A Professional Journal Published by the International Federation of Technical Analysts

23
Inside This Issue
2 Are the Streets Still Smart? Evaluating Swing Trading Strategies inModern Markets
24 Order Flow Analysis
30 Plotting Market Dependencies
37 Modelling Financial Time Series by Generative Adversarial Networks:
With Applications to the Nasdaq Composite Index
46 Using Deep Learning Models for Stock Market Predictions: An
Application of Long Short-Term Memory Algorithms to Micron
Technology, Inc.
55 Price Monitoring of Stock Portfolio—Software Development in Lazarus“We build too many walls
and not enough bridges.”—Isaac Newton

ISSN 2409-0271

Letter From the Editor
By Dr. Rolf Wetzer, CFTe, MFTA

Dear IFTA Colleagues and Friends:
Another very eventful year has passed since the last IFTA Journal. It was a year in which agreat deal of negative news and crises have dominated our daily lives. We are still living in the
midst of a pandemic. In Europe, Russia is waging a brutal war against Ukraine. And aroundthe world, we are experiencing the consequences of climate change more and more clearly.
Therefore, it is more imperative than ever that we all reach out to each other again to bridge
our problems and find good solutions for a peaceful future for all of us.
For us IFTA colleagues too, the last two years have been marked by the consequencesof lockdowns and COVID restrictions. Many events could only take place virtually. I am
therefore very pleased that we will be able to meet again thisyear for a joint conference. The Australian society, ATAA, invites us all to Melbourne forthree days in October. It is a tradition that the IFTA Journal is published in time for the
conference.
The Journal is a new challenge every year. It is produced by only a few people and lives
on the fact that enough colleagues write interesting articles for it. It has been even moreof a challenge over the last two years, as the activities in the national associations haveshrunk somewhat due to COVID.
I am all the more pleased that we were able to find a collection of exciting and highquality contributions this year. Therefore, we would like to thank all the colleagues
who sacrificed their valuable time to write articles for the IFTA Journal. We would
like to extend our special thanks again this year to the National Association of Active
Investment Managers (NAAIM) for allowing us to publish entries from their annual
award.
For myself, it is the 15th edition in which I am involved, so I know from experiencethat the biggest thanks must go to the production team consisting of Linda Bernetich,
Lynne Agoston, and Tiffany Ward. Without their commitment, this Journal would notexist.

... it is more imperative
than ever that we allreach out to each otheragain to bridge ourproblems and find goodsolutions for a peaceful
future for all of us.

Best regards,
Dr. Rolf Wetzer, CFTe, MFTA

IFTA JOURNALEDITORIAL
Dr. Rolf Wetzer, CFTe, MFTA
Editor and Chair of the Editorial Committee
Rolf.Wetzer@ifta.org
Mohamed El Saiid, MFTA, CFTe
melsaiid@hc-si.com
Regina Meani, CFTe
regina.meani@gmail.com

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2023 EDITION

Letter From the Editor
By Dr. Rolf Wetzer, CFTe, MFTA ..........................................................................................Inside front cover
MFTA Paper
Are the Streets Still Smart? Evaluating Swing Trading Strategies in Modern Markets
By Davide Pandini, Ph.D., CFTe, MFTA, CMT.................................................................................................2
ArticlesOrder Flow Analysis
By Anand Behere ...........................................................................................................................................24
Plotting Market Dependencies
By Dr. Oliver Reiss, CFTe, MFTA .................................................................................................................. 30
Modelling Financial Time Series by Generative Adversarial Networks: With Applications to the
Nasdaq Composite Index
By Cezar-Valerian Lupusor, MSc, CFTe ......................................................................................................37
Using Deep Learning Models for Stock Market Predictions: An Application of Long Short-Term
Memory Algorithms to Micron Technology, Inc.
By Cezar-Valerian Lupusor, MSc, CFTe ..................................................................................................... 46
Price Monitoring of Stock Portfolio—Software Development in Lazarus
By Christoph T. Wildensee, Ph.D., MFTA .....................................................................................................55
NAAIM Papers
Active/Passive Blending Based on the Liquidity Premium: A Practical Study
By Garrett H. Brookes, CFA ..........................................................................................................................61
MACD-V: Volatility Normalized Momentum
By Alexandros Spiroglou, DipTA, CFTe........................................................................................................70

Cover Photograph from iStock images

Book Review
Technical Analysis Using Multiple Timeframes by Brian Shannon
Reviewed by Regina Meani, CFTe.................................................................................................................92

Author Profiles.................................................................................................................................................. 93
IFTA Staff............................................................................................................................................................ 95
IFTA Board of Directors................................................................................................................................... 95

The IFTA Journal is published annually by the International Federation of Technical Analysts, 1300 Piccard Dr., Suite LL 14 Rockville, MD 20850 USA.
© 2022 International Federation of Technical Analysts. All rights reserved. No part of this publication may be reproduced or transmitted in any
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IFTA.ORG PAGE 1

IFTA JOURNAL

2023 EDITION

Are the Streets Still Smart? Evaluating Swing
Trading Strategies in Modern Markets
By Davide Pandini, Ph.D., CFTe, MFTA, CMT

Abstract

In 1995, Larry Connors and Linda Bradford Raschke publisheda book titled Street Smarts: High Probability Short Term Trading
Strategies that soon became a reference milestone for many
generations of traders. The book presented multiple strategies
inherently discretionary and mostly focused on equities andfutures. The strategies were based on three simple swing
trading concepts: retracements, pattern breakouts, and climax
reversals, which are among the fundamental pillars of technicalanalysis, and by which support and resistance levels are formed.
Although several traders have used these strategies for many
years, following some structural changes in the markets andan increasing adoption of mechanical trading systems, thestrategies of Street Smarts lately ended up on a sidetrack andwere no longer considered as mainstream by an increasing
number of technical analysts and systematic traders.
In this work, some of the most popular strategies describedin Street Smarts are reviewed. Moreover, an exhaustive
backtesting on historical data across a significant time period,
from 2005 to September 2021, is presented. This time period
includes the most important events in the markets, fromthe global financial crisis (2007–2008) to the more recent
COVID-19 sell-off. The backtesting covered the principal stockindexes, the S&P 500 sectors, real estate, bonds, commodities,
and also the most important Forex currency pairs, whichwere not considered in the original book. Furthermore, arigorous statistical hypothesis testing was performed on theStreet Smarts strategies by means of inferential statistics
multiple hypothesis testing and time series bootstrap. Such acomprehensive analysis of the Street Smarts strategies allows
us to assess their effectiveness on different asset classes
and markets. Moreover, this thorough study also provides a
deeper insight on swing trading techniques in changing market
scenarios and proposes to adopt statistical hypothesis testing
as a best practice to evaluate a trading strategy.

Introduction

Published in 1995 by Larry Connors (LC) and Linda Bradford
Raschke (LBR) (Connors, 1995), Street Smarts is consideredby many to be one of the best books on trading equities,
commodities, and futures. The backbone of this book’s
success is swing trading and the techniques which apply
these methodologies. Moreover, strategies based on patternrecognition and volatility explosion are also presented, alongwith the use of popular technical indicators such as the ADX(Wilder, 1978) and the stochastic oscillator (Lane, 1984).
Although most of the strategies described by LC and LBR were
initially aimed at short-term swing trading, they can also be
PAGE 2 IFTA.ORG

Davide Pandini, Ph.D., CFTe, MFTA, CMT
STMicroelectronics
Agrate Brianza, Italy+39 348 3973247
davide.pandini@hotmail.com

used by longer-term swing traders who could hold a position fordays, weeks, and sometimes even months.
In this work, we will review the most popular strategies
presented in Street Smarts by performing a thoroughbacktesting over several asset classes and across an exhaustive
time window, covering more than 16 years of historical data. The
purpose of this comprehensive study is to assess the validity
and robustness of these strategies after more than 25 years
since they were first published. Since then, most of the equities,
commodities, futures, and Forex markets have changed theirstructural behavior and, unfortunately, most methods do notalways work in all market conditions and market conditions
never persist forever. Therefore, we believe that this work will
provide a new and more in-depth insight on the effectivenessof the Street Smarts techniques. Moreover, a rigorous
statistical hypothesis testing was performed on the Street
Smarts strategies by means of inferential statistics multiple
hypothesis testing and time series bootstrap. Even the mostpowerful strategies, or technical analysis rules, may deliver ahighly variable performance depending on the time series oftested historical data. Statistical analysis is the only scientificapproach to distinguish strategies that have a predictive powerfrom those that do not have an intrinsic merit.
The paper is organized as follows: "Backtesting: Historical
Period and Asset Classes" illustrates the historical period forbacktesting the Street Smarts strategies and the asset classes
considered for this analysis, while "Performance Metrics"
describes the performance metrics used to assess the strategies.
The Street Smarts strategies considered in this work, and the
backtesting results are presented in "Street Smarts Strategies".
The statistical hypothesis testing procedures are discussed
in "Statistical Hypothesis Testing" and "The Bootstrap", while"Conclusion" summarizes our conclusive remarks.

Backtesting: Historical Period andAsset Classes
Look-Back Period
The choice of the time window for backtesting has always
been of interest and concern to technical analysts to assess
the robustness and performance of a strategy, since different
periods and sizes of the window can lead to different
experimental results and conclusions. The work presented
in Inoue, 2012, assessed the robustness of the strategy’s
performance given the window size of the backtesting period.
This study shows the impact that the chosen window canhave on the results and, as such, the authors argue that thewindow should not be arbitrarily selected. In Zakamulin, 2014,

IFTA JOURNAL

it was demonstrated that an active market timing strategy
outperforms the passive buy-and-hold strategy during bearmarkets and vice versa during bull markets. To account for theseresults, this study concluded that the look-back period should
include bear and bull markets to analyze both these market
conditions.
Therefore, the strategies of Street Smarts were tested acrossan historical data length covering the past 16 years (fromSeptember 2005 to September 2021) because it includes multiplebull and bear markets, some of which were quite significant, likethe global financial crisis (2007–2008), the recent COVID-19 selloff (March 2020), and the last bull market lasting over a decade.
Asset Classes
Usually, technical analysis strategies are not equallydistributed and tested across all asset classes. It is frequent
practice to find strategies that have been assessed only onsome specific assets, like the major stock market indexes,
commodities, bonds, or currency pairs. It is well-known that theperformance of a given strategy can vary significantly dependingon the tested asset class and market. Therefore, for a thoroughand comprehensive analysis, the Street Smarts strategies
were evaluated on all the above-mentioned asset classes. The
following ETFs were considered (Figure 1): the most important
U.S. stock market indexes (SPY, QQQ, DIA), the S&P 500 sectors(XLP, XLY, XLE, XLV, XLF, XLI, XLK, XLB, XLU, IYZ), real estate(IYR), gold (GLD), 7–10-year Treasury bonds (IEF), and 20+ year
Treasury bonds (TLT). Furthermore, to complete the assessmentof the Street Smarts strategies, the major Forex currency crosses
were evaluated, as well. All the ETFs historical time series were
downloaded from (Yahoo! Finance, 2022) and the Forex crosses
from the site (Investing.com, 2022). The strategies analyzed inthis work were implemented and tested with MS Excel and all thehistorical data used were on a daily timeframe.
Figure 1. Asset classes and Forex currency pairs
Asset ClassETF Ticker
SP& 500
SPY
DJIA
DIA
Indexes
NASDAQ 100
QQQ
Consumer Staples
XLP
Consumer Discretionary XLY
EnergyXLE
Healthcare
XLV
Financials
XLF
S&P 500 Sectors
Industrials
XLI
Technology
XLK
Materials
XLB
Utilities
XLU
Telecommunications
IYZ
Real Estate
IYR
Gold
GLD
7-10 years Treasury Bonds IEF
U.S. Treasury Bonds
20+ years Treasury Bonds TLT

Performance Metrics

FOREX Cross
EURUSD
GBPUSDEURGBP
USDCHF
USDJPYUSDCADUSDNZD
AUDUSDAUDNZDEURCADEURNZDNZDUSDEURAUDUSDTRY

There are various ways to measure a portfolio performance(Cogneau, 2009). The simplest and most common is the excess
return. It measures the total return less the risk-free rateof return. However, it is not the best performance metricbecause it does not consider risk. A risk-adjusted metric is
more appropriate because investors and traders require

2023 EDITION

compensation for risk. Among the popular methods thatare commonly utilized and include the risk factor, there is
the Sharpe Ratio (Sharpe, 1994), which is the ratio of return,
adjusted for the risk-free return of T-bills, to the annualized
standard deviation of returns, which is considered as a proxy for
risk:
Although the limitations of the Sharpe ratio are known andhave been discussed in the literature (Kirkpatrick III, 2016), in
this study we used it because of its overwhelming popularity.
Additionally, practitioners commonly use the drawdown toassess the riskiness of any given strategy. The most common
performance measure after the Sharpe ratio is the maximum
drawdown, which in this work is measured as a percentage froma highest net asset value (NAV) to the subsequent lowest NAV.
One metric that accounts for the maximum drawdown is theCalmar ratio (Young, 1991):

Therefore, both the Sharpe and Calmar ratios are used inthis study, along with other popular metrics, such as the total
returns, the annualized volatility, and the compound annual
growth rate (CAGR).

Street Smarts Strategies

The strategies of Street Smarts were originally developedand evaluated mostly on U.S. equities and futures, and they
were used for many years in those markets. However, acomprehensive and thorough backtesting also encompassing
the Forex market and across a statistically significant look-backperiod has never been published. Hence, given the structuraldifferences between the Forex and the equities markets, inthis work a detailed analysis of some of the most popular Street
Smarts strategies applied to equities, commodities, bonds,
and the most important currency pairs listed in Figure 1 ispresented.
All the Street Smarts strategies discussed in this paper
were implemented considering both long and short trades,
reversing the trade direction after closing the open trade
when an opposite entry signal was triggered, and rolling overan open position when a new signal in the same direction of
the current trade was generated. For the sake of conciseness,
the Street Smarts strategies are not reviewed in this work andthe interested reader may find their description and set-upin (Connors, 1995), while the principles of swing trading are
outlined in the seminal book by Perry Kaufman (Kaufman,2013).
TurtleBefore looking into the Turtle Soup strategy presented in(Connors, 1995), we first review its background. The Turtle
Soup sets its roots into the famous strategy called Turtle (The
Original Turtle Trading Rules, 2022), which was introducedby Richard Dennis (Schwager, 2006) and William Eckhardt(Schwager, 2008) in the 1980s to a group of novice traders
called the Turtles. The Turtle is a trend-following strategy
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IFTA JOURNAL

2023 EDITION

based on a 20-day breakout of prices, earlier introduced by
Richard Donchian (Donchian, 1974). Like other trend-following
techniques, even the Turtle strategy suffers from false
breakouts. Instead of sustaining strong directional moves inthe direction of the breakout, prices can trace back within the
Donchian channel, originating whipsaws that result in losing
trades. The backtesting of this strategy has demonstrated thatto make it profitable, it is mandatory to implement a carefulmanagement of the stop-loss. Various stop-loss approaches
were tested, and the best performances were obtained with a
trailing stop-loss tracking the opposite limit of the Donchianchannel with respect to the breakout.
Different take-profit targets were evaluated with respect tothe maximum allowed loss. Furthermore, also assessed was the
typical approach of trend-following strategies to let the profits
run and use the trailing stop-loss as a dynamic take-profit level(i.e., to exit the trade when the trailing stop-loss is hit). The
trailing-stop loss allowed to secure most of the gained profits,
and for this trend-following strategy the backtesting evinced tobe the best exit approach.
The monthly NAV for the indexes, equities, commodities, realestate, and bonds over the backtesting time window is reported
in Figure 2, while Figure 3 shows the monthly drawdown. The
best performances were achieved on QQQ (Nasdaq 100) andXLK (technology). It is worth noting that XLK and QQQ arehighly correlated with a correlation coefficient of 0.9598 andconsistently showed the best performances over the look-backperiod. The performances of the Turtle strategy are reported inTable 1.
Figure 2. Turtle strategy asset class monthly NAV

PAGE 4 IFTA.ORG

The Turtle turned out to be less performing in the Forex
market and the NAV results shown in Figure 4 did not reachthe same values reported for the equity indexes and sectors
in Figure 2. However, the drawdowns on the Forex shown in
Figure 5 were smaller than the drawdowns of the other asset
classes. The currency pair where the Turtle strategy’s overall
performance was better than the other currency crosses was
USDTRY, which should be considered more as an outlier since
the behavior of this currency pair over the backtesting period
is significantly different from the typical behavior of the othercurrency pairs, as illustrated in Figure 6.
Given the typical mean-reverting structure of the Forex, thebest approach to protect the gained profits was to close thetrade after three trading days if the profit target had not beenreached within this time window.
The overall performances and the trade statistics in the Forex
market are reported in Table 2.
In summary, the Turtle strategy can deliver good
performances on some S&P 500 sectors and equity indexes
with a particular focus on the technology stocks if used witha trailing stop-loss set on the Donchian channel. In contrast,
its performance was less effective in the Forex market. Thisoutcome is consistent with the strategy’s trend-following
behavior and the structure of the Forex, which essentially ismean reverting. A lower performance of a trend-following
strategy in a typical mean-reverting market should be expected.

IFTA JOURNAL

2023 EDITION

Figure 3. Turtle strategy asset class monthly drawdown

Table 1. Turtle strategy asset classes trade results
XLF
XLI
XLK
XLB
XLU
IYZ
IYR
SPY
DIA
IEF
XLP
XLY
XLE
XLV
TLT
GLD
QQQ
PERFORMANCE
Total Returns 78.1% 179.4% 195.0% 138.5% 122.0% 153.4% 204.1% 157.5% 94.8% 75.3% 146.9% 95.5% 101.1% -8.2% 92.9% 165.1% 281.8%
CAGR 3.7% 6.6%
7.0% 5.6%
5.1%
6.0%
7.2%
6.1% 4.2% 3.6%
5.8%
4.3% 4.4% -0.5% 4.2%
6.2%
8.7%
Volatility 3.3% 5.3%
7.0% 4.9%
4.5%
5.2%
4.8%
4.1% 3.5% 5.0%
4.5%
4.8% 5.0% 2.7% 4.4%
4.6%
5.0%
Maximum DrawDown -4.7% -8.7% -10.7% -5.7% -9.4% -13.9% -6.2% -10.1% -4.9% -12.1% -8.5% -12.0% -14.6% -16.7% -7.0% -5.4% -7.6%
Sharpe Ratio
1.09
1.24
0.99
1.13
1.14
1.14
1.50
1.46
1.20
0.71
1.28
0.88
0.89 -0.20
0.95
1.35
1.75
Calmar Ratio
0.77
0.76
0.65
0.97
0.54
0.43
1.15
0.60
0.87
0.29
0.68
0.35
0.31 -0.03
0.60
1.16
1.14
Max Monthly Return 2.99% 5.69% 16.22% 6.00% 8.11% 5.12% 5.23% 4.32% 3.09% 4.23% 4.93% 3.73% 5.61% 2.66% 5.77% 5.18% 4.36%
Min Monthly Return -4.74% -8.72% -10.05% -4.22% -4.52% -9.30% -6.21% -6.75% -4.87% -5.71% -6.27% -6.34% -8.40% -2.51% -5.48% -4.09% -5.37%% Positive Months 38.3% 48.7% 46.1% 48.2% 39.4% 46.1% 49.7% 46.6% 35.8% 43.0% 49.2% 48.7% 48.2% 25.4% 45.1% 45.1% 62.2%

Figure 4. Turtle strategy Forex monthly NAV

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IFTA JOURNAL

2023 EDITION

Figure 5. Turtle strategy Forex monthly drawdown

Figure 6. AUDUSD and USDNZD vs. USDTRY

Table 2. Turtle strategy Forex trade results
EURUSD GBPUSD EURGBP USDCHF USDJPY USDCAD USDNZD AUDUSD AUDNZD EURCAD EURNZD NZDUSD EURAUD USDTRYPERFORMANCE
Total Returns
24.9%
34.5%
19.0%
50.7%
66.4%
18.3%
41.1%
47.6%
-0.6%
46.9%
18.1%
63.9%
25.4% 112.9%
CAGR
1.5%
2.1%
1.2%
2.9%
3.6%
1.2%
2.4%
2.7%
0.0%
2.7%
1.1%
3.4%
1.6%
5.3%
Volatility
2.8%
2.6%
2.7%
2.4%
2.9%
2.4%
3.3%
4.3%
1.6%
2.6%
2.2%
3.0%
2.9%
3.9%
Maximum DrawDown
-3.7%
-4.4%
-4.6%
-1.6%
-3.4%
-5.4%
-5.1%
-15.7%
-6.1%
-2.5%
-4.6%
-4.3%
-7.4%
-4.5%
Sharpe Ratio
0.56
0.79
0.44
1.18
1.21
0.48
0.73
0.63
-0.03
1.01
0.53
1.13
0.55
1.35
Calmar Ratio
0.41
0.47
0.26
1.75
1.06
0.21
0.47
0.17
-0.01
1.09
0.25
0.80
0.21
1.19
Max Monthly Return
4.11%
4.04%
6.12%
4.04%
4.04%
4.04%
4.04%
4.04%
2.00%
3.62%
3.41%
4.04%
2.12%
8.48%
Min Monthly Return-2.99%-2.32%-2.35% -1.63% -3.36%-2.14% -3.33% -10.04% -2.18%-1.78% -2.14% -1.75%-4.52% -2.41%% Positive Months
31.4%
30.9%
26.3%
37.1%
36.6%
29.7%
26.9%
35.4%
17.1%
32.6%
22.9%
29.1%
31.4%
29.7%

PAGE 6 IFTA.ORG

IFTA JOURNAL

Turtle Soup
The Turtle Soup strategy attempts to identify a false
breakout and to enter the trade trying to capture its reversal,
since quite often when the market is in a strong trend, false
breakouts may have a short duration and the breaks, insteadof producing a strong movement, sometimes generate rapid
and sudden reversals. To take advantage of these changes of
direction, LC and LBR proposed the Turtle Soup. The Turtle Soup
was backtested on the same assets and Forex crosses as the
Turtle strategy. A trailing stop-loss on the Donchian channel
limit where the false breakout occurred was set as soon as
the position became profitable. Figure 7 and Figure 8 show themonthly NAV and the monthly drawdown of the Turtle Soup. The
performance metrics results are summarized in Table 3.
Similarly to the Turtle, even the Turtle Soup generated
worse results on the Forex, as illustrated in Figure 9, but withsignificantly less drawdowns, not exceeding 3%, as reported in
Figure 10. It is worth remarking that in the Forex market the2023 EDITION

overall performance of the Turtle Soup was comparable with
the Turtle’s performance (except for USDTRY). Since the Turtle
Soup attempts to capture a reversal after a false breakout, thisoutcome confirms that a trend-following strategy like the Turtle
does not outperform a reversal strategy such as the Turtle Soup
in a mean-reverting market like the Forex.
The performance metrics for the Turtle Soup backtested on
the currency crosses are reported in Table 4. Even the Turtle
Soup is more effective in the Forex market when the trades areclosed after three days if the profit target has not been reached.
The Turtle and Turtle Soup are two strategies having a
different behavior, and this is confirmed by the correlation
analyses on all the asset classes and currency pairs, which
are summarized in Table 5. Each table entry represents thecorrelation between the daily returns generated by the Turtle
and Turtle Soup on a given asset. The correlation values areclose to zero, which means that the two strategies are basicallyuncorrelated.

Figure 7. Turtle Soup strategy asset classes monthly NAV

Figure 8. Turtle Soup strategy asset classes monthly drawdown

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2023 EDITION

Table 3. Turtle Soup strategy asset classes trade results
XLP
XLY
XLE
XLV
XLF
XLI
XLK
XLB
XLU
IYZ
IYR
SPY
DIA
IEF
TLT
GLD QQQPERFORMANCE
Total Returns 71.2% 103.4% 144.4% 63.0% 47.2% 72.3% 79.6% 86.2% 131.4% 155.0% 90.9% 63.6% 52.5% 31.3% 63.8% 152.8% 106.9%
CAGR 3.4% 4.5% 5.7% 3.1% 2.4% 3.4% 3.7% 3.9% 5.4% 6.0% 4.1% 3.1% 2.7% 1.7% 3.1% 5.9% 4.6%
Volatility 4.0% 4.7% 5.4% 4.2% 3.6% 4.1% 4.1% 3.9% 3.7% 6.3% 3.5% 3.5% 3.5% 2.0% 3.0% 4.3% 4.3%
Maximum DrawDown -8.6% -4.6% -4.5% -9.8% -6.2% -4.2% -4.0% -3.0% -1.5% -3.6% -3.0% -6.5% -8.5% -1.4% -2.6% -1.6% -5.7%
Sharpe Ratio 0.85
0.96
1.06 0.73 0.68 0.84 0.91 1.01
1.44
0.96 1.17 0.89 0.76 0.86
1.03
1.38
1.07
Calmar Ratio 0.40
0.99
1.28 0.31 0.39 0.83 0.92 1.30
3.60
1.67 1.37 0.48 0.31 1.19
1.21
3.62
0.81
Max Monthly Return 6.41% 9.74% 12.32% 5.61% 6.12% 9.13% 6.15% 7.31% 6.12% 20.44% 4.94% 6.01% 4.04% 2.10% 4.04% 6.79% 6.01%
Min Monthly Return -8.37% -4.57% -4.23% -8.29% -4.19% -4.16% -4.02% -1.82% -1.49% -1.52% -1.80% -4.23% -5.61% -0.67% -1.67% -0.83% -3.92%% Positive Months 21.8% 20.2% 20.7% 19.2% 18.7% 17.1% 18.1% 18.1% 25.9% 24.4% 20.2% 17.1% 18.1% 14.0% 18.1% 20.7% 19.7%

Figure 9. Turtle Soup strategy Forex monthly NAV

Figure 10. Turtle Soup strategy Forex monthly drawdown

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2023 EDITION

Table 4. Turtle Soup strategy Forex trade results
EURUSD GBPUSD EURGBP USDCHF USDJPY USDCAD USDNZD AUDUSD AUDNZD EURCAD EURNZD NZDUSD EURAUD USDTRYPERFORMANCE
Total Returns
37.0%
26.3%
25.7%
34.6%
27.2%
43.2%
76.1%
43.9%
27.9%
42.2%
69.5%
49.4%
38.1%
55.4%
CAGR
2.2%
1.6%
1.6%
2.1%
1.7%
2.5%
4.0%
2.5%
1.7%
2.4%
3.7%
2.8%
2.2%
3.1%
Volatility
2.1%
1.9%
2.1%
2.2%
1.6%
2.2%
3.3%
2.3%
1.7%
2.0%
2.7%
2.9%
2.4%
2.5%
Maximum DrawDown
-1.6%
-2.1%
-1.6%
-1.4%
-2.3%
-2.1%
-2.6%
-1.7%
-1.6%
-2.0%
-2.1%
-2.7%
-1.6%
-1.7%
Sharpe Ratio
1.02
0.87
0.74
0.95
1.03
1.11
1.19
1.11
1.00
1.20
1.37
0.96
0.92
1.21
Calmar Ratio
1.37
0.76
1.02
1.47
0.71
1.19
1.50
1.46
1.08
1.25
1.75
1.03
1.36
1.78
Max Monthly Return
3.20%
2.33%
4.84%
4.04%
2.77%
3.47%
4.11%
2.70%
2.63%
2.62%
3.81%
4.04%
4.62%
2.53%
Min Monthly Return-0.73%-1.07%-0.77% -0.89% -1.31%-0.82% -0.68%-0.91% -0.53%-0.94% -1.57% -1.62%-0.85% -1.23%% Positive Months
20.0%
19.4%
17.7%
20.6%
22.9%
22.9%
21.7%
19.4%
20.0%
28.6%
27.4%
20.0%
19.4%
21.7%

Table 5. Turtle vs. Turtle Soup correlations
XLP

XLY

XLE

XLV

XLF

XLI

XLK

XLB

XLU

-0.1216-0.0052-0.0046-0.0036-0.0021-0.0003-0.0057

0.0007-0.0064-0.0027-0.0070-0.0031-0.0030

0.0156-0.0040-0.0072

EURUSD GBPUSD EURGBP USDCHF

USDJPY

IYZ-0.0021IYR-0.0025

SPY-0.0018

DIA-0.0041

IEF-0.0044

TLT

GLD

QQQ

-0.0073

USDCAD USDNZD-0.0019-0.0037

AUDUSD AUDNZD EURCAD EURNZD NZDUSD EURAUD USDTRY-0.00270.0007-0.0043-0.0026-0.0043-0.0019-0.0055

Anti
The Anti strategy is an example of retracement pattern. It enters in the direction of the long-term trend after a retracement (either athrowback or pullback, depending on whether the long-term trend is bullish or bearish) of the short-term trend towards the long-term
trend. The basic principle of this strategy is that often a short-term trend tends to resolve in the direction of the long-term trend. Anti
worked better on the sectors XLF, XLE, XLB, and XLY, which outperformed the technology stocks (QQQ and XLK) and the other assets,
as shown in Figure 11. The drawdowns were less than 7% across the look-back period, as represented in Figure 12. The numerical results
for the Anti are reported in Table 6.
The same Anti setup was used for the Forex market. The monthly NAV and drawdown are illustrated in Figure 13 and Figure 14. The
numerical results are summarized in Table 7, with the worst drawdowns around 4%.
Even the overall performance of the Anti was better on the stock indexes and S&P 500 sectors than on the Forex crosses, thus
showing a consistent behavior with the other Street Smarts strategies.
Figure 11. Anti strategy asset classes monthly NAV

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Figure 12. Anti strategy asset classes monthly drawdown

