IFTA Journal 2022 Edition

A Professional Journal Published by the International Federation of Technical Analysts

22
Inside This Issue
4 Observation of Yield Points ofTrends22 Intraday-Trade-Optimization Via
Fibonacci-DLL
43 The EMD Oscillator
50 Splitting Noise and Useful
Signal in the S&P 500 Members
Correlation Matrix
54 Actively Using Passive Sectors toGenerate Alpha Using the VIX
67 Tribute to Welles Wilder“I am always ready to learn
although I do not always likebeing taught.”—Winston Churchill

ISSN 2409-0271

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

Dear IFTA Colleagues and Friends:
I hope that you, your family, and your friends came through the year healthy and safe. We
are still living through strange times. Something unprecedented keeps us from doing what
we are used to doing. Our world is divided into those who are vaccinated, and thus protected,
and others who are potentially at risk. In some places, life is back to normal. In others, we
still shelter by staying at home, wearing masks, and restricting ourselves from meeting withothers. Unfortunately, this also applies to IFTA. For the second time in our history, there will
be no in-person conference this year. Again, we have canceled Philadelphia and replaced itwith an online conference. Instead of discussing Elliott, we count Corona waves nowadays.
Definitely nothing we should get used to!
But despite the virus and the epidemic, there will be an IFTA Journal. Not business as usual, but nevertheless asnormal as possible. IFTA is international and so is this Journal. Again, we have gathered articles from colleagues
around the world.
In this issue, you will find two papers from our MFTA program. Starting with the first idea until the final
grading of the paper, our colleagues usually spend almost a year achieving their MFTA
designation.
We also have one paper that NAAIM has kindly made available to us. It is the winning
paper of the Wagner Award. Again, we are more than happy about the long-lasting
cooperation with NAAIM. I want to thank NAAIM for their support and especially Susan
Truesdale for her kind cooperation.
We also have two articles from colleagues from Germany and Spain. Both authors
were speakers at an IFTA conference in the past. They share the same passion for using
quantitative elements in their market analysis.
As reported in the last issue of the IFTA Update, J. Welles Wilder Jr. passed away thisspring. He pioneered the use of indicators and data-driven analysis in the 1970s. IFTA
recognized him at last year’s conference for his life’s work. We pay tribute to J. Welles
Wilder Jr. here through memories of his colleagues and present a selection of his ideas.
Last but not least, the Journal traditionally closes with a book review from ourAustralian colleague, Regina Meani. She is something like the faithful soul of the
Journal. Always there, always willing to help and to support. Thank you for that.
Finally, I need to thank Aurélia Gerber for her help and especially Linda Bernetich. Without Linda and her teamthis Journal wouldn’t exist. It's as simple as that. Thanks for your patience and organizational skills.
I hope that you will like the Journal.

I hope that you, yourfamily, and your friends
came through the year
healthy and safe.

Best regards,
Dr. Rolf Wetzer, CFTe, MFTA

IFTA JOURNALEDITORIAL
Rolf Wetzer, Ph.D., CFTe, MFTA
Editor and Chair of the Editorial Committee
Rolf.Wetzer@ifta.org
Regina Meani, CFTe
regina.meani@gmail.com
Aurélia Gerber, MBA, CFA, MFTA
aurelia.gerber@ifta.org

Send your queries about advertisinginformation and rates to admin@ifta.org

2022 EDITION

Letter From the Editor
By Dr. Rolf Wetzer, CFTe, MFTA ..........................................................................................Inside front cover
MFTA Papers
Observation of Yield Points of Trends
By Shinji Okada, CMTA, CFTe, MFTA.............................................................................................................2
Intraday-Trade-Optimization Via Fibonacci-DLL
By Christoph T. Wildensee, Ph.D., MFTA......................................................................................................22
Articles
The EMD Oscillator
By Dr. Oliver Reiss, CFTe, MFTA ...................................................................................................................43
Splitting Noise and Useful Signal in the S&P 500 Members Correlation Matrix
By Carlos Jaureguízar, Ph.D., and Sandra Nieto ........................................................................................50
NAAIM Paper
Actively Using Passive Sectors to Generate Alpha Using the VIX
By Michael A. Gayed, CFA.............................................................................................................................54
Book Review
The Taylor Trading Technique by George Douglas Taylor
Reviewed by Regina Meani, CFTe................................................................................................................ 66

Tribute to Welles Wilder.................................................................................................................................67
Author Profiles..................................................................................................................................................77
Cover Photograph from iStock images

IFTA Staff............................................................................................................................................................79
IFTA Board of Directors...................................................................................................................................79

IFTA Journal is published yearly by The International Federation of Technical Analysts, 1300 Piccard Dr., Suite LL 14 Rockville, MD 20850 USA. ©
2021 International Federation of Technical Analysts. All rights reserved. No part of this publication may be reproduced or transmitted in any form orby any means, electronic or mechanical, including photocopying for public or private use, or by any information storage or retrieval system, without
prior permission of the publisher.

IFTA.ORG PAGE 1

IFTA JOURNAL

2022 EDITION

Shinji Okada, CMTA, CFTe, MFTA

Observation of Yield Points of Trends
By Shinji Okada, CMTA, CFTe, MFTA

Abstract

How long will the trend last? I’ve been pursuing this question
ever since I encountered the financial market. If you could
detect the end point of trends in the stock, bond, exchange,commodity, and other financial markets, you would be able
to avoid following the trend near the end point. Also, if you
have detected the end point of the trend, that means you havedetected the starting point of the next trend. I have been
exploring how to use “regression trends,” one of the methodsof trend analysis, to solve this question. Since I could not findany literature that provides practical explanation on a method
to use regression trends, I decided to create one through thisthesis. I found literature that says prices keep going up anddown and definitely do not continue following the regression.
That’s true, but there was a discovery there. Thinking that prices
are bound to depart from the regression at some time or other,
I studied the importance of regression analysis of trends andsought a way to find the end point of a trend. In this thesis, I will
describe the method and its possibilities so that readers can use
it to avoid following the trend at the ceiling or bottom of a trend.
In this thesis, I named the point at which a trend closes its shortlife the “yield point of the trend,” inspired by the stress-strain
curve.
In this study, I developed an index named the standard error
enhanced index to measure the yield point of a trend and used
it for analysis. As a result of observation using the Nikkei stock
average index, it became easier to observe the yield point of atrend and I could confirm the movement of a trend to its end. On
the other hand, different observations were obtained in AUD/
USD and other markets. I will continue study for verification.
I hope that this study will contribute to the developmentof financial markets in the 21st century and help market
participants make better decisions.

Introduction

How long will the trend last? I’ve been pursuing thisquestion ever since I encountered the financial market. In theapproximately seven years I spent as a securities broker, I saw
many investors buying at the ceiling of an uptrend and sellingat the bottom of a downtrend. If you trade in line with the trend
near the end of the trend, your investment assets will be hurt
badly. You need to detect the end point of the trend. Since thetime I was a securities broker, I have wanted to help investors
in one way or another. Also, if you have detected the end pointof the trend, that means you have detected the starting point of
the next trend. I think it is not too late to trade in line with thetrend after confirming the turnaround of the trend.
To analyze trends, I started with drawing trend lines and
PAGE 2 IFTA.ORG

QUICK Corp. KABUTO ONE,
7-1, Nihonbashi Kabutocho, Chuo-Ku, Tokyo
103-8317, JAPAN+81-80-1285-1546
shinjiokadaresearch@gmail.com

channel lines as a means to grasp the trend. Drawing trend lines
and channel lines seemed to make the trend clearer than in a
price-only chart. However, since trend lines and channel lines
are drawn according to the drawer’s subjectivity, regularity
cannot be found.
Therefore, I chose regression trends as a method to grasp
the trend which has already occurred. I thought arbitrarinessof the drawer could be eliminated by using regression trends,
or regression analysis of price and elapsed time. However,when I researched examples and explanations of the use ofregression trends, all I could find was something like “Enter anarbitrary time axis and trade against the trend with a standard
error of ±2σ.” I generally agree, but I want to use it in a more
specific way. As there is no literature available that explains thepractical use of regression trends, I decided to create one in thisthesis. One literature says that it is impossible that financial
markets, which keep going up and down, continue following theregression. That’s true, but there was my discovery. I only needto measure the point of breaking away.
I think that a trend is a series of “phenomena.” It’s impossiblethat a trend is driven by only one factor. Price movements
continue to be affected by market participants’ decisions
and buy/sell orders for the commodity. As time passes fromthe occurrence of the trend, starting from preceding pricemovements, rumors are generated, factors are announced,
analysts publish reports, specialized magazines cover it, themedia spotlight it, and amateur investors participate by tradingin line with the trend. Then the trend comes to an end. In thisway, trends are affected by a variety of factors. The regression
trend approach enables analysis of a trend, a phenomenon,
from price and elapsed time. I attach importance tocomprehensive analysis of the trend as a whole, a phenomenon
that incorporates detailed analysis and even noise. If you havestudied the Elliott wave, the Ichimoku Kinko Hyo, cycle analysis,
etc., it will be easy to understand that time has a strong impact
on the market. And by analyzing a trend by price and time, you
can understand the current status of the trend.
I named the point at which a trend closes its short life the“yield point of the trend,” inspired by the stress-strain curve. I
created all the following charts in Excel from data provided by
QUICK Corp.

The Factors and the Method

First, I will explain a practical way to use regression trends.
Regression trends are used to understand whether the present
trend is continuing or has already turned around. I will explain
below in an example of an uptrend. Closing prices are used in all
the analyses in this thesis.

IFTA JOURNAL

2022 EDITION

The starting point of a regression trend is the low price before the previous high was overtaken. In Figure 1, this is C. You may wantto draw the line from A, but there is a downtrend from B to C, so A is not suitable for the starting point of the latest trend. And the latest
trend is assumed to be an uptrend because the previous high of B was overtaken at D. Therefore, C is the starting point of the trend.
Figure 1. Nikkei225 (2012/10/01–2012/11/30)

Figure 2 shows a regression trend line drawn from C of Figure 1.
Figure 2. Nikkei225 (2012/10/01–2012/12/28)

The black line in Figure 2 indicates the closing price (¥10395.18), and the green line represents the regression trend (¥10241.85).
The red line indicates the value of the standard error ±1σ (¥10359.94, ¥10123.75), the yellow line ±2σ (¥10478.04, ¥10005.66), andIFTA.ORG PAGE 3

IFTA JOURNAL

2022 EDITION

the blue line ±3σ (¥10596.14, ¥9887.56). Setting November 13,
2012, as Day 1, I calculated the regression trend backward from
December 28, or Day 32 (regression analysis by closing prices of
the 32 days and the elapsed time of 32 days). The standard error
is ¥118.0962.
Next, I will explain the standard error. By using the standard
error in the analysis, the accuracy of the trend estimation canbe measured. A sharp increase in the standard error during themeasurement of a trend means that the estimation accuracy
is decreasing, which suggests that the perception of the trend
during the measurement is incorrect. “Standard error +1σ”
means the value of the regression trend plus the value of thestandard error, and “-1σ” means the value of the regression
trend minus the standard error. Similarly, “Standard error +2σ”
is the value of the regression trend plus two times the standard
error, and “-2σ” is the value of the regression trend minus twice
the standard error. “+3σ” is the value of the regression trendplus three times the standard error, and “-3σ” is the value ofthe regression trend minus three times the standard error. It is
expected that about 68% of the prices that continue to rise or
fall along the trend will be within the range of ±1σ above andbelow the regression trend, and about 27% will be within therange of ±2σ, totaling about 95%.
Let us confirm about a trend itself. An uptrend means thatthe price continues to rise from the starting point of the trend,
whereas a downtrend means that the price continues to fallfrom the starting point of the trend. If the price is falling andmaking the standard error continue to expand beyond the valueof standard error -2σ, we can infer a downward trend. Even
if the price is making the standard error continue to expand
beyond -2σ, it is not a downtrend if the price is rising.
The key point to confirming if an uptrend has turned intoa downtrend is whether the standard error of the regression
trend being measured has expanded while the price has beenfalling. When the price has been falling and the standard error
has been expanding, it is assumed that a downtrend started
from the previous high price. As long as the price continues tofall without recovering to the previous high, the downtrend isrecognized. If the standard error continues expanding as theprice falls while an uptrend is being measured, it is determinedthat a downtrend started from the previous high price.
However, it may be a minor decline during an uptrend, and theprice may resume its rise. Also, the standard error becomeslarger as the upward and downward price movements increase
with the lapse of time. Therefore, it is necessary to check if thetrend continues or not by checking whether the standard error
is expanding rapidly or not.

PAGE 4 IFTA.ORG

The progress of expansion of the standard error cannot be
grasped from a chart simply indicating the price, regression
trend, and standard error. Therefore, I created the “standard
error enhanced index” to check changes in the standard error ina trend.
Standard error enhanced index = Number of days elapsed ×
Change in closing price from previous day (%) × Change instandard error from previous day
In the case of daily time axis, this index is explained asfollows.
• Number of days elapsed: Set the starting point of the trend
as Day 1. If 14 business days have elapsed, it’s Day 14. The
purpose is to reflect the effect of the time elapsed since theoccurrence of the trend.
• Change in closing price from previous day (%): The percent
change in the closing price of the day from the previous day. If
the closing price is 2.1% lower than the previous day, the valueis -2.1. The purpose is to reflect the volatility of the price.
• Change in standard error from previous day: The change inthe standard error calculated from the starting point of thetrend to the latest closing price, expressed in the change fromthe previous day. If the standard error of the day is 95 andthat of the previous day is 15, the value is 80. The purpose isto reflect the extent to which the standard error is affected byprice movements.
In this formula, the longer the trend continues, the higher
the standard error enhanced index tends to rise. I think it is
no problem. The longer the trend continues, the more market
players recognize it and participate in it, which naturally leads
to higher volatility. To reflect this, the number of days elapsed isalso updated daily in the calculation of the index.
If the value is negative, it is converted to an absolute value. In
order to enhance reproducibility, I used standard error values
obtained by regression analysis of the number of days elapsed
and the closing price entered in the Excel data analysis tool.

IFTA JOURNAL

2022 EDITION

Results

In this section, I will explain using examples of the Nikkei stock average.

Figure 3. Nikkei225 (2012/11/13–2013/01/04)

Figure 3 shows measurement of the Nikkei stock average following Figures 1 and 2, in which the closing price of 2012/11/13 is thestarting point of the trend. The lower part of Figure 3 shows the standard error enhanced index of January 4, 2013, which is 1570.98
points (33 days elapsed, closing price up +2.818% from the previous day, and standard error up +16.89 from the previous day: 33 × 2.818
× 16.89 = 1570.98). This is the first yield point. If the price drops to the green regression trend in the middle, the yield point is considered
to have worked. If this yield point is passed, the trend is considered to have shifted from the elastic region to the plastic region. It’stime to refrain from placing new buy orders. In this case, the price moved toward the regression trend, so it is considered that thetrend from November 13 was continuing.
Figure 4. Nikkei225 (2012/11/13–2013/01/23)

In Figure 4, the standard error enhanced index is 1350.517. The closing price has also dropped below -2σ, so it is considered that theyield point has been reached. If the closing price continues to fall after Day 46, the downtrend from the previous high is considered
to be continuing. If the uptrend resumes without turning into a downtrend, it is considered that the minor trend from January 4 wascontained in the uptrend since November 13.
IFTA.ORG PAGE 5

IFTA JOURNAL

2022 EDITION

Figure 5. Nikkei225 (2012/11/13–2013/02/26)

In Figure 5, the standard error enhanced index has exceeded the previous high and the closing price has dropped below -2σ, so it isconsidered to be a yield point. If, after Day 69, the standard error enhanced index exceeds the previous high while the closing pricedeclines, the market is considered to have passed the yield point and shifted to a downtrend.
In Figure 6, the standard error enhanced index has exceeded the previous high, but the closing price has not exceeded +2σ, so it is
not a yield point.
Figure 6. Nikkei225 (2012/11/13–2013/03/08)

PAGE 6 IFTA.ORG

IFTA JOURNAL

2022 EDITIONIn Figure 7, a yield point is observed. The standard error enhanced index has exceeded the previous high, and the closing price has
fallen below -2σ. If the closing price continues to fall and the standard error enhanced index continues to hit new highs, it means thetrend has passed the yield point.
Figure 7. Nikkei225 (2012/11/13–2013/04/01)

Figure 8. Nikkei225 (2012/11/13–2013/04/11)

In Figure 8, a yield point is observed in the latest standard error enhanced index.
IFTA.ORG PAGE 7

IFTA JOURNAL

2022 EDITIONIn Figure 9, too, a yield point is observed in the latest standard error enhanced index.
Figure 9. Nikkei225 (2012/11/13–2013/04/24)

In Figure 10, too, a yield point is observed in the latest standard error enhanced index.
Figure 10. Nikkei225 (2012/11/13–2013/05/07)

PAGE 8 IFTA.ORG

IFTA JOURNAL

2022 EDITION

Figure 11. Nikkei225 (2012/11/13–2013/05/15)

After the yield point was observed in Figure 10, the closing price does not return to the regression trend and the standard error
enhanced index hits a new high. Therefore, it is considered that the trend has broken through the yield point and shifted from theelastic region to the plastic region. The closing price does not fall immediately after the yield point is passed. The trend continues until
the maximum stress is reached, so the uptrend is thought to be continuing as long as the price continues to hit new highs.
When a new high of the standard error enhanced index is no longer observed, it is considered that the maximum stress point has
been passed, suggesting that a downtrend is approaching.
Figure 12. Nikkei225 (2012/11/13–2013/05/20)

IFTA.ORG PAGE 9

IFTA JOURNAL

2022 EDITIONIn Figure 13, the rise of the closing price is continuing, so the uptrend is maintained.
Figure 13. Nikkei225 (2012/11/13–2013/05/22)

In Figure 14, although a decline of the closing price is observed, it is considered within the range of the trend unless the standard
error enhanced index reaches a new high.
Figure 14. Nikkei225 (2012/11/13–2013/05/27)

PAGE 10 IFTA.ORG

IFTA JOURNAL

2022 EDITIONIn Figure 15, the closing price has fallen below -2σ and the standard error enhanced index has reached a new high. Therefore, it isconsidered that the trend that was continuing since November 13 has ended. Deciding that a new trend started on May 22, a market
player should shift to measurement of a downtrend. It is not known whether it is a level trend or a downtrend.
Figure 15. Nikkei225 (2012/11/13–2013/05/30)

The first thing that can be confirmed from the above charts is that in a chart of the standard error and the price, the positional
relationship is updated later with the lapse of time, and as a result, a closing price that was within ±2σ is frequently indicated outside
the range of ±2σ as time passes. Such a phenomenon affects a decision solely based on the regression trend. But it has been foundthat using the standard error enhanced index along with the chart, the yield point can be checked to determine whether the trend willcontinue.
However, not all cases are as simple as the Nikkei stock average. As an example of this method not working well, I will now present
analysis of AUD/USD daily charts.
In Figure 16, as the price is declining and hitting new lows, it is assumed that a downtrend is underway. The starting point of thetrend is the previous high on July 15, 2008, immediately before the trend.
Figure 16. AUD/USD (2008/05/21–08/04)

IFTA.ORG PAGE 11

IFTA JOURNAL

2022 EDITIONIn Figure 17, a yield point is observed due to the increase in the standard error enhanced index.
Figure 17. AUD/USD (2008/07/15–08/08)

In Figure 18, a yield point is observed due to the increase in the standard error enhanced index. If the closing price continues to rise,
it is inferred that the downtrend has come to an end.
Figure 18. AUD/USD (2008/07/15–08/21)

PAGE 12 IFTA.ORG

IFTA JOURNAL

2022 EDITIONIn Figure 19, a yield point is observed due to the increase in the standard error enhanced index.
Figure 19. AUD/USD (2008/07/15–08/28)

In Figure 20, an increase in the standard error enhanced index is observed, but this is not a yield point because the position of theclosing price is not standard error ±2σ.
Figure 20. AUD/USD (2008/07/15–09/02)

IFTA.ORG PAGE 13

IFTA JOURNAL

2022 EDITIONIn Figure 21, an increase in the standard error enhanced index is observed, but this is not a yield point because the position of theclosing price is not standard error ±2σ.
Figure 21. AUD/USD (2008/07/15–09/11)

In Figure 22, an increase in the standard error enhanced index is observed, but this is not a yield point because the position of theclosing price is not standard error ±2σ.
Figure 22. AUD/USD (2008/07/15–09/12)

PAGE 14 IFTA.ORG

IFTA JOURNAL

2022 EDITIONIn Figure 23, a yield point is observed due to the increase in the standard error enhanced index.
Figure 23. AUD/USD (2008/07/15–09/18)

In Figure 24, the yield point observed in Figure 23 has been passed, so the trend is considered to have shifted from the elastic region
to the plastic region. In other words, the downtrend is approaching its end.
Figure 24. AUD/USD (2008/07/15–09/19)

IFTA.ORG PAGE 15

IFTA JOURNAL

2022 EDITIONIn Figure 25, the yield point of the trend has already been passed, so the closing price is expected to continue rising.
Figure 25. AUD/USD (2008/07/15–09/23)

In Figure 26, the closing price has begun falling again and the standard error enhanced index has hit a new high. Therefore, theearlier observed yield point is considered to have been false. The short uptrend seen earlier is thought to have been contained in the
downtrend that began on July 15.
Figure 26. AUD/USD (2008/07/15–10/06)

PAGE 16 IFTA.ORG

IFTA JOURNAL

2022 EDITIONIn Figure 27, the yield point observed in Figure 26 has been passed, so the trend is considered to have shifted from the elastic region
to the plastic region. In other words, the downtrend is approaching its end.
Figure 27. AUD/USD (2008/07/15–10/08)

In Figure 28, as long as the closing price continues falling, it is considered that the downtrend is continuing.
Figure 28. AUD/USD (2008/07/15–10/10)

IFTA.ORG PAGE 17

IFTA JOURNAL

2022 EDITIONAs shown in Figure 29, if both the closing price and the standard error enhanced index hit new values, it is considered that the
downtrend is continuing.
Figure 29. AUD/USD (2008/07/15–10/15)

In Figure 30, both the closing price and the standard error enhanced index have hit new values, so it is considered that the
downtrend is continuing.
Figure 30. AUD/USD (2008/07/15–08/21)

PAGE 18 IFTA.ORG

IFTA JOURNAL

2022 EDITIONAs shown in Figure 31, if the closing price continues to rise and an increase in the standard error enhanced index is observed, it isinferred that the downtrend has come to an end.
Figure 31. AUD/USD (2008/07/15–11/04)

As in Figure 32, if both the closing price and the standard error enhanced index hit new values, it is considered that the downtrend iscontinuing.
Figure 32. AUD/USD (2008/07/15–11/20)

IFTA.ORG PAGE 19

IFTA JOURNAL

2022 EDITIONIn Figure 33, because neither the closing price nor the standard error enhanced index hit new values, resumption of the downtrend
was not observed. The downtrend is considered to have ended unless a new low is reached.
Figure 33. AUD/USD (2008/07/15–12/08)

Consideration

In this study, I analyzed charts of the Nikkei stock averageand AUD/USD by regression trends and the standard error
enhanced index. It was found that we can detect the end of atrend by using these two factors. On the other hand, there werecases where a short-term rebound was judged to be the endof the trend, as seen in AUD/USD. It is notable that a reboundoccurred after the yield point of the trend was observed in
Figure 24. As explained in the section “Factors and the Method,”
it is necessary to judge that the downtrend has resumed when
the price has hit a new low again. I also tested it with CME crude
oil futures and obtained similar results to those of AUD/USD.
On the contrary, when I tested it with uptrends of AUD/USD, theyield point observation worked as in the case of the Nikkei stock
average.
We cannot detect the end of a trend by using regression
trends in the way generally explained in literature because an
ongoing trend continues to increase the standard error with thelapse of time. It is necessary to use the standard error enhanced
index employed in this study in combination with regression
trends and to observe the impact of the expansion of thestandard error on the trend.
PAGE 20 IFTA.ORG

Conclusion

In this study, I utilized regression trends to observe trends
and their end points. I also developed the standard error
enhanced index to measure the expansion of the standard error.
It was confirmed that the end point of a trend can be determinedby using them. However, this method seems to work better in an
uptrend, so I will continue to improve it. In addition, there may
be events in the market big enough to change the trend, so careshould be exercised in actual use.
While I used regression trends to observe the yield point of atrend, I believe that regression trends are also compatible with
the Elliott wave, cycle analysis, etc. I have a hypothesis thatby measuring each Elliott wave by regression trend, the end of
the wave can be predicted. I want to work on this study in the
future. I also want to study a method to measure a downtrendof a 60-minute candlestick included in an uptrend of daily
candlestick. Through my studies in technical analysis, I hope tocontribute to the betterment of society. It would be my pleasure
if this thesis would be of help to financial traders, sales people,
and investors around the world.

IFTA JOURNAL

2022 EDITION

References
Nippon Technical Analysts Association (2004) Nippon Technical Bunseki
Taizen (Complete Technical Analysis of Japan), Nikkei Inc.
Nippon Technical Analysts Association (1986) Nippon no Kabuka
Bunseki (Stock Price Analysis of Japan), Nikkei Inc.
Kakuya Kojoh (2019) Technical Bunseki ga Wakaru (Understanding
Technical Analysis), Nikkei Inc.
Katsuhiro Tanaka (1998) Technical Bunseki Daizenshu (Complete
Collection of Technical Analysis), Sigma Base Capital Corporation.
Jon Andersen (1996) “Standard Error Bands,” Technical Analysis of
STOCKS & COMMODITIES magazine.

Acknowledgements

I am greatly indebted to Mr. Kakuya Kojo, chairman of Koichi
Nosaka and general manager of the Research Department, andother members of the Nippon Technical Analysts Association(NTAA) for helping me write this thesis. As a technical analyst, I
have continued studies following my predecessors to this day. I
would also like to express my gratitude to Securities Japan, Inc.
for teaching me the basics of the financial market, QUICK Corp.
for providing me with various inspiration, and my family forwatching over and supporting my study.
This thesis is the author’s personal statement and not theintention of the institution to which he belongs. The institution
is in no way responsible for it.