Table 6. Anti strategy asset classes trade results
XLP
XLY
XLE
XLV
XLF
XLI
XLK
XLB
XLU
IYZ
IYR
SPY
DIA
IEF
PERFORMANCE
TLT
GLD
QQQ
Total Returns 88.6% 174.7% 247.3% 72.6% 282.4% 171.1% 162.5% 214.2% 55.0% 156.8% 200.4% 113.3% 81.2% 46.0% 132.2% 144.8% 135.0%
CAGR 3.8% 6.2% 7.7% 3.3% 8.3% 6.1% 5.9% 7.0% 2.6% 5.8%
6.8% 4.6% 3.6% 2.3% 5.1% 5.5% 5.2%
Volatility 3.1% 3.9% 6.0% 3.2% 4.4% 4.1% 4.6% 3.9% 2.8% 3.7%
3.7% 3.6% 3.3% 2.0% 3.0% 3.4% 3.6%
Maximum DrawDown -3.5% -1.7% -5.2% -3.7% -2.3% -2.5% -3.8% -3.6% -3.1% -3.6% -6.3% -3.5% -6.8% -3.0% -2.1% -2.6% -4.2%
Sharpe Ratio
1.22
1.59
1.29
1.04
1.89
1.50
1.29
1.82
0.94
1.57
1.81
1.27
1.09 1.16
1.73
1.60
1.45
Calmar Ratio
1.11
3.69
1.47
0.88
3.66
2.45
1.54
1.96
0.84
1.60
1.07
1.30
0.53 0.75
2.50
2.07
1.25
Max Monthly Return 4.67% 5.43% 16.22% 3.78% 8.11% 6.11% 12.92% 4.52% 2.07% 4.57% 5.37% 6.72% 4.57% 3.55% 4.03% 4.26% 6.27%
Min Monthly Return -3.12% -1.55% -5.03% -3.55% -2.27% -1.74% -3.15% -3.38% -2.67% -2.97% -3.06% -3.53% -6.58% -1.88% -2.06% -1.68% -4.07%% Positive Months 35.8% 38.8% 40.8% 30.3% 38.8% 35.8% 36.8% 40.3% 30.8% 41.8% 44.8% 34.8% 33.8% 37.8% 42.3% 36.8% 41.8%

Figure 13. Anti strategy Forex monthly NAV

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Figure 14. Anti strategy Forex monthly drawdown

Table 7. Anti strategy Forex trade results
EURUSD GBPUSD EURGBP USDCHF USDJPY USDCAD USDNZD AUDUSD AUDNZD EURCAD EURNZD NZDUSD EURAUD USDTRYPERFORMANCE
Total Returns
34.8%
39.7%
31.9%
57.2%
45.4%
45.6%
35.1%
55.8%
8.0%
15.7%
33.7%
70.4%
44.0%
76.4%
CAGR
2.0%
2.2%
1.8%
3.0%
2.5%
2.5%
2.0%
2.9%
0.5%
0.9%
1.9%
3.5%
2.4%
3.8%
Volatility
2.0%
2.0%
1.9%
2.0%
2.0%
2.0%
2.5%
2.3%
1.4%
2.1%
2.0%
2.3%
2.2%
2.4%
Maximum DrawDown
-2.2%
-1.8%
-2.1%
-1.6%
-2.3%
-1.3%
-4.4%
-4.2%
-4.3%
-3.5%
-3.1%
-2.3%
-2.5%
-2.8%
Sharpe Ratio
0.99
1.08
0.96
1.50
1.20
1.24
0.78
1.28
0.35
0.45
0.93
1.55
1.06
1.55
Calmar Ratio
0.89
1.24
0.85
1.81
1.06
1.92
0.45
0.70
0.12
0.27
0.62
1.54
0.96
1.34
Max Monthly Return
2.21%
2.60%
2.30%
2.38%
2.75%
2.01%
4.06%
3.03%
1.21%
2.01%
2.01%
2.59%
2.01%
4.56%
Min Monthly Return-1.21%-1.33%-1.67% -1.28% -1.23%-1.12% -3.39%-1.98% -1.31%-2.18% -2.36% -1.37%-2.07% -1.90%% Positive Months
29.3%
32.1%
30.4%
39.1%
31.0%
33.2%
28.8%
34.2%
21.7%
23.9%
25.5%
35.9%
31.0%
34.2%

ID-NR4
Swing trading can be profitable when there are priceoscillations and a good amount of volatility (Kaufman, 2013).
The internal-day narrow-range 4 (ID-NR4) strategy attempts
to identify a pattern where a period of volatility expansion
usually follows a period of volatility contraction. When thevolatility is cyclical, then the market can experience sequencesof range contractions followed by range expansions, and usually
after the market has been inactive (or in a period of range
contraction), a trend period often follows (Crabel 1990). The
ID-NR4 strategy was backtested closing an open position after
three days, since volatility explosions are not often followed bytrend movements. The experimental results are shown in Figure
15 and Figure 16. GLD delivered the best performance along the
backtesting period. The numerical results are summarized inTable 8.
It is quite important to assess the effectiveness of stopping
and reversing in a whipsaw (or trading range). This meansthat if the trade is a loser, not only it will be stopped out witha small loss, but it will reverse direction. The Stop & Reverse
technique was part of the ID-NR4 set-up and it was backtested
with the strategy. The overall performance, with respect tothe implementation without Stop & Reverse, has only slightly
improved, as shown in Figure 17 and Figure 18. After a Stop &Reverse pattern, it is more likely to enter a trading range thana true trend reversal. The numerical results summarizing theperformance of the Stop & Reverse technique are shown in
Table 9.
The ID-NR4 strategy was also tested on the Forex currency
pairs. The monthly NAV and drawdown are reported in Figure 19
and Figure 20. In the Forex market, large volatility movements
after a period of volatility compression are not likely to happen
very often. Therefore, a better performance was obtained
locking in the accrued profits by closing the positions after threedays, instead of relying on a trailing stop-loss to exit the trade.
The numerical results are outlined in Table 10 and they confirm
that ID-NR4 is not suited for the Forex.

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Figure 15. IN-NR4 strategy asset classes monthly NAV

Figure 16. IN-NR4 strategy asset classes monthly drawdown

Table 8. ID-NR4 strategy asset classes trade results
XLP
XLY
XLE
XLV
XLF
XLI
XLK
XLB
XLU
IYZ
IYR
SPY
DIA
IEF
TLT
GLD
QQQ
PERFORMANCE
Total Returns 71.6% 97.0% 244.3% 71.3% 259.0% 209.6% 105.6% 136.8% 129.1% 129.6% 173.6% 181.3% 110.7% 35.2% 104.4% 348.2% 134.8%
CAGR 3.3% 4.1% 7.6% 3.3% 7.9% 6.9% 4.4% 5.3% 5.0% 5.1% 6.2% 6.3% 4.5% 1.8% 4.3% 9.3% 5.2%
Volatility 3.7% 4.3% 7.4% 3.4% 6.6% 6.0% 4.6% 5.1% 4.0% 5.3% 6.4% 5.4% 4.2% 1.8% 4.3% 5.6% 5.5%
Maximum DrawDown -7.5% -5.1% -17.3% -6.5% -5.3% -6.0% -6.4% -4.8% -3.8% -6.2% -4.7% -5.8% -6.6% -1.8% -3.7% -2.2% -6.1%
Sharpe Ratio 0.88
0.95
1.04 0.95
1.19
1.16
0.96
1.04
1.25
0.96
0.96
1.17
1.07 1.03
1.02
1.67
0.94
Calmar Ratio 0.44
0.80
0.44 0.50
1.48
1.16
0.68
1.09
1.34
0.82
1.32
1.10
0.69 1.02
1.17
4.20
0.86
Max Monthly Return 3.89% 6.41% 9.27% 3.64% 13.74% 10.24% 6.09% 6.09% 5.18% 6.50% 15.19% 8.95% 7.40% 2.63% 10.73% 8.39% 9.27%
Min Monthly Return -2.65% -5.08% -9.79% -3.02% -5.33% -3.17% -3.16% -3.41% -1.77% -2.60% -3.35% -4.11% -6.58% -1.10% -2.09% -1.61% -4.52%% Positive Months 36.3% 30.8% 31.8% 34.8% 34.3% 36.3% 33.8% 33.3% 35.8% 32.3% 34.8% 37.8% 42.8% 35.3% 35.3% 48.3% 33.3%

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Figure 17. ID-NR4 strategy asset classes NAV with Stop & Reverse

Figure 18. ID-NR4 strategy asset classes monthly drawdown with Stop & Reverse

Table 9. ID-NR4 strategy asset classes trade results with Stop & Reverse
XLP
XLY
XLE
XLV
XLF
XLI
XLK
XLB
XLU
IYZ
IYR
SPY
DIA
IEF
PERFORMANCE
TLT
GLD
QQQ
Total Returns 71.9% 104.9% 286.1% 77.3% 277.8% 216.0% 111.7% 155.4% 135.5% 138.9% 178.9% 207.4% 118.3% 38.1% 108.6% 363.5% 160.6%
CAGR 3.3% 4.4% 8.4% 3.5% 8.2% 7.1% 4.6% 5.7% 5.2% 5.3% 6.3% 6.9% 4.7% 1.9% 4.5% 9.5% 5.9%
Volatility 3.8% 4.5% 7.4% 3.4% 6.7% 6.1% 4.5% 5.2% 4.0% 5.3% 6.5% 5.5% 4.0% 1.8% 4.3% 5.9% 5.6%
Maximum DrawDown -7.6% -5.1% -17.3% -6.0% -5.3% -7.2% -6.4% -4.5% -5.3% -7.7% -4.9% -5.3% -4.2% -1.8% -3.7% -2.2% -4.1%
Sharpe Ratio 0.86
0.98
1.13 1.02
1.23
1.16
1.01
1.11
1.29
1.01
0.97
1.25
1.18 1.09
1.04
1.63
1.05
Calmar Ratio 0.43
0.85
0.48 0.58
1.54
0.99
0.71
1.28
0.99
0.69
1.29
1.31
1.13 1.09
1.21
4.29
1.44
Max Monthly Return 3.89% 6.41% 9.27% 3.64% 13.74% 10.24% 6.09% 6.09% 5.18% 6.50% 15.19% 8.95% 7.40% 2.63% 10.73% 8.39% 9.27%
Min Monthly Return -2.73% -5.08% -9.79% -3.02% -5.33% -4.39% -3.16% -3.41% -1.77% -2.82% -3.35% -4.11% -3.78% -1.10% -2.09% -1.72% -2.94%% Positive Months 37.3% 32.3% 33.8% 35.8% 35.3% 36.8% 34.8% 34.3% 37.3% 33.8% 36.3% 38.3% 42.8% 36.8% 35.8% 47.8% 34.8%

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Figure 19. ID-NR4 strategy Forex monthly NAV

Figure 20. IN-NR4 strategy Forex monthly drawdown

Table 10. IN-NR4 strategy Forex trade results
EURUSD GBPUSD EURGBP USDCHF USDJPY USDCAD USDNZD AUDUSD AUDNZD EURCAD EURNZD NZDUSD EURAUD USDTRYPERFORMANCE
Total Returns
11.5%
19.1%
4.3%
33.9% 83.5%
45.2%
26.3%
56.8%
4.1%
8.4%
21.5%
25.6%
19.5% 106.8%
CAGR
0.7%
1.1%
0.3%
1.9%
4.0%
2.4%
1.5%
3.0%
0.3%
0.5%
1.3%
1.5%
1.2%
4.8%
Volatility
2.6%
2.6%
2.2%
3.5%
3.6%
3.0%
3.2%
3.6%
2.0%
2.2%
2.9%
3.5%
2.5%
4.2%
Maximum DrawDown
-7.6%
-3.2%
-6.8%
-5.7%
-2.6%
-3.0%
-7.1%
-5.9%
-5.7%
-8.3%
-5.3%
-5.1%
-5.3%
-3.1%
Sharpe Ratio
0.27
0.43
0.12
0.55
1.12
0.82
0.47
0.82
0.13
0.23
0.44
0.43
0.46
1.14
Calmar Ratio
0.09
0.35
0.04
0.33
1.54
0.82
0.21
0.51
0.05
0.06
0.24
0.29
0.22
1.53
Max Monthly Return
4.10%
5.26%
3.00%
6.42% 6.09%
4.47%
4.74%
4.72%
2.27%
3.00%
4.42%
4.42%
3.01%
6.09%
Min Monthly Return -2.17% -2.06% -3.39% -2.01% -1.50% -1.46% -2.13% -2.53% -1.79% -2.26% -2.55% -2.49% -2.52% -2.66%% Positive Months
26.6%
26.6%
21.7%
23.4% 37.0%
34.8%
30.4%
31.5%
23.9%
29.3%
28.8%
26.6%
25.5%
38.0%

Holy Grail
This pattern is based on Welles Wilder’s Average Directional Index (ADX) (Wilder, 1978) and is supposed to work in any market
and in any timeframe. The Holy Grail is a strategy that enters a position after a retracement. Once we are in the trade, we look fora continuation of the previous trend. In the Holy Grail, when prices retrace after a strong move, a 20-period exponential moving
average acts as support/resistance for these retracements. The monthly NAV and drawdown are reported in Figure 21 and Figure 22.
The numerical results of the Holy Grail for the equity indexes and sectors are summarized in Table 11. A trailing stop-loss with a fixed
amplitude of 1% was used and positions were closed after three days if the profit target had not been reached.
Even on the Forex crosses, the performance of the Holy Grail was worse than on the other asset classes, as confirmed by the results
shown in Figure 23, Figure 24, and Table 12, respectively.

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Figure 21. Holy Grail strategy asset classes monthly NAV

Figure 22. Holy Grail strategy asset classes monthly drawdown

Table 11. Holy Grail strategy asset classes trade results
XLF
XLI
XLK
XLB
XLU
IYZ
IYR
SPY
DIA
IEF
XLP
XLY
XLE
XLV
PERFORMANCETLT
GLD QQQ
Total Returns 94.4% 121.6% 125.3% 52.3% 119.8% 122.7% 260.5% 117.3% 70.4% 178.7% 69.8% 153.3% 57.0% 20.3% 56.9% 39.7% 123.6%
CAGR 4.2% 5.1% 5.2% 2.6% 5.0% 5.1% 8.3% 4.9% 3.4% 6.6% 3.3% 5.9% 2.8% 1.2% 2.8% 2.1% 5.1%
Volatility 4.3% 4.4% 5.1% 3.8% 7.2% 5.2% 7.6% 5.8% 5.7% 5.5% 5.3% 6.4% 4.1% 1.4% 4.1% 2.7% 4.8%
Maximum DrawDown -1.1% -1.7% -1.7% -2.0% -5.5% -2.9% -4.6% -0.5% -1.9% -0.4% -4.7% -1.8% -1.9% -0.7% -2.1% -1.9% -3.8%
Sharpe Ratio
0.97
1.14
1.01
0.70
0.69
0.97
1.09
0.85
0.59
1.21
0.64
0.93
0.69 0.81
0.68 0.77
1.06
Calmar Ratio
3.80
3.05
3.01
1.33
0.91
1.77
1.80 10.21
1.79 15.07
0.71
3.36
1.48 1.60
1.33 1.08
1.37
Max Monthly Return 10.20% 7.41% 9.04% 10.72% 17.41% 10.86% 13.34% 13.67% 20.03% 9.93% 14.20% 12.94% 11.12% 2.79% 13.18% 7.50% 8.02%
Min Monthly Return -1.11% -1.66% -1.72% -0.86% -3.36% -2.88% -4.60% -0.48% -1.48% -0.44% -2.59% -1.77% -1.47% -0.72% -1.77% -1.95% -3.75%% Positive Months 16.6% 17.1% 12.4% 11.9% 12.4% 12.4% 17.6% 10.4% 15.5% 19.2% 13.5% 15.5% 9.8% 11.4% 10.9% 11.9% 15.0%

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Figure 23. Holy Grail strategy Forex monthly NAV

Figure 24. Holy Grail strategy Forex monthly drawdown

Table 12. Holy Grail strategy Forex trade results
EURUSD GBPUSD EURGBP USDCHF USDJPY USDCAD USDNZD AUDUSD AUDNZD EURCAD EURNZD NZDUSD EURAUD USDTRYPERFORMANCE
Total Returns
23.2%
24.1%
22.1%
37.3% 54.5%
26.6%
18.5%
46.8%
27.3%
20.5%
45.4%
60.8%
43.0%
52.2%
CAGR
1.4%
1.5%
1.4%
2.2%
3.0%
1.6%
1.2%
2.7%
1.7%
1.3%
2.6%
3.3%
2.5%
2.9%
Volatility
2.1%
1.7%
1.7%
2.2%
3.1%
2.6%
2.0%
2.5%
2.0%
1.9%
3.7%
3.5%
2.7%
3.1%
Maximum DrawDown
-2.7%
-0.8%
-1.5%
-0.7%
-2.0%
-2.0%
-3.4%
-0.7%
-1.2%
-1.7%
-1.9%
-2.6%
-0.9%
-1.7%
Sharpe Ratio
0.68
0.87
0.80
1.00
0.99
0.63
0.57
1.07
0.85
0.68
0.71
0.94
0.91
0.96
Calmar Ratio
0.54
1.77
0.93
3.07
1.52
0.82
0.34
3.58
1.36
0.74
1.40
1.25
2.68
1.69
Max Monthly Return
4.04%
3.02%
4.31%
4.36% 5.99%
8.64%
5.13%
4.53%
4.37%
3.89%
7.51%
6.34%
5.91%
6.83%
Min Monthly Return -1.87% -0.84% -1.34% -0.72% -2.00% -1.15% -2.08% -0.74% -1.08% -1.47% -1.85% -0.92% -0.56% -1.73%% Positive Months
20.0%
13.7%
13.1%
17.1% 17.1%
17.1%
13.7%
14.3%
14.9%
16.0%
13.7%
14.9%
14.3%
18.3%

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Statistical Hypothesis Testing“There are three types of lies: lies, damn lies, and statistics…”–Benjamin Disraeli (1804–1881), Prime Minister of Great Britain(1874–1880)
The strategies of Street Smarts were backtested on several
times series of historical data, and we used inferential statistics
to have a better insight on whether they can generate excess
returns different than and above zero. The hypothesis testingis a rigorous inference procedure to decide when a trading
rule or a strategy has some intrinsic value (i.e., it can generate
positive excessive returns and, therefore, it can help us todecide whether it can be used for trading in the future). In thiswork, we considered multiple hypothesis testing adjustments
and time series bootstrap. All the results presented in Appendix
A and Appendix B were obtained with the statistical software R(The R Project for Statistical Computing, 2022).
Multiple Hypothesis TestingMultiple hypothesis testing consists of statistical inference
by not rejecting or rejecting assumptions on an unknown
population parameter, such as mean, standard deviation,
skewness, or kurtosis, from its representative or random
samples associated statistics1 with a specific degree ofstatistical significance or confidence. The statistical inference
parameter for hypothesis testing considered in this work is
the mean return by means of probability value (i.e., p-value)assessment.
First, we calculate the multiple hypothesis testing p-values,
and then we perform the corresponding adjustments. The
p-value is the probability that the observed value of the test
statistic could have occurred given that the hypothesis being
tested (i.e., the null hypothesis) is true. The smaller the p-value,
the greater is the justification to challenge the truth of the null
hypothesis H0 and reject it in favor of the alternative hypothesis
H1. When the p-value is less than a given threshold, then H0 is
rejected and H1 is accepted. Therefore, a statistically significant
result has a p-value low enough to justify the rejection of thenull hypothesis H0.
The p-value adjustments are done through the family-wiseerror rate or Bonferroni procedure (Bonferroni, 1936) andthe false discovery rate or Benjamini-Hochberg procedure(Benjamini,1995), where these adjustments are compared withthe corresponding original p-value calculations. The population
mean p-value is evaluated through the following steps:
1. Define the unknown population mean null (H0) andalternative (H1) hypothesis, which must be mutually exclusive
and exhaustive propositions. In the two-tail test hypothesis
we define H0:μ = μ0; H1:μ ≠ μ0 . In the one-tail (i.e., right-tail) test
hypothesis we define H0:μ ≤ μ0; H1:μ > μ0 . For both tests, theunknown population mean is assumed μ0 = 0;
2. Define the unknown population mean degree of statisticalsignificance or confidence with the associated non-rejection(where the null hypothesis cannot be rejected) and rejection
regions. For the two-tail test, the critical values for therejection vs. non rejection region are: ±t* = ±cdft (1-α ⁄2),
where α is the level of statistical significance and ±cdft2023 EDITION

is the cumulative distribution function of the t-student
probability distribution. Therefore, for the two-tail test, thenull hypothesis non-rejection region is [ -t*,t* ]. For the one-tailtest, the critical value is given by t* = cdft (1-α) and the null
hypothesis non-rejection region is [ -∞,t* ];3. Calculate the standardized representative or random samples
mean statistics and test whether their values are within
the multiple hypothesis testing non-rejection or rejection
regions.
The standardized representative of a random sample mean
statistic is the t-statistic, which is equal to the corresponding
random sample mean μ̂ minus the null hypothesis mean μ0= 0 divided by the random sample standard error (σ̂ is therandom sample standard deviation, while n̂ is the number ofobservations within the random sample):

Therefore, the H0 two-tail test non-rejection region is, while the H0 one-tail test non-rejection region is. The t-statistic p-value is tested as follows:• Ifthen do not reject the null hypothesis H0 with(1-α) of statistical confidence.
• Ifthen reject the null hypothesis H0 with (1-α) of
statistical confidence.
In the hypothesis testing, if α is the level of statisticalsignificance, then (1-α) is the degree of statistical confidence. In
this assessment, we use a level of statistical significance of 5%,
which is translated into a 95% degree of statistical confidence. It
is worth noting that when computing the cdft for a two-tail test,
α is divided by two because we are considering both the lower
and upper distribution tail.
Probability Value Adjustment
The population mean p-value adjustment consists ofdecreasing the expected rate of false positives when conducting
multiple comparisons through the family-wise and the false
discovery error rate filtering methods. The type I error (or false
positive) consists of incorrectly rejecting an assumption on an
unknown population mean parameter from its representative or
random sample associated statistic. The statistical significancelevel α is the probability of making a type I error. A type IIerror (or false negative) consists of incorrectly not rejecting
an assumption on an unknown population mean parameterfrom its representative or random sample associated statistic.
Reducing the probability of making a type I error increases theprobability of making a type II error and vice versa if the sample
size remains constant.
The methods for multiple hypothesis testing adjust α, sothat the probability of getting at least one significant result
due to chance remains below a significance level α. Type I
error leads to mistakenly rejecting the null hypothesis H0, thus
investing in a worthless strategy which exposes the capital torisk without the prospect of gain. The Bonferroni correction
can be quite conservative, leading to a higher rate of false
negatives (type II error). However, while the Bonferroni
correction is considered too conservative in many fields, thehigher bar to significance may be regarded as appropriate
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by many traders and investors for backtesting a trading
strategy. Type II errors cause a potentially profitable strategy
to be ignored, thus resulting in lost investing opportunities.
From the investor or trader’s perspective, a type I error ismore serious because lost capital is considered worse thanlost investment opportunities. The family-wise error rate, orBonferroni procedure, adjusts the population mean p-values
by decreasing the expected rate of false positives (type I
errors). The false discovery rate, or Benjamini-Hochberg
procedure, yields a more relaxed p-value adjustment thanthe Bonferroni procedure. With respect to the Bonferroni
correction, there is a slight increase in type I error rate, but at
the same time a significant reduction in type II error rate.
Strategy Evaluation
The techniques of multiple hypothesis testing and p-value
adjustments were applied to the Street Smarts strategies on
the daily returns of all the asset classes and Forex crosses forthe length of the look-back period from September 2005 to
September 2021. The purpose of this evaluation was to assess
whether the mean returns of the strategies were statisticallysignificant with respect to the null hypothesis and could
consistently bring some excess returns with respect to the zero
return of the null hypothesis. The results for each strategy arereported in Appendix A and the tables summarize the p-values
and their adjusted values according to the Bonferroni and false
discovery rate (i.e., fdr) procedures. All the p-values greaterthan 0.05 (the level of statistical significance considered for thisassessment), where the null hypothesis cannot be rejected, aremarked in light red. The p-values show that the null hypothesis
for most of the asset classes and currency pairs can be rejectedin favor of the alternative hypothesis.
Table 13 confirms that the Turtle does not generatestatistically significant excess returns above zero on IEF andthe null hypothesis (both for the two-tail and one-tail test)
cannot be rejected. In the Forex market, in agreement with theresults shown in Figure 4, the null hypothesis cannot be rejected
for the currency cross AUDNZD. Furthermore, the Bonferroni
adjustment (to reduce the type I errors) does not reject the
one-tail test null hypothesis for EURUSD, EURGBP, USDCAD,
AUDUSD, AUDNZD, EURNZD, and EURAUD. This result may
seem quite conservative since these currency crosses have apositive CAGR from the backtesting. However, it is worth notingthat the returns generated by these currency pairs are smaller
than the other returns and more likely to incur in type I errors.
It is the investor or trader’s responsibility to decide whether thisconservative filtering is consistent with her/his own risk profile.
The Turtle Soup (Table 14) generated statistically significant
excess returns on all asset classes after the fdr filtering
procedure (the Bonferroni did not reject the null hypothesis only
for the one-tail test of XLF).
Both the two-tail and one-tail test for the ID-NR4 (Table15) showed a consistent statistical significance (confirmed by
Bonferroni and fdr adjustments) on all the equity indexes andsectors, bonds, gold, and real estate. In contrast, the ID-NR4
results were less significant on the Forex crosses, where only
USDJPY, USDCAD, AUDUSD, and USDTRY delivered statisticallysignificant excess returns according also to the p-value
PAGE 18 IFTA.ORG

adjustments of both the Bonferroni and fdr procedures. This
statistical analysis confirms the backtesting results shownin Figure 19 and reported in Table 10, where these currency
pairs have the higher CAGR values. In summary, the multiple
hypothesis testing supported the conclusion that ID-NR4
delivered a robust performance on the stock indexes andsectors, but it is not particularly suited for the Forex market.
The Holy Grail strategy generated statistically significant excess
returns on all the asset classes and most of the currency pairs(Table 16) also based on the Bonferroni and fdr procedures.
Even the Anti (Table 17) yielded statistically significant excess
returns on all asset classes and most of the currency pairs, also
confirmed by the Bonferroni and fdr adjustments. It is worth
pointing out that the p-value adjustments obtained with the
Bonferroni procedure are more conservative, thus reducing theprobability of type I errors, but also the trading opportunities.
In general, the backtesting results presented in "Street Smart
Strategies" were validated by the multiple hypothesis testing.
The strategies generated excess returns on all the asset classes,
except for ID-NR4, that on most of the Forex currency pairs did
not deliver statistically significant excess returns with respect
to the null hypothesis.

The Bootstrap

The bootstrap method derives a sampling distribution
shape of the test statistic2 (or sample statistic) by randomly
resampling with replacement from an original sample ofobservations. The test statistic is a point estimate (in our case,the population mean) and is computed on each sample (i.e.,time series historical data). Assuming that certain conditions
are satisfied, the bootstrap technique converges to a correct
sampling distribution as the sample size goes to infinity. In
practice, this means that given a single sample of observations,bootstrapping can produce the sampling distribution needed totest the significance of a technical analysis rule, parameter, or
strategy.
Resampling with replacement reuses the same data in theoriginal sample (Efron, 1993). For stationary data, random
resamples are used (Politis, 1994), while for non-stationary data,
random fixed-block resamples or random distributed blockresamples are used (Kuensch, 1989). In this work, the simulationof the population mean probability distribution is performedby means of random fixed-block resampling with replacement,with blocks of fixed length equal to 10, while the number ofresamplings is equal to 1000. At the end of the procedure,
we calculate the test statistic for the bootstrap, which is thearithmetic mean, where B is the number of bootstrap estimatesand is the mean of each bootstrap resampling:

The bootstrap statistical inference parameter estimations
are point estimates with their associated confidence
intervals. Such interval estimate is a range of values within
which the (unknown) population mean lies with a given
level of probability (1‒α).

IFTA JOURNAL

Bootstrap Hypothesis Testing
The bootstrap statistical inference parameters hypothesis
testing is given by the probability value estimations(MacKimmon, 2007) and by not rejecting or rejecting
assumptions on an unknown population mean from its
representative or random sample associated bootstrap test
statistic, with a specific degree of statistical significance orconfidence, similarly to what was described in "Statistical
Hypothesis Testing".
Bootstrap Probability Value Adjustment
The bootstrap population mean p-value multiple test
adjustment consists of decreasing the expected rate of false
positives in the individual statistical significance test when
conducting multiple comparisons through the family-wiseerror rate or the Sidak filtering method (Sidak, 1967). The
Sidak procedure assumes that the trials are independent andthe corresponding probability value adjustment is done for anindividual time series bootstrap hypothesis testing. It is slightly
less conservative than the Bonferroni procedure.
Bootstrap Strategy Evaluation
The bootstrap confidence intervals for the test statistic point
estimates are reported in Appendix B for each Street Smarts
strategy and for all the asset classes and currency pairs used forbacktesting. The critical values marked in light yellow highlightwhen the confidence range (DiCiccio, 1996) includes thecondition μ0 = 0, where the null hypothesis cannot be rejected.
Moreover, the tables in Appendix B also show the mean values ofthe original time series and the mean values obtained from thebootstrap sampling distribution. The bootstrap mean values arein good agreement with the original sample means.
It is possible to observe that the statistical significance tests
based on the two-tail test p-values obtained with the multiple
hypothesis testing described in "Statistical Hypothesis Testing"and summarized in Appendix A are consistent with the p-values
generated by the bootstrap procedure (two-tail test) reported inAppendix B. The results obtained with the Sidak procedure arealigned with the adjusted p-values generated by the Bonferroni
procedure, since both methods are family-wise error rate
procedures. The numerical results summarized in Appendix B
confirm that Sidak is slightly less conservative than Bonferroni.

Conclusions

In this work, some of the most popular strategies published in
the book Street Smarts (Connors, 1995) by LC and LBR more than
25 years ago were backtested across stock indexes, S&P 500
sectors, real estate, commodities, bonds, and all the major Forex
currency pairs. The strategies of Street Smarts are inherently
discretionary and were proposed for the stock and futures
markets of a quarter of a century ago. Since then, most of themarkets have changed their structure and behavior. Therefore,
in this paper the addressed problem was to determine whether
those strategies are still valid in the current markets and canbe profitably traded. The robustness of the backtesting resultspresented in this work is supported by the completeness of theasset classes considered and by the length of the historical data
look-back period.

2023 EDITION

The settings of the strategies were kept substantially alignedwith the original settings proposed by the authors. Moreover, by
testing the strategies on many different markets and for a very
representative look-back period, we assume that the resultspresented in this paper are robust and not over-fitted. The
backtests confirmed that the performance of the strategies canvary depending on the underlying assets and markets.
Another relevant contribution of this work has been arigorous and comprehensive statistical assessment of theStreet Smarts strategies. We believe that randomness canhave a larger impact in the financial markets than in othersectors. Hence, a complete evaluation and a deeper insight on
a trading strategy and on its intrinsic value can be achieved
through hypothesis testing with the techniques of inferential
statistics and bootstrap. The backtesting results and thestatistical assessment presented in this work confirm that theStreet Smarts strategies have delivered statistically significant
results across the look-back period on most of the asset classes.
Only ID-NR4 (a volatility explosion pattern) did not produce
statistically significant excessive returns on most of thecurrency pairs given the typical mean-reverting structure of theForex.
After more than 25 years since they were presented, theStreet Smarts techniques can still deliver good performances on
several asset classes and in a changing market scenario. Even if
these strategies are inherently discretionary, the robustness ofthe statistical assessment performed in this work makes someof the strategies’ underlying techniques, like swing trading,pattern breakouts, and retracements, still effective options to
be implemented in automatic trading systems.
In conclusion, the Street Smarts strategies can still beof interest to many traders and investors, both from an
educational and trading perspective. Reading Street Smarts ishighly recommended to all traders. It probably remains one of
the most valuable books on trading and every trader should befamiliar with the techniques proposed by LC and LBR.