IFTA.ORG PAGE 21

IFTA JOURNAL

2022 EDITION

Christoph T. Wildensee, Ph.D., MFTA

Intraday-Trade-Optimization
Via Fibonacci-DLL

Nordstr. 7
Seelze-Letter, Niedersachsen
30926 Germany

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

Abstract

The first unsatisfactory thing is that, despite the frequent
use of Fibonacci resistance and support lines, the scientificreputation is rather poor. The proof about the mathematicalpower and functionality is difficult—despite achievablesuccesses. Software manufacturers naturally implement suchfunctionalities in their trading software, which also play aweighty role in the various strategies for trading. However,the question also arises whether it is possible to use simplified
empirical methods to determine the turning points in the pricedevelopment in such a way that there is sufficient time for a
trading reaction.
This is done by using statically fixed distances to the current
price value (left and right edge) and determining the slope ofthe moving edge from this. The determination points movecontinuously at the same distance.
This representation permits a reliable view of the possible
turning points. However, this takes place only with coursechanges. Constant courses over a longer period do not playa role. The effectiveness is proven in my opinion with thefollowing work. The basic data is available for review and can be
discussed with more advanced analysis features.
With existing data, the methodology and conclusions
drawn from it withstand any resistance. The approach differs
significantly from common approaches, as these otherwise
allow for significant influence on traders’ application of thehelp and support lines. This approach does not allow for any
particular influence and is only variable in the definitionof the left and right secant points, keeping the approach
methodologically simple and fixed within its framework

Introduction
Fibonacci Number Series
The Fibonacci number series and the ratios derived from it
open up the possibility of calculating both striking support
points and resistances as well as potential price targets ofcurrent movements, adapted in the price trend of stocks
and indices. These are often provided in trading systems asfunctionally adaptable overlays. The Shoulder-Head-Shoulder
formation (first and third middle high as Shoulder, middle
stronger high as Head) is certainly worth mentioning (see e.g.,
Savin/Weller/Zvingelis [2003]) but will not play a role in thefollowing.
The discovery of this number sequence goes back to Leonardo
Fibonacci da Pisa (1170–1240) and his work “Liber Abaci.”
The interesting thing about the number sequence is not the

PAGE 22 IFTA.ORG+00495114302128
christoph@wildensee.de

result itself, but the relations of the numbers to each other. If
one looks at the Fibonacci number ranges: 0, 1, 1, 2, 3, 5, 8, 13,
21, 34, 55, 89, 134, 233, 377, 610..., it can be used to determine
the irrational number Phi (Φ, ϕ, φ, more rarely tau or g) for
the ratio of the golden ratio, which can be used to determine
retracements (price corrections at resistance and support lines)
and extensions (price movements that strongly exceed theprevious impulse). However, Kempen already stated or provedin his 2015 paper “Fibonaccis are Human (made)” that a) pricereversal is most likely for all trend classes in the range of 50%of the movement, b) trend correction is more likely than trend
break regardless of trend class, and c) there is no empiricalreason for the restriction to a few excellent retracement levels.
This last point means that 100% retracement is not empiricallyconfirmed as a support line because there is no clear statisticalsignificance for any trend class and, most importantly, thesignificance of Fibonacci retracements is empirically refuted
for all trend classes. However, the 100% level is significant in asmall environment, but the size of this environment depends on
the trend class and is opposite to the trend duration. The same
applies in a weakened way to the 33%, 50%, and 67% levels forsecondary and tertiary trends (see Kempen [2015], p. 21). The
calculation is carried out via the quotient formation with thelimit value consideration (Kempen [2015], p. 10):and following also (cf. Gaucan/Maiorescu [2011], McLean[2005]).

F3 = ….

≈ 0.236067

He clearly concludes that the “empirical investigations[...] have exposed the myth of Fibonacci retracements as
human (made). Moreover, it has been shown that the choiceof retracement forecasts can be optimized with the help of
empirical evaluations. Although the recommendations set by
Murphy [...] are a good choice, added value has been created with

IFTA JOURNAL

the (cumulative) probability trajectories produced.” (Kempen[2015], p. 22) Although mathematically refuted to a large extent,
it is empirically consistent in use, because including Kempen,
one can postulate that the inclusion of auxiliary lines in the priceobservation of stocks very well expresses a certain probability
that a trend reversal is imminent. This is no proof and noguarantee, especially since the price development depends
on the actions of the market participants and expresses the
expectation horizon of these. Nevertheless, the presentationof trend lines shows that statistically significant supports areuseful in anticipating the possible course of the price. This
does not have to be done using explicit Fibonacci-based lines;
it can be other line definitions, but Fibonacci lines can also be
considered valuable.
If we look at trading software (i.e., professional trading
systems), we can see that the inclusion of trend lines is acommon practice and is recognized as beneficial. Thus, there
are many traders who have their trading strategy supported
by Fibonacci lines for both short and long-term trends (seeMcLean [2005], p. 12ff). However, this must also be understoodin terms of content. “It is our job to interpret a chart and then totranslate that interpretation into a language that is understoodby the non-professional technical analyst, keeping it as simple
and jargon-free as possible. Anyone can draw a trendline; only
a few can interpret Elliott wave or Gann theories.” (McLean[2005], S. 30)
Fibonacci Ratios
Fibonacci retracements indicate potential supportand resistance levels. If the range of a previous price swing isonly corrected, it is a retracement, but if this range is exceeded(“extended”), it is an extension. For the representation of theretracements with the upward trend, the low point (100%retracement) is first connected with the following high point(0% retracement). With the difference of these two points,
starting from the high point, the retracements are measured inpercentages of 23.6%, 38.2%, 50%, 61.8%, and 78.6% and drawn
in as a horizontal line by the trading software. For plotting theretracements on the downtrend, it is the converse, but with thelines 127.2%, 150%, and 161.8%, for example. These are the mostfavored lines for support (see also Prasad [2010], pp. 16ff, 54ff).
The most favored line is that of the 61.8% retracement as
the critical zone, which signals whether a current swing isa countertrend swing or a swing into a new trend direction.
Thus, countertrends or corrections should not cross the 61.8%
retracement. However, if it is exceeded, it is usually assumed
that the market is taking a new trend direction and is not justa countertrend. Here, however, one must object that the 61.8%
retracement represents an important potential support orresistance, but cannot always be seen as a trend signal, because
it is not uncommon for a wave to end at a 78.6% retracement
before the next strong wave starts. For this reason, a 78.6%
price correction is also an important retracement level thatshould not be undercut, provided the previous trend direction iscontinued.
Ultimately, this methodology can be used in intraday trading
as well as in long-term market monitoring to locate potential
trend direction changes.

2022 EDITION

Materials and Methods
Approach of Change Points on the Time Axis
In the following, a supplementary approach shall be presented
that does not include all trend components of the price course,
but only includes the price changes and anticipates the further
course from this via Fibonacci lines.
This approach is to set a marker at the points with a higher
probability that the price trend will rise or fall. This can also be
used to identify small jumps. The procedure shows that its use
can be empirically proven.
By means of a small example, the procedure shall first be
explained. In the following are the date format dd.mm.yyyy andthe time format hh:mm (german).
Figure 1. Adidas share price performance as of March 31,
2021

Figure 1 shows the price development of the Adidas share in
the period from 9:00 in the morning to 18:00 in the evening for
March 31, 2021. In addition to the phases of rise and fall, theconstant values over longer periods can also be seen here. In the
period from around 10:02 to 10:34, for example, the share priceis unchanged at EUR 265.90.
Figure 2. Change points of the Adidas share pricedevelopment from 31.03.2021

Figure 2 again shows only the change points with the change
values of Adidas. It is therefore an identical representation interms of content as Figure 1, but the phases of constant values
are not included.

IFTA.ORG PAGE 23

IFTA JOURNAL

2022 EDITION

Table 1. Excerpt of the Adidas price history as of 31.03.2021 with consideration in Figures 1 and 2

In this respect, there are fewer points in the price history toconsider, but the informative value of this representation is thesame with fewer time stamps. The relevant price changes can be
identified more quickly, even with small jumps. This view forms
the basis for further development. There is also a large numberof IT systems that do not offer such support lines (e.g., in thefield of energy trading). The further explanations can serve as abasis for this, and the results can be integrated there later.
Derivation of the Markers
The current price value forms the reference point. The trendline is generated, for example, with a 2_8 F-step definition fromthe value two points back as the right value and, starting from
this, the point eight further values back as the left value. Thus,
the relations of the trend development to the current value are
to be represented in the following:

PAGE 24 IFTA.ORG* 2_8: Right value two values before the current value
standing, from this, eight values to the left running as left value
defined,* 1_8: Analog one value in front of the current value, eightvalues running from this to the left,* 2_10: Analog two values before the current value, 10 values
running from this to the left,* 2_5: Analog two values before the current value, five values
running from it to the left, etc.
If the right point in the value is larger than the left point, a
positive gradient of the trend results; if this is not so, it concernsa negative trend (fiboricht = Direction). From these two values(left and right) in dependence of the trend direction, theexpected Fibonacci reference values are determined from thedifference between right and left value as absolute value (abs[right-left]). The calculation in LAZARUS looks as follows:(Wildensee [2021a]), Source Code from procedure TForm1.
Fibo1;IFTA JOURNAL

2022 EDITION

Table 2. Excerpt of Source Code Fibonacci Limits[...]
diff1:=abs(wertmax1-wertlow1); // positiver Wert der Differenz (absolut); right=wertmax1
if (fiboricht = true) then// bei positiver Steigung; left=wertlow1
begin
fibborder62:=wertmax1-(((wertmax1-wertlow1)*62)/100); // roundedfibborder50:=wertmax1-(((wertmax1-wertlow1)*50)/100);
fibborder38:=wertmax1-(((wertmax1-wertlow1)*38)/100);
fibborder162:=wertmax1+(((wertmax1-wertlow1)*162)/100);
fibborder150:=wertmax1+(((wertmax1-wertlow1)*150)/100);
fibborder127:=wertmax1+(((wertmax1-wertlow1)*127)/100);end;
if (fiboricht = false) then // bei negativer Steigung
begin
fibborder62:=wertmax1+(((wertlow1-wertmax1)*(100-62))/100); // different showing
fibborder50:=wertmax1+(((wertlow1-wertmax1)*50)/100); // in 62+38 invers showing
fibborder38:=wertmax1+(((wertlow1-wertmax1)*(100-38))/100); // without dec. point calculation
fibborder162:=wertmax1-(((wertlow1-wertmax1)*162)/100);
fibborder150:=wertmax1-(((wertlow1-wertmax1)*150)/100);
fibborder127:=wertmax1-(((wertlow1-wertmax1)*127)/100);
end;
[...]

In case of a negative slope, it is necessary to swap the display labels for the Fibonacci limits in the value 38 and 62 (inverse showing);
otherwise, a wrong order will be displayed. This is not mandatory, but it makes sense for the display in order not to confuse. Thus, theprogram can be represented first as shown in Figure 3.
Figure 3. Example representation, German version, of the program development (rising phase)

It can be seen in Figure 3 that the price values are read continuously (every half minute), the change points are marked with an “x”
in the Chk (Check) field, and only these are shown in the price development. Base values like the first value (f), lowest value (l), andmaximum value (m), and also values for slope (S1 for first-middle slope and S2 for first-low slope) and return (Pd for average-minreturn, Pl for max-average-return, and Pz for max-min-return), are provided. Via the “Fib” button, other F-Step values can also be used
for a short time (after switching off the update cycle) to recognize the Fibonacci values (F-Step = left and right value), and the last five
Change values are provided with the current value. The values are taken from a rounded point of view (i.e., the decimal places are notincluded) because this is too small.
The calculation of the potential turning points (the labels are empty at the time) results as follows: (source code from procedure
TForm1.Fibo1).