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Efron, B., and R. Tibshirani. An Introduction to Bootstrap. Chapman andHall, 1993.
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Notes
The term sample statistic refers to the parameter being used to testa hypothesis, like the average or mean return. The term sample
statistic is interchangeable with the term test statistic.
2
A test statistic is a statistic (i.e., a quantity derived from the sample)
used in statistical hypothesis testing.
1

Acknowledgements

In memory of my beloved father Alberto, 09/15/1930–
10/29/2021.

Appendix A: Multiple Hypothesis Testing
Table 13. Turtle strategy p-values
Turtle (two-tail)
Turtle (one-tail)
Turtle FOREX (two-tail)
Turtle FOREX (one-tail)two-tail test bonferroni
fdr
one-tail test bonferroni
fdr
two-tail test bonferroni
fdr
one-tail test bonferroni
fdr
XLP
6.000E-06 1.060E-04 1.000E-05 3.000E-06 5.300E-05 5.000E-06 EURUSD 2.903E-02 4.065E-01 4.517E-02 1.452E-02 2.032E-01 2.258E-02
XLY
0.000E+00 5.000E-06 1.000E-06 0.000E+00 3.000E-06 1.000E-06 GBPUSD 2.914E-03 4.080E-02 6.800E-03 1.457E-03 2.040E-02 3.400E-03
XLE
7.600E-05 1.286E-03 1.070E-04 3.800E-05 6.430E-04 5.400E-05 EURGBP 4.585E-02 6.418E-01 5.349E-02 2.292E-02 3.209E-01 2.674E-02
XLV
3.000E-06 4.300E-05 6.000E-06 1.000E-06 2.200E-05 3.000E-06 USDCHF 2.000E-05 2.770E-04 9.200E-05 1.000E-05 1.390E-04 4.600E-05
XLF
6.000E-06 1.090E-04 1.000E-05 3.000E-06 5.500E-05 5.000E-06 USDJPY
6.000E-06 8.400E-05 4.200E-05 3.000E-06 4.200E-05 2.100E-05
XLI
4.000E-06 7.600E-05 8.000E-06 2.000E-06 3.800E-05 4.000E-06 USDCAD 8.908E-02 1.000E+00 9.593E-02 4.454E-02 6.235E-01 4.797E-02
XLK
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 USDNZD 4.563E-03 6.388E-02 9.126E-03 2.281E-03 3.194E-02 4.563E-03
XLB
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 AUDUSD 1.319E-02 1.846E-01 2.308E-02 6.593E-03 9.230E-02 1.154E-02
XLU
3.000E-06 5.600E-05 7.000E-06 2.000E-06 2.800E-05 4.000E-06 AUDNZD 9.456E-01 1.000E+00 9.456E-01 5.272E-01 1.000E+00 5.272E-01
IYZ
3.873E-03 6.584E-02 4.115E-03 1.936E-03 3.292E-02 2.057E-03 EURCAD 6.200E-05 8.650E-04 1.730E-04 3.100E-05 4.330E-04 8.700E-05
IYR
0.000E+00 7.000E-06 1.000E-06 0.000E+00 3.000E-06 1.000E-06 EURNZD 4.384E-02 6.138E-01 5.349E-02 2.192E-02 3.069E-01 2.674E-02
SPY
2.050E-04 3.481E-03 2.490E-04 1.020E-04 1.740E-03 1.240E-04 NZDUSD 4.800E-05 6.740E-04 1.690E-04 2.400E-05 3.370E-04 8.400E-05
DIA
3.070E-04 5.217E-03 3.480E-04 1.530E-04 2.609E-03 1.740E-04 EURAUD 3.915E-02 5.481E-01 5.349E-02 1.958E-02 2.741E-01 2.674E-02
IEF
4.580E-01 1.000E+00 4.580E-01 7.710E-01 1.000E+00 7.710E-01 USDTRY
1.000E-06 1.500E-05 1.500E-05 1.000E-06 8.000E-06 8.000E-06
TLT
1.090E-04 1.851E-03 1.420E-04 5.400E-05 9.250E-04 7.100E-05
GLD 0.000E+00 2.000E-06 0.000E+00 0.000E+00 1.000E-06 0.000E+00
QQQ 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00

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Table 14. Turtle Soup strategy p-values
Turtle Soup (two-tail)
Turtle Soup (one-tail)
Turtle Soup FOREX (two-tail)
Turtle Soup FOREX (one-tail)two-tail test bonferroni
fdr
one-tail test bonferroni
fdr
two-tail test bonferroni
fdr
one-tail test bonferroni
fdr
XLP
6.420E-04 1.091E-02 8.480E-04 3.210E-04 5.453E-03 4.240E-04 EURUSD 1.860E-04 2.609E-03 3.220E-04 9.300E-05 1.304E-03 1.610E-04
XLY
4.400E-05 7.400E-04 9.200E-05 2.200E-05 3.700E-04 4.600E-05 GBPUSD 1.424E-03 1.993E-02 1.424E-03 7.120E-04 9.965E-03 7.120E-04
XLE
3.000E-06 4.700E-05 1.200E-05 1.000E-06 2.400E-05 6.000E-06 EURGBP 8.150E-04 1.142E-02 8.780E-04 4.080E-04 5.707E-03 4.390E-04
XLV
1.851E-03 3.147E-02 2.098E-03 9.250E-04 1.573E-02 1.049E-03 USDCHF 2.300E-04 3.221E-03 3.220E-04 1.150E-04 1.610E-03 1.610E-04
XLF
1.476E-02 2.509E-01 1.476E-02 7.379E-03 1.254E-01 7.379E-03 USDJPY
2.240E-04 3.138E-03 3.220E-04 1.120E-04 1.569E-03 1.610E-04
XLI
5.540E-04 9.414E-03 8.480E-04 2.770E-04 4.707E-03 4.240E-04 USDCAD 1.700E-05 2.430E-04 6.100E-05 9.000E-06 1.220E-04 3.000E-05
XLK
1.850E-04 3.143E-03 3.140E-04 9.200E-05 1.571E-03 1.570E-04 USDNZD 1.000E-06 9.000E-06 8.000E-06 0.000E+00 5.000E-06 4.000E-06
XLB
2.400E-05 4.150E-04 6.900E-05 1.200E-05 2.080E-04 3.500E-05 AUDUSD 4.200E-05 5.930E-04 9.900E-05 2.100E-05 2.960E-04 4.900E-05
XLU 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 AUDNZD 3.040E-04 4.253E-03 3.870E-04 1.520E-04 2.127E-03 1.930E-04
IYZ
1.760E-04 2.990E-03 3.140E-04 8.800E-05 1.495E-03 1.570E-04 EURCAD 3.900E-05 5.460E-04 9.900E-05 1.900E-05 2.730E-04 4.900E-05
IYR
3.000E-06 5.000E-05 1.200E-05 1.000E-06 2.500E-05 6.000E-06 EURNZD 1.000E-06 1.500E-05 8.000E-06 1.000E-06 8.000E-06 4.000E-06
SPY
6.480E-04 1.102E-02 8.480E-04 3.240E-04 5.511E-03 4.240E-04 NZDUSD 6.300E-05 8.870E-04 1.270E-04 3.200E-05 4.430E-04 6.300E-05
DIA
3.633E-03 6.176E-02 3.860E-03 1.817E-03 3.088E-02 1.930E-03 EURAUD 5.210E-04 7.300E-03 6.080E-04 2.610E-04 3.650E-03 3.040E-04
IEF
9.100E-04 1.547E-02 1.105E-03 4.550E-04 7.737E-03 5.530E-04 USDTRY
1.700E-05 2.380E-04 6.100E-05 9.000E-06 1.190E-04 3.000E-05
TLT
3.300E-05 5.690E-04 8.100E-05 1.700E-05 2.850E-04 4.100E-05
GLD 0.000E+00 1.000E-06 0.000E+00 0.000E+00 0.000E+00 0.000E+00
QQQ 1.000E-05 1.740E-04 3.500E-05 5.000E-06 8.700E-05 1.700E-05

Table 15. ID-NR4 strategy p-values
ID-NR4 (two-tail)ID-NR4 (one-tail)ID-NR4 FOREX (two-tail)ID-NR4 FOREX (one-tail)two-tail test bonferroni
fdr
one-tail test bonferroni
fdr
two-tail test bonferroni
fdr
one-tail test bonferroni
fdr
XLP
1.010E-03 1.717E-02 1.010E-03 5.050E-04 8.583E-03 5.050E-04 EURUSD 2.578E-01 1.000E+00 3.281E-01 1.289E-01 1.000E+00 1.641E-01
XLY
1.630E-04 2.779E-03 1.740E-04 8.200E-05 1.390E-03 8.700E-05 GBPUSD 7.590E-02 1.000E+00 1.181E-01 3.795E-02 5.313E-01 5.904E-02
XLE
1.000E-06 1.500E-05 3.000E-06 0.000E+00 8.000E-06 2.000E-06 EURGBP 6.030E-01 1.000E+00 6.030E-01 3.015E-01 1.000E+00 3.015E-01
XLV
1.040E-04 1.761E-03 1.170E-04 5.200E-05 8.800E-04 5.900E-05 USDCHF 2.435E-02 3.408E-01 6.817E-02 1.217E-02 1.704E-01 3.409E-02
XLF
0.000E+00 5.000E-06 1.000E-06 0.000E+00 3.000E-06 1.000E-06 USDJPY
7.000E-06 9.200E-05 6.000E-05 3.000E-06 4.600E-05 3.000E-05
XLI
0.000E+00 2.000E-06 1.000E-06 0.000E+00 1.000E-06 0.000E+00 USDCAD 1.396E-03 1.954E-02 6.357E-03 6.980E-04 9.769E-03 3.178E-03
XLK
8.300E-05 1.409E-03 1.010E-04 4.100E-05 7.050E-04 5.000E-05 USDNZD 7.379E-02 1.000E+00 1.181E-01 3.689E-02 5.165E-01 5.904E-02
XLB
6.000E-06 9.600E-05 1.100E-05 3.000E-06 4.800E-05 5.000E-06 AUDUSD 1.816E-03 2.543E-02 6.357E-03 9.080E-04 1.271E-02 3.178E-03
XLU
1.000E-06 2.300E-05 4.000E-06 1.000E-06 1.200E-05 2.000E-06 AUDNZD 5.606E-01 1.000E+00 6.030E-01 2.803E-01 1.000E+00 3.015E-01
IYZ
9.000E-06 1.500E-04 1.500E-05 4.000E-06 7.500E-05 7.000E-06 EURCAD 2.894E-01 1.000E+00 3.376E-01 1.447E-01 1.000E+00 1.688E-01
IYR
2.100E-05 3.510E-04 2.700E-05 1.000E-05 1.760E-04 1.400E-05 EURNZD 7.393E-02 1.000E+00 1.181E-01 3.696E-02 5.175E-01 5.904E-02
SPY0.000E+00 1.000E-06 0.000E+00 0.000E+00 0.000E+00 0.000E+00 NZDUSD 9.372E-02 1.000E+00 1.312E-01 4.686E-02 6.561E-01 6.561E-02
DIA
6.000E-06 9.800E-05 1.100E-05 3.000E-06 4.900E-05 5.000E-06 EURAUD 6.592E-02 9.229E-01 1.181E-01 3.296E-02 4.614E-01 5.904E-02
IEF
1.300E-05 2.200E-04 1.800E-05 6.000E-06 1.100E-04 9.000E-06 USDTRY
9.000E-06 1.210E-04 6.000E-05 4.000E-06 6.000E-05 3.000E-05
TLT
3.000E-06 5.500E-05 8.000E-06 2.000E-06 2.700E-05 4.000E-06
GLD 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
QQQ 1.000E-05 1.630E-04 1.500E-05 5.000E-06 8.200E-05 7.000E-06

Table 16. Holy Grail strategy p-values
Holy Grail (one-tail)
Holy Grail (two-tail)
Holy Grail FOREX (two-tail)
Holy Grail FOREX (one-tail)two-tail test bonferroni
fdr
one-tail test bonferroni
fdr
two-tail test bonferroni
fdr
one-tail test bonferroni
fdr
XLP
0.000E+00 3.000E-06 1.000E-06 0.000E+00 2.000E-06 0.000E+00 EURUSD 6.244E-03 8.742E-02 6.724E-03 3.122E-03 4.371E-02 3.362E-03
XLY
1.000E-06 2.100E-05 3.000E-06 1.000E-06 1.100E-05 2.000E-06 GBPUSD 1.830E-04 2.556E-03 3.450E-04 9.100E-05 1.278E-03 1.730E-04
XLE
2.000E-06 3.200E-05 4.000E-06 1.000E-06 1.600E-05 2.000E-06 EURGBP 1.123E-03 1.572E-02 1.429E-03 5.610E-04 7.858E-03 7.140E-04
XLV
1.498E-03 2.547E-02 1.592E-03 7.490E-04 1.274E-02 7.960E-04 USDCHF 1.900E-05 2.620E-04 5.600E-05 9.000E-06 1.310E-04 2.800E-05
XLF
2.600E-04 4.419E-03 4.350E-04 1.300E-04 2.209E-03 2.170E-04 USDJPY
3.000E-06 3.800E-05 3.500E-05 1.000E-06 1.900E-05 1.800E-05
XLI
1.000E-06 1.000E-05 2.000E-06 0.000E+00 5.000E-06 1.000E-06 USDCAD 4.540E-04 6.349E-03 6.750E-04 2.270E-04 3.175E-03 3.370E-04
XLK
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 USDNZD 6.603E-02 9.244E-01 6.603E-02 3.302E-02 4.622E-01 3.302E-02
XLB
2.000E-06 3.800E-05 4.000E-06 1.000E-06 1.900E-05 2.000E-06 AUDUSD 1.600E-05 2.230E-04 5.600E-05 8.000E-06 1.110E-04 2.800E-05
XLU
5.740E-04 9.758E-03 6.840E-04 2.870E-04 4.879E-03 3.420E-04 AUDNZD 2.000E-05 2.800E-04 5.600E-05 1.000E-05 1.400E-04 2.800E-05
IYZ
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 EURCAD 5.095E-03 7.133E-02 5.944E-03 2.548E-03 3.567E-02 2.972E-03
IYR
3.520E-04 5.983E-03 4.980E-04 1.760E-04 2.991E-03 2.490E-04 EURNZD 1.970E-04 2.764E-03 3.450E-04 9.900E-05 1.382E-03 1.730E-04
SPY
0.000E+00 2.000E-06 1.000E-06 0.000E+00 1.000E-06 0.000E+00 NZDUSD 5.000E-06 7.100E-05 3.500E-05 3.000E-06 3.500E-05 1.800E-05
DIA
6.030E-04 1.026E-02 6.840E-04 3.020E-04 5.129E-03 3.420E-04 EURAUD 1.800E-04 2.516E-03 3.450E-04 9.000E-05 1.258E-03 1.730E-04
IEF
3.810E-04 6.479E-03 4.980E-04 1.910E-04 3.240E-03 2.490E-04 USDTRY
4.820E-04 6.747E-03 6.750E-04 2.410E-04 3.374E-03 3.370E-04
TLT
2.810E-04 4.780E-03 4.350E-04 1.410E-04 2.390E-03 2.170E-04
GLD
3.920E-03 6.664E-02 3.920E-03 1.960E-03 3.332E-02 1.960E-03
QQQ 1.000E-06 1.400E-05 2.000E-06 0.000E+00 7.000E-06 1.000E-06

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2023 EDITION

Table 17. Anti strategy p-values
Anti (two-tail)Anti (one-tail)Anti FOREX (two-tail)Anti FOREX (one-tail)two-tail test bonferroni
fdr
one-tail test bonferroni
fdr
two-tail test bonferroni
fdr
one-tail test bonferroni
fdr
XLP
1.000E-06 2.000E-05 1.000E-06 1.000E-06 1.000E-05 1.000E-06 EURUSD 8.300E-05 1.167E-03 1.170E-04 4.200E-05 5.840E-04 5.800E-05
XLY
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 GBPUSD 4.300E-05 5.980E-04 7.500E-05 2.100E-05 2.990E-04 3.700E-05
XLE
0.000E+00 5.000E-06 0.000E+00 0.000E+00 2.000E-06 0.000E+00 EURGBP 5.900E-05 8.210E-04 9.100E-05 2.900E-05 4.110E-04 4.600E-05
XLV
1.100E-05 1.810E-04 1.100E-05 5.000E-06 9.000E-05 6.000E-06 USDCHF 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
XLF
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 USDJPY
1.000E-06 1.700E-05 3.000E-06 1.000E-06 8.000E-06 1.000E-06
XLI
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 USDCAD 1.000E-06 1.700E-05 3.000E-06 1.000E-06 9.000E-06 1.000E-06
XLK
1.000E-06 1.300E-05 1.000E-06 0.000E+00 7.000E-06 1.000E-06 USDNZD 9.250E-04 1.296E-02 1.080E-03 4.630E-04 6.478E-03 5.400E-04
XLB
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 AUDUSD 1.000E-06 1.700E-05 3.000E-06 1.000E-06 9.000E-06 1.000E-06
XLU
2.540E-04 4.311E-03 2.540E-04 1.270E-04 2.155E-03 1.270E-04 AUDNZD 2.042E-01 1.000E+00 2.042E-01 1.021E-01 1.000E+00 1.021E-01
IYZ
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 EURCAD 6.167E-02 8.634E-01 6.641E-02 3.083E-02 4.317E-01 3.321E-02
IYR
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 EURNZD 3.370E-04 4.712E-03 4.280E-04 1.680E-04 2.356E-03 2.140E-04
SPY
0.000E+00 1.000E-06 0.000E+00 0.000E+00 0.000E+00 0.000E+00 NZDUSD 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
DIA
1.000E-05 1.620E-04 1.100E-05 5.000E-06 8.100E-05 5.000E-06 EURAUD 2.100E-05 2.950E-04 4.200E-05 1.100E-05 1.480E-04 2.100E-05
IEF
0.000E+00 3.000E-06 0.000E+00 0.000E+00 2.000E-06 0.000E+00 USDTRY 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
TLT
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
GLD
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
QQQ 0.000E+00 4.000E-06 0.000E+00 0.000E+00 2.000E-06 0.000E+00

Appendix B: Bootstrap
Table 18. Turtle strategy bootstrap confidence intervals and p-values
Turtle (two-tail bootstrap)
Turtle FOREX (two-tail bootstrap)sample mean boot mean ci lower ci upper
p-value p-value Sidak
sample mean boot mean ci lower
ci upperp-value p-value Sidak
XLP
1.450E-04 1.454E-04 8.044E-05 2.087E-04 0.000E+00 0.000E+00 EURUSD
6.323E-05 6.387E-05 6.016E-06 1.182E-04 3.000E-02
3.472E-01
XLY
2.597E-04 2.616E-04 1.593E-04 3.655E-04 0.000E+00 0.000E+00 GBPUSD
7.832E-05 7.704E-05 2.878E-05 1.261E-04 2.000E-03
2.764E-02
XLE
2.777E-04 2.765E-04 1.369E-04 4.217E-04 0.000E+00 0.000E+00 EURGBP
4.674E-05 4.712E-05 9.063E-07 9.828E-05 4.400E-02
4.674E-01
XLV
2.196E-04 2.144E-04 1.190E-04 3.067E-04 0.000E+00 0.000E+00 USDCHF
1.091E-04 1.079E-04 6.010E-05 1.563E-04 0.000E+00 0.000E+00
XLF
2.015E-04 1.987E-04 1.065E-04 2.953E-04 0.000E+00 0.000E+00 USDJPY
1.357E-04 1.373E-04 8.164E-05 1.966E-04 0.000E+00 0.000E+00
XLI
2.356E-04 2.331E-04 1.187E-04 3.380E-04 0.000E+00 0.000E+00 USDCAD
4.548E-05 4.590E-05 -9.539E-06 1.004E-04 9.000E-02
7.330E-01
XLK
2.795E-04 2.776E-04 1.808E-04 3.640E-04 0.000E+00 0.000E+00 USDNZD
9.220E-05 9.487E-05 3.162E-05 1.590E-04 8.000E-03
1.064E-01
XLB
2.376E-04 2.385E-04 1.493E-04 3.221E-04 0.000E+00 0.000E+00 AUDUSD
1.060E-04 1.086E-04 1.955E-05 1.849E-04 2.000E-02
2.464E-01
XLU
1.677E-04 1.683E-04 9.373E-05 2.341E-04 0.000E+00 0.000E+00 AUDNZD -1.104E-06 -1.652E-06 -3.451E-05 3.015E-05 9.420E-01 1.000E+00
IYZ
1.442E-04 1.457E-04 3.234E-05 2.457E-04 6.000E-03
9.725E-02 EURCAD
1.024E-04 1.017E-04 4.965E-05 1.555E-04 0.000E+00 0.000E+00
IYR
2.279E-04 2.269E-04 1.324E-04 3.125E-04 0.000E+00 0.000E+00 EURNZD
4.478E-05 4.522E-05 -1.354E-06 8.989E-05 5.600E-02
5.537E-01
SPY
1.703E-04 1.703E-04 8.156E-05 2.521E-04 0.000E+00 0.000E+00 NZDUSD
1.317E-04 1.331E-04 7.027E-05 2.044E-04 0.000E+00 0.000E+00
DIA
1.780E-04 1.781E-04 7.093E-05 2.720E-04 0.000E+00 0.000E+00 EURAUD
6.123E-05 6.096E-05 3.918E-07 1.193E-04 4.600E-02
4.828E-01
IEF-1.974E-05 -1.846E-05 -7.013E-05 3.295E-05 4.860E-01 1.000E+00 USDTRY
2.020E-04 2.024E-04 1.247E-04 2.880E-04 0.000E+00 0.000E+00
TLT
1.664E-04 1.655E-04 8.099E-05 2.499E-04 0.000E+00 0.000E+00
GLD
2.457E-04 2.450E-04 1.524E-04 3.371E-04 0.000E+00 0.000E+00
QQQ
3.370E-04 3.379E-04 2.294E-04 4.287E-04 0.000E+00 0.000E+00

Table 19. Turtle Soup strategy bootstrap confidence intervals and p-values
Turtle Soup (two-tail bootstrap)
Turtle Soup FOREX (two-tail bootstrap)sample mean boot mean ci lower ci upper
p-value p-value Sidak
sample mean boot mean ci lower
ci upperp-value p-value Sidak
XLP
1.364E-04 1.357E-04 4.683E-05 2.132E-04 2.000E-03
3.346E-02 EURUSD
8.377E-05 8.337E-05 4.196E-05 1.291E-04 0.000E+00 0.000E+00
XLY
1.796E-04 1.811E-04 9.528E-05 2.710E-04 0.000E+00 0.000E+00 GBPUSD
6.209E-05 6.180E-05 2.464E-05 1.028E-04 2.000E-03
2.764E-02
XLE
2.259E-04 2.233E-04 1.246E-04 3.239E-04 0.000E+00 0.000E+00 EURGBP
6.086E-05 6.173E-05 2.461E-05 1.032E-04 0.000E+00 0.000E+00
XLV
1.243E-04 1.245E-04 4.425E-05 1.995E-04 0.000E+00 0.000E+00 USDCHF
7.901E-05 8.140E-05 4.124E-05 1.274E-04 0.000E+00 0.000E+00
XLF
9.906E-05 9.875E-05 2.912E-05 1.704E-04 6.000E-03
9.725E-02 USDJPY
6.383E-05 6.447E-05 3.334E-05 9.826E-05 0.000E+00 0.000E+00
XLI
1.378E-04 1.394E-04 6.225E-05 2.239E-04 0.000E+00 0.000E+00 USDCAD
9.533E-05 9.657E-05 5.684E-05 1.463E-04 0.000E+00 0.000E+00
XLK
1.480E-04 1.482E-04 7.864E-05 2.345E-04 0.000E+00 0.000E+00 USDNZD
1.505E-04 1.491E-04 9.159E-05 2.125E-04 0.000E+00 0.000E+00
XLB
1.566E-04 1.578E-04 8.741E-05 2.370E-04 0.000E+00 0.000E+00 AUDUSD
9.919E-05 9.926E-05 5.270E-05 1.468E-04 0.000E+00 0.000E+00
XLU
2.106E-04 2.107E-04 1.354E-04 2.937E-04 0.000E+00 0.000E+00 AUDNZD
6.532E-05 6.500E-05 3.290E-05 1.011E-04 0.000E+00 0.000E+00
IYZ
2.393E-04 2.379E-04 1.309E-04 3.885E-04 0.000E+00 0.000E+00 EURCAD
9.360E-05 9.409E-05 5.073E-05 1.409E-04 0.000E+00 0.000E+00
IYR
1.625E-04 1.628E-04 9.734E-05 2.309E-04 0.000E+00 0.000E+00 EURNZD
1.403E-04 1.407E-04 9.066E-05 1.987E-04 0.000E+00 0.000E+00
SPY
1.245E-04 1.268E-04 5.684E-05 2.040E-04 0.000E+00 0.000E+00 NZDUSD
1.070E-04 1.060E-04 5.193E-05 1.618E-04 0.000E+00 0.000E+00
DIA
1.073E-04 1.074E-04 2.867E-05 1.789E-04 8.000E-03
1.276E-01 EURAUD
8.595E-05 8.565E-05 3.566E-05 1.458E-04 0.000E+00 0.000E+00
IEF
6.821E-05 6.865E-05 3.154E-05 1.130E-04 0.000E+00 0.000E+00 USDTRY
1.172E-04 1.164E-04 6.386E-05 1.709E-04 0.000E+00 0.000E+00
TLT
1.240E-04 1.241E-04 6.721E-05 1.862E-04 0.000E+00 0.000E+00
GLD
2.332E-04 2.311E-04 1.525E-04 3.162E-04 0.000E+00 0.000E+00
QQQ
1.835E-04 1.821E-04 1.038E-04 2.702E-04 0.000E+00 0.000E+00

PAGE 22 IFTA.ORG

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Table 20. ID-NR4 strategy bootstrap confidence intervals and p-values
ID-NR4 (two-tail bootstrap)
ID-NR4 FOREX (two-tail bootstrap)sample mean boot mean ci lower ci upper
p-value p-value Sidak
sample mean boot mean ci lower
ci upperp-value p-value Sidak
XLP
1.320E-04 1.333E-04 4.836E-05 2.136E-04 2.000E-03
3.346E-02 EURUSD
2.870E-05 2.785E-05 -2.092E-05 8.121E-05 2.980E-01
9.929E-01
XLY
1.748E-04 1.741E-04 9.282E-05 2.578E-04 0.000E+00 0.000E+00 GBPUSD
4.525E-05 4.493E-05 3.462E-07 9.926E-05 4.600E-02
4.828E-01
XLE
3.303E-04 3.288E-04 2.031E-04 4.662E-04 0.000E+00 0.000E+00 EURGBP
1.167E-05 1.080E-05 -3.436E-05 5.492E-05 6.080E-01 1.000E+00
XLV
1.386E-04 1.375E-04 7.185E-05 2.068E-04 0.000E+00 0.000E+00 USDCHF
7.557E-05 7.589E-05 1.173E-05 1.480E-04 1.800E-02
2.245E-01
XLF
3.240E-04 3.258E-04 2.040E-04 4.457E-04 0.000E+00 0.000E+00 USDJPY
1.550E-04 1.545E-04 8.713E-05 2.278E-04 0.000E+00 0.000E+00
XLI
2.789E-04 2.779E-04 1.876E-04 3.803E-04 0.000E+00 0.000E+00 USDCAD
9.550E-05 9.458E-05 3.544E-05 1.583E-04 0.000E+00 0.000E+00
XLK
1.826E-04 1.809E-04 9.021E-05 2.749E-04 0.000E+00 0.000E+00 USDNZD
6.103E-05 6.174E-05 -2.591E-06 1.280E-04 5.600E-02
5.537E-01
XLB
2.279E-04 2.267E-04 1.333E-04 3.203E-04 0.000E+00 0.000E+00 AUDUSD
1.159E-04 1.158E-04 4.295E-05 1.959E-04 0.000E+00 0.000E+00
XLU
2.072E-04 2.075E-04 1.313E-04 2.867E-04 0.000E+00 0.000E+00 AUDNZD
1.087E-05 1.132E-05 -2.518E-05 4.826E-05 5.440E-01 1.000E+00
IYZ
2.115E-04 2.137E-04 1.243E-04 3.114E-04 0.000E+00 0.000E+00 EURCAD
2.490E-05 2.443E-05 -2.108E-05 7.237E-05 3.140E-01
9.949E-01
IYR
2.508E-04 2.508E-04 1.395E-04 3.642E-04 0.000E+00 0.000E+00 EURNZD
5.061E-05 5.093E-05 3.113E-07 1.136E-04 4.600E-02
4.828E-01
SPY
2.717E-04 2.722E-04 1.810E-04 3.678E-04 0.000E+00 0.000E+00 NZDUSD
5.993E-05 5.997E-05 -1.083E-05 1.315E-04 8.400E-02
7.072E-01
DIA
1.890E-04 1.900E-04 1.120E-04 2.703E-04 0.000E+00 0.000E+00 EURAUD
4.597E-05 4.585E-05 -3.075E-06 9.495E-05 6.000E-02
5.795E-01
IEF
7.728E-05 7.708E-05 4.457E-05 1.120E-04 0.000E+00 0.000E+00 USDTRY
1.863E-04 1.868E-04 1.086E-04 2.602E-04 0.000E+00 0.000E+00
TLT
1.777E-04 1.754E-04 9.886E-05 2.531E-04 0.000E+00 0.000E+00
GLD
3.706E-04 3.731E-04 2.712E-04 4.790E-04 0.000E+00 0.000E+00
QQQ
2.333E-04 2.335E-04 1.425E-04 3.338E-04 0.000E+00 0.000E+00