IFTA.ORG PAGE 25

IFTA JOURNAL

2022 EDITION

Table 3. Excerpt of source code Fibonacci derivation of potential turning points[...]
LabelFib38.Caption:=’F38: ‘+copy(FloatToStr(fibborder38),1,6);
LabelFib38.Refresh;
LabelFib50.Caption:=’F50: ‘+copy(FloatToStr(fibborder50),1,6);
LabelFib50.Refresh;
LabelFib62.Caption:=’F62: ‘+copy(FloatToStr(fibborder62),1,6);
LabelFib62.Refresh;
LabelFib162.Caption:=’F162: ‘+copy(FloatToStr(fibborder162),1,6);
LabelFib162.Refresh;
LabelFib150.Caption:=’F150: ‘+copy(FloatToStr(fibborder150),1,6);
LabelFib127.Caption:=’F127: ‘+copy(FloatToStr(fibborder127),1,6);
LabelFib127.Refresh;if ((fiboricht = true) and (length(LabelNewValue.Caption)>0)) then // positive direction
begin
if ((StrToFloat(LabelNewValue.Caption) <= fibborder62) and (fibborder62 <> 0)) then
begin
LabelFib62.Caption:=’F62: CHANGE?’;LabelFib62.Refresh;end;
if ((StrToFloat(LabelNewValue.Caption) <= fibborder50) and (fibborder50 <> 0)) then
begin
LabelFib50.Caption:=’F50: CHANGE?’;LabelFib50.Refresh;end;
if ((StrToFloat(LabelNewValue.Caption) <= fibborder38) and (fibborder38 <> 0)) then
begin
LabelFib38.Caption:=’F38: CHANGE?’;LabelFib38.Refresh;end;
if ((StrToFloat(LabelNewValue.Caption) >= fibborder162) and (fibborder162 <> 0)) then
begin
LabelFib162.Caption:=’F162: CHANGE?’;LabelFib162.Refresh;end;
if ((StrToFloat(LabelNewValue.Caption) >= fibborder150) and (fibborder150 <> 0)) then
begin
LabelFib150.Caption:=’F150: CHANGE?’;LabelFib150.Refresh;end;
if ((StrToFloat(LabelNewValue.Caption) >= fibborder127) and (fibborder127 <> 0)) then
begin
LabelFib127.Caption:=’F127: CHANGE?’;LabelFib127.Refresh;
end;
end;
if ((fiboricht = false) and (length(LabelNewValue.Caption)>0)) then // negative direction
begin
if ((StrToFloat(LabelNewValue.Caption) >= fibborder62) and (fibborder62 <> 0)) then
begin
LabelFib62.Caption:=’F62: CHANGE?’;LabelFib62.Refresh;end;
if ((StrToFloat(LabelNewValue.Caption) >= fibborder50) and (fibborder50 <> 0)) then
begin
LabelFib50.Caption:=’F50: CHANGE?’;LabelFib50.Refresh;end;
if ((StrToFloat(LabelNewValue.Caption) >= fibborder38) and (fibborder38 <> 0)) then
begin
LabelFib38.Caption:=’F38: CHANGE?’;LabelFib38.Refresh;end;
if ((StrToFloat(LabelNewValue.Caption) <= fibborder162) and (fibborder162 <> 0)) then
PAGE 26 IFTA.ORG

IFTA JOURNAL

2022 EDITION

begin
LabelFib162.Caption:=’F162: CHANGE?’;LabelFib162.Refresh;end;
if ((StrToFloat(LabelNewValue.Caption) <= fibborder150) and (fibborder150 <> 0)) then
begin
LabelFib150.Caption:=’F150: CHANGE?’;LabelFib150.Refresh;end;
if ((StrToFloat(LabelNewValue.Caption) <= fibborder127) and (fibborder127 <> 0)) then
begin
LabelFib127.Caption:=’F127: CHANGE?’;LabelFib127.Refresh;
end;
end;
[...]

Since the constant phases of the value (i.e., over a certain period of time with identical value) can last shorter or also longer, a slopeof the successive points is suggested, which is not actually present. Therefore, the actual gradient is also represented under S1 and S2.
However, this is not intended otherwise. The tool to be developed is not intended to highlight the reality; this is already done by themain application that integrates this functionality. Rather, it is intended to show the change points in relation to each other and to
the trend to be assumed. To view an initial result, Figure 4 shows the trend from Figure 2, but with possible inflection points from the
March 31, 2021, calculation.
Figure 4. Change points in the Adidas share price from 31.03.2021 with possible turning points with 2_8

First of all, it can be seen that the beginning phase does not generate any markers. The next phase then shows a price loss withreference to the trend, which leads to a minimum at around 12:00. Subsequently, the price rises strongly, so that the previous markers
actually represent entry points for buying as turning points for this day. Afterwards, a falling price development is indicated again.
Around 15:00, a phase of increase begins again, but the high around 17:50 is no longer marked. The recognized need for adjustmentshows that beside the main line, which was defined as a 2_8 line, an additional correcting auxiliary line is needed, which—as adifferentiated definition—shows the developments, which are not recognized from the main line.
The program was redesigned and extended accordingly, so that values are also available at the beginning after a short time. As longas one cannot go back suitably, the first value is used. The source code for this looks as follows:

IFTA.ORG PAGE 27

IFTA JOURNAL

2022 EDITION

Source code from procedure TForm1.RangeFiboErmitteln;// Identify left and right border
Table 4. Excerpt of source code definition of the two trend outer values[...]
i:=StringGridValues.RowCount; k:=0;[...]
if (i > 0) thenbegin
for t:=i-1 downto 1 do
begin
if ((TRIM(StringGridValues.Cells[4,t]) = ‘x’)) thenbegin
k:=k+1;// Counter for relevant Values
if (k = fstep0) then // Edit of right Value, mostly 2
begin
wrechts:=StringGridValues.Cells[3,t]; // right Valueend;
if (k = fstep1+fstep0) then // when k = right Value + left Value, thenbegin // 8 as default, left and right Value can be changed between 2 and 100
wlinks:=StringGridValues.Cells[3,t];
end;
end;
if (length(wlinks)<2) then wlinks:=ersterwert;
[...]
end;
end;
[...]

However, this would also be the case if no values are provided abruptly at a later time. Thus, the provision should only occur if novalues for the left boundary arise in the initial phase.
In addition, a second Fibonacci line was drawn in as auxiliary line, which should have another verification mode, so beside e.g., 2_8
still 1_5. The consequence would be that identifications not occurring in the first line are recognized with the second line.
Figure 5. Example representation of the program development after adaptation with change point display

Development of a DLL for Trend Analysis
The result is provided as a Dynamic Link Library, or DLL, so
that it can be included in software products as supplementaryfunctionality. “A DLL is a library that contains code and datathat can be used by more than one program at the same time.”(https://docs.microsoft.com/en-us/troubleshoot/windowsclient/deployment/dynamic-link-library). The DLL is to be
downloaded under Wildensee (2021b) as a free program. A“kurse.dll” is provided for German support without second
auxiliary line, and a “fiboengl.dll” as an English-language
version, in the listing single without second auxiliary line, in thelisting double with second auxiliary line. Especially the lattershould be integrated into other software products.
PAGE 28 IFTA.ORG

Results
Data Collection and Initial Evaluation
In the period from March 31 to April 14, 2021, several runs
were conducted to collect stock price data using the test tool
created for this purpose. In total, the following data wascollected for the shares• Adidas• Bechtle• Airbus• BMW• Allianz• Evonik• BASF• Fresenius• Bayer• GEA

IFTA JOURNAL

2022 EDITION

Price data was determined, processed in table processing, and presented in price change graphs. Since results are available for thedifferent lines 2_8, 2_10, 2_12, 1_8, and 2_5, covers of the turns to the trend could be identified. The error rate of the determineddatasets is max. 2.5% so that a solid data basis can be assumed.
First, several 2_8 histories as of April 1, 2021, are to be presented. They show that the adjustments in the program logic were
important, because errors in the view still occurred here.
Figure 6. Airbus price development on April 1, 2021, change points

Figure 6 clearly shows that no changes were detected in the front area until about 12:00. The early beginning of the rise would havebeen an entry point. From approximately 13:00, the change points with 2_8 (red) and 2_10 (green) were recognized; 2_10 advances
here to the possible auxiliary line.
Figure 7. Allianz share price development on April 1, 2021, change points

Figure 7 shows a corresponding picture as Figure 6 for the Allianz share. In the rear area, both lines recognize the various turning
points quite reliably. However, it should be noted that the overall unsteady course with rapid changes must indicate a correspondingly
large number of results, does not allow a clear conclusion in the middle area with regard to the turning points, and in this respect,should not be used to check the plausibility of the results.
Figure 8. BASF share price development on April 1, 2021, change points

IFTA.ORG PAGE 29

IFTA JOURNAL

2022 EDITION

This looks equally interesting for the BASF share in Figure 8. Here, the 1_8 line was also used (blue). 2_8 and 2_10, with the
exception of the end of the day at about 17:50, clearly show the performance from about 10:30, but the trend is only minimally upward.
1_8 comes at the end again in its display to a short rise and directly afterwards to a fall of the value.
Figure 9. Bayer share price development on April 1, 2021, change points

When looking at the Bayer share price development in Figure 9, the previous results can be confirmed. With the lines 2_8 and 2_10,
meaningful turning points are recognizable. (Trajectories of other stocks such as BMW, GEA, etc. are therefore not shown here.)
Need for Adjustment
Accordingly, the run on April 1, 2021, clearly shows that adjustments to the program run are necessary. In addition, it can be seenthat other step definitions, such as 1_8 and 2_5, also need to be reviewed. Accordingly, a run was performed on April 7, 2021, using thevarious definitions. This presented the following results.
Figure 10. Adidas share price development on April 7, 2021, change points

Figure 10 clearly shows that the 2_8 definition (red) achieves reliable results as long as the rate is unambiguous. Rapidly successive
price changes, as in Figure 7, can also be detected here between 10:30 and 13:10. On the one hand, they are reliably displayed, but they
are not optimal as a trend display. Only with decreasing values from approximately 14:00 and especially with 2_8 around 16:50 to
17:15, unambiguity arises.

PAGE 30 IFTA.ORG

IFTA JOURNAL

2022 EDITION

Figure 11. Airbus price trend on April 7, 2021, change points

As shown in Figure 11, the Airbus change line of April 7, 2021, from about 13:30 onwards, consistently correctly shows the turning
points both in the strongly rising and subsequently falling phase with certainty. Gaps are to be identified beside the phase to 10:15 asinitially not recognized phase in particular at the time points 10:30 and 11:45.
Figure 12. Allianz price trend on April 4, 2021, change points

Figure 12 shows a reliable recognition of all phases of the decline and the fall by the lines. The exceptions here are also the initial
phase until about 10:00 and the slight rise at about 11:45, which, however, also does not seem to be clear enough. The 2_8 definition is
also the clearest here. The 2_5 definition advances to an equally good auxiliary line as the 2_10 before.

IFTA.ORG PAGE 31

IFTA JOURNAL

2022 EDITION

Figure 13. BASF share price development on April 7, 2021, change points

Figure 14. Bayer share price development on April 7, 2021, change points

In fact, Figures 13 and 14 are analogous to Figure 12. Clearly, the turning points with the definitions 2_8, 2_5, and also 1_8 are very
well recognized. Thus, there is only a need for adjustment in the front area until about 10:00. Here, the recognition quality is not given.
Adaptation Requirement
Accordingly, the run on April 7, 2021, shows that further adjustments of the program flow are necessary, especially in the front areaof the curve generation. Additionally, it can be seen that the step definitions 1_8 and 2_5 need further verification.
The source code was adapted in procedure TForm1.Fibo1. As long as there are no left outer values after F-Step, the first generated
value is used as the outer value.
Table 5. Excerpt source code definition of the two trend outer values after adjustment[...]
i:=StringGridValues.RowCount; k:=0;[…]
if (i > 0) thenbegin
for t:=i-1 downto 1 do
begin
if ((TRIM(StringGridValues.Cells[4,t]) = ‘x’)) thenbegin
k:=k+1;// Counter for relevant Values
if (k = fstep0) then // Edit of right Value, mostly 2
begin
wrechts:=StringGridValues.Cells[3,t]; // right Value
end;
PAGE 32 IFTA.ORG

IFTA JOURNAL

2022 EDITION

if (k = fstep1+fstep0) then // when k = right Value + left Value, thenbegin// 8 as default, left and right Value can be changed between 2 and 100
wlinks:=StringGridValues.Cells[3,t];countnotleft:=false; // if enough Values, don’t use first Value. Otherwise real one
end;
end;
if ((length(wlinks)<2) and (countnotleft = true)) then wlinks:=ersterwert;
[...]
and
[…]
procedure TForm1.SGFill;varda1: String;uh1: String;na1: String;ku1: String;
rc: integer;
begin
da1:=LabelDate1.Caption;
uh1:=LabelTime1.Caption;na1:= ComboBoxStock.Text;
ku1:=LabelNewValue.Caption;
rc:=StringGridValues.RowCount-1;
StringGridValues.RowCount:=StringGridValues.RowCount+1;
StringGridValues.Cells[0,rc]:= da1;
StringGridValues.Cells[1,rc]:=uh1;
StringGridValues.Cells[2,rc]:=TRIM(na1);
StringGridValues.Cells[3,rc]:=ku1;
StringGridValues.Cells[4,rc]:=‘_‘;
if ((length(LabelW1.Caption)>0)) thenbegin
if (LabelNewValue.Caption <> letzterwert) then
begin
StringGridValues.Cells[4,rc]:=’x’;
if (ersterwert = ‘0’) then ersterwert:=LabelNewValue.Caption; // ‘0’=default, store value
end;// in variable ersterwert
end;
end;

Result Verification
On April 12, 2021, another half-day only run was performed for the detail view with different definitions. This one presented theresults conveyed in Figure 15a-m..
To first show the previous results again in a single case view, the time period between 14:36 to 16:46 is chosen for April 12, 2021,
which presents the results sequentially. The right outer edge is relevant here.
Figure 15a-m. Sequential representation of an example development of the Adidas share on April 12, 2021
a. 14:36, indicated a strong phase.

IFTA.ORG PAGE 33

IFTA JOURNAL

2022 EDITION

b. 14:44, 2_8 Change and 2_5 Change (each with different sides) indicate an intermediate upswing and stronger
upswing phase, and possible start of the head phase of a shoulder-head-shoulder formation. Here is possibly a good
position to sell.

c. 14:51

d. 15:03, indicated a downturn phase.

e. 15:47, smaller right phase indicated shoulder share, with further downward trend?

PAGE 34 IFTA.ORG

IFTA JOURNAL

2022 EDITION

f. 15:57, no, slight upward trend again is shown in both lines.

g. 16:08, range of the lower step definition identical, therefore no display at 2_5.

h. 16:13, rise of the price, which is also displayed as a change. Start of the subsequent high?

i. 16:23, no, trend is downwards.

j. 16:30, and remains.

IFTA.ORG PAGE 35

IFTA JOURNAL

2022 EDITION

k. 16:36, as before, no turning point display, while further decreasing.

l. 16:46, continuously decreasing.