Table 21. Holy Grail strategy bootstrap confidence intervals and p-values
Holy Grail (two-tail bootstrap)
Holy Grail FOREX (two-tail bootstrap)sample mean boot mean ci lower
ci upperp-value p-value Sidak
sample mean boot mean ci lower
ci upperp-value p-value Sidak
XLP
1.667E-04 1.680E-04 9.898E-05 2.544E-04 0.000E+00 0.000E+00 EURUSD
5.556E-05 5.568E-05 1.219E-05 1.021E-04 6.000E-03
8.080E-02
XLY
2.004E-04 1.988E-04 1.200E-04 2.891E-04 0.000E+00 0.000E+00 GBPUSD
5.720E-05 5.753E-05 2.554E-05 9.663E-05 0.000E+00 0.000E+00
XLE
2.047E-04 2.086E-04 1.164E-04 3.171E-04 0.000E+00 0.000E+00 EURGBP
5.301E-05 5.325E-05 2.077E-05 8.841E-05 0.000E+00 0.000E+00
XLV
1.064E-04 1.075E-04 4.562E-05 1.847E-04 0.000E+00 0.000E+00 USDCHF
8.415E-05 8.335E-05 4.411E-05 1.363E-04 0.000E+00 0.000E+00
XLF
2.009E-04 2.012E-04 7.959E-05 3.358E-04 0.000E+00 0.000E+00 USDJPY
1.155E-04 1.148E-04 6.449E-05 1.723E-04 0.000E+00 0.000E+00
XLI
2.014E-04 1.991E-04 1.053E-04 3.054E-04 0.000E+00 0.000E+00 USDCAD
6.262E-05 6.310E-05 2.305E-05 1.142E-04 0.000E+00 0.000E+00
XLK
3.225E-04 3.242E-04 2.034E-04 4.730E-04 0.000E+00 0.000E+00 USDNZD
4.576E-05 4.625E-05 4.059E-06 9.128E-05 2.800E-02
3.281E-01
XLB
1.956E-04 1.947E-04 8.836E-05 3.134E-04 0.000E+00 0.000E+00 AUDUSD
1.020E-04 1.020E-04 5.841E-05 1.508E-04 0.000E+00 0.000E+00
XLU
1.350E-04 1.360E-04 5.365E-05 2.456E-04 0.000E+00 0.000E+00 AUDNZD
6.397E-05 6.329E-05 2.825E-05 1.042E-04 0.000E+00 0.000E+00
IYZ
2.571E-04 2.594E-04 1.704E-04 3.529E-04 0.000E+00 0.000E+00 EURCAD
4.971E-05 5.048E-05 1.825E-05 8.770E-05 4.000E-03
5.457E-02
IYR
1.339E-04 1.356E-04 4.995E-05 2.339E-04 0.000E+00 0.000E+00 EURNZD
9.979E-05 1.009E-04 3.830E-05 1.716E-04 0.000E+00 0.000E+00
SPY
2.341E-04 2.355E-04 1.351E-04 3.632E-04 0.000E+00 0.000E+00 NZDUSD
1.264E-04 1.260E-04 6.989E-05 1.927E-04 0.000E+00 0.000E+00
DIA
1.139E-04 1.140E-04 4.860E-05 1.981E-04 0.000E+00 0.000E+00 EURAUD
9.521E-05 9.476E-05 4.902E-05 1.516E-04 0.000E+00 0.000E+00
IEF
4.612E-05 4.697E-05 2.157E-05 7.455E-05 0.000E+00 0.000E+00 USDTRY
1.125E-04 1.115E-04 4.606E-05 1.714E-04 0.000E+00 0.000E+00
TLT
1.134E-04 1.121E-04 4.714E-05 1.898E-04 0.000E+00 0.000E+00
GLD
8.455E-05 8.527E-05 3.052E-05 1.454E-04 0.000E+00 0.000E+00
QQQ
2.026E-04 2.016E-04 1.188E-04 3.050E-04 0.000E+00 0.000E+00

Table 22. Anti strategy bootstrap confidence intervals and p-values
Anti (two-tail bootstrap)
Anti FOREX (two-tail bootstrap)sample mean boot mean ci lower ci upper
p-value p-value Sidak
sample mean boot mean ci lower
ci upperp-value p-value Sidak
XLP
1.528E-04 1.523E-04 9.369E-05 2.139E-04 0.000E+00 0.000E+00 EURUSD
7.597E-05 7.693E-05 4.025E-05 1.141E-04 0.000E+00 0.000E+00
XLY
2.435E-04 2.431E-04 1.736E-04 3.219E-04 0.000E+00 0.000E+00 GBPUSD
8.496E-05 8.623E-05 4.408E-05 1.264E-04 0.000E+00 0.000E+00
XLE
3.029E-04 3.021E-04 2.014E-04 4.323E-04 0.000E+00 0.000E+00 EURGBP
7.024E-05 7.086E-05 3.694E-05 1.097E-04 0.000E+00 0.000E+00
XLV
1.316E-04 1.318E-04 7.635E-05 1.919E-04 0.000E+00 0.000E+00 USDCHF
1.147E-04 1.158E-04 7.769E-05 1.564E-04 0.000E+00 0.000E+00
XLF
3.229E-04 3.264E-04 2.404E-04 4.159E-04 0.000E+00 0.000E+00 USDJPY
9.496E-05 9.381E-05 5.484E-05 1.329E-04 0.000E+00 0.000E+00
XLI
2.398E-04 2.395E-04 1.646E-04 3.165E-04 0.000E+00 0.000E+00 USDCAD
9.537E-05 9.604E-05 5.680E-05 1.365E-04 0.000E+00 0.000E+00
XLK
2.340E-04 2.347E-04 1.504E-04 3.314E-04 0.000E+00 0.000E+00 USDNZD
7.677E-05 7.624E-05 2.987E-05 1.228E-04 0.000E+00 0.000E+00
XLB
2.754E-04 2.771E-04 2.030E-04 3.536E-04 0.000E+00 0.000E+00 AUDUSD
1.127E-04 1.126E-04 6.532E-05 1.611E-04 0.000E+00 0.000E+00
XLU
1.060E-04 1.069E-04 5.091E-05 1.638E-04 0.000E+00 0.000E+00 AUDNZD
1.985E-05 2.009E-05 -7.482E-06 4.951E-05 1.680E-01
9.238E-01
IYZ
2.267E-04 2.269E-04 1.649E-04 2.900E-04 0.000E+00 0.000E+00 EURCAD
3.741E-05 3.692E-05 -2.310E-06 7.650E-05 5.600E-02
5.537E-01
IYR
2.644E-04 2.620E-04 1.863E-04 3.322E-04 0.000E+00 0.000E+00 EURNZD
7.404E-05 7.448E-05 3.440E-05 1.128E-04 0.000E+00 0.000E+00
SPY
1.823E-04 1.821E-04 1.157E-04 2.478E-04 0.000E+00 0.000E+00 NZDUSD
1.353E-04 1.346E-04 8.872E-05 1.813E-04 0.000E+00 0.000E+00
DIA
1.435E-04 1.455E-04 8.491E-05 2.041E-04 0.000E+00 0.000E+00 EURAUD
9.274E-05 9.378E-05 4.883E-05 1.367E-04 0.000E+00 0.000E+00
IEF
9.057E-05 9.158E-05 5.504E-05 1.305E-04 0.000E+00 0.000E+00 USDTRY
1.440E-04 1.440E-04 9.908E-05 1.915E-04 0.000E+00 0.000E+00
TLT
2.021E-04 2.019E-04 1.457E-04 2.581E-04 0.000E+00 0.000E+00
GLD
2.151E-04 2.161E-04 1.479E-04 2.844E-04 0.000E+00 0.000E+00
QQQ
2.064E-04 2.068E-04 1.289E-04 2.919E-04 0.000E+00 0.000E+00

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Order Flow Analysis

Anand Behere
Duesseldorf, Germany+49 1703602576
behere.anand23@gmail.com

By Anand Behere

What Is Order Flow Analysis and Its
Importance?

Order flow analysis (OFA) is a tool that helps to analyze thestrength of bulls or bears in the market—in other words, who isin control, buyers or sellers? Markets are driven by what we call“smart money”, and if traders are able to get a hint of what the
big institutions are doing, then the analysis would help them toalign their trades with the trend. Most indicators are lagging
in nature and will only trigger a buy/sell signal after part of thetrend is over, but data, on the other hand, is a leading indicator,
which gives an edge to retail traders.
Another significant use of this tool is to identify whether
breakouts/breakdowns are real or fake. The tool will also help topoint out the exhaustion levels for trending up moves or down
moves in intraday.

What Are Some of the ImportantParameters to Be Considered in
OFA and When Should They Be
Monitored?

Big orders are normally executed through limit orders ormarket orders. OFA talks about aggressive market buy/sellorders and the data needs to be analyzed only at reference
points. These reference levels could be previous day high/Figure 1. OFA parameters

PAGE 24 IFTA.ORG

low, weekly high/low, and higher timeframe swing highs/
lows, which act as resistances or supports. Refer to Figure 1
for all the parameters described below. The numbers in green
on the right side of every candle show the aggressive buyers,
while the numbers in red on the left side of every candle show
the aggressive sellers during that timeframe. The table at thebottom in the picture shows the four parameters that have been
described below.
Delta: The sum of aggressive market buy orders andaggressive market sell orders. If Delta is positive, buyers arestrong. So, a big positive Delta value above a resistance would
be a buying indication, and a big negative Delta below a support
would be a selling indication.
Max Delta: The maximum value of Delta during the selected
timeframe. Similar to Delta, Max Delta has to be observed only
above a resistance, and a combination of Delta and Max Delta
indicate whether buying pressure is going to sustain or not.
Min Delta: The minimum value of Delta during a selected
timeframe. This parameter is observed below a support, andthe combination of Delta and Min Delta indicate whether sellingpressure is going to increase or not.
Cumulative Delta: The sum of Delta from the first minute ofthe day to the last minute.

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2023 EDITION

How to Identify Momentum

When the market is moving higher, the cumulative Delta needs to be increasingly positive and above a reference point; if the Deltaand Max Delta have big values, then a bullish momentum is likely. The Delta for every subsequent candle above a resistance should
keep increasing, suggesting a continuation of the up orientation.
On the other hand, for a bearish momentum, the cumulative Delta preferably needs to be increasingly negative, and a break below a
support should be accompanied with big negative values for Min Delta and Delta.

Breakout

Once reference levels are identified, the Delta and Max Delta above a resistance need to be observed. For a successful bullish
breakout, Delta needs to be at least 65% of Max Delta above a resistance (a Delta value closer to Max Delta indicates that buyers arestill in control at the end of the candle). If the momentum condition and breakout condition are met, there is a higher probability thatthe up move would sustain. In such a case, a bullish trade can be initiated with a stop-loss below the breakout candle and a 1:2 risk
reward ratio. Refer to Figure 2 for an example of a successful breakout. The Cum Delta had been increasing, and the 15 min candle
closed above the resistance at 33,000 with a huge Delta (160.25k). A bullish entry is made above the high of the breakout candle.
Figure 2. Successful breakout

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On the other hand, when the positive Delta above a support is not big enough (3.4K as shown in Figure 3), there is a good possibility
that the breakdown will fail and the market would eventually move lower. A small positive Delta value indicates that the buyers
are not strong enough to take the price higher. Refer to Figure 3 for an example of a failed breakout. The bullish entry itself wasn’t
triggered, and the market headed lower even after it crossed the resistance.
Figure 3. Failed breakout

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Breakdown

Delta and Min Delta below a support are observed. Both need to have big values with Delta value at least 65% of Min Delta below a
support (a Delta value close to Min Delta indicates that sellers are still in control). The momentum condition and bearish breakdown
conditions together are necessary for a down move. A bearish trade can be initiated with minimum 1:2 risk-reward ratio and stoploss above the breakdown candle. Refer to Figure 4 for a successful breakdown example. Although the support was at 33,260, oncethe price moved below it, there wasn’t any indication of major selling in prior candles, and the down move was gradual. When buyers
finally gave up, sellers took control below 32,950 (Delta -45.18K and Max Delta -55.9K), which can be seen in the breakdown candle. A
bearish momentum followed suit with only a few retracements.
Figure 4. Successful breakdown

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On the other hand, when the negative Delta below a support is not big enough, there is a good possibility that the breakdown will fail, andthe market would eventually move higher. A small negative Delta value indicates that the sellers do not have full control, and the operator isable to take the price high enough to trigger most of the SLs in the system. Refer to Figure 5 for an example of a failed breakdown.
Figure 5. Failed breakdown

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Stop-Loss Hunting

Stop-loss hunting can happen if buyers are not in control above a resistance or sellers are not in control below a support. The
strength of the buyers or sellers has to be gauged by using OFA. Refer to Figure 6, which shows an example of stop-loss hunting. The
market was strong throughout the day, which is shown by the positive Cum Delta (120K), before a candle suddenly closes below the
support at 35,040. The big negative Delta (74K) in this case indicates that the SLs of buyers got triggered, owing to the big value. No
follow-up big negative Delta confirmed the view that the down move was only a stop-loss hunting one. The market did not move down
significantly, and a bearish trade can be avoided.
Figure 6. Stop-loss hunting

Summary

OFA is a great tool to gauge the strength of buyers or sellers in the market. Some important points to be kept in mind are as follows:
1. The OFA parameters have to be observed only at reference points. They do not hold much importance in a consolidation zone.
2. OFA shows the presence of aggressive buyers/sellers in the market, and this helps to differentiate between a trending and a
nontrending day.
3. The most important use of OFA is to identify a successful bullish breakout or a bearish breakdown and avoid stop-loss hunting
moves by the operators.

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Dr. Oliver Reiss, CFTe, MFTA

Plotting Market Dependencies
By Dr. Oliver Reiss, CFTe, MFTA

Am Bonneshof 30
40474 Dusseldorf
Germany+49 175 5613395
dr.oliver.reiss@gmail.com

Abstract“The trick is to take risks and be paid for taking those risks,
but to take a diversified basket of risks in a portfolio.”–Jeffrey Gundlach, DoubleLine
Diversification is the key to successful portfolio construction
for every trader or investor. But it is not sufficient just to split
the portfolio into several positions. The positions themselves
should be least dependent to gain the optimal risk reduction. In
institutional risk management, the dependencies between theassets are often measured by correlations and those are used toestimate the risk of a certain portfolio. But for a discretionary
trader, such a correlation matrix is just a mess of numbers andnot really helpful to construct a well-diversified portfolio.
This paper presents methods to construct a plot of thecorrelation matrix based on so called “force-directed graphdrawing.” The result is a graph showing the instruments totrade and these instruments are laid out in such a way thathigher correlated assets are closer together and less correlated
assets have a larger distance in the plot. Hence, for a goodrisk management the trader picks the assets which fit to theindividual trading strategy and are far away in this market
dependency plot.

Introduction

This paper demonstrates how to plot the dependencies in
the market, which are usually expressed by correlations of theassets. A plot of the assets is provided in such a manner thathighly correlated assets lie closer together and less dependent
assets are plotted more away from each other. Three methods
to construct such market dependency plots are provided and,even if they look quite different, their interpretation is always
the same: A trader should pick promising assets which are farapart on these plots in order to increase the diversification in
the portfolio.
The construction of these plots is based on the technique of“force-directed graph drawing,” which are, for example, used
to visualize relationships obtained from the analysis of big data
(Kobourov, 2013). One traditional force-directed graph drawing
approach is based on the work of (Eades, 1984) and is used inthis paper. The idea is quite simple: Assume that each asset is aparticle and there are two forces interacting on the particles:
1. A repulsive force driving all particles apart.
2. An attracting force pulling each pair of particles together.
This force depends on the correlation of the two assets(particles) and is stronger if the correlation is higher.

PAGE 30 IFTA.ORG

These particles are laid out on the two-dimensional plane andthe core idea is that this physical system should attain a state ofminimal energy.
This paper starts with a first market dependency plot and an
explanation of how to use it for trading or investment. A simple
algorithm for the construction of this first example is presented
thereafter. Throughout this paper, all examples are based on
the stocks contained in the Dow Jones Industrial Average Index;
hence, we assume that the portfolio is composed by some ofthese stocks and the reader is free to choose the actual trading
strategy for the single stocks.
Even if the correlation is quite popular to measuredependencies, correlations work fine in general only for certain
distributions (Embrechts et al, 1999). A warning example isprovided and therefore another mathematical concept should beconsidered to measure dependencies: The Gaussian copula.
The first example uses a heuristic to formulate the attracting
force. In the second example, the attracting force is modified
such that it is based on a metric, a proper mathematical way
to describe distances. The resulting plot looks different at firstglance, but the general interpretation of this plot remains thesame.
The third and last example is based on the idea of (Kamada
and Kawai, 1989). In their approach, a metric is needed and there
is only one kind of force: The particles are linked by springs
which have individual spring constants and rest lengths.
In the final conclusion, the three different market dependency
plots are reviewed. Regarding the purpose to compose aportfolio with reduced risks due to a rather high diversification,
all three methods provide similar results. Hence the usage offorce-directed graph drawing to display market dependencies israther independent from the concrete definition. Hence choose
your favorite layout to find less dependent assets for yourportfolio!

A First Market Dependency Plot
How to Use the Market Dependency Plot
To get an impression of a market dependency plot, an example
based on the stocks of the Dow Jones Industrial Average Index isprovided in Figure 1. The index is printed in blue and each stockis presented in a color based on a certain trading strategy: Greenfor buying, red for selling, and gray for stocks without a signal.
In all examples of this paper, these signals are based on a trend
following strategy, but any trading system can be used to define
the colors of the stocks.

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Figure 1. The first example of a market dependency plot

2023 EDITION

reduce the risks of the portfolio. The lower the correlation of theassets, the higher the effect of the diversification, and the mostsuitable positions for a portfolio can be obtained in the market
dependency plot by the dots of the right color which lie mostapart from each other.
The Model Behind This Plot
The model is inspired by (Eades 1984) and consists ofrepulsive and attracting forces between particles which
represent the assets. Let pi be the position of the particle i withi = 0 being the Dow Jones Index and i = 1 ... n the single stocks.
The repulsive force for each stock is defined by a constant force
pushing the particle away from the center c of all particles. The
center is defined by:

There is no repulsive force for the index (i = 0) and therepulsive force
for the stocks (i = 1 ... n) is given by:

The closer the stocks lie together, the higher thecorrelation between them. So, without surprise, somestocks are plotted closely together:• The financial stocks: J.P. Morgan, Goldman Sachs, American
Express, Visa
• The pharmaceutical companies: Merck, Johnson & Johnson,
Amgen• The software companies: Apple, Microsoft, Salesforce
These groups, based on the same industry of the companies,
are well known to all traders and that these lie together inthe chart indicates how this plot works. But, at first glance, a
portfolio of Visa, Microsoft, and Nike may look diversified fromthe sector point of view, but the plot shows that these stocks arealso highly correlated.
Let’s assume a trader wants to construct a portfolio withthree positions from the Dow Jones constituents. In a first step,
the trader applies the favorite trading system on each stock andgets, for example, the three results for each stock: Buy (Green),
Sell (Red), or Neutral (Gray). Hence, only the Green plotted
equites are relevant for the long-only portfolio.
In the second step, the trader choses the green equites which
lie most apart in Figure 1. In this example, this results obviously
in buying Chevron, Procter & Gamble, and Apple.
A short-seller on the other hand would focus on red dots
and would diversify the short portfolio with 3M, Salesforce,and either J.P. Morgan or Boeing. Maybe the short investor willreconsider in this example to construct the portfolio of four
shorts instead of three.
The concrete trading system used to color the equities in
the plot is not relevant. For any successful trading system,
regardless of short-term or long-term, regardless of trend
following or mean reversion, a well-diversified portfolio will

Since ||p|| denotes the Euclidian Norm,||p|| =, so theabsolute value of this force is either 1 (in the first case) or 0 (ifthe particle is in the center or the particle is the index). Theenergy related to the repulsive forces is given by

To link the particles together, an attracting spring force
between the particles is established. The spring constant ishigher if the particles (assets) are higher correlated. If two
assets are uncorrelated, there is no spring at all. If assets are
perfectly anti-correlated, these assets would also not contributeto some diversification, hence it is reasonable to define themodel by spring constants ki,j which depend on the correlation
ρ i,j between the two assets.
Hence for a correlation of almost ±1, the spring constant isvery high. For a correlation of 0, the spring constant is 0. The
force acting on particle i induced by the spring to particle j isgiven by:The energy of the attracting springs is given by:

The total energy of the system is given by E = Er+Ea and forthe plot, the particles should be located such that the energy ofthe system is minimal. The bad news is that optimal solution
may not obtained. But the good news is that a rather good
approximation is fine for this application.
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The construction of the forces implies that there is someenergy minimum. If all particles are on the same spot, hence
the center of the system, the total energy is obviously zero. If
the particles move only a small distance away from the center,the total energy is approximated by the linear repulsive energy
term Er and hence negative if the distances are quite big. The
positive attracting energy Ea dominates the total energy due toits quadratic behavior with respect to the distances.
The solution will not be unique since any rotation or mirroringof a solution provides another solution with the same energy.
Therefore, there is a freedom to rotate or mirror the result. For
the purpose of this paper, all plots are oriented such that thefinance stocks are at the bottom and Chevron is on the left.
Also, a proper scaling of the result for the plot must be
considered.
The Steepest Descent Algorithm to Minimize theEnergyThe algorithm to find an approximate solution is based on asteepest descend algorithm, which is also used to train neutral
networks. The idea behind this algorithm is quite simple. For
the initialization, let all particles be randomly placed on thetwo-dimensional plain. Then the force of the system drives all
particles for a small moment (called learning-rate in the context
of neural networks) into a certain direction and then the systemis frozen again, hence all particles are fixed at the new position.
If the energy of the new system got smaller, the step is repeated.
If the energy of the system increased, then the learning-rate isdecreased.
Here is the algorithm in pseudo-code based on the formulas
presented above, especially the formulas for the forces andenergy are not stated explicitly again. The forces and positions
are two-dimensional vectors. The learning rate λ, the energies,
and the small constant ε are numeric values. The final positions
are the result of the algorithm and can be plotted after rescaling(and possible rotation).

How to Measure Dependencies: Correlation orGaussian Copula
If everything behaves benignly, the correlation is a goodmeasure for dependencies. But as (Embrechts 1999) pointed
out, there are several pitfalls. For a warning example that
correlation may be a bad measure for dependency, let Ai be somedrawings of a standard-normal variable and define Bi = exp (Ai)and Ci = exp (5 Ai). Then B and C are perfectly dependent, sincefrom any value of Bi one can compute the corresponding value of
Ci . But note, the correlation of B and C is just around 66%!
To describe general dependencies of stochastic variables, Abe
Sklar introduced the concept of copulas, see (McNeil 2005 andthe references therein). A special case of copula dependency
is the Gaussian copula. Each random variable is transformed
into a standard normal distributed random number and thenthe correlation between these transformed random variables
is measured. Hence the Gaussian copula is a correlation again
and, in the warning example above, the Gaussian copula willbe 100%. To clarify this procedure, the calculation of the Gauss
copula of two stocks is explained.
Let Xt and Yt with t = 0. . . T the close quotes of the stocks. The
log-returns of the stocks are given by ΔXt = ln(Xt) - ln(Xt-1) andΔYt = ln(Yt) - ln(Yt-1) with t = 1 ... T. The data ΔXt and ΔYt will be used
to estimate the usual Person correlation ρ. Using the notation
andthe formula for thecorrelation is given by:

In order to compute the Gaussian copula, the values of ΔXt
need to be ranked. Hence for the value of t where ΔXt is thesmallest value= 0, for the value of t of which ΔXt attains
the second smallest value= 1, and so on up to= T - 1, forthe t where ΔXt is maximal. Let N() be the cumulative normal
distribution function and N-1() its inverse, then we define:

Algorithm 1. The steepest descent algorithm

Sinceobtains each integer value from 0 to T - 1, isapproximately standard normal distributed. The similartransformation can be performed with the data ΔYt to obtain. The correlation based on the Pearson correlation formula
between and is the Gaussian copula. Note that the mean ofand and is zero by construction:

Of course, if the distribution of the random variables is close
to the normal distribution, the correlation and the Gaussian
copula will be quite similar. For the results in this paper, theGaussian copula based on the daily returns over a one-year
horizon is used as correlation. So even if the stock returns are
not as benign as expected, the measure of their dependency isbased on a robust mathematical foundation.

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A Second Market Dependency PlotIn the first example, the heuristic distance -ln(ρ) between two
assets has been used based on their correlation (or Gaussian
copula) ρ. Even if the results are reasonable, this kind of
distance does not fit to the mathematical concept of a metric.
So, it’s worthwhile to introduce a distance which fulfills theaxioms of a metric and to review a market dependency plot
based on a metric.

A Mathematical Distance Between the Assets
In mathematics, a well-defined distance d(A,B) between A and
B is called a metric if it fulfills three axioms.
1. d(A,B) ≥ 0 and d(A,B) is zero if and only if A = B
2. d(A,B) = d(B,A)
3. d(A,B) < d(A,C) + d(C,B)
The third and last axiom is called the triangular inequality
and states that any detour via point C is never shorter than the
direct way.
For this discussion, A, B, and C are the random variables
which may represent the returns of the stocks. Working within
the framework of Gaussian copulas, we now assume that A, B,
and C are standard normal distributed random variables. Hencethe transformed equity returns. The distance shall be expressedby their correlation, which is again commutative—hence thesecond axiom holds:d(A,B) = d(ρ B,A)
To find a suitable expression for the distance of A and B
expressed by their correlation, basic stochastics and geometry
is combined. The idea of the following discussion is that thestandard normal distributions (A, B, C) can be identified bypoints (A, B, C) on the unit-sphere.
Let K1, K2 and K3 be the orthogonal coordinates in thegeometric interpretation and independent standard normal
distributed random variables in the stochastics view. Define
three points on the unit sphere:

From the stochastics point of view, A, B, and C are standard
normal distributed random variables since they are a sum of
normal distributed random variables and have again a mean of
0 and a variance of 1.
The squared Euclidian metric between the points A and B canbe expressed by:‖A-B‖2= ‖A‖2+ ‖B‖2 -2 ⟨A│B⟩=2-2⟨A│B⟩
where ⟨A│B⟩ = a1b1 + a2b2 + a3b3 denotes the scalar productand for the last equality recall that ‖A‖2= ‖B‖2 = 1 holds bydefinition.

2023 EDITIONIn the stochastics view, the correlation between A and B isgiven by its covariance since the expectation of A and B is 0 andtheir variance is 1. As a result, the correlation of A and B is justthe scalar product due to the linearity of the covariance andthe fact that K1, K2 and K3 are independent standard normal
distributed:
ρ A,B = Cov(a1K1 + a2K2 + a3K3, b1K1 + b2K2 + b3K3) = a1b1 + a2b2 + a3b3
Since the discussion started with the Euclidian metric,
the term
is a metric for the stochastic variables
expressed by their correlation. The multiplication of the metricwith any positive number fulfills the axioms, as well. Hence a
simplified expression for a metric expressed by the correlation
is given by:

In our application, the distance of anti-correlated assets
should be small too since anti-correlated assets do notcontribute to diversification. Therefore, this distance ismodified to bring anti-correlated assets close together by taking
the absolute value of the correlation:̂To show that d(A,B)
still fulfills the triangular inequality, a
discussion of eight possible cases regarding the signs of ρ A,B ,ρ B,C and ρ A,C must be performed. Such a proof of the triangular̂
inequality of d(A,B)
is provided in the appendix of (Chen et al.
2019).
The ModelThis second model is quite analogous to the first model. Only
the attracting force between two particles (stocks) is defined
based on the previously introduced metric. The spring constantused in this model between stock i and stock j is given by the
inverse of the metricand the attracting force is again given by Hook’s law:Hence the attracting energy is given by

These are the only modifications to the first model and therepulsive forces are unchanged. This model can also be solved
with the steepest descend Algorithm 1.

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The Resulting Plot
Figure 2. The second example of a market dependency plot

The result shown in Figure 2 arranges the single stocks almost
on a circle. As in the first plot, the stocks of certain sectors areagain arranged closely together:• The financial stocks: J.P. Morgan, Goldman Sachs, American
Express, Visa
• The pharmaceutical companies: Merck, Johnson & Johnson,
Amgen• The software companies: Apple, Microsoft, Salesforce

is no general repulsing force and there is no special treatmentof the Dow Jones Index particle anymore. In order to push theparticles apart, the rest length of the springs is greater than 0.
In general, the rest length should be proportional to the metricand the spring constant should be proportional to the inverse of
the squared metric. Using the previously introduced metric, thespring constant k i,j̃ and the rest length l i,j̃ of the spring between
particles i and j are given by:

To compare the usage of this plot to the first plot, we look
for the decision a trader makes who wants to pick three mostfar apart but green stocks from the graph. The result from thesecond plot will be Apple, Chevron, and Procter & Gamble, as in
the decision based on the first plot.
Also, the short seller would prefer to build a portfolio basedon the same short positions as in the first plot (3M, Salesforce,
J.P. Morgan, or Boeing). Hence even if the forces to create theplot are changed and the plot looks different, the resulting
portfolio build from the positions most apart from each other do
not differ.

The force F i,j̃ on particle i induced by the spring to particle j isdependent on the position of the particles pj,pi:

A Third Market Dependency Plot
The Model
The third model is based on the idea of (Kamada and Kawai,1989) and this model consists of spring forces only. Hence there
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And the energy of spring between particles i and j is given by:

The Algorithm to Solve This Model
To solve for a solution of this model, the steepest descendalgorithm fails due to too much local minima. But there is a
simple way to modify the steepest descend algorithm such that

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it will yield proper results. Instead of moving all particles atthe same time, only the particle which is exposed to the largest
force will be moved until it attains a position of rest. Then thenext particle, which is then exposed to the highest force, ischosen to relocate while all other particles are fixed. Since only
one particle is moving in every step, the computational effort ishigher than for the steepest descend algorithm.
Algorithm 2 presents the Kamada and Kawai algorithm inpseudo-code based on the formulas presented above. Please
note that the formulas for the forces F ̃ and energy E ̃ dependon the positions of the particles and their value changes if
any particle is moved. The index of the particle to move isan integer value denoted by m. The forces and positions are
two-dimensional vectors. The learning rate λ, the energies,
and the small constant ε are numeric values and the variable
isimproving is Boolean.

2023 EDITION

The Resulting Plot
Figure 3. The third example of a market dependency plot

Algorithm 2. The algorithm of Kamada and Kawai

Figure 3 spreads the particles (stocks) over the whole plane
without a circular structure anymore. Even if there is no
special treatment of the index, it is placed in the centerof the plot. As in the previous plots, stocks of the same
industry (e.g., financial, pharmaceutical, software) areplaced closely together.
The market dependency plot will be used by the samemanner as before. The long-investor is spotting for thegreen stocks most far apart and the selection will again
yield to a portfolio of Apple, Chevron, and Procter &Gamble. Hence the portfolio consisting of three longpositions is again unchanged.
For a portfolio consisting of three short positions, thisplot is more clear than the previous one and the selected
stocks would be 3M, Salesforce, and Boeing. In theprevious plots, the selection of either Boeing or J.P. Morgan
was considered and there was a tendency to use four stocks
in a short portfolio. But if a fourth short position should be
added based on this plot, it would certainly be J.P. Morgan.

Conclusion

While it is quite simple to identify stocks which are highly
dependent, for example by acting in the same industry, it isinconvenient to imagine which stocks are least dependent. But
this task is important to construct a portfolio which gains mostfrom the effect of diversification. To visualize the dependenciesof the stocks, some market dependency plots have been
provided.
The technique behind plotting of these dependencies isknown as “force-directed graph drawing” and three models
have been analyzed. The core idea is to embed the correlation
or Gaussian copula into the attracting forces. This can bedone either by some heuristic approach (first model) or by anapproach which utilizes a metric (second and third model). Even
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if the resulting plots look different at first glance, the application
to build a portfolio of a few mostly independent stocks basedon these plots yield mostly to the same (or at least quite similar)
portfolio. Even if the list of models can easily be extended, theirresults in the application to construct a portfolio will almost
have the same outcome. That seems likely from the portfolio
discussions of the three models in this paper.
The degree of dependency is often expressed by thecorrelation, but keep the warning example in mind: correlation
may be misleading. To cover the dependence of stochastic
variables, a general approach of copulas exists and the special
case of a Gaussian copula is presented. The Gaussian copula
differs mathematically from the usual correlation but can betreated like a correlation again. Hence, one should easily getused to it.
The presented algorithms to search for an energy minimum
will work for this purpose, but they are just basic and may
be trapped in a local minima without finding a better global
minimum. To overcome this issue, there are algorithms
containing some stochastic components based on the ideaof “Simulated annealing” (Press et. al., 1992) and which arerecommended to improve the minimization task.
The market dependency plots provide the freedom to color
each stock based on a signal of your favorite trading systemand the construction of the market dependency plot does notdepend on a certain trading strategy. You are also free to choose
your convenient time frame to measure the dependencies ofthe financial instruments. Therefore, market dependency plots
provide a general tool to reduce the portfolio risk as well for the
short-term trader as for the long-term investor.

PAGE 36 IFTA.ORG

References
Chen, Jiaxing, et al. “On triangular Inequalities of correlation-based
distances for gene expression proﬁles”, bioRxiv, www.biorxiv.org/
content/10.1101/582106 (2019)
Eades, Peter. “A heuristic for graph drawing”, Congressus Numerantium,
Vol 42, pp.149-160, (1984)
Embrechts, Paul, et. al. “Correlation : Pitfalls and Alternatives”, Risk,
pp. 69-71, (1999)
Kamada, Tomihisa and Satoru Kawai. “An algorithm for drawing
general undirected graphs”, Information Processing Letters, Elsevier,Vol. 31 (1) pp. 7–15 (1989)
Kobourov, Stephen G. “Force-Directed Drawing Algorithms” inHandbook of Graph Drawing and Visualization, Chapter 12, CRC
Press (2013)
McNeil, Alexander J., et. al. Quantitative Risk Management. Princeton
Series in Finance, Princeton University Press (2005)
Press, William H., et al. Numerical Recipes in C: The Art of Scientific
Computing. Cambridge University Press, 2nd Edition, (1992)

Software and Data

The market data used for this research has been obtainedby the software TAI-PAN End-of-Day from the provider
Lenz+Partner GmbH (www.lp-software.com), which is part ofInfront ASA (www.infrontfinance.com).

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Modelling Financial Time Series by Generative
Adversarial Networks: With Applications to the
Nasdaq Composite Index
By Cezar-Valerian Lupusor, MSc, CFTe

Introduction

This study aims to introduce TimeGANs to the field offinancial modelling or more generally to the field of artificial
intelligence (AI) in finance. TimeGANs belong to the family of
GANs (Generative Adversarial Networks), which are a neuralnetworks architecture developed for generating images. They
are increasingly used for generating time series and othertypes of financial data. The purpose of this study is to give an
introduction to the modelling problem in finance, to describe
the architecture of TimeGANs and how they are implemented
in the language Python, to assess the quality of the generated
synthetic time series data, to present some stylized facts about
financial time series and to verify whether synthetic data can
reproduce them and to conclude with an outlook of future
developments and limitations of this technique. The overallfinding is that GANs are able to produce solid results withrespect to synthetic time series data generation and modelling.

The Modelling Problem in Finance

The finance industry is one of the most influential fields
impacted by new developments in AI. Machine learning (ML)tools have been used for forecasting, risk management, fraud
detection, and portfolio management. ML tools are by theirvery nature data intensive, and a lack of (financial) data due
to regulations and privacy laws may limit their potential. In
this respect, GANs are useful for generating synthetic data
where real data is scarce. In addition to this, GANs are used
for data-driven modelling, and their application can improvethe modelling of complex and unknown statistical dynamics
present in financial data. Before the advent of ML, financial
modelling was mainly based on families of models (i.e., ARCH/
GARCH for modelling and forecasting volatility and stochastic
models such as Black Scholes [1973], Merton [1976], and Heston[1993]). ARCH/GARCH models describe the variance as timevarying (heteroskedastic) and as a function of current and past(squared) error terms. They do not have a stochastic component
since volatility is completely dependent on previous values.
On the other hand, stochastic volatility models introduce (astheir name suggests) stochastic components in the form ofBrownian motions to the modelling of volatility and ultimately
to logarithmic return series and options pricing. The limitationof Black Scholes, for example, is that it produces (by its model
assumptions) constant (implied) volatilities where, in practice,implied volatilities are not constant (in practice, implied
volatilities may be described by a U-shape called “volatility
smile”). More advanced stochastic models like the Merton model

Cezar-Valerian Lupusor, MSc, CFTe
Polgarweg 28
Linz, 4030 Austria+43 660 5691291
cezar.lupusor@yahoo.com

introduce so-called random jumps following a Poisson process
to allow for discontinuities beside (standard) Brownian motions
for modelling return series and to capture the stylized facts of
implied volatilities.
In sum, these models rely on assumptions, whereas MLmodels are much more empirical (i.e., data driven). Thus, a greatrisk in financial modelling, model risk, which is the risk of using
an inappropriate model, can be mitigated.

Machine Learning Versus Deep
Learning

ML is an area within the fields of AI and computer sciencethat enables computers to learn by using data and advanced
statistical methods. In short, ML consists of the creation oflearning algorithms that receive data (e.g., training data) as an
input and return a classification—a label of a prediction related
to this input. The traditional tasks that ML models perform areregression, classification, clustering, and prediction. A closely
related field is deep learning with more innovative solutions.
Deep learning algorithms are based on so called artificial
neural networks, which are networks of connected layers of
nodes (neurons) inspired by the biological neural networksof brains. These networks are called “deep” because they arecomposed of more than two layers: an input layer, an output
layer, and at least one hidden layer that enables the network tolearn complex nonlinear functions that are required to carryout complicated tasks of AI. The simplest neural network is thefeed-forward network since data flows from the input layer tothe output layer.
Figure 1. A feed-forward neural network

A more sophisticated type of neural network is the Recurrent
Neural Network (RNN). An RNN not only has neurons withconnections from the input layer to the output layer but also
neurons with connections from the output layer back to the
input layer. This additional connection enables the RNN to store
information over time, which is called dynamic memory. RNNs
are particularly useful for time series predictions.

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Figure 2. A recurrent neural network

One important distinction is between generative models
and discriminative models, and another is between supervised
learning and unsupervised learning. Learning means “learningfrom data,” and it is called “supervised” because of the presenceof the outcome variable to guide the learning process (oneexample of supervised learning is linear regression analysis,
where the linear model learns from the input (X1,…,Xp ) on which
it is trained to predict an output (Y1,…,Ym ). In the “unsupervised
learning problem” or “learning without a teacher”, only thefeatures or inputs are observed while there is no measurementof the output. The task is rather to describe how the data isorganized or clustered. Most discriminative models fall in the
category of supervised learning, while most generative models
are labeled as unsupervised.

GANs

GANs were introduced in 2014. Goodfellow et al. proposeda model made up of two components: a generator (G) and adiscriminator (D). Their tasks can be described as follows. The
G captures the data distribution and generates new data. The
second model is a classifier, the D, which estimates the probability
that a sample came from the training data and not from G.
The training process of the G is to maximize the probabilityof its output being misclassified by the D. The D has the taskof assessing the quality of the generated data and providing
feedback to the G. These neural networks are optimized undergame-theoretic aspects: the G is optimized to generate data
to fool the D, and the D is optimized to detect the source of the
input, namely the G or the real data set. The overall aim is togenerate data that is indistinguishable from the real data in key
aspects, in which case we do not need the D anymore. This meansthat both models are competing against each other in a gamecalled adversarial in Game Theory, and they are playing a zerosum game. This means that when the D successfully identifies
a sample, it is rewarded or no update is done to the model
parameters, whereas the G is penalized with large changes tomodel parameters. From the other perspective, when the G tricks
the D, it is rewarded, or no update is done to its parameters, but
the D is penalized, and its model parameters are changed.
The GAN training process uses loss functions that measure
the distance between the distributions of the generated data
and the real data to assess their similarity. There are manymethods that can be used to solve this task. In the original“vanilla” GAN, a so-called minimax function was introduced:
minG maxD V(D,G)= Ex [logD(x)] + Ez [log(1-D(G(z)))]PAGE 38 IFTA.ORG• D(x) is the Discriminator’s estimate of the probability thatthe real data instance x is real.
• Ex is the expected value over all data instances.
• G(z) is the Generator’s output given noise z or given the fakeinstance.
• D(G(z)) is the Discriminator’s estimate of the probability thata fake instance is real.
• Ez is the expected value over all generated fake instancesG(z).
Thus, the G minimizes the loss, which is equivalent to log(1-D(G(z)) since it cannot directly affect the D(x) term in
the function. As the G distribution approaches the real data
distribution, the D distribution will be unable to distinguishthem and stabilizes at D(x) = ½.

The GAN Family

A number of GANs can be divided into two categories,
namely by Architecture and by the design of the Lossfunction. TimeGANs, for example, use the Kullback-Leibler
divergence as Loss function, WGANs (WassersteinGANs) use
the Wasserstein distance as an alternative to the originallyproposed Loss function. FIN-GANs could successfully produce
synthetic time series that replicate the main stylized facts offinancial time series. What makes GANs particularly useful istheir ability to learn the properties of data without requiring
explicit assumptions or mathematical formulations, somethingthat stochastic processes cannot do without non-trivial
assumptions.

The TimeGAN Architecture and the
Scope of This Study

The scope of this study is to use the Nasdaq Composite Index
as the quantity of interest and apply TimeGANs to it in order
to ultimately create synthetic financial data. The quality of thecreated synthetic financial data is evaluated by three criteria:
1. Diversity: The distribution of the synthetic samples shouldroughly match that of the real data.
2. Fidelity: The sample series should be indistinguishable fromthe real data.
3. Usefulness: The synthetic data should as useful as its realcounterparts for solving a predictive task.
Furthermore, it should be verified if synthetic data created by
TimeGANs represent the main stylized facts of financial timeseries:• Linear unpredictability or absence of linear autocorrelation:
Except for short intraday time scales, it is expected that
asset returns show minimal linear autocorrelations.
• Fat-tailed distribution: The distribution of returns exhibits
fat tails, which means that the probability of extreme
returns, either positive or negative, is much higher thanunder the Gaussian distribution.
• Volatility clustering: Volatility displays a positive
autocorrelation over several days. This means that large
price changes tend to be followed by large price changes
and small price changes tend to be followed by small pricechanges.

IFTA JOURNAL

2023 EDITION• Gain/loss asymmetry: Large plunges in asset prices do not share equally large upward movements.
• Aggregational gaussitanity: Over large time scales, the distribution of returns looks like a normal distribution.
The data for this study is EOD (End of Day) and comprises 20 years, from April 18, 2002, until April 18, 2022. It uses six features,
namely open, high, low, close, adjusted close, and volume.
Figure 3. 20 years of daily data of the Nasdaq Composite Index, 2002–2022

Figure 4. The Logarithmic return series of the Nasdaq Composite Index, 2002–2022

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Figures 3 and 4 show different pictures of the same quantityof interest. Figure 3 depicts the Nasdaq Composite Index inlevels, whereas Figure 4 depicts its logarithmic return series.
While the former is called a nonstationary or trending process,the latter is called a stationary or nontrending process. The
phenomenon of volatility clustering is easily detectable,
particularly around the years 2008 and 2020.
Figure 5 shows the distribution of the logarithmic returnsof the Nasdaq Composite Index. It can be easily seen that the
distribution is leptokurtic (i.e., there is a large excess kurtosis)(3 being the Gaussian distribution).

Table 1 shows some descriptive statistics of the Nasdaq
logarithmic returns distribution. The kurtosis is muchgreater than 3 (3 being the value characterizing a Gaussian
distribution), and the skewness is negative (0 being theGaussian distribution), suggesting more weight on the righttail of the distribution. Together, kurtosis and skewness
suggest a fat-tailed distribution. The absolute minimum of thelogarithmic return series was -13.1%, whereas the absolute
maximum was 11.1%.

Table 1. Some descriptive statistics of the Nasdaq
logarithmic returns distribution
Kurtosis10.209Skewness-0.325Min-0.131Max

0.111

Figure 5. The Nasdaq logarithmic returns distribution (blue) and the Gaussian PDF (red)The TimeGAN architecture is comprised of two main categories with a total of four components. The two main categories are:
• The Autoencoder: It comprises the embedding and recovery networks.
• The Adversarial network: It comprises the generator and discriminator.
The embedding and recovery networks of the autoencoder map the feature space into the latent space and vice versa. The latent
space is simply a representation of compressed data. Compressed data is obtained by transforming complex forms of data into simpler
representations (e.g., dimensionality reduction from 3D to 2D). This is done because it is more convenient for a deep learning algorithm
to process and analyze compressed data.

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One of the specific characteristics of the TimeGAN architecture is the joint training of the autoencoder and adversarial networks
by means of three different loss functions: the reconstruction loss optimizes the autoencoder, the unsupervised loss trains theadversarial network ,and the supervised loss is responsible for the temporal dynamics. Consequently, the TimeGAN simultaneously
learns to encode features, generate representations, and iterate across time.

Assessing the Quality of the Synthetic Time-Series Data

Having outlined the broad architecture of TimeGANs, the next step is to create synthetic time-series data. A total of 24 observations
were created by the TimeGAN framework.
Figure 6. Synthetic time-series data (yellow) versus real time-series data (blue)

As can be seen from Figure 6, the yellow graph (synthetic data) replicated the blue graph (real data) reasonably well. However, it isnecessary to take a closer look at the quality of the synthetic data. For this task, the three aforementioned criteria (diversity, fidelity,
and usefulness) are employed.
Diversity
For a qualitative assessment of diversity, I use two methods of dimensionality reduction (in order to plot them in 2D), principal
component analysis (PCA) and t-SNE (t-distributed Stochastic Neighbor Embedding) to visually inspect how closely the distribution of
the synthetic samples resembles that of the original data. PCA is a linear method that is applied when many of the variables are highly
correlated, and it is desirable to reduce their number to an independent set while preserving as much of the data’s variation as possible.
t-SNE is a nonlinear method for dimensionality reduction and is used when data is not linearly separable.
Figure 7. Assessing diversity—visualization using PCA and t-SNE

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As can be seen from Figure 7, both methods reveal strikingly similar patterns and significant overlap, suggesting that the synthetic
data captures important aspects of the real data characteristics. Upon closer examination, it is interesting to note that the t-SNE
result is better than the PCA result, suggesting the existence of nonlinearities in the data.
Fidelity
For this task, I trained a time-series classifier to distinguish between real and fake data and evaluate its performance on a heldout test set. Therefore, the first 80% of the data was selected for training and the last 20% was selected as a test set. A simple RNN
with six units that receives mini batches of real and synthetic data is used. It is optimized using binary cross-entropy loss and theAdam optimizer, while the AUC (Area Under the Curve; the curve in this case is the receiver operating characteristics [ROC]) andother accuracy metrics are tracked. The higher the AUC, the better the performance of the model at distinguishing between real andsynthetic data.
Figure 8. Assessing fidelity—time-series classification performance

Figure 8 (right panel) suggests that the model is able to distinguish between real and synthetic data quite well on the train set (highAUC) but this does not generalize to the test set (low AUC). This result suggests that the quality of the synthetic data meets the fidelity
standard.
Usefulness
The last step involves a prediction task (one step ahead prediction) and assesses whether real data or synthetic data are more
useful for accomplishing this. Specifically, the first 23 observations of each sequence are selected as input to a one-layer RNN with 12
GRU (gated recurrent units) and the last observation as output. I trained the RNN model twice—on synthetic data and on real data
for training, and the out-of-sample performance is evaluated by the MAE (mean absolute error). The MAE is a statistical measure of
accuracy that averages the sum of the absolute errors, which are the absolute difference between a prediction and the true value. The
lower this value, the more accurate the model is.
Figure 9. Assessing usefulness—time series prediction performance

Figure 9 suggests that the MAE is lower after training on the synthetic dataset. This means that training a simple model (e.g., an
RNN) on synthetic TimeGAN data delivers equal or better performance than training on real data.
In conclusion, the three evaluation criteria show that TimeGANs are able to produce high-quality synthetic data that resembles thereal data in important characteristics.

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Stylized Facts of Financial Time Series

The last section of this study aims to reproduce some of the stylized facts mentioned in the section on TimeGAN architecture by
TimeGAN synthetic data. For this purpose, the focus lies on logarithmic returns and not on level data, as in the preceding sections.
A sample of 100 observations of TimeGAN synthetic data has been generated. At this point, it is worth mentioning that generating
synthetic data is a computationally intensive process. Working on a MacBook Pro with a 1.4 GHz Quad-Core Intel Core i5 processor
took approximately four hours for this task to be completed. Consequently, it was not possible to prove all stylized facts, especiallyvolatility clustering and aggregational gaussitanity, due to the relatively small sample of synthetic data.
Figure 10. Synthetic (yellow) and real (blue) logarithmic returns

The above figure shows that synthetically generated logarithmic returns are able to reproduce the time series of real logarithmic
returns. The synthetic returns series is centered around zero, but it exhibits greater oscillations. Due to the small sample size, it is
not possible to check whether the phenomenon of volatility clustering could be satisfactorily reproduced. In conclusion, there is somedoubt about this finding.
Figure 11. PDF of the real return series (blue) versus PDF of the Gaussian distribution (red)IFTA.ORG PAGE 43

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Figure 11 depicts the distribution of the sample of the real logarithmic return series. The distribution is asymmetric with a kurtosisof 3.363 and a skewness of -0.304. The sample exhibits the same properties as the its larger counterpart containing 20 years of daily
observations.
Figure 12. PDF of the synthetic return series (blue) versus PDF of the Gaussian distribution (red)Figure 12 depicts the distribution of the sample of the synthetic logarithmic returns. In this case, the kurtosis is 1.949 and theskewness is -0.070. The distribution is platykurtic and approximately symmetric with a skewness parameter close to zero. It therefore
fails to reproduce the fat tails that are a characteristic of financial time series data.

Figure 13. Autocorrection function (ACF) of the real
logarithmic return series

For financial returns, the autocorrelation is expected to bevery low, given the stylized fact of linear unpredictability. Figure
13 depicts this stylized fact for the real logarithmic returnseries.

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Figure 14. ACF of the synthetic logarithmic return series

Figure 14 is very similar to Figure 13, which means thatsynthetically generated logarithmic returns are mostly linearly
unpredictable, as are their real counterparts.

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Conclusion

This study introduced one version of Generative Adversarial
Networks, namely TimeGANs. Starting the conclusion
backwards, an attempt was made to show how TimeGAN
synthetic data reproduces some of the stylized facts offinancial time series. This attempt was made to show that
there are no unified quantitative metrics by which to assess
the performance of synthetic financial data. Some of theresults were satisfactory and some were not, partially due tothe small sample size of the synthetic data. Maybe one of thepresent limitations for individual practicioners of this tool is theimmense computational power needed for generating a large
enough sample of synthetic data. Another caveat is that thisstudy dealt with daily data. Assessing diversity, it was shownthat there are nonlinearities present in financial time series as
the t-SNE performed better than the PCA. Working with highfrequency data (e.g., tick data, generally intraday data) would
presumably make temporal dynamics more complex and require
adjustments to be made to the TimeGAN architecture.
On the other hand, this study attempted to highlight or rather
to suggest a set of quantitative metrics, namely diversity,
fidelity, and usefulness, for assessing the quality of thegenerated financial data—and consequently to provide unified
metrics. Thus, it forms a contrast to the previous literature,
which is basically summarized in the Stylized Facts of Financial
Time Series section of this study.
By their very nature, GANs generate synthetic data that
can also be used for training deep learning models when real
data is scarce due to privacy laws. Seen this way, GANs are an
indispensable component of deep learning and machine learning
tools. In addition to this, it was also shown that predictions
based on synthetic data are at least as good as those based onreal data.
In sum, GANs are a promising new tool for modelling
purposes and add new possibilities to the challenging world of
quantitative finance.

2023 EDITION

References
Stefan Jansen (2020), Machine Learning for Algorithmic Trading, 2ndedition, Packt.
Hastie, Tibshirani, Friedman (2008), The Elements of Statistical
Learning, 2nd edition, Springer.
Eckerli, Osterrieder (2021), Generative Adversarial Networks in Finance:
an Overview, A preprint.
Torres (2018), Generation of Synthetic Data with Generative Adversarial
Networks, KTH Royal Institute of Technology, Sweden.
Lecture Notes on Numerical Methods: Financial Models with Jumps,
Bayes Business School, UK.

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Using Deep Learning Models for Stock Market
Predictions: An Application of Long Short-Term
Memory Algorithms to Micron Technology, Inc.

Cezar-Valerian Lupusor, MSc, CFTe

By Cezar-Valerian Lupusor, MSc, CFTe

Micron Technology, Inc.

Polgarweg 28
Linz, 4030 Austria+43 660 5691291
cezar.lupusor@yahoo.com

Figure 1. Difference between a feedforward neuron and arecurrent neuron

This study examines the chart of Micron Technology (MU), a
stock listed on the Nasdaq Global Select (GS) for the purpose offinancial predictions. This particular stock has been selectedby the author of this study because it is a big player in thesemiconductor industry. The company is headquartered in
Boise, Idaho, in the United States and has approximately 43,000
employees. Its market capitalization is at about $78 billion
US, and its EPS (earnings per share) are at $5.14 US per share,
which means the company is profitable. Furthermore, the stock
has been chosen because, according to financial news media,
it was a favorite short of David Einhorn of Greenlight CapitalManagement, a famous U.S. hedge fund.

About This Study

This study employs deep learning algorithms for predicting
the stock price of Micron Technology. The analysis is regressionstyle (i.e., the aim is to model the chart/time series of Micron
Technology). Therefore, the root mean square error (RMSE) as
well as the R-squared statistic have been used as performance
metrics. The reason for this style of analysis is straightforward:
Long short-term memory (LSTM) algorithms are atheoreticalmodels that learn from historical data. The advantage of using
such models is that no theoretical models (i.e., models that
use the fundamental determinants of Micron Technology’s
stock price as regressors) are necessary. This fact alone is atremendous simplification. Furthermore, the aim of the study
is the comparison between LSTM models and Gated Recurrent
Unit models that are the modern variant of plain vanilla LSTMs.
Both types of models are run over three different time spans ofhistorical data—one long-term and two short-term. The study
concludes with 1-step ahead predictions of Micron Technology’s
stock price.

LSTM Algorithms—A Special Kind of
RNNs

LSTM constitutes a special case of recurrent neural networks(RNNs), which were originally proposed to model both shortterm and long-term dependencies. As the name suggests, a RNN
contains, in addition to a feedforward, a recurrent connection.
The main difference between a feedforward neuron and arecurrent neuron is shown in Figure 1. The feedforward neuron
possesses only connections from its input to its output. In
contrast, a recurrent neuron has an additional connection fromits output to its input. This extra connection is called “feedback
connection”; thus, the information can flow around in a loop.

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In conclusion, an RNN is formed by the combination/connection of many feedforward and recurrent neurons.
An RNN offers two main advantages:
1. Store Information
The RNN can take advantage of its feedback connection inorder to store information over time. Therefore, an RNN
has some form of memory.
2. Learn Sequential Data
The RNN is able to handle sequential data. This meansthat a simple feedforward network can compute one
fixed size input to one fixed size output (similar to a linear
function). The RNN instead can handle one to many, many
to one, or many to many inputs to outputs (similar to anonlinear function). See Figure 2.
Figure 2. RNN inputs to outputs

Note: RNNs were first introduced in 1982 by J.J. Hopfield.

However, one significant drawback of RNNs is their inability
to learn to store information over extended time intervals. This
problem is called “vanishing gradient problem” or “exploding
gradient problem”. When the network is learning to bridge longtime lags, the network takes either too much time or it stops

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working (vanishing gradient problem). On the other hand, theexploding gradient leads to oscillating weights, which is anotherdrawback.
Therefore, the solution to this problem was presented in 1997
by Hochreiter and Schmidhuber in the form of LSTM algorithms.
LSTMs are able to model both short-term and long-term
dependencies. The major novelties in a LSTM network are thememory block and the adaptive gate units. More specifically, thestructure of the memory cell Ct is composed by three gates: theinput gate, the forget gate, and the output gate. At every time
step t, the input gate xt determines which information is added
to the cell state Ct (memory); the forget gate ft determines which
information is thrown away from the cell state; the output gate
σt determines which information from the cell state will be usedas output.
First, the forget gate looks at ht-1 (output at time step t-1) and xt(input at time step t) to compute ft which is a number between 0
and 1. This is multiplied by the cell state Ct-1 (i.e., Ct-1 * ft). If ft takes
on a value of 1, the cell keeps all information, and at a value of 0,
the cell forgets all information.
Second, the outputs it and C̃t are multiplied, which constitutes
an update of the cell. This update is then added to the previous
input Ct-1 * ft .
Finally, the output value ht is computed by the multiplicationof ot with the tanh of the result of the second step (i.e., ht = ot *tanh (Ct), where ot = σ* (W0 [ht-1,xt ]+b0)), tanh being the hyperbolic
tangent function and W0 and b0 being the weighting matrix anda bias vector, respectively.

Gated Recurrent Unit

The Gated Recurrent Unit (GRU) was introduced in 2014.
Whereas a LSTM has three gates, a GRU has two gates. GRUs do
not have a memory cell Ct . Instead, GRUs use the hidden state totransfer information.
In many tasks, both models yield comparable performance.
Therefore, tuning hyperparameters like layer size is important.

2023 EDITION

GRUs have fewer parameters and thus may train a bit faster orneed less data to generalize. On the other hand, LSTMs work
better with more data. Thus, GRUs are parsimonious in naturewhen compared to LSTMs; they have fewer parameters andare presumably able to work with less data. These are the main
advantages of GRUs.

Data Analysis and Tests of Normality
The scope of this section is to inspect the data for Micron
Technology, first, visually, by the means of a histogramand a probability—probability plot (P-P plot), and secondly,
quantitatively, by employing specific tests for evaluating
the null hypothesis of normality of the distribution of thelogarithmic returns. The significance level for these tests is set
at 5%. Therefore, a pValue of less than 5% or 0.05 means thatthe null hypothesis of a normal distribution is rejected. The
following tests were used: Jarque-Bera and Shapiro-Wilk.
The first dataset for Micron Technology was chosen toencompass its whole history (i.e., since its IPO). The time span
ranges from June 1984 to October 2021. 80% of the data has been
reserved for training the models, and the remaining 20% wasused for model validation. The data has been normalized using the
MinMaxScaler, and the data frequency is EOD (End of Day). Usinga scaler should boost the predictive performance of the models.
The second and third datasets encompass three years and one
year, respectively, and should purposefully test whether GRU
models perform better than LSTM models when the availabilityof data is scarce.
The Jarcque-Bera statistic is a measure of whether the data
has the skewness and kurtosis matching a normal distribution.
The test statistic is defined as follows:

where n is the sample size, S is the sample skewness (the third
moment), and K is the sample kurtosis (the fourth moment; aFigure 3. The architecture of LSTMs

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kurtosis greater than 3 means leptokurtosis [i.e., a higher peak than the normal distribution, which is quite representative for mostfinancial data]).
The Shapiro-Wilk test is another test for normality of the data. The test statistic is defined as follows:

where xi is the ith order statistic (i.e., the ith smallest number in the sample), x̅ is the sample mean, the coefficients ai are given by(ai ..., ai) =, where C is a vector norm: C = ‖V -1 * m‖ = (m' V -1 V -1 m)1/2, and the vector m (transposed) = (m1 ..., mn)' is made of the
expected values of the order statistics of identically and independently distributed (IID) random variables sampled from the standard
normal distribution. V is the covariance matrix of these normal order statistics.
Figure 4. Price chart of Micron Technology, Inc. (MU)

Figure 4 shows the price chart of MU. There are some strong trends, particularly from 1995 to 2000, when the dot.com bubble had its
full strength. After 2000, the bubble burst and prices declined to pre-1995 levels. Then, 2012–2013 was the beginning of another bullrun, and MU reached the level of the dot.com climax. Since then, prices have been declining.
Figure 5. Chart of the logarithmic returns

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Figure 5 shows the logarithmic returns of MU. For theircalculation, the close has been used, as this is traditionally themost important price of the day when compared to the otherfeatures, such as open, high, and low.
As expected, this time series is stationary. There are frequentinstances when the logarithmic returns oscillated strongly
either up or down, with a maximum of 20% to the upside andnearly -30% to the downside.
Figure 6. Logarithmic returns distribution

Figure 6, which shows the distribution of the logarithmic
returns of MU, suggests that the distribution is not Gaussian.
The first visual impression is that the distribution is leptokurtic.
The red-colored distribution is the probability density functionof the Gaussian distribution.
Figure 7. Probability plot of the logarithmic returns

Figure 7 shows the probability plot of the logarithmic returns.
It can be seen that the logarithmic returns exhibit fat tails,
which means that extreme returns (either positive or negative)
are more likely than under the assumption of a Gaussian
distribution.
The results of the normality tests can be seen in the Table 1.
Table 1. Test results of two normality tests
Test Statistic

pValueJarcque-Bera5836.72

0.0

Shapiro-Wilk

0.96091.5e-442023 EDITION

Employing a significance level of 5%, a pValue less than 0.05
rejects the null hypothesis of a Gaussian distribution. This istrue for both tests.