Up to this point, all switches were also displayed as a possibility of switching. The high phases could have been used as selling times,
provided that the shares were bought at a time with a lower value. The difference in this example is 3.00 EUR.

m. 17:57, low phase not displayed.

However, the last low phase at 17:57 is not shown. This corresponds to the expected error pattern for the first morning and last evening
minutes. However, with the other F-Step definitions, such as 2_10 and 1_8, this can often be narrowed down as well.

Finally, the following graphs represent the day of April 12, 2021, as of 12:30 am.
Figure 16. Adidas price trend on April 12, 2021, change points

PAGE 36 IFTA.ORG

IFTA JOURNAL

2022 EDITION

2_8 (red) and 2_5 (yellow) are largely recognized reliably, but the rise is not recognized in the start phase, which can also result
from the late start at 12:30 pm. The other phases are also recognized sufficiently, but 1_8 (blue) is insufficient.
Figure 17. Airbus share price development on April 12, 2021, change points

A corresponding picture also emerges in Figure 17 for the Airbus share. 2_8 and 2_5 serve well as F-step definitions.
Figure 18. Allianz share price development on April 12, 2021, change points

Figure 18 shows, however, that the definition of 1_8 as a supplementary line is also possible and provides solid results at certain
points in time.

IFTA.ORG PAGE 37

IFTA JOURNAL

2022 EDITION

Figure 19. BASF share price development on April 12, 2021, change points

However, Figure 19 clearly highlights again the definitions 2_8 and 2_5 as common indicators.
Figure 20. Bayer share price development on April 12, 2021, change points

Finally, Figure 20 confirms the previously favored combination of 2_8 and 2_5.
The inclusion of the special case of the F-step definition 1_3 of April 14, 2021, shows that a shorter step definition does not lead toany significant improvements of the expected course.
Figure 21. Adidas share price development on April 14, 2021, change points 1_3

PAGE 38 IFTA.ORG

IFTA JOURNAL

2022 EDITION

Figure 22. Bayer share price on April 14, 2021, change points 1_3

There are too many gaps in the observations here with 1_3 (purple), so that 1_3 appears unsuitable as an auxiliary line.
Consequences of Data Analysis
The previous explanations have proven that:• The data basis for the empirical demonstration of the thesis that the present program can display the turning points of the pricetrend is solid.
• The display of the turning points is timely, and a high percentage of the time is correctly displayed.
• The F-step definitions 2_8 and 2_5 are suitable to provide a solid support.
• The provided DLL as integrable program resources under Windows is able to call the form calculation functionality in alreadyexisting applications.
Implementation Procedure/Special Features
The implementation was carried out in an agile manner (i.e., initially, it was exclusively tested as to whether stock prices can be readand displayed at all from https://www.finanzen.net). This is done using the following constructs:
Table 6. Reading and decomposing the price value from the internet page[...]// link check
url:=‘https://www.finanzen.net/aktien/‘+EditNameStock.Text+‘-aktie‘; // urlLabelUrl.Caption:=url;
LabelUrl.Refresh;if ((url <> q1)) then // if url changed
begin// Variables and Labels must be empty
q1:=url;end;
httpclient := TFPHttpClient.Create(Nil); // Create; Get from *html := httpclient.Get(url);// Get; Get from *httpclient.Free;// Free; Get from *MemoHTMLText.Text := html; // Memotext filled with html-Code; Get from *MemoHTMLText.Refresh;
SuchStart := 0;
SuchStart := FindInMemo(MemoHTMLText, ‘Aktueller Kurs:’, SuchStart + 1); // Get from *if (SuchStart > 0) thenLabelTextPosition.Caption := ‘Found at Position Memo1.SelStart[‘+IntToStr(SuchStart)+’] !’else
LabelTextPosition.Caption := ‘No Position found!’;LabelTextPosition.Refresh;
LabelNewValue.Caption:=copy(MemoHTMLText.Text, SuchStart+15 , 12); // String with 12 chars
Wertzerlegen(LabelNewValue.Caption);LabelNewValue.Refresh;
Wertesetzen;
IFTA.ORG PAGE 39

IFTA JOURNAL

2022 EDITION

SGFill;[…]letzterwert:=LabelNewValue.Caption;* [see Lazarus-TMemo]

Twelve characters are read each time, these are then divided using the Value Decomposition procedure, and the value without text
components is determined.
Table 7. Determining value without text components
procedure TForm1.Wertzerlegen(S: String);
const
ErlZeichen: Array[1..11] of String = (‘0’, ‘1’, ‘2’, ‘3’, ‘4’, ‘5’, ‘6’, ‘7’, ‘8’, ‘9’, ‘,’);[...]z:=Length(S);if (z > 0) thenbegin
for i:=1 to z do
begin
v:=copy(S, i, 1);// compare v in ErlZeichen
q:=AnsiMatchStr(v, ErlZeichen);if (q = true) thenbegin
t:=t+v;q:=false;
end;
end;
end;
if (length(t)=0) then t:=letzterwert;
LabelNewValue.Caption:=t;LabelNewValue.Refresh;
end;

Test Environment
In addition, a test program was developed, which is methodically the same as the main application, but which can read the values
for several stock prices in quick succession. This is controlled by the variable tglob, which serves as an index for variables like
„Aktienname: Array[1..10] of String;“ (arbitrarily expandable) and can then be addressed as Aktienname[tglob] (stock name).
Table 8. Adjustment of the table fill via array with tglob[...]
for t:=1 to alleaktien do
begin
tglob:=t;url:=‘https://www.finanzen.net/aktien/‘+Aktienname[t]+‘-aktie‘;// url wird gebildet[...]
httpclient := TFPHttpClient.Create(Nil); // Get from *html := httpclient.Get(url);// Get from *httpclient.Free;// Get from *MemoHTMLText.Text := html;// Get from *MemoHTMLText.Refresh;
SuchStart := 0;
SuchStart := FindInMemo(MemoHTMLText, ‘Aktueller Kurs:’, SuchStart + 1); // Get from *if (SuchStart > 0) thenLabelTextPosition.Caption := ‘Found at Memo1.SelStart[‘+IntToStr(SuchStart)+’] !’else
LabelTextPosition.Caption := ‘No position found!’;LabelTextPosition.Refresh;
LabelNewValue.Caption:=copy(MemoHTMLText.Text, SuchStart+15 , 12);Wertzerlegen(LabelNewValue.Caption);LabelNewValue.Refresh;[...]
SGFill;BisherValue[tglob]:=LabelNewValue.Caption;
end;

PAGE 40 IFTA.ORG

IFTA JOURNAL

2022 EDITION

procedure TForm1.SGFill;
[...]
begin
da1:=LabelDate1.Caption;
uh1:=LabelTime1.Caption;na1:=Aktienname[tglob];
ku1:=LabelNewValue.Caption;
rc:=StringGridValues.RowCount-1;
StringGridValues.RowCount:=StringGridValues.RowCount+1;
try
StringGridValues.Cells[0,rc]:= da1;
StringGridValues.Cells[1,rc]:=uh1;
StringGridValues.Cells[2,rc]:=TRIM(na1);
StringGridValues.Cells[3,rc]:=ku1;
StringGridValues.Cells[4,rc]:=’_’;
if ((length(LabelNewValue.Caption)>0)) thenbegin
if ((LabelNewValue.Caption <> BisherValue[tglob])) then
begin
StringGridValues.Cells[4,rc]:=’x’; // set „x“if (ersterwert[tglob] = ‘0’) then ersterwert[tglob]:=LabelNewValue.Caption;
end;
end;
[...]

Then the Fibonacci values are determined, and it is recognized whether the lines were exceeded or not. This is marked in the table in
the fields provided (F38 to F162). The values are then transferred to a file at the end of the day after 18:00 and stored on the computer.
This larger number of files can be evaluated to draw conclusions about further adjustments.
Gradually, over the further sprints, the adjustments were made so that finally, the program including DLL is available.
The following results are available:• German, App, simple line definition (KursDeuSingleApp)• German, DLL, simple line definition (KursDeuSingleDLL)• English, App, simple line definition (KursEnglSingleApp)• English, DLL, single line definition (KursEnglSingleDLL)• German, App, double line definition (KursDeuDoubleApp)• German, DLL, double line definition (KursDeuDoubleDLL)• English, App, double line definition (KursEnglDoubleApp)• English, DLL, double line definition (KursEnglDoubleDLL).
For verification, the test tool is provided in German and English (KursTesttoolDeu and KursTesttoolEngl). The English language
versions can be found at [Wildensee (2021a+c)].
The data dumps from the test data provision are also stored in tabular form, from which the graphs of the course trajectories arethen displayed and the turning points are plotted.
Figure 23. Price data dump with turning point definition (GGF. WENDE = CHANGE?)

IFTA.ORG PAGE 41

IFTA JOURNAL

2022 EDITION

Discussion

References

Final Conclusion
First, we need to clarify, with an IT-technical illustration inthis rather simple surrounding field, such as Lazarus, whether
a fastidious solution is possible. As it shows up, the application
development is fast and high performance convertible. Lazarus
produces a high-quality and performance conversion that canalso be made available as DLL. Such DLL can be integrated again inarbitrary environments. The updated DLL contains access to theinternet side (https://www.finanzen.net) to the current collectionof the share prices of selected titles. There are currently 24
different titles, mainly from Germany. The procedure is explained,
and the price is queried every half minute and displayed in thetable. An extension to other stocks and the change to anotherquote provider is possible without any problems.
In this respect, the application offers a positive view of theapproach and clearly shows that professional applications canbe extended without problems.
As far as the methodological approach is concerned, it must
be explained that a market event cannot be forecast, but
probabilities can very well be calculated that phases of rising andfalling alternate. The error rate is known, and the prediction is
statistically limited. Nevertheless, as shown above, support lines
are an expression of exactly this probability. This has alreadybeen sufficiently demonstrated by other authors (see McLean[2005], p. 61ff). The presented approach assumes that drawing
resistance and support lines to the price trend or, in particular, tothe price change points, is a legitimate way to mark the probableturning points. There is no guarantee it will turn around, but
the tearing of the support lines is at least a sufficiently coherent
suspicion. Over time, a feeling for the correct points of time willdevelop. It should be noted that if the difference between theleft and right limits is too small, the presentation of a possible
turning point is problematic. If the difference is sufficiently large,
the trend reversal can be recognized with a high hit rate of up to
approximately 90%, even if this occurs with a slight time delay.
Nevertheless, by centering on the change points, the trader
usually has enough time for a trading reaction even if the pricedifference is minimal.
As it turns out, the F-Step definitions 2_8 as the main and 2_5
as the complementary correction line are well suited to present
solid results on probable turning points.
As mentioned, too choppy progressions with deflections
occurring in short succession are insufficient for recognition,
but meaningfully sustained movements can be clearly
identified. For the future, if necessary, further F-step
definitions, such as 1_4, 2_4, 1_6, 2_6, should be checkedwith regard to their effect. In conclusion, however, a very solid
result is available. In particular, it should be noted that thisapproach should also be investigated for the energy trading
field. This trading field is especially known for volatile day
trading patterns. Other stock markets are good targets for thisapproach, too.

PAGE 42 IFTA.ORG

Gaucan/Maiorescu (2011). How to use Fibonacci retracement to predict
forex market, in: Journal of Knowledge Management, Economics andInformation Technology,
http://www.scientificpapers.org/wp-content/files/volume1_
issue_2_2011.pdf.
Kempen (2015). Fibonaccis are Human (made) – Wissenschaftliche
Analyse von Retracement-Level (citations translated), http://www.
instmath.rwth-aachen.de/~maier/publications/Kempen2015b.pdf.
McLean (2005). Fibonacci and Gann Applications in Financial Markets,
Practical Applications of Natural and Synthetic Ratios in TechnicalAnalysis, Wiley & Sons, 2005.
Prasad (2010). Technical Analysis, http://www.karvycommodities.com/
downloads/Technical%20Analysis.pdf.
Savon/Weller/Zvingelis (2003). The Predictive Power of “Head-andShoulders” Price Patterns in the U.S. Stock Market, University of
Iowa, January 2003.
Wildensee (2021a). http://www.wildensee.de/fiboquelle_eng.zip.
Wildensee (2021b). http://www.wildensee.de/AlsDLLAufruf.zip.
Wildensee (2021c). http://www.wildensee.de/testtool.zip.
Wildensee (2021d). http://www.wildensee.de/Hist1.zip.

Software and Data
Lazarus: https://www.lazarus-ide.org/index.php?page=downloads.
Lazarus-TMemo: https://wiki.lazarus.freepascal.org/TMemo/de.

Acknowledgements

I would like to thank my wife Nina and my little 9-year-old
twins, Jonas and Simon.
Copyright © 2021 Christoph Tobias Wildensee

IFTA JOURNAL

2022 EDITION

Dr. Oliver Reiss, CFTe, MFTA
Am Bonneshof 30
40474 Dusseldorf
Germany

The EMD Oscillator
By Dr. Oliver Reiss, CFTe, MFTA

Abstract

The Empirical Mode Decomposition (EMD) and its applicationin technical analysis was the topic of my MFTA thesis (Reiss
2019). The results of that paper cover the adaption of the EMD
to financial time series, an EMD-based price projection, thedevelopment of an EMD-based moving average, and, finally, two
trend following trading systems. The research was awarded
with the John Brooks Memorial Award and this honor was the
incentive for me to continue this work.
In this paper, the EMD approach is now elaborated to swing
trading. For the convenience of the reader, the EMD algorithm
and the EMD moving average are recalled. This builds thebasis to introduce the EMD Oscillator, present its computation,and the generation of buy and sell signals. Furthermore, therecommended settings for the oscillator are provided, as well
as a quantitative distinction between “oversold” and “veryoversold.” The usage of this indicator is shown by presenting
two swing trading strategies based on this new oscillator.