LSTM ArchitectureThis section describes a selection of relevant
hyperparameters of the LSTM and GRU models theoreticallyand numerically.
Number of Hidden Layers and Dropout: The employed LSTM
and GRU models are so-called stacked models. This means that
there are multiple hidden layers stacked one on top of another. A
hidden layer is the connection between inputs and outputs. For
this study, the first LSTM layer has hidden units varying from 64
to 128 to 256. This LSTM layer is followed by a dropout layer witha keep probability of 70% (or a dropout of 30%). A dropout layer
mitigates overfitting in training by bypassing randomly selected
neurons. These are followed by a second LSTM layer with hidden
units varying from 32 to 64 to 128. Again, these are followed bya second dropout layer with a keep probability of 70%. The same
holds true for the GRUs.
Optimization: Adam (Adaptive Moment Estimation)
optimization was chosen for all models. Adam optimization is astochastic gradient method that is based on adaptive estimationof first-order and second-order moments.
Dense Layers: A dense layer is a layer where each neuron
receives input from all neurons in the previous layer. Dense
layers improve overall accuracy. For the models, one dense layer
was used.
Activation Function: As an activation function, the Rectified
Activation Function (ReLU) was chosen. An activation function
defines the output of a node as either being on or off. These
functions are used to introduce nonlinearities to models, thus
allowing deep learning models to learn nonlinear prediction
boundaries. The ReLU function can be described by a simple
if-statement:
if input>0:
return input
else:
return 0or mathematically: g(x)=max{0, x}.
Number of Epochs: An epoch is how many iterations of thedataset are to be run. The number of epochs has been set at 100.
Batch Size: The batch size defines the number of samples
to work on before the internal parameters of the model are
updated. The batch size was chosen to be 32.

Results

As outlined before, the dataset was split into 80% training
data and 20% test data. This corresponds approximately tousing 2014 as the cutoff. The blue time series represents thetraining set whereas the orange dataset represents the test set(i.e., the dataset used for regression). The aim is to model thisdataset as accurately as possible. For this purpose, two metrics
were used to describe the goodness of the fit: RMSE and theR-squared statistic. A low RMSE as well as a high R-squared (i.e.,an R-squared close to 1) describe a good fit. The data has beennormalized by using the MinMaxScaler. This last step should
boost the performance of the models.
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Figure 8. Splitting the dataset Into 80% training and 20% testing

Figure 9. The actual (blue) vs. predicted (orange) test set

Figure 9 shows an accurate modeling/regression of the test dataset. As can be seen, the LSTM model learns from the training data to
reproduce the test data. Figure 9 is representative for all models. Table 2 summarizes the test results by means of RMSE and R-squared
statistic.

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Table 2. Test results of LSTMs and GRUs

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Table 3. Test results for 3-year and 1-year data

RMSE

R-squared

3-Year Data

RMSE

LSTM 64x32

0.036140.98587

LSTM 256x128

0.02619

LSTM 128x64

0.03374

0.98768

GRU 256x128

0.03650

LSTM 256x128

0.03263

0.98848

1-Year Data

GRU 64x32

0.034100.98742

LSTM 256x128

0.02216

GRU 128x64

0.03467

0.98700

GRU 256x128

0.01331

GRU 256x128

0.03288

0.98830

For answering this question, only the RMSE was used. As canbe seen, the LSTM performs better than the GRU on the 3-Yeardataset, whereas the GRU performs better than the LSTM on the
1-Year dataset.

As can be seen from Table 2, the most complex LSTMs and
GRUs in terms of hidden layers perform best. The best modelis the LSTM 256x128 with a RMSE of 0.03263 and a R-squared
statistic of 0.98848, which means that the model describes over
98% of the variation of the test data. The second-best model is
the GRU 256x128, with a nearly equal RMSE of 0.03288 and a
R-squared statistic of 0.98830.
The next area of analysis is determining whether LSTMs or
GRUs perform better when financial data is scarce. For thispurpose, the two strongest models (i.e., LSTM 256x128 and GRU
256x128) have been tested on three-year and one-year data,
respectively. Table 3 summarizes the results.

1-Step Ahead Predictions

For this last area of analysis, the last 100 data points from thefull dataset of MU are used to make 1-step ahead predictions
into the future and compare the predictions with the actual
trend direction of the test set. This means that 100 last data
points are used to predict number 101, the next point (number
102) is predicted by 98 last data points, number 103 is predictedby 97 last data points, and so on. I repeat these steps 60 times
for every model out of the set of six models. The results areshown in Figure 10.

Figure 10. Rolling 1-step ahead predictions: LSTM 64x32

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Figure 11. Rolling 1-step ahead predictions: LSTM 128x64

Figure 12. Rolling 1-step ahead predictions: LSTM 256x128

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Figure 13. Rolling 1-step ahead predictions: GRU 64x32

Figure 14. Rolling 1-step ahead predictions: GRU 128x64

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Figure 15. Rolling 1-step ahead predictions: GRU 256x128

The conclusion of the rolling predictions is that mostmodels do not get the predictions right all the time. Quite
to the contrary, the more complex the model, the worse thepredictions, especially at the very tops and the very bottoms(see Figure 15 for example). Nevertheless, GRU 64x32 performs
quite well, getting the majority of predictions right, or at least
the big moves, which is the holy grail recipe for every trader.

Conclusion

This study was about analyzing deep learning models, namely
LSTMs and GRUs. The chosen style of analysis was regression
type. The last part of the study ventures some predictions, which,according to the author of this study, is the most relevant part.
There is no real performance difference between LSTMs
and GRUs. In fact, LSTMs perform slightly better the more
historical data is available, and GRUs presumably performbetter the less historical data is available. However, GRUs are to
be preferred, as they have fewer parameters and train faster.
As a comparison, the most complex LSTM (LSTM 256x128)
has a total of 461,441 parameters, while the GRU 256x128 has
347,265 parameters in total. The run time for these two models
on the full dataset is 1h 5min 15s and 52min 48s, respectively.
(Calculations were performed on a MacBook Pro with a 1.4 GHz
Quad-Core Intel i5 CPU with 8 GB 2133 MHz LPDDR3 memory.)
Furthermore, one has to use many different LSTMs and/or
GRUs when doing predictions, as not all models perform well.
In fact, most models get the big moves wrong, which translates
into financial losses for the trader. Only one model (GRU 64x32)
showed an adequate prediction capacity.
As far as stocks and the stock market are concerned, manyfactors (macroeconomic factors such as inflation expectations,
PAGE 54 IFTA.ORG

interest rates and bond yields, and consumer sentiment, butalso company specific events such as earnings and earning
outlooks) play a relevant role. Whereas it is true that the price ofa stock is the most important variable and it should incorporate
all relevant factors (in accordance with the EMH), other sourcesof information besides the price could be used with deeplearning models.
Another point is that no trader should only rely on one modelor one tool for making predictions. Other tools are technicalanalysis and fundamental analysis, which is a combination ofmacroeconomic and company-specific variables. I think thatthese tools should be used as complements to deep learningmodels.
Last but not least, deep learning or, more broadly, AI, is afairly new scientific discipline that is expected to progress
at a fast pace. Therefore, there is a good reason why traders,investors, and financial institutions should study these models,as they may become the foundation for more complex andaccurate models in the future.

References
Hilpisch, Y. (2020), Artificial Intelligence in Finance: A Python-Based
Guide, O’Reilly.
Hilpisch, Y. (2020), Python for Algorithmic Trading: From Idea to Cloud
Development, O’Reilly.
Hamoudi, H. & Elsefi, M. (2018), Stock Market Prediction using CNN and
LSTM, CS230, Stanford University.
Ahmed, W. & Bahador, M. (2018), The accuracy of the LSTM model for
predicting the S&P 500 index and the difference between prediction
and backtesting, KTH Royal Institute of Technology, School ofElectrical Engineering and Computer Science.

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Christoph T. Wildensee, Ph.D., MFTA

Price Monitoring of Stock Portfolio—
Software Development in Lazarus

Nordstr. 7
Seelze-Letter, Niedersachsen
30926 Germany+49 511 4302128
christoph@wildensee.de

By Christoph T. Wildensee, Ph.D., MFTA

Introduction

In my MFTA thesis from 2021, I have shown by using the
programming language Lazarus (Object-Pascal, similar
to Delphi, cross-platform development) that it is possible
to produce software for the observation of intraday stock
developments and to include insights of Fibonacci trading. This
does not produce a compelling result for a buy or sell decision,
but this supplementary view of the price development can help
to make such a decision. Forecasting is not possible, but thedevelopment can be upgraded with probability estimation. In
doing so, the separation between observation and trading has tobe taken care of in order to take a consciously active role and to
execute a trading action only after careful consideration and, if
necessary, with the help of further information. High frequency
trading is of course not possible.
Finally, the focus is on the presentation of one’s own
portfolio. In particular, stock developments that do notcorrespond to the desired course must be observed.
Currently (i.e., at the end of February 2022), the stock
market developments show dramatically negative due to the
Ukraine crisis as a result of the invasion of Russian troop
units with Belarusian support in the context of the violationof international law. Provided that one does not sell inpanic, but holds, it is purposeful to observe the deficit stock
developments in one’s own portfolio both intraday and over
several months. Of course, now is not a time to trade withspecial strategies; every strategy is influenced by the war andcurrent market movements. There are winners and losers
every day, but this is not due to the common parameters of
the enterprises. However, the current volatile markets withextreme movements are purposeful for the demonstration ofcertain effects.
In the following article, the development of a small
administration software in Lazarus for 10 stock titles tobe observed is represented. The system can be extended at
any time. I added example data to simulate a possible loss
risk identification. The basis portfolio lies exemplarily withapproximately 15,000 EUR evaluation sum, the current
loss risk with approximately -3,900 EUR. The values can beextrapolated analogously.

IT System Development

As in the master’s thesis, the IT system is based on reading
the prices for all the titles to be monitored via website (https://www.finanzen.net), and this is done every two minutes. In
this way, 30 values per title are generated per hour. If a pricecannot be read, the last correct price is used as an alternativevalue. To get an overview of the portfolio and its development,
certain values must be held and mirrored against the current
development. Essential points can be, for example:• “own avg. price” average price, including all fees of a stock
title.
• “P2S”
target price at which a number of stocks is
to be sold• “New Value”
current market value (NV, „new value“)• “P2B”
price at which a subsequent purchase isbeing considered• “Num.”number of stocks in the portfolio.
This can be used to map both the development and the user’s
own preferences. If the software is connected to a database, thevalues can be stored over a long period of time. The software
saves permanently but copies all values [year - 1] into ahistorical table after one year so that the productive table does
not expand unnecessarily.

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Figure 1. Main form

On the left to just above the center, the above-mentioned values are held for the 10 stock titles in Figure 1. In addition, certain
difference values (P2S - NV and P2B - NV) are calculated. If the threshold values are exceeded and/or fallen below, the system produces
a beep so that the user receives a reference to look at the values. This way, he can run the software in the background during the day
and does not miss important points of the intraday development. On the right side, the price development intraday is displayed both intabular form and visually, provided that a fast view for every title is selected with a mouse click.

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Figure 2. Show hist-data, here from TUIIn Figure 2, the previous developments of the stock can be viewed (F5). Several time ranges can be activated, such as today,yesterday (-1D), last month (1M), the last three months (3M), the entire year (this year) and all existing values. The button „Check“ isused to narrow down the development. “DS” shows the number of records that fit into the narrowing down. On the right side, as usual,are the last values of the series.

Inclusion of Fibonacci

Fibonacci inclusion means that a right and left point in the trend view of the stock performance is used to create a difference ofthe left and right value. This is used to generate the Fibonacci support lines. In such a view, the right-hand value is only marginally
removed from the latest price value, while the left-hand value may well be several hundred points away, depending on the will to know.
In my original work, I used only the change points of the intraday development, only to see with the intraday change performance,
constant prices were ignored, so the distance of the left and right secant value was not so large.
Here, however, I bring in each new price value so that the secant values are located with long distancy. The trackbar (i.e., theslide, sets this distance and of course cannot be larger than the total number of existing records. The buttons F150/50, F162/62, andF200/100 create the support lines according to Figure 3.
Figure 3. Development with support lines

The price of the TUI share, for example, fell back from almost EUR 3.60 to near EUR 2.80 on this day. Accordingly, the lower support
line struck. The other support line definitions also showed an identical result.

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Import of New Values

Of course, it must be possible to insert new values, including fees, automatically adjusting the average price. This can be seen in
Figure 4.
Figure 4. Add new value

Further Analytics

First of all, any analyses can be run with regard to the existing values stored in the database. These are limited only by the stored
raw data itself. The speed is hardly burdening since the keeping of historical data larger than one year is not permanently needed. The
raw data width can be extended as desired with additional fields and then saved to the new price value with more complex calculated
attribute values.
An example is the relationship between the current and average price value (upper graph from Figure 5). This is solved by calculating the
average value of the selected stock title. Another example in Figure 5 is the ratio of the last to the newly read price value (lower graph).
Figure 5. Examples of different data views

It can also be useful to see if there were records that exceeded or fell below previous defaults. This is shown in Figure 6. The
corresponding SQL statement is ‘SELECT Name1, OAP, P2S, NV, P2B, OSNUM, Date1, Time1 FROM 10Stocks WHERE ((CDbl(NV) CDbl(P2S) >= 0) OR (CDbl(NV) - CDbl(P2B) <= 0)) ORDER BY ID DESC’.

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Figure 6. Exceeding or falling below favored values

At the calculation point shown in Figure 3, it is possible toimplement any additional calculation model, e.g., univariate
ARMA, GARCH ..., possibly via Python or MATLAB integration.
The results can be conveyed in a new Form like Figure 5, perhaps
shown with a probable range of future value. This is difficult
and tricky but can be done quite well. I extracted the generationof a value prediction to a DLL. Therefore, in the case of acalculation change, only the DLL has to be changed, not the main
component; ArrayPred[1..2]: Double = DLL (ArrayVal[]: Double;
numberofval:integer; ArrayModelParam[]: Variant). The result isa range of a value prediction.

Note

The default values are fictitious, the price values were read in
March 2022.

References
Adegboye/Kampouridis/Otero (2021): Improving trend reversal
estimation in forex markets under a directional change paradigm
with classification algorithms, International Journal of Intelligent
Systems, https://doi.org/10.1002/int.22601.
Aloud (2016): Time Series Analysis Indicators under Directional
Changes: The Case of Saudi Stock Market, International Journal of
Economics and Financial Issues, 2016, 6(1), 55-64.
Butgereidt (2019): Analyse der Prognosegüte alternativer
Prognosemethoden bei kleinen Stichproben, TU Wien.
Hyndman (2018): Forecasting: principles and practice, Monash
University Business School, https://robjhyndman.com/
acemsforecasting2018/2-ARIMA.pdf.
Montgomery et al (2015): Introduction to Time Series Analysis andForecasting, Wiley, 2015.
Schmelzer (2009): Die Volatilität von Finanzmarktdaten, Theoretische
Grundlagen und empirische Analysen von stündlichen
Renditezeitreihen und Risikomaßen, Diss., Universität Köln, 2009.
Sun/Cui/Xu (2014): Design and Implementation of a Time-frequency
Analysis System for Non-stationary Vibration Signals Using
Mixed Programming, International Journal of Hybrid Information
Technology Vol. 7, No. 6 (2014), pp. 283-294, https://gvpress.com/
journals/IJHIT/vol7_no6/24.pdf.

Wildensee (2021): Intraday-Trade-Optimization via Fibonacci-DLL, IFTA
Journal 2022, 22-42.
Wildensee (2022): Extension of the Intraday Fibonacci-DLL, IFTA
Update, Volume 28, Issue 4, 7-15.

Data and Software
DEWLAB: Dew Lab Studio for Delphi 2021, High performance
numerical, statistical and dsp library for Delphi/C++, https://dewlab-studio-for-delphi.software.informer.com/2021/.
FM Labs (2020): Technical Analysis Programmer’s Toolkit, https://www.fmlabs.com/toolkit.htm.
Wildensee (2022): http://www.wildensee.de/fibo_view.zip . http://
www.wildensee.de/laz1a.htm.

Appendix
Selected Sample Source Code // Delphi - Lazarus[…]
for i:=1 to anzds do // number of records selected
begin// New Valuetry
q:=DBGridShowData.DataSourceReadData.DataSet.
FieldByName(‘NV’).AsString;
exceptq:=’0’;
end;// NV*100/AVG
tryt:=DBGridShowData.DataSourceReadData.DataSet.
FieldByName(‘NVPROCAVG’).AsString;// nv / avg is stored in Database every reading of new value
exceptt:=’0’;
end;
try
ArrayNumNV[i]:=StrToFloat(q);exceptIFTA.ORG PAGE 59

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//
end;
try
ArrayNVAVG6[i]:=StrToFloat(t);except//end;// add. calculations (here you can implement any calculation
you want, put an array// in a form, initialize it at [1..200000] to 0 and implement any
calc here). Maybe with// Python4Delphi / Lazarus or Matlab integration; Forecast
model with probability calc// implementation, display; …then ...
if (i > 1) then
begin
try
if (buyprice = 0) then // diff. calc, when own avg. price equal
or unequal 0
begin
ArrayNVQ6[i]:=(-100*((ArrayNumNV[i]ArrayNumNV[i-1]))/ArrayNumNV[i]);
end
else
begin
ArrayNVQ6[i]:=(-100*((ArrayNumNV[i]ArrayNumNV[i-1]))/buyprice);end;
except//end;
end;// ***[…]CreateAVGStock(StockName1, selected_stockid, NewValue);
procedure TForm1.CreateAVGStock(Name1: String; stid:
integer; nv: Double);var
anzds1: integer; i: integer; q: String; p: Double; sum1: Double;
sum2: Double; proc1: Double;
begin
anzds1:=0; i:=0; q:=’’; sum1:=0; sum2:=0; proc1:=0; p:=0;
try
SQLTransactionReadData1.Active := true;
SQLQueryReadData1.UsePrimaryKeyAsKey := false;
SQLQueryReadData1.SQL.Text :=‚SELECT Name1, OAP, P2S, NV, P2B, OSNUM,
Date1, Time1, NVPROCAVG FROM 10Stocks
WHERE Name1 = ‘+QuotedStr(Name1);
SQLQueryReadData1.Open;
SQLQueryReadData1.Last;
anzds1:=SQLQueryReadData1.RecNo; // number of records
SQLQueryReadData1.First;
except//end;
PAGE 60 IFTA.ORG

if (anzds1 > 1) thenbegin
for i:=anzds1 downto 1 do
begin
try
q:=DataSourceReadData1.DataSet.FieldByName(‘NV’).
AsString;
exceptq:=’0’;
end;
try
p:=StrToFloat(q);exceptp:=0;
end;
sum1:=sum1+p; // sum of all Values
end;
sum2:=sum1/anzds1; // sum of all values / number of records
proc1:=(nv*100)/sum2; // new value in relation to sum2
end;
avgv1[stid]:=FloatToStrF(proc1, fffixed, 8,2);// array with proc1 for all time stamps
end;IFTA JOURNAL

2023 EDITION

Garrett H. Brookes, CFA

Active/Passive Blending Based on the
Liquidity Premium: A Practical Study

Slingshot Financial
Denver, CO USA+1 (303) 993-7839
gbrookes@slingshotfin.com

By Garrett H. Brookes, CFA

Abstract

The merits of active and passive investing have been exploredextensively in volumes of academic research where thesuperiority of each approach has been debated at length. We
acknowledge the advantages of each by preferring a blended
portfolio approach that includes both active and passive
strategies to achieve our objectives.
Our study is conducted from a practical perspective. It relies
on widely available information, accessible real investments,and operationally feasible processes. We propose the liquidity
premium described by the spread between the yield of U.S.
Treasury 10-Year and 3-Month securities as an indicator forallocating to active or passive strategies. Our proposal is tested
by simulating an active/passive blended portfolio allocating
regular bimonthly new money contributions through a 14-year
period of wealth accumulation. Our total blended portfolio
includes a passive strategy represented by an unmanaged
buy-and-hold portfolio of an equally weighted S&P 500 ETF,
and an active strategy represented by a Cap Weighted S&P
500 ETF & Cash portfolio that tactically manages its equity
allocation according to the NAAIM Exposure Index. Our
proposed allocation method, the Liquidity Premium Blend,
allocates its new money portfolio contributions to the active
strategy in periods of low liquidity premium and to thepassive strategy in periods of high liquidity premium. The
intent is to achieve enhanced portfolio efficiency through risk
management while minimizing its opportunity cost to returns.
Investment performance presentation includes total returns
with reinvested dividends. Our final analysis uses internal rateof return as its performance measure to evaluate alternative
active/passive allocation sequences. We draw conclusions
primarily based on risk-adjusted portfolio efficiency.
As background for our strategy simulation, the study begins
with a review of the U.S. Treasury 10-Year Minus 3-Month spread
data. We explore the performance of the S&P 500 throughperiods of high and low liquidity premium. The chosen ETFs arealso examined through these periods for perspective. Our active
strategy is defined after a review of the NAAIM Exposure Indexhistorical data.
Ultimately, the simulation results supported our proposal,suggesting liquidity premium serves as an effective indicatorfor efficiently blending active and passive management throughportfolio contribution allocations. The rate of return for our
Liquidity Premium Blend outperformed all other blended
portfolio methods we tested. Its portfolio efficiency describedby our modified Sharpe ratio was second only to the active
strategy. It beat its comparable randomized allocation method’srate of return by 50 bps and was more efficient. The mostsignificant implications for wealth management and financial
planning practitioners are:In all simulations, blending the active strategy: NAAIM
Tactical Risk Managed with the passive strategy improved
portfolio efficiency and reduced drawdowns versus the passiveonly methodologies.
Liquidity premium measured by the spread between the U.S.
Treasury 10-Year and3-Month serves as an effective indicator for efficiently
allocating between the active and passive strategies.
This Liquidity Premium Blend method can be customized forclient objectives and risk tolerance.

Introduction

The merits of active and passive investing have been exploredextensively in volumes of academic research where thesuperiority of each approach has been debated at length. We
acknowledge the advantages of each by preferring a blended
portfolio approach that includes both active and passive
strategies to achieve our objectives.
In this paper, we will explore liquidity premium as anindicator for blending active and passive strategies throughallocations of regular new-money portfolio contributions. We
will consider a passive strategy represented by an unmanaged
buy-and-hold exposure to equity beta, and an active strategy
represented by an equity/cash portfolio that tactically manages
its equity beta level. Our proposed method, the Liquidity
Premium Blend, allocates its new money portfolio contributions
to the active strategy in periods of low liquidity premium and to
the passive strategy in periods of high liquidity premium. The
intent is to achieve enhanced portfolio efficiency through risk
management while minimizing its opportunity cost to returns.
Our study is conducted from a practical perspective. It relies
on widely available information and accessible real investments
and aims for operational feasibility. We will simulate our
proposed blending method through a wealth accumulation
pattern of regular, bimonthly contributions made by the typicalinvestor saving for retirement. Investment performance
presentation will account for total returns, including thecompounding effect of reinvested dividends. Our final analysis
uses internal rate of return as its performance measure toevaluate alternative active/passive allocation sequences. We
draw conclusions primarily based on risk-adjusted portfolio
efficiency.
The liquidity premium occurred as a natural fit for our
indicator, owing in part to its pattern of cyclicality and our
acceptance of The Liquidity Preference Theory.1,2 While there
are many measures of liquidity premium, some directly derived
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IFTA JOURNAL

2023 EDITION

from U.S. equity market data, we selected U.S. Treasury yield spreads as our strategy’s indicator. From a practical perspective, yieldspread data is readily available. From a philosophical perspective, as “risk-free” assets, we believe treasuries are a purer indicationof broad liquidity premium and are less susceptible to “noise”. We accept this broader measure of liquidity premium, believing that
capital flows freely between public markets.

Background
Studying the Law Yield Spread Data: 1/4/1982–2/23/2021
In preparation for this study, we considered a variety of U.S. Treasury yield spreads and settled on the 10-Year Minus 3-Month todefine our liquidity premium periods. This spread was selected for its relatively smooth cycles over decades of our observation. This
would allow our proposed methodology to be practical for real-world implementation. Additionally, we felt these durations best matchthe durations of the assets included in the study: equities carrying a long duration while “cash” assets are fairly represented by the
3-Month maturity. This information is readily available on the Federal Reserve Bank of St. Louis economic research website3 in aconstant maturity format that is free and easy to access.
Figure 1. U.S. Treasury 10-year minus 3-month constant maturity

Table 1. U.S. Treasury 10-year minus 3-month constant maturity statistics

1/4/1982–2/23/2021
Total observations

9,787

Maximum Value

5.18

Minimum Value-0.96

Average

1.74096761

Median

1.8

Mode

1.92

Standard Dev

1.120893684

Kurtosis-0.957030843

Skew-0.10971558

Days greater than .999

6,986.00

Avg consecutive Days

136.98Days Less than 1

2,800.00

Average Consecutive Days

56.00

PAGE 62 IFTA.ORG

This data led us to designate 1% as the threshold to define
periods of low liquidity risk premium and high liquidity risk
premium, which determine the active/passive allocation of newmoney contributions to our blended portfolio. We intentionallysought a level that led to longer high premium periods while
avoiding frequent signal changes. This was because ourLiquidity Premium Blend strategy is intended to be applied
over long periods of wealth accumulation, and we believe that
equity prices rise over time. The 1% level achieved both of theseobjectives, with days at or above 1% representing approximately
70% of observations, and days below 1% representing
approximately 30% of all observations. After selecting the 1%
level as our threshold we defined start and stop dates for highpremium and low premium periods by requiring 15 consecutive
days at a new level (above or below the 1% threshold) to
confirm a period change. Fifteen days was chosen as thesmoothing number because no transitionary period exceeded
this timeframe, and the study does not include new money
contributions more frequently than 15 days.

IFTA JOURNAL

2023 EDITION

Table 2. Smoothed liquidity premium periods
HIGH PREMIUM PERIODS: 1% +LOW PREMIUM PERIODS: LESS THAN 1%

Beginning Date

Ending Date

Number of Days

Beginning Date

Ending Date

Number of Days

1/8/21

2/23/2131

6/15/18

1/7/21640

1/22/08

6/14/18

2,604

6/22/05

1/18/08646

4/9/01

6/21/05

1,049

1/31/00

4/6/01299

12/28/99

1/28/00

23

10/29/99

12/27/99

39

6/1/9910/28/99

105

10/22/97

5/28/99401

2/20/96

10/21/97

421

5/5/95

2/16/96198

8/6/905/4/95

1,186

11/14/88

8/3/90432

5/19/82

11/10/88

1,619

3/2/82

5/18/8255

1/4/82

3/1/82

39

Total

7,046

338.75

Average Days in Period

880.75235.8812
27.78%

StD

917.5686

Percent of Time72.22%

2710

S&P 500 Through Our Defined Liquidity Premium Periods
With Liquidity Premium Periods defined, we observed the S&P 500 through these timeframes to better understand how the broad
equity market performed and anticipate any impact to our proposed methodology. This would provide an initial indication if thestrategy could achieve its intended objectives and potentially explain future results. Cumulative returns for each liquidity premium
period were annualized, along with standard deviation of daily returns. A weighted average was then applied to compare returns andprice volatility between periods of high liquidity premium and low liquidity premium.
Figure 2. S&P 500 through liquidity premium periods

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2023 EDITION

Table 3. S&P 500 performance by liquidity premium periods
Liquidity Premium
Environment

PeriodCumulative
ReturnAnnualized Return

StDev of Daily Returns

Annualized StD ofDaily Returns

Low

6/15/18 - 1/07/21

36.84%

19.59%

0.01520.2460High

1/22/08 - 6/14/18

112.30%11.13%

0.01280.2061Low

6/22/05 - 1/18/08

9.17%

5.08%

0.00820.1328High

4/09/01 - 6/21/05

6.68%

2.28%

0.01160.1875Low

1/31/00 - 4/06/01-19.08%-22.77%0.01450.2342High

12/28/99 - 1/28/00-6.69%-66.67%0.01420.2286Low

10/29/99 - 12/27/99

6.91%

86.89%

0.00810.1303High

6/01/99 - 10/28/99

3.72%

13.54%

0.01160.1871Low

10/22/97 - 5/28/99

34.42%

30.90%

0.01320.2131High

2/20/96 - 10/21/97

51.76%

43.57%

0.00870.1402Low

5/05/95 - 2/16/96

24.58%

49.95%

0.0057

0.0917High

8/06/90 - 5/04/95

55.65%

14.59%

0.00730.1177Low

11/14/88 - 8/03/90

28.81%

23.85%

0.00810.1315High

5/19/82 - 11/10/88

138.20%21.61%

0.01160.1881Low

3/02/82 - 5/18/82

2.80%

20.11%

0.00820.1319High

1/04/82 - 3/01/82

7.14%

90.69%

0.01090.1754

Avg Annualized Return

Avg Annualized StD of Daily Returns

Average for Low Liquidity Premium Periods

17.01%

0.1793

Average for High Liquidity Premium Periods

14.96%

0.1800

The results were interesting and likely carry implications for
additional research beyond the scope of this study. Risk, or pricevolatility, was nearly identical for the high- and low-premium
periods. Returns, on the other hand, were approximately
2% annualized higher in our low liquidity premium periods.
Considering that low liquidity premium is typical in later stagesof the business cycle, we assume this is the result of strong
price momentum. This was interesting to observe because
our Liquidity Premium Blend method will allocate new money
contributions to the active strategy during these low premium
periods when momentum is strong and likely to cause anincrease in the passive strategy’s proportional share of thetotal blended portfolio. The original motivation of our Liquidity
Premium Blend was to have new money contributions actively
allocated between equity and cash when there is little premium
being paid for the illiquidity risk of long duration assets. This
analysis of S&P 500 performance through our liquidity premium
periods shows that our methodology should also strategically
help maintain balance between active and passive allocations.