Introduction

Based on Charles Dow, there are three trends in the market.
He illustrated the primary trend as the tide of the sea, thesecondary reaction as the large waves of the sea (swell), and thedaily fluctuations in the markets correspond to the ripples of thewater (wind sea). Having this analogy in mind, it makes sense to
apply results from hydrospheric research to technical analysis.
To eliminate the disturbing interference of sea waves from
data, researchers from several hydrospheric research institutes(Huang and others 1998) developed the Empirical Mode
Decomposition (EMD). A first adoption of the EMD to financial
price series has been performed by Dürschner (2014), but there
was still the need for further adaptions. These are presented inReiss (2019) and, with regard to trading, that paper was focusedon trend following approaches, hence investing in the primary
trend. However, it did not cover how to trade the secondary
reactions, and the current paper will close the gap to EMD based
swing trading.
To recapitulate the EMD, a characteristic example is shown.
The result is a decomposition of a financial time series into thebasis trend and several smooth modes (waves) which are called
Intrinsic Mode Functions (IMF). The IMFs of a decomposition
are ordered. The wavelength and amplitude of the IMF are
increasing with the order of the IMFs. The algorithm to obtain
this decomposition is empirical, hence driven only by the input
data without further assumptions. For the convenience of thereader, the EMD algorithm based on the previously cited results
is recalled.

+49 175 5613395
oliver-reiss@freenet.de

One application of the EMD is recalled, namely theconstruction of a moving average (EMDMA). The fundamental
idea of any moving average is to smooth the price over a certain
period. Using the EMD one can construct a moving average
which erases the smaller waves in the price signal which are
identified as the IMFs with a lower order.
Typically, a swing trading approach is based on overboughtor oversold states of the market, indicated by an oscillator.
Following the definition of the Commodity Channel Index,
which is given as a scaled difference of the price and its moving
average, the EMD Oscillator is defined by two steps. At first, thedifference of the price and the EMDMA is computed. Secondly,
this difference is rescaled by its average amplitude. This result
is the EMD Oscillator which oscillates around zero and, likethe Commodity Channel Index, the EMD Oscillator exceeds
the values of -1 or 1, which are important trigger lines. The
mathematical algorithms needed for all computations used inthis paper can be found in standard literature (e.g. Press andothers 1992), and the computation of the amplitude based on theHilbert transform is explained in this paper.
To illustrate the effectiveness of the EMD Oscillator, twoswing trading strategies are presented to complete the paper.
The first one is related to trade one instrument only (forexample the S&P 500 Index) and highlights the distinction
between “oversold” and “very oversold.” The second one
provides a short-term stock selection strategy, hence selecting
the most auspicious stocks, e.g., from the constituent equities of
the S&P 500 Index.

The Empirical Mode Decomposition
Characteristics of the EMD
Let us start with an introductive example. Figure 1 shows
the EMD of the S&P 500 Index over the period of one year. In
the top window, the S&P 500 is presented in black, and the bluelines represent the result of the EMD. The blue line in the top
window is the trend component and lies in the area of the S&P
500. The windows below show the Intrinsic Mode Functions(IMF) of the decomposition. These IMF fluctuate around zero
since all maxima are positive and all minima are negative.
With increasing order, the IMFs become smoother, and theiramplitude and their wavelength increases.

IFTA.ORG PAGE 43

IFTA JOURNAL

2022 EDITION

Figure 1. An example of the Empirical Mode
Decomposition

Hence, the IMFs are designed to cover non-stationary waves
in the market. The wavelengths and amplitudes vary overtime for each IMF. Therefore, the EMD can be regarded as a
generalization of the classical cycle theory which comes clear
if we recall the five principles of cycle theory and check themagainst the IMFs:• Summation: The price movement is exactly explained by
the movements of all underlying waves (IMFs) and the trend
component.
• Proportional: Each subsequent IMF has an increased
wavelength and amplitude.
• Synchronization: Often a high or a low of an IMF wave
corresponds with a high or low of its preceding IMF, but thisproperty does not hold strictly.
• Constant cycle length: The wavelength or amplitude of an
IMF is not constant over time, but usually of similar order.
• Harmonics: The wavelength of an IMF is not an integer
multiple of its preceding IMF. As a rule of thumb, it is often afactor between two and three.
EMD Algorithm
Typically, the technical analyst starts the analysis from thelarge timescale and refines the analysis by breaking down thetime frame. The EMD works the other way around. The smallest
wave is extracted at first and the next iteration identifies thesmallest remaining wave, and so on until all waves have been
segregated. The core algorithm is shown in the flow chart(Figure 2). The initial signal is the price series and as long as
the signal includes a wave, a so-called sifting process is applied
until an IMF has been isolated. The determined IMF is stored
and subtracted from the input signal and this decomposition
will be repeated until the remaining signal is not wavy anymore.
Finally, the remaining signal gives the trend component, and thecomplete decomposition consists of this trend component andall identified IMFs.

Figure 2. Flow chart of the EMD algorithm

By construction it is clear that the sum of all IMFs and thetrend component yield to the original input, since at the endof each iteration of the outer loop (blue) the identified IMF issubtracted from the input signal and the result is the input for
the next iteration. Hence the following relation holds, where N
denotes the number of identified IMFs:

The inner loop of the algorithm, which is shown in red in theflow chart, is used to identify the next and smallest available
wave from the data. This wave will be the next IMF and issegregated by multiple application of the sifting process. The
stopping criteria for the iteration of the sifting process is given
by Reiss (2019):• The sifting process has been performed at least five times,
and• all local maxima of the IMF are positive, and all local minimaof the IMF are negative.
Sifting Process
The essential part of the EMD algorithm is the sifting process,which is used to identify the wave with the shortest wavelengthfrom the signal. To explain the sifting process by using terms
from the technical analysis, at first some bands are determinedto capture the input signal, then an average is defined by thearithmetic mean of the upper and lower band. The difference
between the input signals the average results in an oscillator,
which is the result of the sifting process.
Including the additional boundary conditions introduced inReiss (2019), the mathematical and precise definition of thesifting process is given by the following steps:
1. Identify the upper band
The upper band is defined as the cubic spline with natural
boundary conditions supported by all local maxima of thesignal and two points at the left and right edge. Their value
is given by the maximum of the signal at the edge and thenearest local maximum.
For the definition and an algorithm to compute a cubic spline,
see Press and others (1992).

PAGE 44 IFTA.ORG

IFTA JOURNAL

2. Identify the lower band
According to the upper band, the lower band is computed as
the cubic spline with natural boundary conditions supportedby all local minima of the signal and two points at the left andright edge. Their value is given by the minimum of the signal
at the edge and the nearest local minimum.

2022 EDITION

Figure 4. The S&P 500, the corresponding EMDMA(6), andthe standard SMA(200)

3. Calculate the mid line
The mid line is computed as the arithmetic mean of thepreviously identified upper and lower band.
4. Determine the potential IMF
The potential IMF is obtained as the difference of the input
signal and the mid line. If the result is not an IMF or thesifting process has not been iterated at least five times,
this potential IMF serves as input signal for the next sifting
process.
To clarify the sifting process, the first iteration of the sifting
process is shown in Figure 3 inspired by the example of Kim
and Oh (2009). From the input signal (blue line), the upper andlower band are identified as cubic splines (red lines) based on
the local maxima/minima of the signal and the additional points
defined at the boundary. The average of both splines is the midline (black line). The difference between the input signal (blueline) and the mid line (black line) is the result of the sifting, thepotential IMF (green line).
Figure 3. Explaining one iteration of the sifting process

One Sifting iteration:
From input signal to the potential IMF

One simply identifies two important differences between thetwo moving averages:
1. In periods of a strong upward trend, the price is locatedabove the SMA while the EMDMA is always located in thearea of the price action—even in trending phases. That isclear from the definition, since the EMDMA is the price minus
some IMFs which fluctuate around zero by definition.
2. After a correction, the EMDMA usually turns faster frombeing falling to rising than the SMA. This point inspired
Dürschner (2014) for a simple interpretation of the EMDMA.
A rising EMDMA is a long signal. A falling EMDMA is a short
signal. A trading strategy and its backtest based on this idea
is analyzed in Reiss (2019).

The EMD Oscillator
Motivation and Definition
The EMD Oscillator is inspired by the well-known Commodity
Channel Index (Lambert 1980) which is defined by:

8
6
4
2
0
-2

1

5

9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77 81 85 89 93 97
input signal

top spline

low spline

mid linepotential IMF

The EMD Moving Average
Definition of the EMDMA
Generally, a moving average is used by a technician to smooth
any time series. From the characteristics of the EMD it becomes
obviously clear that this task can also be performed by thistechnique. To remove the smaller “ripples” of the market from atime series, one can just subtract the low order IMFs. That’s thedefinition of the EMDMA:

Properties of the EMDMA
For a deeper understanding of the EMDMA, Figure 4 shows
the S&P 500, the corresponding EMDMA(6), and the classicalsimple moving average of 200 days. The parameter value of six
for the EMDMA has been chosen to let the EMDMA swing in asimilar fashion as the simple moving average.

In this formula, MA is the moving average of the price and MD
denotes the absolute mean derivation of the price with respect
to its simple moving average. Traditionally, price denotes the
typical price which is given by the average of the high, low,
and close quote. Of course, the CCI could also be computed on
close quotes only and can be summarized as scaled difference
between the price and the moving average.
This summary also holds for the EMD Oscillator; but now—as
one might expect—the moving average is given by the EMDMA
and the scaling will be adopted to the techniques used in thecontext of the empirical mode decomposition:

Using the definition of the EMDMA, this can be simplified toand the scaling is given by A(m, n, t), the average over m periodsof the amplitude of. The computation of thisamplitude will be presented in a later section.
Even if the EMDOSC is defined similar to the CCI, there is one
essential difference. Lambert designed the CCI originally as a
IFTA.ORG PAGE 45

IFTA JOURNAL

2022 EDITION

trend following index: buy if the index is over 100 and exit if
it falls below 100. This approach is based on the idea that in astrong upward trend the price is far above its moving average.
Nowadays, the CCI is also often interpreted as an oscillator: amarket is oversold if the CCI is below -100 and overbought if the
CCI is above 100.
Since the EMDMA stays always in the area of the price action
as discussed before, the EMD Oscillator can only be interpreted
as oscillator. Due to its scaling based on the average amplitude,
the typical range of the oscillator is between -1.0 and 1.0, but it
will exceed this range regularly. If the EMDOSC is less than -1.0,
the market is oversold, and if the EMDOSC is larger than 1.0, it
is overbought. Furthermore, the EMD Oscillator also provides
a quantitative measure to state a “very” oversold (overbought)
market condition if the EMDOSC is below -2 (above 2).
Parametrization
As explained, the EMD Oscillator cannot be used for trend
following and is hence designed to support swing trading. Prior
to trading, we have to care about its parametrization, hence thenumber of IMFs to consider. In this respect, there is a conflict of
two objectives:• The larger the number of IMFs used, the larger is the wave tosurf, hence a larger n should be considered.
• The smaller the number of IMFs used, the shorter is theholding period yielding to more trading opportunities, hence asmaller n should be considered.
For a successful trading, other aspects also need to beconsidered. At first, a too volatile trading might be too
expensive. Secondly, economic research has shown that due
to psychological effects of the market participants, the pricemovements are mean-reverting in shorter timeframes, but
surveys of longer periods also show that the price action istrendy. Usually, trend following techniques start to work out if ahorizon of six months or more is considered. For very long timeframes (roughly starting at three years), markets often behave
mean-reverting again, that is related to business cycles and thelong-term consideration of fundamentals (value-investing).
After considering all these facts, the idea is to take a larger
number of IMFs, but the wavelength of the largest IMF toconsider should be clearly less than six months. Therefore, thestandard parameter for the number of intrinsic mode functions
used for the EMD Oscillator on daily data is given by four (n=4).
Since the EMD is designed to detect non-stationary waves,the amplitudes of the IMF vary in time. For the computation of
the EMDOSC, the parameter m needs to be fixed: the number ofdays used to compute the average of the amplitude. To facilitate
the computations, m should be a power of two, and to match to
the larger waves, the period to average the amplitude should belarger than a month. For that reason, the default choice is m=32.
Throughout this paper, only this default setting (n=4 andm=32) is used. Each empirical mode decomposition is performed
on a moving time window based on a 3-year horizon.

PAGE 46 IFTA.ORG

Trading Signals
Figure 5. The S&P 500 and the corresponding
EMDOSC(4,32) with the -1 and +1 thresholdTo get an impression of the EMD Oscillator, an example isshown in Figure 5. The underlying in this example is the S&P
500 Index. The indicator oscillates around 0 and exceeds thevalues of -1 (oversold area) and 1 (overbought area). In rarecases, the absolute value of the EMD Oscillator exceeds 2—inthis case one can define the market as “very overbought” or“very oversold.” Oscillator values far below -1 are especiallyeasy to understand: The amplitude which defines the scaling of
the oscillator is obtained by an average of 32 days. During an
intensive downturn the volatility in the markets often increases
and hence the scaling needs some time to catch up.
Keeping the market wisdom “overbought does not mean it’sover” in mind, the signals are not generated by entering theoverbought or oversold area, but by leaving them. A buy signal
is triggered when the oscillator crossed the -1 level from below
and a sell signal is triggered if the oscillator crossed the 1 fromabove. To analyze, if this approach is effective, a trading system
based on this simple rule is presented below.

Computation of the Amplitude Using
the Hilbert Transform
The Amplitude of Oscillations Centered at Zero
The Hilbert transform is a linear transformation which
provides for a given oscillation, another oscillation with thesame amplitude, and the output is orthogonal to the input.
Simple closed form examples are:

Let X(t) be an oscillation centered at 0 and define Y(t):=H{X(t)},then the amplitude A(t) is given by:
Example: Let X(t)=cos(ω t), hence Y(t)=sin(ω t) and theamplitude of cos(ω t) is 1 as expected, since:IFTA JOURNAL

The Scaling of the EMD Oscillator
In the case of the EMD Oscillator, the input X(t) is an
oscillation centered at zero by definition.

and let Y(t):=H{X(t)} be its Hilbert transform. This computation
is usually based on the last m data points of X denoted by Xi andthe result of the Hilbert transform. Y also has m data points Yi .
The amplitude used for scaling the EMD Oscillator is given by:

The Amplitude of Non-Centered Oscillations
To complete the discussion, and as a warning remark, one
should note that the property of an oscillation to be centeredat zero is necessary. So let X(t)=1+cos(ω t) then its Hilberttransform is given byY(t):=H{1+cos(ω t)}=H{1}+H{cos(ω t)}=sin(ω t)anddoes not yield to the correct amplitudeof one.
In such situations, the Hilbert transform needs to be applied
twice to obtain the amplitude of X(t):Fortunately, for the computation of the EMD Oscillator
we have to compute the amplitude of a sum of IMFs which iscentered at zero. Hence, there is no need to compute the Hilberttransform twice to determine the amplitude.

2022 EDITION

others 1992), which is the reason to choose the number of data
points as a power of two.
1. Compute the Fourier transform of X.
2. Multiply the result with +i for s>0, with –i for s<0, and with 0for s=0.
3. Compute the inverse Fourier transform of the previous result
to obtain H{X(t)}.

Swing Trading With the EMD
Oscillator
Trading the EMD Oscillator Signals on the S&P 500
As already stated, a buy signal is triggered if the EMD
Oscillator crosses the level of -1 from below and a sell signal is
triggered when the EMD Oscillator crosses the level of 1 fromabove. This simple approach is the basis for this trading system.
It is just augmented with a basic risk management. Whenevera buy signal is triggered and the financial instrument ispurchased, a stop loss order is established at the low of the last
five days. The position is closed either on stop loss or if the EMD
Oscillator triggers the sell signal.
This system is examined on the S&P 500 index from 2000 to
2020. Additionally, one could modify the system and accept only
the buy signals based on a “very oversold” state. Hence, if theminimum of the current downturn of the oscillators exceeds thelevel of -2.
The results of these trading approaches are listed in Table 1
and the equity curves are shown in Figure 6. The initial capitalfor the backtest was 100,000 USD and on every entry signal the
total available cash is invested. There are no transaction costs,
interest, or dividend payments considered.
Figure 6. The equity curve of the S&P 500 and the two
trading systems

Numerical Computation of the Hilbert TransformIn the following definition of the Hilbert transform theintegral is taken over the domain of X(t) and the integral should
be taken as Cauchy principal value:

This integral forms a convolution which can efficiently becalculated using the Fourier transform with this convention:

Due to the properties of the Fourier transform on
convolutions for the first equality, and some integral
computations for the second equality, we obtain:
This formula provides the complete guide for the computationof the Hilbert transform of X(t) by utilizing the Fouriertransform. For numerical applications, the Fourier transform isoften calculated based on the Fast Fourier Transform (Press and

The results show clearly that both systems have a considerable
reduced drawdown than the buy and hold approach. The system,
which by every signal provides enough signals to outperform theindex, and the second system, which only buys the very oversold
signals, has too less trading opportunities (only about two peryear), so that there is no outperformance achieved even if thewinning rate of this system is higher compared to the system
investing at each long signal.
To utilize the higher hit rate of the second system andcombine it with the first system, one could create a new system
IFTA.ORG PAGE 47

IFTA JOURNAL

2022 EDITION

which uses the information on the state “oversold” or “veryoversold” for the money management. Every long signal of
the EMD Oscillator is used, the stop loss is considered at the
low of the last five days, there is a full investment for the“oversold” signals, and the investment is leveraged up forthe “very oversold” signals by an equally sized investmentin the S&P 500 future, hence the leverage is two if the EMD
Oscillator went below -2 in the current move. Due to the partial
leverage, the return is drastically improved for the costs of ahigher drawdown in this case, see Table 1. But even this higher
drawdown is still significantly lower compared to the buy-andhold approach.
The equity curves shown in Figure 7 confirm the effectivenessof the idea to link the minimum level of the EMD Oscillator ateach downturn to the money management of the combined
trading system.

Figure 7. The equity curves of S&P 500, the previous
systems, and the combined system

Table 1. The statistics of the systems traded on the S&P 500 index
Trade Count

Percentage Profitable Average Profit Per Trade

19.6%

169

37.9%

1.26%

220,257 USD

15.9%

39

48.7%

2.05%

1,619,264 USD

30%

169

37.9%

1.66%

SystemFinal Equity

Maximum Drawdown

Buy-and-Hold

256,554 USD

57.6%

All Long Signals

829,879 USD

Very Oversold Only
The Combined System

Buying the Most Oversold Stocks

Besides trading of a certain instrument, there is thealternative approach to select the instruments to invest infrom a given set. Such selection strategies are well known andworking strategies in technical analysis, e.g., investing in thestocks with highest momentum was presented in Levy (1968)
and also the idea of buying the stocks with low volatility is alsoquite old (Haugen and Heins 1972). For this paper, a selection
strategy based on the idea of purchasing the most oversold
stocks based on the EMD Oscillator is introduced.
The basic idea of this system is based on the assumption thatthe stock price will return to its EMDMA since its level is basedin the center of the price action. Remember that the following
relationship holds:
EMDMA = Price – Amplitude * EMDOSC
Hence from the calculation of the EMD Oscillator, the levelof the corresponding EMDMA is also known. Since the current
level of the EMDMA is the price target, the expected return isgiven by:

The idea is now to purchase each day the stock with the highest
expected return. To be concrete, the basic set of stocks has beenchosen to be the constituents of the S&P 500 and the maximum
number of stocks to hold is set to 10. At each day where thenumber of current positions in the portfolio is less than 10, there
is one position to buy if there is at least one stock which• is not already in our portfolio, and• which is oversold, hence EMDOSC< -1.0.
PAGE 48 IFTA.ORG

If there are several stocks which meet this condition at one
day, the stock with the highest expected return is chosen. The
new position is either sold at the price target (take profit order)or four weeks after the purchase date (time stop). Based on thediscussion of the parametrization of the EMD Oscillator, themaximum holding period of four weeks becomes plausible.
To be honest, the following analysis of the strategy is not astringent backtest since it is performed based on the current
constituents of the S&P 500 and is therefore exposed to thesurvival bias. This shortcoming is consciously accepted since
the purpose of this paper is rather to present the range ofapplications for the EMD Oscillator than to provide an optimal
trading strategy.
The equity curve of this strategy is presented in Figure 8 andis starting at the beginning of 2000 with 100,000 USD raised to
7,666,244 USD at the end of 2020. The strategy turns out to berather risky. The high performance comes at the expense of ahigh maximum drawdown of 70%. To complete the statistics, theshare of profitable trades is about 58%.
Even if the return is clearly overestimated due to the survivalbias, this trading system is presented to provide an alternative
usage of the EMD Oscillator to select the most oversold stocks.

IFTA JOURNAL

Figure 8. The equity curves of S&P 500 and the mostoversold stocks system

Conclusion

In Reiss (2019), the EMD has been enhanced to utilize thismethod in technical analysis. The trading systems presented
in that paper were designed to apply the EMD in the context
of a trend-following investment approach. Since the EMD also
detects the smaller waves, it was necessary and obvious toelaborate this technique for swing trading too.
The characteristics of the EMD are presented and thedata driven algorithm is shortly summarized. The EMDMA is
also recalled and there is one important difference to otherbroadly used moving averages. Even in strong trend phases,
the EMDMA always stays within the area of price action. Dueto this property, the EMD Oscillator, which is defined along thelines of the Commodity Channel Index, can only be interpreted
as an overbought/oversold oscillator. Furthermore, also aquantitative definition of “very” overbought/oversold states canbe provided because the scaling of the EMD Oscillator is basedon the current amplitude of the oscillation.
The proposed default parametrization is well-suited for swing
trading and is based on the fact that there is a mean reversion
property in financial time series on shorter time frames. Thisdefault parametrization is also used for the backtest of two
trading strategies which demonstrate the usage of the EMD
Oscillator. The first strategy combines the EMD Oscillator witha stop-loss based risk management to trade one instrument
only and it is also shown that the characterization of themarket state as “oversold” or “very oversold” can improve
the performance of the trading system, e.g., by using thisinformation in the money management applied. It is shown that
this strategy is superior to the buy-and-hold approach in termsof risk and return.
Another approach to use the EMD Oscillator is based on a“most oversold selection system” which buys each day the mostoversold stock of a certain market, if any, and to limit the riska time stop is applied. This approach ranks the stocks based on
the current oscillator value and the amplitude of the unscaled
oscillator. Just buy the stock with the highest expected return
based on the assumption that the stock will return to its mean
defined as the current level of the EMDMA.
Regardless if you prefer trend-following or swing-trading, inany case the EMD provides you the adequate tools to navigate
successfully through the financial markets.

2022 EDITION

References
Dürschner, Manfred G. Technische Analyse mit EMD. Wiley-VCH, 2014.
Haugen, Robert A. and A. James Heins. “On the Evidence Supporting
the Existence of Risk Premiums in the Capital Market”, Wisconsin
Working Paper 4-75-20, University of Wisconsin-Madison(December 1972).
Huang, Norden E., et al. “The empirical mode decomposition and theHilbert spectrum for nonlinear and non-stationary time series
analysis.” Proceedings of the Royal Society A, Vol. 454, 1998, pp.
903-995.
Kim, Donghoh and Hee-Seok Oh. “EMD: A Package for Empirical Mode
Decomposition and Hilbert Spectrum” The R Journal, Vol 1, May
2009, pp. 40-46.
Lambert, Donald R. “Commodity Channel Index: Tool for Trading Cyclic
Trends”, Commodities [now Futures] Magazine, October, 1980, pp.
40-41.
Levy, Robert A. The Relative Strength Concept of Common Stock Price
Forecasting, Investors Intelligence, 1968.
Press, William H., et al. Numerical Recipes in C: The Art of Scientific
Computing. Cambridge University Press, 2nd Edition, 1992.
Reiss, Oliver. “Empirical Mode Decomposition: Application to Financial
Time Series With Chart Projection.” IFTA Journal 2019, pp. 40-48.

Market 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).
Copyright ©2021 Dr. Oliver Reiss, CFTe, MFTA

IFTA.ORG PAGE 49

IFTA JOURNAL

2022 EDITION

Splitting Noise and Useful Signal in the
S&P 500 Members Correlation Matrix
By Carlos Jaureguízar, Ph.D., and Sandra Nieto

Abstract

Correlation matrices allow the estimating of the relationshipbetween the price movements of different assets, something
fundamental not only to estimate risks or create portfolios,
but also in order to interpret technical signals in an asset
historical data due to its relationship with other series and theirown technical signs. In this article, a way to filter the random
part out of the signal information in the correlation matrices
is established by the distribution of the eigenvalues of thecorrelation matrix of the S&P 500 members.

Motivation

As is shown in Murphy’s “Intermarket Technical Analysis…,”
there are important relationships between sectors and assetsthat a technical analyst must follow. One of the key metrics
widely used is the assets' historical prices correlation matrix. Of
course, this matrix is not only used in technical analysis, but in
portfolio construction, both with classic and modern machinelearning algorithms, risk management, and many other areas of
the financial sector. This broad exposure and use of correlation
between assets requires a methodology that allows removing, orat least reducing, any random element.

Random Matrices Theory (RMT)

Today, interest in large random matrices is high due to theirstriking practical applications. Although the beginnings of therandom matrices theory (RMT) can be found in the publicationof Wishart (1928), it was the work of the physicist Eugene
Wigner from 1955 that made it advance due to the usefulnessof certain types of matrices in the quantum mechanicalinvestigations applications in nuclear physics. To know more
about random matrices, Lal Mehta (1990) can be consulted.
As Bouchaud et al. (1999) states, “an important aspect of risk
management is the estimation of the correlations between theprice movements of different assets…The study of correlation(or covariance) matrices thus has a long history in finance.”
For this reason, the advances in the RMT aroused interest in
the financial field, and as of 1999 it took off after the publicationof the first works in which the correlation of financial assets
was related to the theory of random matrices by Bouchaud et al.
(2000) and Amaral et al. (1999). Since those papers, many others
have followed. A review of the state of the art is available atBouchaud et al. (2017).
As it is the subject of this article, in recent years financial
research has drawn attention over the need to split between
the (random) noise and the informative signal that exists incorrelation matrices.
Bouchaud et al. (2000) observed the results of:
PAGE 50 IFTA.ORG

Carlos Jaureguízar, Ph.D.
Robexia IA TechConsulting
Sandra Nieto
Robexia IA TechConsulting
info@robexia.com• Calculating a correlation matrix of the historical prices of the
S&P 500 companies.
• Studying the density of its associated eigenvalues.
They found that the bulk part of its spectral density can beassociated to purely random data: “In particular, the present
study raises serious doubts on the blind use of empiricalcorrelation matrices for risk management.”