Methods
Defining Investments and Their Performance
Measures
For practicality, this study uses a couple of the largest
and most tenured Exchange Traded Funds (ETFs) to simulate
PAGE 64 IFTA.ORG

investment results. They are available on most no-transaction
fee trading platforms and are increasingly available infractional shares, adding to their accessibility. All performance
presentation of investment results for our active and passive
strategies, including final simulations, are calculated using
the Total Return Price (Forward Adjusted) available through
YCharts.4 The Total Return Price (Forward Adjusted) allows us tosimulate dividend reinvestment, a key component of long-term
investing. Its formula is:
Total Return Level = Actual Price x Split Factor x Dividend
Adjustment Factor
Split factor = 0.5 for a 2 for 1 split, 0.33 for a 3 for 1 split, etc.
Dividend Adjustment Factor = (1 + Value of Dividend/Previous
Day’s Close Price)
Risk is presented as standard deviation of daily returns
calculated as a weighted average of portfolio components’ daily
returns.
Transaction costs and taxes were intentionally omitted
from the calculation, assuming no transaction fees for our
ETF trading and a qualified account for wealth accumulation.
Expense ratios of the ETFs are reflected in their performance,with no other hypothetical fees applied.

IFTA JOURNAL

Active Strategy: NAAIM Tactical Risk Managed
The active strategy: NAAIM Tactical Risk Managed or
NAAIM TRM implements the National Association of Active
Investment Manager’s (NAAIM) Exposure Index 5 as an equity/
cash allocation strategy. This indicator represents the averagelevel of exposure to U.S. equity markets reported by the group’s
membership. The NAAIM Exposure Index is a very credible
indication of professional risk manager’s sentiment, widely
cited by major financial press.6-10 It provides over 14 years oflive data spanning four of our most recent liquidity premium
periods.

2023 EDITION“NAAIM member firms who are active money managers
are asked each week to provide a number which represents
their overall equity exposure at the market close on a specificday of the week, currently Wednesdays. Responses canvary widely as indicated below. Responses are tallied andaveraged to provide the average long (or short) position of all
NAAIM managers, as a group.
Range of Responses: 200% Leveraged Short, 100% Fully
Short, 0% (100% Cash or Hedged to Market Neutral), 100%
Fully Invested, 200% Leveraged Long.”5

Figure 3. NAAIM exposure index

Table 4. NAAIM exposure index simple statistics
Number of Observations

764

Maximum Allocation

120.56

Minimum Allocation

-3.56

Mean

65.3270

Median69.665

Mode

97.44

Standard Deviation

24.2367

Skew-0.6016

Kurtosis-0.3224

Number of Observations Above 100, percentage of total

28

3.66%

Number of Observations Below 0, percentage of total

3

0.39%

We modeled the NAAIM Tactical Risk Managed Portfolio by applying the Exposure Index numbers since its inception as a percentageof exposure to the daily performance of SPY—State Street SPDR S&P 500 ETF Trust. SPY was selected as the most common, longest
tenured ETF available as broad representation of “the market”. Any unallocated cash received the daily yield of the 3-Month U.S.
Treasury. Exposure levels were not constrained, so market exposures less than 0% and greater than 100% were allowed. Although

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2023 EDITION

many practitioners are limited in their ability to implement
leverage or short exposure especially in qualified accounts,
these instances were not extreme, with -4% being the“shortest” observation and 121% the most “levered”. We
assume these levels could be creatively replicated with noobservable impact, given that the occurrences of “short”
and “levered” observations were rare at 0.39% and 3.66% of
total observations, respectively. The NAAIM TRM portfolio’s
equity/cash allocation was held constant for each day between
reported changes in the exposure number.
Passive Strategy
The passive strategy is represented as a buy-and-holdaccumulation of RSP—Invesco S&P 500 Equal Weight ETF,
which holds the S&P 500 constituents in equal proportions andrebalances quarterly. While it can be fairly argued that quarterly
rebalancing and annual reconstitution is not purely passive
ownership, this investment was selected as our passive strategy
for a few reasons. Our study includes regular contributions
to the portfolio, and RSP’s quarterly rebalancing ensures that

contributions to the passive strategy will be made nearly
equally among its stocks. Additionally, our proposed Liquidity
Premium Blend is intended to be easily implemented for wealthmanagement practitioners. As fiduciaries, none would actually
hold an investment completely unmanaged (even allowing it tofall to $0.00). As a result, we felt RSP is as philosophically close
to passive ownership as is practical.
Market Cap Weight Versus Equal WeightThe decision to implement the active and passive strategies
using investments that weigh the S&P 500 stocks differently
was made for philosophical reasons, fully aware this resultsin tilting towards different factor risk premia. The SPY cap
weighted index is expected to provide a higher exposure
towards the momentum factor, whereas the equally weighted
RSP tilts towards (small) size and value factors. Knowing
these risk factors tend to be rewarded differently through thecourse of a business cycle, we observed performance of the capweighted SPY and equal weight RSP through our periods of highand low liquidity premium.

Figure 4. RSP and SPY performance

Table 5. RSP and SPY performance through liquidity premium periods
Liquidity Premium

PeriodAnnualized Return

Annualized StD

SPY

RSP

SPY

RSP

Low

6/15/18 - 1/07/21

22.89%

17.56%

0.24210.2654High

1/22/08 - 6/14/18

14.57%

16.10%

0.20570.2251Low

6/22/05 - 1/18/08

7.55%

5.50%

0.13150.1400High

4/30/03(inception)- 6/21/05

24.44%

37.28%

0.11960.1333

PAGE 66 IFTA.ORG

IFTA JOURNAL

The equally weighted RSP is more volatile than the market
cap weighted SPY through all periods, unsurprising given its
tilt towards the (small) size and value factors. However, it wasinteresting to discover the cap-weighted portfolio outperforms
in our periods of low liquidity premium while the equallyweighted portfolio outperformed in periods of high liquidity
premium. This is noteworthy since our proposed Liquidity
Premium Blend allocates its contributions to the active strategy
using SPY in the low liquidity premium periods and to thepassive RSP strategy in high liquidity, and is likely to have afavorable impact on performance while also potentially helping
to maintain balance in our blended portfolio.
Simulation Methods
Simulations spanning 14.5 years were conducted to compare
the effects of blending our active and passive strategies throughallocations of regular bimonthly new money contributions
to the portfolio. The intent is to replicate the typical wealthaccumulation pattern of an average investor saving for
retirement. The beginning date of 7/5/2006 coincides with the
inception of the NAAIM Exposure Index while the end date of
1/7/2021 marks our most recent change of liquidity premium
periods.
Each simulation begins with a total portfolio value of$200,000. All active/passive blending methods begin with thetotal portfolio divided equally: $100,000 allocated to active,
and $100,000 allocated to passive. The active NAAIM TRM
Only, Passive Only, and SPY Only simulations begin with thefull $200,000 allocation to their respective single investment
portfolios. Regular bimonthly contributions of $1,000 are madethrough the course of the study on the same dates in eachmethod simulation.

Liquidity Premium Blend
Our proposed method for active/passive blending allocates its$1,000 new money portfolio contributions to the active strategy
in periods of low liquidity premium and to the passive strategy
in periods of high liquidity premium.
Passive Only
Holds and allocates to RSP exclusively.
NAAIM TRM Only
Holds and allocates to the active strategy exclusively.
SPY Only
Holds and allocates to SPY exclusively.

2023 EDITION

1:1 Random Contribution
Randomized contributions with a simulated “coin flip”
determining the allocation of the $1,000 contributions to theactive or passive strategy.
Reverse Contribution
Reverse Contribution allocates the $1,000 contribution to
the active strategy in periods of high liquidity premium and thepassive strategy in periods of low liquidity premium. This is the
opposite of our proposed Liquidity Premium Blend.
2:1 Random Contribution
Randomized allocation of the $1,000 contribution to thepassive strategy in 2/3 of instances, active in 1/3 of instances.
This was intended to compare directly with our proposed
Liquidity Premium Blend by approximating the historicalamount of time in each liquidity regime.
Simulation Analysis
Because our study explores the effects of new money
allocation sequences through a common timeframe, we choseto analyze the simulation results using their Internal Rateof Return. For each simulated method, the total annual newmoney contributions were subtracted from the gross change
in portfolio value for each calendar year to represent net “cashflows”. For example:
Cf0 = -$200,000, Cf1 = (2006 ending value – $200,000– 2006 contributions), Cf2 = (2007 ending value – 2007
beginning value – 2007 contributions), Cf3 = (2008 ending
value – 2008 beginning value – 2008 contributions), etc.
Portfolio efficiency is presented with a modified Sharpe ratio(Rp – Rf)/ StDp:
Rp = the portfolio’s IRR
Rf = The 10-Year U.S. Treasury Inflation-Indexed Security,
Constant Maturity rate on our 7/5/2006 inception
StD = The portfolio’s annualized standard deviation of daily
returns
An analysis of annual drawdowns was calculated todetermine the maximum drawdown for each simulation. All
occurred through the 2008–2009 financial crisis. The 2020
drawdown was also included in the study’s results, as it was thesecond greatest drawdown for all simulations.

50–50 Contribution
Equally divides each $1,000 bimonthly contribution with$500 allocated to the active strategy and $500 to the passive
strategy.

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2023 EDITION

Figure 5. Liquidity premium blend, NAAIM TRM only and passive only

Figure 6. Liquidity premium blend vs. others

PAGE 68 IFTA.ORG

IFTA JOURNAL

2023 EDITION

Table 6. Final simulation results

Portfolio

EndingPortfolio Value

Internal
Rate of
ReturnAnnualized
StD

Liquidity Premium Blend$1,560,579.28

15.080%0.15780.79-30.83%-30.09%

63.5%

36.5%

Passive Only

$1,672,786.31

16.348%0.22600.61-55.19%-38.43%100.0%

0.0%

NAAIM TRM Only

$1,344,154.47

11.744%0.0956

0.95-13.43%-11.71%0.0%

100.0%SPY Only Portfolio$1,758,883.25

15.813%0.20670.64-52.66%-30.43%NANA

50–50 Contribution$1,508,470.39

14.197%0.15020.77-32.32%-26.05%

50.0%

50.0%

1–1 Random Contribution$1,511,648.38

14.252%0.15000.77-32.19%-25.71%

48.7%

51.3%

Reverse Contribution$1,420,104.33

13.298%0.14340.74-33.25%-21.81%

36.5%

63.5%

2–1 Random Contribution$1,534,154.44

14.573%0.15850.75-33.60%-28.61%

61.7%

38.3%

Conclusion

The Liquidity Premium Blend results support our proposal,suggesting liquidity premium serves as an effective indicatorfor efficiently blending active and passive management throughportfolio contribution allocations. Our overall rate of returnfor the Liquidity Premium Blend was 15.08%, outperforming
all other blended methods and the active-only strategy. Its
portfolio efficiency described by our modified Sharpe ratio of
0.79 is second only to the active-only strategy.
The active-only strategy: NAAIM Tactical Risk Managed
produced impressive portfolio efficiency, handedly
outperforming all other strategies with its modified Sharpe
ratio of 0.95. Its max drawdown was less than 1/3 of the SPY
Only Portfolio. However, its superior efficiency and downsideprotection comes at the expense of returns; nothing is free inthis world. The purely passive strategies including SPY Only
finished with the highest portfolio values and rates of return
but were soundly the worst from a risk-adjusted efficiency
perspective.
In most blended portfolio methods, we observed an
improvement in portfolio efficiency as more new money
contributions were allocated to the risk managed active
strategy. The major exception is our Reverse Contribution
methodology, which posted the worst modified Sharpe ratio of
all active/passive blended portfolios despite allocating 64% of
contributions to the active risk-managed strategy, more thanany other blending method. The Reverse Contribution results
support our proposal, indicating that allocating contributions
between active and passive strategy according to the liquidity
premium has significant impact on the blended portfolio’s
efficiency.
Further evidence is apparent when comparing the Liquidity
Premium Blend to its 2:1 Random Contribution counterpart.
These methods allocated roughly the same amount of newmoney to their active and passive strategies but in different
sequences. Our proposed Liquidity Premium Blend method
prevailed with 50 bps greater rate of return and superior
portfolio efficiency.

Max%
Contributions
Modified Drawdown:
2020
Sharpe‘08-’09
Drawdown
Passive%
Contributions
ActiveImplications for Practitioners

Our proposed Liquidity Premium Blend strategy was designed
for real-world implementation. It relies on readily available
information and includes widely accessible investments for
operational feasibility. The most significant implications for
wealth management and financial planning practitioners are:
1. In all simulations, blending the active strategy: NAAIM
Tactical Risk Managed with the passive strategy improved
portfolio efficiency and reduced drawdowns vs. thepassive-only methodologies.
2. Liquidity premium measured by the spread between the
U.S. Treasury 10-Year and 3-Month serves as an effective
indicator for efficiently allocating between the active andpassive strategies.
3. This Liquidity Premium Blend method can be customized
for client objectives and risk tolerance.

References
Keynes, John Maynard. The General Theory of Employment, Interest
and Money. 1936.
2
Modigliani, Franco. “Liquidity Preference and the Theory of Interest
and Money.” Econometrica, vol. 12, no. 1, 1944, pp. 45–88. JSTOR,
www.jstor.org/stable/1905567. Accessed 8 Apr. 2021.
3
The Federal Reserve Bank of St. Louis economic research website(https://fred.stlouisfed.org).
4
YCharts (https://ycharts.com/glossary/terms/total_return_forward_adjusted_price).
5
National Association of Active Investment Manager’s (NAAIM)
Exposure Index (https://www.naaim.org/programs/naaimexposure-index).
6
Seeking Alpha (https://seekingalpha.com/article/4411396-diana-rossupside-down-stock- market).
7
Bloomberg (https://www.bloomberg.com/news/articles/2020-08-18/
rallying-stock-market-is- forcing-everyone-to-become-a-believer).
8
CNBC (https://www.cnbc.com/2020/05/15/assessing-the-stockmarket-after-one-of-the- fastest-declines-and-subsequentcomebacks-in-history.html).
9Wall Street Journal (https://www.wsj.com/articles/one-reason-foroptimism-bearish- investors-1523006335).
10
Barron’s (https://www.barrons.com/articles/the-stock-market-isbouncing-back-thank-you- chuck-norris-51583846070)is-bouncingback-thank-you- chuck-norris-51583846070)
1

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Alexandros Spiroglou, DipTA, CFTe

MACD-V: Volatility Normalised Momentum
By Alexandros Spiroglou, DipTA, CFTe

Introduction
What Is This Topic About?
This paper will focus on the study of momentum using avery popular technical analysis indicator, the Moving Average
Convergence Divergence (MACD), created by one of the mostrespected analysts of our time—Gerald Appel.1
This paper is comprised of six parts.
In the first section, we will focus on the MACD itself. We will
do a brief description of its construction, the most elementary
ways to use it, and then a review of the five limitations it has.
This is a section that is familiar territory to all technicians.
In the second section, we will show a widely known
suggestion to deal with these limitations that does improve one,but does not solve all of them.
In the third and fourth sections, we will present our own
solution, which remedies the shortcomings while creating
unique advantages (edges) that would not be possible to obtain
via the classic MACD.
In the last two sections, we will use our framework to improveexisting tools in TA literature and explore new techniques.
Why Does This Topic Matter to Us?
Most price-based momentum indicators fall into roughly two
camps:

Range Bound Oscillators
These operate within a finite range of values, usually 0–100(e.g., RSI, Stochastics, Williams %R, etc.). They offer theadvantage of having objectively defined momentum readings,
while at the same time making these readings uniform acrosssecurities for cross market comparison purposes. On the other
hand, the very fact that these tools can only obtain a limited
range of values presents problems during extended price trends,
as their extreme readings (aka “overbought/overbought”)
remain at high (or low) levels for a prolonged period of time,
thereby giving many false signals. In fact, some analysts
have created some counterintuitive techniques, based on thisphenomenon, whereby “overbought” is a sign of future strengthand “oversold” is a sign of future weakness.2 Oscillators are
not trend-friendly and one could argue that these are not truly
momentum measuring yardsticks, but range identification
indicators. For example, a 14 period stochastic oscillator states
where you are as a % in a 14 period Donchian channel anddoes not measure price momentum per se. Thus, the terms“overbought, oversold” become a bit of a misnomer.

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SMART Trader Systems Ltd.
London, UK
alex@TradeTD.com
www.AlexSpiroglou.com

Trend-following Indicators
These measure price change over some period of time andusually are boundless indicators (but not exclusively), as theirreadings can be increasing (or decreasing) along with pricetrends (e.g., RoC, MACD, etc.). Their very freedom makes it
almost impossible to have objectively defined “overbought”“oversold” levels or have meaningful momentum comparisons
between different asset classes (e.g., individual equites vs.
currencies).
Of course, the aforementioned categorization of indicators is
not a fully detailed taxonomy, but a rather broad distinction for
definitional purposes…
Irrespective of which family (category) of momentum tool isused, it would appear that in technical analysis literature there
is certainly no shortage of indicators. One could even argue that
there are more indicators than traders…
So, why attempt to build another tool?
It is not the author’s intention to simply design yet “another”
indicator that would provide approximately the same
informational value as numerous ones already do, thus resulting
in a tool that exacerbates the already existent issue of indicator
multicollinearity.
Our goal is to improve an existing tool (MACD) so that, by
eliminating its shortcomings, we will be creating a unique typeof hybrid “boundless oscillator,” that opens the doors for several
pattern recognition opportunities which would not be definable
using the classic MACD.
We are big believers in creating new techniques rather than
new tools, thus we will use the improved MACD to define ageneral Momentum Lifecycle RoadMap (framework), new entry
and exit techniques, and versatile cross asset (intermarket)
strategies, among other uses, that would not be achievable via
the venerable MACD.

MACD: A Measure of Momentum
Construction
One of the available tools to define momentum is the Moving
Average Convergence Divergence (MACD) indicator. The MACD
was created by Gerald Appel in the late 1970s. It is a trendfollowing momentum indicator that shows the relationshipbetween two moving averages of prices.
The MACD is constructed in four steps :1. Calculate a 12 bar Exponential Moving Average
2. Calculate a 26 bar Exponential Moving Average
3. MACD Line = 12 bar EMA – 26 bar EMA
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What is momentum?
Momentum is closely tied to physics and is the rate (speed)that prices change (velocity = d/t, where d = distance, t =time).
Momentum in market prices is a direct challenge to the
Efficient Market Hypothesis (EMH), as it implies that prices
trend and are not randomly distributed, thus it is possible tooutperform the broad market.
Momentum Strategies are broadly distinguished between(i) Time Series (absolute) Momentum—establish long (short)positions by determining the trend of each asset individually(e.g., go long positive 12-month price return).
(ii) Cross Sectional (Relative) Momentum Strategies—
ranking assets and going long top and shorting bottom
performers.

The MACD is a versatile tool with many non-conventional
uses, but it nevertheless has five key shortcomings. Three ofthem are regarding the MACD values themselves and two haveto do with signal line crossovers. Let’s see these in detail.

Further to the MACD, Thomas Aspray in 1986 created theMACD Histogram, which is constructed as follows:
5. MACD Histogram = Signal Line – MACD Line

Table 1. MACD ranges

Thus in essence:• The 12 & 26 EMAs are the 1st derivative of price.
• The MACD Line is the 2nd derivative of price.
• The Signal Line is the 3rd derivative of price.
• The MACD-H is the 4th derivative of price.

Limitation 1: The MACD Across TimeBy way of design, the MACD is an “absolute price indicator”
as it takes absolute price inputs (price MAs) and produces
an output (spread of raw price MAs) without any kind of
normalisation. This creates the following situation:
Although the MACD in 2020 has a bigger value than in 1957, that
does not imply that the market has more momentum. That was
simply a function of the underlying security having a larger
absolute value when it was calculated in the second instance(2020) than the first (1978). The problem is exacerbated thefurther one goes back in time.

S&P 500

1957–1971

2019–2021

MACD Maximum

1.56

86.31

MACD Minimum-3.3-225.40

The implication of this is that MACD (and MACD Histogram)readings are not comparable across time for the same security,especially if the market in question has had substantial priceappreciation or depreciation.

Figure 1. S&P 500 & MACD (1957–2021)

The MACD is not time stable (comparable across time).
Limitation 2: The MACD Across Markets
The second limitation of the MACD and MACD Histogram are that they are not comparable across securities. Any differences in theindicator readings are attributable to comparing securities that have different absolute values, rather than depicting varying levels of
momentum strength.
For example, the MACD for the S&P 500 at the time of writing is 65 and for the euro currency is -0.0070.
Again, this does not mean that the S&P has more momentum than the euro, but its bigger MACD reading is a function of the bigger
absolute price of the underlying security.
Cross market momentum comparisons are not possible, as it would be the case with say using a (0–100) scaled indicator. The RSI for
the S&P and euro in this instance would be directly comparable, but not for the MACD.
The MACD is not comparable across securities.
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Limitation 3: MACD Momentum Lifecycle
The MACD is an improved version of a moving averagecrossover system.
When a market is trending in a particular direction, theshorter term EMA responds quicker to price than the longer
term EMA, moving away from (closer to) it and consequently
their difference/spread increases (decreases). Thus, the MACD
indicates the direction of momentum (bullish if above thesignal line or bearish if below the signal line). When this isviewed against the prevailing trend, it highlights momentum
acceleration or deceleration and the beginning and end of thisprocess can be identified via signal line cross overs. Moreover,the further away the MACD is from the equilibrium line, thestronger momentum is (please refer to Figure 4, bottom panel).
However, since MACD values are not comparable acrosstime and across securities, it is impossible to standardize theintensity (strength) of (MACD-defined) momentum into an
objectively and quantitatively defined framework, where “High(fast) vs Low (slow)” and/or “overbought vs. oversold” levels
would exist.
The MACD momentum readings cannot be objectively scaled.
Limitation 4: Signal Line Accuracy
When directional strength is low, the MACD will be near theequilibrium line and/or close to the signal line. As such, signal
line crossovers will be frequent, giving many (false) signals. Thisphenomenon is one of the “Achilles' heels” of trend-following
system behavior in low momentum environments in general.
The MACD is no exception.
In Figure 5, this is easily observed during the May to August
2016 period, where six loss producing crossovers signals
occurred in a range bound, low momentum environment. As aconsequence of limitation #3 (lack of momentum level scaling),
these cannot be avoided by way of rejecting the signals that
occur within an objectively and quantitatively defined low
momentum environment.

Figure 2. MACD behavior in low momentum - FTSE 100 (February–August 2014)

MACD signal line crossovers are unreliable in low momentum environments.
Limitation 5: Signal Line Timing
When momentum is high, MACD signal accuracy is (one) of its main strengths. However, when the market is pushing higher (lower)with too much force, to the point where the MACD line has built significant distance from the signal line but then changes its trend to
the downside (upside) abruptly, it takes some time before the lagging MAs catch up to the new data (raw price), which translates into a
directionally correct (accurate) but late (from a timing point of view) signal.
This phenomenon is more often observed in fast bearish trends, which then proceed to form a V-shaped bottom (when a countertrend bounce occurs). Given the trend following nature of the MACD, it is guaranteed that it will signal the turn, but it will produce a
signal line cross over that may be some distance away from the actual price bottom itself.
For example, the S&P 500 bottomed at 2532.69 on the February 9, 2018, but the MACD signaled the turn at 2747.30 on February 23,
which means it was “late” by 8.47%!!

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Figure 3. MACD in high momentum trend reversal—S&P 500 (February 2018)

Again, as a direct consequence of limitation #3 (and the lagging nature of the signal line), it is impossible to improve signal timing by
first identifying a high momentum environment.
MACD crossover signals are late in high momentum trend reversals.

PPO: An Improvement, But Not a Solution
Construction
A solution to deal with limitations #1 and #2 is to normalize the readings of the MACD, so as to become comparable across time andsecurities. A well-known suggestion is to place the raw MA spread as a function of the absolute price of the underlying security so thatmomentum (MACD) is placed in context. This is then multiplied by 100 to obtain the output on a percent (%) basis.
Thus, the formula for the MACD Line now becomes:[ (12 period EMA - 26 period EMA) / (close) ] x 100 or [ (12 period EMA - 26 period EMA) / (26 period EMA) ] x 100
This resulting indicator is commonly known as the PPO (percent price oscillator).
Let’s see what the effect of the PPO on the MACD limitations is.
Figure 4: MACD & PPO—FTSE 100 (February to October 2016)

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Limitation 1: The PPO Across Time
Since the PPO readings are expressed on a percent basis, that means that they should be comparable across time for the same
security on an “apples to apples” basis. Let’s confirm this by revisiting the S&P 500.
Figure 5: S&P 500 & PPO (1970–2021)

Although specific stationarity tests could be employed to prove the point, we can easily observe that the range of fluctuation(variables dispersion around zero) is more stable as the MA spread is normalized on a percentage basis. In fact, if we set lower andupper boundaries in such a way that it contains 95% of the observations, since the February 3, 1975, the PPO has oscillated within 2%
and -2%.
Table 2: PPO Ranges (S&P 500)
PPO Ranges> 2%

2% to -2%

< - 2%% of time

2.2%

94.3%

3.5%

The PPO retains all of the advantages that the MACD has but also adds reading uniformity across time for the same security. It would
appear that limitation #1 is solved.
PPO readings are time stable (comparable across time).
Limitation 2: The PPO Across Markets
One would be tempted to assume that since the PPO is expressed on a percent (%) basis and is comparable across time, then crossmarket comparisons would also be feasible. However, upon closer inspection it would appear that the PPO fails the test. Let’s see this
via an example:
Figure 6. German Bund and PPO (1991–2021)

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Using the aforementioned upper/lower boundaries used for the S&P 500, it would appear that the Bund has never traded above theupper level of 2% and never below the lower -2% level in its entire history. It is evident that there is considerable variation in the dataand in order to see where 95% of the PPO values for the Bund reside we would need to establish different levels.
Table 3. PPO Ranges (German Bund futures)
PPO Ranges> 0.7%

0.7% to -0.7%< - 0.7%% of time

3.5%

93.6%

2.9%

Thus, a PPO reading higher than 0.5% for the Bund would constitute a strongly trending environment. The same reading for the S&P
would be indicative of an almost range bound market. What constitutes “high momentum” in one market may very well be classified as“low momentum” in another.
Figure 7. Natural gas futures and PPO (1990–2021)

The aforementioned differences become more pronounced as we examine a very volatile market, such as natural gas futures.
Figure 7 depicts the PPO ranging most of the time (94.2%) from +7% to -7%.
Table 4. PPO ranges (across markets)
NG - PPO Ranges> 7%

7% to -7%

< - 7%% of time

1.4%

94.2%

4.4%

SP 500 - PPO Ranges > 2%

2% to -2%

< - 2%% of time

2.2%

94.3%

3.5%

BUND - PPO Ranges> 0.7%

0.7% to -0.7% < - 0.7%

% of time

3.5%

93.6%

2.9%

Thus, it appears that the PPO is not a truly normalized momentum comparison tool for cross market purposes as it fails to provide
uniform benchmarks levels due to fact that markets may have significantly different volatility structures.
The PPO is not comparable across securities.
Limitation 3: PPO Momentum Framework
Since the PPO cannot be standardized both across time AND securities, it is then not possible to deal with momentum level
definition in a uniform framework.
It would be perhaps feasible on a per individual market basis to create levels where historically each market in question is deemed
as “overstretched” or with adequate levels of trend strength, but this would not be practical as it would require massive amounts of
optimization for an almost limitless universe of securities and the findings for each market would not be transferable to another.
Limitations 4 and 5: PPO Signal Line Accuracy and Timing
Consequently, the lack of a uniform “high/low” momentum definition renders limitations #4 and #5 unsolved under the PPO as well,as cross over signal filtering is not feasible.
The PPO improves some but not all of the MACD shortcomings.
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MACD-V: Volatility Normalised
MomentumConstruction
Since “normalization by price” results in cross market
momentum valuation discrepancies due to differences involatility, then it would be preferable to normalize by volatility
itself.
We will be using Welles Wilder’s Average True Range (ATR) as
the tool for the measurement of volatility.
Thus, the MACD line formula now becomes:[( 12 bar EMA - 26 bar EMA) / ATR(26) ] * 100
The output of the indicator is the amount of momentum
a security has that is in excess of its average volatility
expressed as a percentage.
We are measuring directional strength “purified” fromvolatility fluctuations.

What is ATR ?
Average true range (ATR) is a technical analysis volatility
indicator originally developed by J. Welles Wilder Jr. forcommodities.
The true range indicator is taken as the greatest of thefollowing: current high less the current low; the absolutevalue of the current high less the previous close; and theabsolute value of the current low less the previous close.
The indicator does not provide an indication of price trend,
simply the degree of price fluctuation.
The average true range is an N-period smoothed moving
average (SMMA) of the true range values.
In order to distinguish the new indicator from the classic
MACD I will name it by adding a “V” at the end of the original
name (“MACD-V”) and refrain from creating a completely newname altogether, so as to honour the original inventor.
Let’s examine now how MACD-V measures against the five
shortcomings of the classic MACD.

The MACD-V Across TimeWe will first be checking how MACD-V behaves across time for the S&P 500.
Figure 8. S&P 500 and the MACD-V (1975–2021)

It is easily observable that MACD-V fluctuates within a finite range of a values around its equilibrium line (similar to the PPOs
behaviour). Any indicator reading discrepancies across time have been eliminated due to normalization.
If we try to find the range where 95% of the data fluctuate and define the rest as “extremes,” then since February 1975 for the S&P
500 the MACD-V oscillates between 150 and -150.
Table 5. MACD-V ranges (S&P 500)
MACD-V Ranges> 150

150 to -150

< - 150% of time

4.4%

95%

0.6%

MACD-V readings are time stable (comparable across time).

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The MACD-V Across Markets
Will the MACD-V succeed where the PPO failed? Does the range of 150 to -150 also hold 95% of the MACD-V values for other markets?
Below we feature the figures of the German Bund and natural gas futures and the levels.
The range of fluctuations for the two MACD-Vs is considerably more uniform than when comparing the equivalent ones for the two
PPOs. They essentially oscillate the same amount around the equilibrium line as differences in volatility have been eliminated.
Slight and sporadic extremes are strictly attributable to strong momentum (prolonged moves in a particular direction), since theMACD at its core is a boundless indicator.
Figure 9. German Bund and the MACD-V (1990–2021)

Figure 10. Natural gas and the MACD-V (1990–2021)

Table 6. MACD-V extreme ranges (S&P 500, 1975–2021)

Table 7. MACD-V extreme ranges (Bund, 1991–2021)

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Table 8. MACD-V extreme ranges (natural gas, 1990–2021)

All three markets share similar exhaustion levels (when momentum is 1.5 times its volatility), despite the fact that they havecompletely different absolute volatilities in general. In addition, the min and max values differ for each market since the MACD-V is aboundless indicator and not constrained by a 0 to 100 scale.
MACD-V values are comparable across securities.
MACD-V Ranges
Since MACD-V readings are comparable across time and markets, that means that we can create a Momentum Lifecycle RoadMap
that will rank both the momentum’s direction (“bullish” or “bearish”) and strength, as well as “low” vs. “high” momentum and“overbought” vs. “oversold”. However, since the MACD-V is an unbounded indicator it will have the added advantage that it will not belimited by the scaling boundaries (0–100) of conventional oscillators and will avoid the problem of “pegging” at high levels.
OBOS (Extreme) Momentum: When the market has advanced too far and too fast the EMA spread will have reached a point where
historically it becomes unstainable to progress any further in the short to intermediate term. This should be around 5% of the data andis located when momentum is 1.5 or -1.5 times its volatility.
Strong (High) Momentum: When the market begins to gain some directional strength, then distance between the two EMAs (12 and26) begins to increase as the shorter EMA is being driven away from the longer one and thus the MACD-V would move significantly
away from the equilibrium line. This should be around 35%–40% of the data and is located when momentum is over +0.5 or -0.5 times
its volatility.
Weak (Low) Momentum Range: When there is little directional conviction (low momentum), the MAs (12 and 26) should be relatively
close and thus their spread (MACD-V) should be close to zero, the equilibrium line. This should be around 45%–50% of the data and iswhen momentum is between 0.5 or -0.5 times its volatility
Based on this framework, we can test the objective momentum levels that would hold across securities using the MACD-V.
Table 9. MACD-V ranges (S&P 500, 1975–2021)

Using data since 1975 (11,817 days) for the S&P 500, we observe that the index has been above the overbought benchmark (>150)
around 4% of the time and below the oversold level (-150) around -1% of the time, reflecting the “upward drift” (bullish bias) of themarket. The time spent between the “neutral zone” that is close to the equilibrium line (50 to -50) is around 45% of the time. Finally,time spent on the strong momentum zone (50<x<150 and -150<x<-50) is respectively 36% and 14%, reflecting the bullish bias for the
S&P 500.
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Table 10. MACD-V ranges (Bund, 1991–2021)

Using data on the German Bund (a fixed income market with different volatility characteristics), we observe that the data that falls
into the aforementioned brackets is roughly the same with the S&P 500.
Table 11. MACD-V ranges (natural gas, 1991–2021)

Table 11 reflects the data for natural gas, a market with completely different trend and volatility DNA. However, the data supportsthat again we have achieved a unified definition of “fast vs. slow” vs. “overbought/oversold” without having presented boundaries tothe values that the indicators can have (e.g., RSI, etc.).
The extreme levels (>150 and <-150) capture roughly 5% of the data in the market again, while the “fast” range (50–150 and -50–-150)
is around 50% of the data.
Based on this framework, we can test the objective momentum levels under different trend regimes and across markets.

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Figure 11. MACD-V ranges and trend regime filter v.1

Table 12. MACD-V ranges and trend regime filter v.1 (S&P 500, 1975–2021)

If we were to dissect the MACD-V data by a basic trend rule (above or below a 200 EMA), we would see that the S&P 500 stands above
the EMA 76% of the time (i.e., having an “upward drift,” bullish bias) and 24% below. Let’s examine how the MACD-V behaves in each ofthese conditions. A similar concept (observation) has been suggested by Andrew Cardwell (RSI range rules). Thus, I will keep the same
term (range rules) to study the behavior of the MACD-V.
All of the occurrences (100%) of the MACD-V reaching the overbought range have been recorded in the bullish stage and it has neverreached the oversold level while over the 200 EMA. While in the bullish stage, 99.4% of market action is contained with readings ofthe MACD-V > -100. If we observe the data more closely, 5% of the data on the downside are captured within the -50 to -150 range, thus
becoming the “new” oversold level while the market stands above the 200 EMA. As long as the market stays above the 200 EMA, wewould not expect it to fall below the – 100 range of the MACD-V.
Analogous behavior is observed on the bearish stage (< 200 EMA) as there are zero occurrences of the indicator reaching theoverbought range (>150) and 100% readings of the oversold range. While in the bearish stage, 99.8% of market action is contained withreadings of the MACD-V < 100, which is a quite similar number to the bulls (99.4%).
Thus, while the market is bearish (< 200 EMA) we would expect a maximum stretch until the MACD-V reaches the 100 level (bearmarket rally).
Table 13. MACD-V ranges and trend regime filter v.1 (Bund, 1991–2021)

Table 13 displays the data for the Bund, a market with different trend characteristics (i.e., > 200 EMA 67% of the time vs. 76% of thetime for the S&P 500) and certainly different volatility DNA. However, the same observations (range rules) can be made.
While the market is in the bullish stage (> 200 EMA), it has 100% of the occurrences of overbought readings (>150), 0% of the oversold
readings (<-150), and 98.9% of the data is captured by the >-100 level. Thus, similarly to the S&P 500, any bull market decline can be
expected to stop at the -100 MACD-V level (if the market is to stay above the 200 EMA).
Symmetrically for the bearish stage, it has 100% of the occurrences of oversold readings (<-150), 0% of the overbought readings(>150), and 99.8% of the data are captured by the <100 level. Thus, similarly to the S&P 500, any bear market rally can be reasonably
expected to stop at the 100 MACD-V level (if the market is to stay below the 200 EMA).
Figure 12: Bund and cxtreme MACD-V readings (1994–2021)

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Table 14. MACD-V ranges and trend regime filter v.1 (natural gas, 1991–2021)

The data for NG are even more compelling, as this market has completely different trend characteristics (spends an equal amount oftime in bullish/bearish stages, each one is 50% of the data) and is considerably more volatile than the aforementioned ones. However,
the exact same observations (range rules) can be made.
While the market is in the bullish stage (> 200 EMA), it has 100% of the occurrences of overbought readings (>150), 0% of the oversold
readings (<-150), and 99.8% of the data is captured by the >-100 level. Thus, similarly to the S&P 500, any bull market decline can be
expected to stop at the -100 MACD-V level (if the market is to stay above the 200 EMA).
Symmetrically for the bearish stage, it has 100% of the occurrences of oversold readings (<-150), 0% of the overbought readings(>150), and 99.5% of the data is captured by the < 100 level. Thus, similarly to the S&P 500, any bear market rally can be reasonably
expected to stop at the 100 MACD-V level (if the market is to stay below the 200 EMA).
Figure 13. Natural gas and the bear market rallies (2014–2016)

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MACD-V Ranges and Trend Regime Filter v.1 and Swing Filters
Another way to help study the data even further would be to create a swing line as an additional price filter and then observe where
market tops and bottoms occur.
For the S&P 500, we will use a 3% swing line. Our personal preference for this type of filtering work is using swing based on ATR (notpercents), but for this study we will use percentage calculations to keep things relatively simpler.
Table 15 records where these swing highs/lows are placed within the Trend Regime Filter v.1 . Since 1975, the S&P 500 has made 651
swings that had a magnitude of 3% or more. 233 swing highs were recorded in the bullish stage and 93 in the bearish stage.
Table 15. 3% Swing line stats per stage (S&P 500, 1975–2021)

We will provide more context to the total number of highs and lows per stage by relating them to the MACD-V.
Table 16. 3% Swing line stats per MACD-V ranges (S&P 500, 1975–2021)

Table 16 sheds more light. When the market is in the bullish stage, almost 60% of swing highs occur in the “Strong Momentum”
Range (50 to 150) and almost all (99.1%) above the -100 range of the MACD-V. Similarly, 72% of swing lows in the bullish stage occur
in the weak momentum range (50 to -50), while almost all (99.7%) are above the -100 level for the MACD-V. This confirms the findingsof tables 11–13 that should the market stay above the 200 EMA, then the “maximum” decline it can have should be around -100 of theMACD-V.
Table 17. 3% Swing line stats per MACD-V ranges (S&P 500, 1975–2021)

Table 16 shows the data for the bearish stage and they are analogous to the bulls.
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Table 18. Trend regime filter v.1, swing line (1%), and MACD-V stats (Bund, 1991–2021)

To study the Bund, we will use a 1% swing line since the volatility for fixed income markets is considerably less than for theirequity counterparts. However, the results are very similar to the ones presented for the S&P 500. The range rules for one market are
applicable across other markets as well.

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Table 19. Trend regime filter v.1, swing line (5%), and MACD-V stats (NG, 1991–2021)

In order to complete our cross-market validation, we will present the same study for natural gas. The difference is with the swing
line again. In this instance, we employ a 5% swing filter in order to deal with the elevated inherent volatility of this market.
The rest of the data leads to the same results, which we will leave to the reader to validate and explore further.
MACD-V Ranges and Trend Regime Filter v.2
The numbers in tables 11–13 could be more insightful by using a more detailed Trend Regime Filter. The rules for Trend Regime Filter
v.2 (Figure 14) were created, to our knowledge, by Chuck Dukas.3 We will examine the bullish stages (1,2,3).
The swing line percentages will remain the same for each market.
Figure 13. MACD-V ranges and trend regime filter v.2

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Table 20. MACD-V ranges and trend regime filter v.2, stage 2 (S&P 500, 1975–2021)

These are the relevant numbers for the S&P 500 in Stage 2 (i.e., C >50>200). This time the maximum downside stretch of the MACD-V
is -50, as the range 150 to -50 contains 99.8% of the data.
Thus, if one thinks that on any pullback the market will not break the 50 EMA, then any dive that would cause the MACD-V > -50
would provide a definition of a stage-specific oversold level.
Table 21. MACD-V ranges, trend regime filter v.2 (stage 2), and 3% swings (S&P 500, 1975–2021)

The table above shows that out of the 233 swing highs above the 200 EMA, 87.1% of these (203) have occurred in Stage 2 (C > 50
EMA > 200 EMA). The vast majority of these (59.6%) were in the 50–150 range of the MACD-V, while around 10% occurred while in the
overbought range. Almost all of the highs (99.5%) were over the -50 range of the MACD-V.
Turning our attention to swing lows in Stage 2, these are really rare events as we have seen 29 occurrences in the past 46 years.
100% of these were over the -50 range of the MACD-V.
It would seem that if one expects a larger than 3% correction that would not extend below the 200 EMA, then the odds greatly favourthat the S&P 500 would breach the 50 EMA (Stage 3) and the MACD-V to be in the -50 to -50 range (or -50 to -100 in the case of stronger
corrections).
Table 22. MACD-V ranges and trend regime filter v.2, stage 3 (S&P 500, 1975–2021)

When the market has progressed into Stage 3, the vast majority of times (72.4%) the MACD-V is in the neutral range (50 to -50).
In quite rare occurrences we may have a dip below the -100 level, but it would be an exception as 96.7% of the values in the stage areabove that.
Table 23. MACD-V ranges, trend regime filter v.2 (stage 3), and 3% swings (S&P 500, 1975–2021)

When the market has slid below the 50 EMA, in the vast majority of cases, the reversal swings associated in the stage are lows (101)vs. highs (11). A notable statistic is that 82.2% of the swing lows that occur in this stage are in the “neutral zone” of 50 to -50 and a few
extend to the -50 to -150 range. In total, 97% of swing lows in Stage 3 occur over the -100 range of the MACD-V.
Thus, pullbacks into this stage could end in the aforementioned ranges for a possible resumption of the trend.

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Table 24. MACD-V ranges and trend regime filter v.2, stage 1 (S&P 500, 1975–2021)

Stage 1 does not occur very often or rather does not register for long. It is usually an explosive move to the upside coming off of a low.
Hence, it is the only stage (except 2) that manages to drive the market into the overbought zone (>150). In the vast majority of cases,
the market is in the “fast” range of the MACD-V (50 to 150) and in 100% of the cases the MACD-V stays above -50
Table 25. MACD-V ranges, trend regime filter v.2 (stage 1), and 3% swings (S&P 500, 1975–2021)

There aren’t many reversals (swings) occurring in this stage and almost all are high (19) vs. lows (2) in the 46-year history of thedata. Notable stats are that these aforementioned highs occur in the 50 to 150 range of the MACD-V (73.7% of the occurrences).
Note: The following pages will display the same studies for the Bund and natural gas markets. They exhibit similar behavior thus
we will leave it up to the readers to dive deeper into the data without our commentary. Please note that we used a 1% swing line for
the Bund and a 5% swing line for natural gas to account for different volatility levels. Moreover, in our private work we use ATR-based
swing lines and more sophisticated Trend Regime Filters.

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Table 26. Trend regime filter v.2 Key statistics (Bund, 1991–2021)

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Table 27. Trend regime filter v.2 key statistics (natural gas, 1991–2021)

MACD-V Momentum Lifecycle RoadMap
At this stage we can introduce the signal line (9 period EMA of the MACD line), as it is the tool that signals changes in momentum. The
signal line is guaranteed to highlight momentum shifts, but its lagging nature does so at the expense of accuracy and timing sometimes(please refer to “Limitation 4: Signal Line Accuracy” and “Limitation 5: Signal Line Timing”). Thus, we chose to replace it with another
tool that deals (to some extent) with the aforementioned issues. However, we made a conscious choice not to present the modifications
we have made on the signal line and just focus on the MACD line, as the length of this paper would increase significantly. Therefore,
henceforth any mention of the signal line assumes that we would use the 9 period EMA.

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Table 28 presents the ranges and how the MACD-V line
relates to the signal line. There are in total eight ranges that the
MACD-V can take, which of course can be easily programmed in
any language of your choice (Python, AmiBroker AFL, etc.).
Table 28. MACD-V and signal line combinationsRANGE

ABOVE SIGNAL LINEBELOW SIGNAL LINE

> 150

Risk

50 < x < 150

Rallying

Retracing (in price or time)-50 < x < 50

Ranging

Ranging-150 < x < -50

Rebounding

Reversing-150 <

Risk

Figure 15. MACD-V momentum lifecycle roadmap

2023 EDITION

MACD-VH: Volatility Normalised
Histogram

Further to the MACD, Thomas Aspray in 1986 created theMACD Histogram, which is constructed as follows:
MACD Histogram = Signal Line – MACD Line.
Since the MACD line has now been normalized, similar
properties should also be shared by the 4th derivative of price,
the MACD-V Histogram (MACD-VH). That means that it ispossible to detect indicator levels which are associated withshort term extreme price levels. This is a unique property of theMACD-VH, as thus far the applications of the MACD Histogram
were confined to comparisons of the height of each bar of thehistogram relative to the preceding ones (higher vs. lower) andnot relative to the absolute level that each bar has.
It appears that when the MACD-VH is above 40 (or below –40) that would imply that the market is mildly stretched to theupside (downside).
Figure 16. MACD-VH Momentum Lifecycle RoadMap

This opens up new and unexplored opportunities to use
the MACD. Up until today, the MACD could be used in two
ways: either above/below the signal line and/or above/below
the 0-line. The MACD-V now presents us with eight different
scenarios to explore and of course these are multiplied in thecase of cross asset comparisons.

Table 29. MACD-VH Extreme Levels for Three Markets

Figure 17. MACD-VH Mildly Overbought/Oversold (>40, <-40) (FTSE 100, 2014–2015)

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Figure 18. MACD-VH mildly overbought/oversold (>40, <-40) (FTSE 100, 2015–2016)

Teaching New Tricks to Old “Tools”

At the final part of the paper, I would like to apply the concept of volatility normalization to other well-known indicators, thus
expanding their informational value.
LBR 3/10 Oscillator “Sardine”4
The first tool would be the LBR 3/10 oscillator by the esteemed trader Linda Bradford Raschke. Linda has publically disclosed many
trading setups using this tool (“Anti” setup, divergences, new momentum highs/lows). The oscillator is a MACD(3,10), thus it would beeasy to create range rules for this indicator as well. The new formula would be:[EMA(3,C) – EMA(10,C) ] / ATR(10).
The data in table 30 behaves in a similar fashion as do the MACD-V and MACD-VH.
Figure 19. LBR 3/10 oscillator & 100/125, -100/-125 levels (S&P 500)

Table 30. LBR 3/10 oscillator extreme levels for three markets

Alex Elder Impulse “Plus” System
The “Elder Impulse System” was designed by Alexander Elder.5 The system, according to its creator, “identifies inflection points wherea trend speeds up or slows down.”
The price bars are color coded as follows:• Green: EMA(13,C) > previous (EMA(13,C) and (MACD-H> previous MACD-H)• Red: EMA(13,C) < previous (EMA(13,C) and (MACD-H< previous MACD-H)• Blue: In all other cases

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In this particular case, additional rules could be added so as towarn the trader when the market has been overstretched in the
short term. Thus, the rules could look like:
Green: EMA(13,C) > previous (EMA(13,C) and (MACD-VH>
previous MACD-VH)
Red: EMA(13,C) > previous (EMA(13,C) and (MACD-VH>
previous MACD-VH) and MACD-VH > 40
Blue: In all other cases
Red: EMA(13,C) < previous (EMA(13,C) and (MACD-VH<
previous MACD-VH)
Green: EMA(13,C) < previous (EMA(13,C) and (MACD-VH<
previous MACD-VH) and MACD-VH < - 40
Blue: In all other cases
There are certainly more possibilities to explore, but the
point is to exhibit the additional value that volatility normalized
momentum presents to the existing toolset.
Chuck Dukas Diamond “Refined”
Figure 13 presented in brief the rules for the “Chuck Dukas
Diamond,” a trend classification system. Using volatility
normalization, this can be improved in a few ways.
One possible solution to “refine” the diamond would be thefollowing:
1. Each of the EMAs would be expressed as a MACD-V—i.e.,the 50 EMA would be MACD-V(1,50), the 200 EMA would
be MACD-V(1,200), and the 50 EMA/200 EMA crossoverrules would be MACD-V(50,200).
2. Create extreme levels for each of the MACD-Vs—i.e.,
for the MACD-V(1,50) we would use +/- 4, for the
MACD-V(1,200) we would use +/- 8, and for the
MACD-V(50,200) we would use +/-5.
3. Create a weighted condition scoring system that would
serve as a warning for overbought/oversold conditions
within each of the six stages— i.e., MACD-V(1,50) > 4, 1
point; MACD-V(1,200) > 8, 2 points; and MACD-V(50,200)> 5, 3 points.
In addition to an OBOS warning system, anotherpossible solution would be then to use the readings of theMACD-V(50,200) as a relative strength ranking tool for theuniverse of the markets classified by the system. Thus, one
would not just classify securities in a stage, but also within thatstage. The higher (lower) the reading, the stronger (weaker) themarket would be.
The 70 & 77 System (Strong Momentum Range
Rules)As mentioned in “Momentum Lifecycle RoadMap,” theMACD-V Momentum Lifecycle RoadMap opens up opportunities
that would not exist with the simple MACD.
One simple example would be to filter buy signals whena market enters high in the strong momentum range. The
following equity curve was created by buying one DAX futurescontract (long only) when the MACD-V is above 70 (market entry
order) and selling at target exit of 2.85% (next bar limit) or after
15 days if in profit (but the target exit had not been reached) orafter 77 days if neither of these conditions held true. (€25 perroundtrip trade were deducted for slippage and commissions.)

2023 EDITION

Figure 20. 70 & 77 System equity curve (DAX, 1991–2021)

Table 31. 70 & 77 System key stats (DAX, 1991–2021)

Of the 201 profitable trades, 95 trades managed to reach theirtarget exit price (77.23% of all winning trades). Of course this is
not a tradeable system on its own, but serves as inspiration forfurther strategy idea development.

Epilogue

This paper is the definition of “standing on the shouldersof giants,” as it would not have been possible without theknowledge shared by esteemed technicians past and present. I
sincerely hope that we have added a small brick on the huge wallof the Body of Knowledge of Technical Analysis.

Notes
Gerald Appel, “Technical Analysis: Power tools for active investors,”
FT Press; Reprint edition (21 Mar. 2005).
2
Tom Demark, “The New Science of Technical Analysis,” Wiley; 1stedition (10 Dec. 2007).
3
Chuck Dukas, “The TrendAdvisor Guide to Breakthrough profits,”
John Wiley & Sons; 1st edition (16 Mar. 2006).
4
Linda Raschke, “Trading Sardines,” Self-published (2018).
5
Alex Elder, “Come Into My Trading Room,” Wiley; 1st edition (16 May
2002).
1

Acknowledgements

This research paper is dedicated to my wife and parents andin memory of Gerald Appel (June 2, 1933–February 13, 2020).

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Technical Analysis Using Multiple Timeframes by Brian Shannon
Reviewed by Regina Meani, CFTe

Brian Shannon’s Preface focuseson the passions in our life andquestions whether we are
passionate enough about themarkets. He expresses this as themental challenge and the senseof satisfaction … knowing that I
have attained success on my own
terms.1 It is Shannon’s passionthat fills this book with a goal tohelp us understand and be able
to recognize market structure, and from there, to discover ourown trading edge. An edge that will allow us to identify low-risk,
high-profit trades with a planned risk management strategy.
Chapter 1 deals with technical analysis and examines whether
it works. Shannon, from his observations, concludes that it does
work and that the market speaks the language of supply anddemand, and that message is broadcast on price charts.2
In Chapters 2 through to 6, Shannon outlines the four stages
for stocks, which he terms Accumulation, Markup, Distribution,
and Decline. These stages are present in all timeframes, and hebelieves that the ability to recognize them allows one to keep
our analysis unbiased and objective.
The author uses very clear and simple language withpertinent examples to explain the concepts of support andresistance, trend following, volume, and the use of moving
averages. He suggests that support and resistance may help
us to uncover potential turning points, but he goes further topropose that they help us to objectively work out conceivablerisk/reward ratios.
Volume is dealt with in Chapter 9, and Shannon believes thatafter price, it is the next most important analysis to add. It
allows us a window into market psychology as a measure of theemotional intensity level of the market participants.

PAGE 92 IFTA.ORG

We are introduced to “trend alignment” in Chapter 11. The
concept deals with the use of multiple timeframes to analyze
the risk/reward relationship. He looks at how short-term
traders and longer term investors hold different objectives andviews of the value for an entity and how quickly that value may
change—hence, the need for trends in multiple timeframes. We
are provided with the example of when a short-term trader may
well be best served by entering a position when the short-term
trend confirms the longer term trend. Regardless of whether you
are an investor, swing trader or day trader, a minimum of three
timeframes should be studied before you commit capital to a
trade.3
The last chapters take a look at stock selection both from thelong and short side, how to integrate news and fundamentals,
and most importantly, risk management techniques. Shannon
gives us a guide to the different types of stop losses and whereto place them with chart examples. Finally, we end up with some
Trading tips and truisms to think about4 and how to plan our
trades and put it all together. Included are two wall charts—on
the market structure and truisms.
Overall, Shannon has given us a very easy-to-read adventure
into technical analysis for the beginner, and for the moreadvanced among us, perhaps a refresher and a reminder that
our techniques can be used across all timeframes.

Notes
Shannon, B., Technical Analysis, Using Multiple Timeframes,
Alphatrends Publishing, LLC, Canada, 2008 p. vi.
2
Ibid. p. 4
3
Ibid. p. 101
4Ibid. p. 165
1

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Author Profiles
Anand Behere
Anand Behere graduated from EDHEC Business
School with a master’s degree in finance. He
currently works as a technical market analyst in
the energy sector at a large German utilities
company. He has previously been involved in
option trading by analyzing order flow andmarket depth.

(Accredited Market Technician). She has regular columns in thefinancial press and appears in other media forums. Her
freelance work includes market analysis, webinars, and larger
seminars; advising and training investors and traders in market
psychology; CFD; and share trading and technical analysis. She
is also a former director of the Australian Technical Analysts
Association and has belonged to the Society of TechnicalAnalysts, UK for over 30 years.

Garrett H. Brookes, CFA
Garrett Brookes has worked in the financial
industry for more than 20 years, serving in amarketing and sales capacity to registeredinvestment advisors, independent financial
advisors, and money management firms
throughout the United States on behalf of major
investment companies and small boutique investment
providers. In January 2021, he formed Slingshot Financial topartner with the “hidden gems” of money managers focused on
quantitative strategies, alternatives, strategic income, andinnovative fintech, offering strategic guidance on wholesale
product development and marketing as well as tacticalexecution through Slingshot Financial’s turnkey wholesaler
program (https://slingshotfin.com).

Davide Pandini, Ph.D., CFTe, MFTA, CMTDavide Pandini, Ph.D., CFTe, MFTA, CMT, joined
STMicroelectronics in Agrate Brianza, Italy, in
1995, where he is a technical director and afellow of ST technical staff. He was previously aresearch intern at Philips Research Labs inEindhoven, the Netherlands, and at Digital
Equipment Corp., Western Research Labs, in Palo Alto,
California. He holds a Ph.D. in electrical and computerengineering from Carnegie Mellon University. Davide has
authored or co-authored more than 50 papers in international
journals and conference proceedings and served on the programcommittee of several premiere international conferences. He
received the STMicroelectronics Corporate STAR Gold Award in2008 and 2020 for R&D excellence. Since June 2015, he has been
the chair of the ST Italy Technical Staff Steering Committee.
Davide is a professional member of SIAT (Societa’ Italiana
Analisi Tecnica). In 2021, he was the recipient of the prestigious
XII SIAT Technical Analyst Award in the Open category. He was a
speaker at SIAT Trading Campus in May 2022 and at theInvesting and Trading Forum in June 2022. He served as avolunteer at the Universal Exhibition Expo2015—Feeding thePlanet, Energy for Life—in Milano, Italy.

Cezar-Valerian Lupusor, MSc, CFTe
Cezar-Valerian Lupusor, MSc, CFTe, is an avid
follower of financial markets and has been
trading them systematically for many years. He
holds a degree in economics from Vienna
University of Economics and Business in Austria
and an MSc in quantitative finance from Bayes
Business School, London, UK. Lately, he has become involved
with the fascinating field of machine learning for algorithmic
trading, where he explores financial time series data by utilizing
sophisticated machine learning algorithms. He uses these tools
as a complement to technical analysis. Currently, he is based inAustria.
Regina Meani, CFTe
Regina Meani, CFTe, covered world markets as atechnical analyst and associate director for
Deutsche Bank prior to freelancing. She is anauthor in the area of technical analysis and is asought-after presenter both internationally andlocally, lecturing for various financial bodies anduniversities as well as the Australian Stock Exchange. Regina isa founding member and former president of the AustralianProfessional Technical Analysts and a past Journal director for
IFTA, carrying the CFTe designation and the Australian AMT

Dr. Oliver Reiss, CFTe, MFTA
Dr. Oliver Reiss, CFTe, MFTA, received a master’s
degree in physics from the University ofOsnabrueck (1998) and a Ph.D. in mathematics
from the University of Kaiserslautern (2003)—
the latter for his research on financial
mathematics performed at the Weierstrass
Institute in Berlin. Since then, he has worked in the banking
industry and today is a self-employed consultant for financial
institutions, with a focus on risk controlling, derivatives pricing(quant), and related IT implementations. As a private investor,
Oliver is interested in technical analysis, and, due to hismathematical and programming expertise, he is now focused on
developing and back-testing midterm trading strategies basedon more sophisticated algorithms. He joined the VTAD in 2011,
when he became a freelancer, and currently serves as deputy
manager of the VTAD’s regional group in Dusseldorf, Germany.

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Oliver received his MFTA for his thesis on the applicationof the Empirical Mode Decomposition to technical analysis,
for which he was recognized with the John Brooks Memorial
Award in 2019. As a frequent attendee of IFTA’s conferences,
he also presented the results of his MFTA research at the IFTA
Conference in Cairo.
Alex Spiroglou, DipTA (ATAA), CFTe
Alex Spiroglou, DipTA (ATAA), CFTe, is aquasi-systematic, cross-asset proprietary
futures trader, currently trading his own book.
He is active in all major liquid futures markets
and across all major asset classes (equity,interest rates, FX, commodities). Spiroglou has
worked with various proprietary trading and investment
management firms in the UK and Greece. Based in the United
Kingdom, he is founder and CEO of SMART Trader Systems Ltd,
London, a firm focused on the training, support, anddevelopment of institutional traders. Visit www.AlexSpiroglou.
com for more information on Alex.
Christoph T. Wildensee, Ph.D., MFTA
Christoph Wildensee, Ph.D., MFTA, is a wellknown auditor and data/process analyst at
enercity AG in Hannover, Germany. Christoph’s
special focus is on finding errors andoptimization potential in IT systems relevant toaccounting, including, in particular, the Energy
Trade and Risk Management system, which is used to handle allenergy trading activities at enercity. He was also a member of
the team evaluating the new Pioneer/Hitachi-ABB ETRM
system.

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2023 EDITIONIFTA Staff

IFTA Board of Directors

Senior Member Services Manager
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IFTA HEADQUARTERS
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Advanced
tools for
Advancedtradersoftools forall levels
tradersof
all levels

Get a 1-month free trial at MetaStock.com/iftaCertified Financial Technician (CFTe) Program
IFTA Certified Financial Technician (CFTe) consists of the
CFTe I and CFTe II examinations. Successful completionof both examinations culminates in the award of
the CFTe, an internationally recognised professional
qualification in technical analysis.

Examinations

The CFTe I exam is multiple-choice, covering a wide
range of technical knowledge and understanding of theprincipals of technical analysis; it is offered in English,
French, German, Italian, Spanish, Arabic, and Chinese;it’s available, year-round, at testing centers throughout
the world, from IFTA’s computer-based testing provider,
Pearson VUE.
The CFTe II exam incorporates a number of questions
that require essaybased, analysis responses. The
candidate needs to demonstrate a depth of knowledge
and experience in applying various methods of technicalanalysis. The candidate is provided with current chartscovering one specific market (often an equity) to beanalysed, as though for a Fund Manager.

The CFTe II is also offered in English, French, German,
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Curriculum

The CFTe II program is designed for self-study, however,
IFTA will also be happy to assist in finding qualified
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To Register

Please visit our website at http://www.ifta.org/
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Master of Financial Technical Analysis (MFTA) Program
IFTA’s Master of Financial Technical Analysis (MFTA)
represents the highest professional achievement in thetechnical analysis community, worldwide. Achieving thislevel of certification requires you to submit an original
body of research in the discipline of international
technical analysis, which should be of practicalapplication.

Examinations

Timelines & Schedules

There are two MFTA sessions per year, with thefollowing deadlines:
SESSION 1“Alternative Path” application deadline February 28
Application, outline and fees deadline May 2
Paper submission deadline
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In order to complete the MFTA and receive your
Diploma, you must write a research paper of no lessthan three thousand, and no more than five thousand,words. Charts, Figures and Tables may be presented inaddition.

SESSION 2“Alternative Path” application deadline July 31
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Your paper must meet the following criteria:• It must be original• It must develop a reasoned and logical argument andlead to a sound conclusion, supported by the tests,
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