Eigenvalues and Eigenvectors

The distribution of the eigenvalues ​​in a random matrix, as
the RMT describes, can be used to identify deviations from theexpected non-random elements or, in other words, useful signal
against random noise.
In order to give a very brief explanation, according to Malik(2019), “the eigenvector is an array with n entries where nis the number of rows (or columns) of a square matrix. The
below equation states that we need to find eigenvalue (λ)
and eigenvector (x) such that when we multiply a scalar λ(eigenvalue) to the vector x (eigenvector) then it should equal
to the linear transformation of the matrix A once it is scaled byvector x (eigenvector).”A*x=λ*x
It’s usual to represent eigenvalues as lambda (λ).

Marchenko-Pastur Law

Elaborating on the distribution of random matrices
eigenvalues, Plerou et al. (1999) found that the distributions ofmost of the eigenvalues of the empirical correlation matrices
correspond to what was expected by the random matrix theory.
They could be associated with simple randomness, but they saw
deviations for a few of the largest eigenvalues.
In this sense, to determine what part of the distribution would
correspond to signal information and what part to pure noise,
the use of the Marchenko-Pastur law (1967) has been proposed.
The Marchenko-Pastur theorem states that if the elements of amatrix are random, its eigenvalues will be distributed in a given
range and density. In this way, the eigenvalues that deviate fromthe expected theoretical Marchenko-Pastur distribution would
contain useful information, such as the number of non-random
factors (just by counting those eigenvalues). Not only that but
the eigenvalues could be used to clean up or filter the correlation
matrices, thus keeping the meaningful signal and reducing therandom useless and confusing noise.
To check this let’s see how it behaves in practice. Let’s createa random matrix R containing 10,000 rows and 1,000 columns
and compare:IFTA JOURNAL• The blue line: shows the density that the eigenvalue
distribution adopts when the elements of the matrix are
random according to the Marchenko-Pastur law.
• The orange distribution: eigenvalues of the random matrix R
are graphed thanks to the implementation of python’s scikitlearn kernel density estimation (KDE).1
In Figure 1 the eigenvalues of this random matrix are shownin orange and it can be seen that they accurately adjust to thetheoretical distribution, which means random elements.
Figure 1. Fit of eigenvalues o​ f a random matrix (orange)
to its theoretical density (blue)

2022 EDITION

Some eigenvalues of the matrix correspond to random
behavior (blue line range) and others to non-random behavior.
In other words, a part of the correlation matrix corresponds tonoise and another part to signal. The question that arises almost
immediately is how can we remove this random behavior?
Can we modify the matrix to get rid of these eigenvalues? The
answer is yes, by filtering or denoising it.
To help understand the denoising method, let’s change theway in which we see the same eigenvalues of the previous
figure. In Figure 3, the horizontal x-axis becomes the y-axis,
and the horizontal simply show the eigenvalues from the firstto the last (800).
Figure 3. Eigenvalues of previous random matrix (8000 *800) with some added signal

If this were the distribution of the eigenvalues of the portfolio’s
correlation matrix, it would provide no signal at all but purerandom behavior (noise). However, what happens when there issignal and noise? That is, what happens when part of the behaviorof the correlation matrix is ​random and another part is not?
Let’s generate a new random matrix (8000 * 800), as we havedone before, and add some signal—as is explained by López dePrado (2020)—to the correlation matrix, for example, with 100
signal factors. Following the same steps, in Figure 2 we get:Figure 2. Random matrix (8000 * 800) with some added
signalSupposing the variance σ is 0.8 instead of 1 (for a deeper
explanation see López de Prado [2020]), any eigenvalue above λ+corresponds to signal:

λ+ = 0.8 * (1 + sqrt(8000/800)) ^ 2 = 0.8 * (1.316) ^2 = 1.386
So, once ordered from lowest to highest, 700 corresponds tonoise (below 1.386, the λ+ level) and 100 to signal (above 1.386).

Correlation Denoising

There are several ways to clean (filter) matrices. As Bun et al.
(2016) quotes:
1. Basic linear shrinkage
2. Advanced linear shrinkage
3. Eigenvalues clipping (Bouchaud and Potters, 2011)
4. Eigenvalues substitution
5. Rotationally invariant, optimal shrinkage

Note: We have adjusted the variance to 0.8 for a better fit (consult
López de Prado [2020]).

According to Bouchaud and Potters (2011), a way to denoise
the matrix is keeping the top eigenvalues (all above theMarchenko-Pastur upper edge λ+) and shrink the others to a
constant one.

Practical Case: S&P 500 Members
Correlation Matrix

To carry out this research, the closing prices of the S&P 500
members have been used from approximately five years sinceJune 1, 2016. Once insufficient data assets and dates have been
removed, the logarithmic returns are calculated in a 1,349 x 474
matrix (1,349 dates and 474 assets).
IFTA.ORG PAGE 51

IFTA JOURNAL

2022 EDITION

The red line shows the theoretical distribution of the random
eigenvalues according to Marchenko and Pastur (1967) and the
distribution of the empirical correlation matrix, as can be seen,
and assuming that the variance for all of the standardized log
returns is 1 (σ = 1).

Figure 5. Comparison of eigenvalues before and after
denoising

The maximum theoretical eigenvalue is 2.537, so there are 18
eigenvalues higher than the maximum level:[4.626, 3.748, 3.681, 3.457, 3.297, 3.115, 3.0476, 2.915, 2.883,
2.834, 2.818, 2.777, 2.762, 2.695, 2.674, 2.626, 2.576, 2.567]
and 456 eigenvalues related to noise.
Figure 4. Empirical correlation S&P 500 members’
eigenvalues distribution vs. Marchenko-Pastur

So, in order to denoise the correlation matrix, let’s substituteall the 456 eigenvalues by a constant one, like the average,
0.91864.
After doing that we must reconstruct the covariance and thecorrelation matrices to get a filtered one.
Again, we follow López de Prado (2020). So, being:• eVec: Correlation matrix eigenvectors• eVal: New eigenvalues (keeping the top ones and shrinking
the others to a constant one average)• eVec’ = eVec.T = Trasposed eVec matrix

Or, using python code:
covariance = np.dot(eVec,eVal).dot(eVec.T)
That is, the covariance matrix than can be easily normalized
into a correlation matrix.
Note that getting the eigenvectors and eigenvalues in Excel ispossible, but there are no direct functions so some VBA code or add-in
may be used. Once the eigenvalues and eigenvectors are set, just direct(but array) formulas can be used to denoise the matrix.2
Let’s plot the results.

PAGE 52 IFTA.ORG

Although there are some criticisms about the denoising of
the correlation matrices—“However, this cleaning overlooks thefact that the large empirical eigenvalues are overestimated,”(Bun et al., 2016) and “However, ‘no information’ or ‘pure noise’
assumption in the bulk region is too strict…the residuals from real
data are not necessarily pure noise, and more general correlation
structure needs to be considered to assess the empiricaldensities,” (Papanicolau and Yeo, 2016)—many researchers defend
its use, as is the case of López de Prado (2020).
“Working with denoised and detoned covariance matrices
renders substantial benefits. Those benefits result from themathematical properties of those treated matrices and can beevaluated through Monte Carlo experiments.” Furthermore,
he analyzes the case of two characteristic portfolios at theefficient frontier, such as the minimum variance and maximum
Sharpe ratio, concluding a very significant improvement of theroot-mean-square errors (RMSE) across all weights when thecorrelation matrices are denoised (López de Prado, 2020).

Conclusion

In the field of financial markets, asset correlation matrices
are widely used to establish the relationship between theevolution of their prices. However, since signal-to-noise ratioin financial data sets is very low, prior filtering of the matrix
is recommended. This technique, known as denoising, isperformed according to the Marchenko-Pastur law.
Explanatory Note on the Use of Python
Although the fact of using Python (or another similar
language) could be a handicap for the dissemination of thismethodology, two things may be said:
1. Being strict, Excel could be used, but with a large numberof array formulas or array code that make it somewhat
uncomfortable. Additionally, the calculation of theeigenvalues and eigenvectors is more complex, but possible.
2. Although programming requires knowledge and experience, theuse of a third-party code, for example in Python, is not complex.
Unix and Apple come with Python by default, while Windows
requires a relatively simple installation. The repository, both forthe code and an explanation of the Python installation, can beaccessed at www.github.com/Robexia/Denoising.
Both López de Prado (2020) and Rome (2016) offer usefulsnippet code, although they differ in some aspects, especiallyin the way in which the denoising of the correlation matrix is ​​carried out.

IFTA JOURNAL

References
Amaral, L.N., P. Gopikrishnan, V. Plerou, B. Rosenow, and H. E. Stanley.
"Universal and non-universal properties of cross-correlations infinancial time series," Physical Review Letters, 83:1471{1474, (1999).
Bouchaud, J.P, J. Bun, and M. Potters. "Cleaning large correlation
matrices: Tools from random matrix theory," Physics Reports, 666:1109 (2017).
Bouchaud, Jean-Philippe, Pierre Cizeau, Laurent Laloux, and Marc
Potters: "Noise Dressing of Financial Correlation Matrices," PhysicalReview Letters 83(7), 1467 (1999).
Bouchaud, Jean-Philippe, Pierre Cizeau, Laurent Laloux, and Marc
Potters. "Random matrix theory and financial correlations,"
International Journal of Theoretical and Applied Finance, Vol. 3, No. 3,
pp. 391–97 (2000).
Bouchaud, Jean-Philippe and Marc Potters. The Oxford Handbook of
Random Matrix Theory: Chapter 40 Financial Applications (2011).
Bun, Joël, Marc Potters, and Adam Rej. "Cleaning correlation matrices."
Risk Magazine (April 2016).
Jones, M.C. and B.W. Silverman. "E. Fix and J.L. Hodges (1951): An
Important Contribution to Nonparametric Discriminant Analysis
and Density Estimation: Commentary on Fix and Hodges (1951)."
International Statistical Review / Revue Internationale De Statistique,Vol. 57, no. 3, 1989, pp. 233–238.
Lal Mehta, Madan: Random Matrices, 2nd Edition. Academic Press(1990).
López de Prado, M. Machine Learning for Asset Managers (Elements in
Quantitative Finance). Cambridge: Cambridge University Press,(2020). doi:10.1017/9781108883658
Malik, Farhad. "What are Eigenvalues and Eigenvectors?" (Jan 2019).
https://medium.com/fintechexplained/what-are-eigenvaluesand-eigenvectors-a-must-know-concept-for-machine-learning80d0fd330e47.
Marchenko, V.A. and L. A. Pastur. "Distribution of eigenvalues for somesets of random matrices," Matt. USSR-Sbornik, 1:457486 (1967).
Murphy, John J. Intermarket Technical Analysis: Trading Strategies for the
Global Stock, Bond, Commodity, and Currency Markets (1991).
Papanicolaou, George and Joongyeub Yeo. “Random matrix approach toestimation of high-dimensional factor models” (2016).
Rome, Scott. "Eigen-vesting III. Random Matrix Filtering in Finance."
March 30, 2016. https://srome.github.io/Eigenvesting-III-RandomMatrix-Filtering-In-Finance/.
Rosenblatt, Murray. "Remarks on Some Nonparametric Estimates of a
Density Function," Ann. Math. Statist. 27 (3) 832 - 837, September,1956. https://doi.org/10.1214/aoms/1177728190.
Wishart, J. "The generalised product moment distribution in samples
from a normal multivariate population," Biometrika, 20A, 32–2.
(1928) https://doi.org/10.1093/biomet/20A.1-2.32
Wigner, E. "Characteristic Vectors of Bordered Matrices with Infinite
Dimensions, Ann. of Math. 62, 548-564 (1955).

2022 EDITION

Notes
1

In statistics, kernel density estimation (KDE) is a non-parametricmethod that estimates the probability density function of a randomvariable from some observations (called sample). It was proposedby Rome (2016) and Silverman and Jones (1951). There are numerous
ways to implement it in Python, for example, using the SciPy,
Statsmodels, Scikit-learn, or seaborn libraries.

2

Array formula is a special type of formula that must be entered by pressing
Ctrl+Shift+Enter in a range.

IFTA.ORG PAGE 53

IFTA JOURNAL

2022 EDITION

Michael A. Gayed, CFA

Actively Using Passive Sectors to Generate
Alpha Using the VIX
By Michael A. Gayed, CFA

Abstract

A significant amount of academic research has documented
momentum within and across broad sectors of the stock market
as a means of generating alpha over a passive benchmark.
However, few studies approach sector allocation from a mean
reversion perspective using the Chicago Board of Exchange(CBOE) Volatility Index (VIX) as the trigger. We find that
positioning into defensive sectors during periods of low
volatility for the stock market, and into cyclical sectors during
periods of high volatility, produces significant long-term alpha.
Using this framework, we backtest a dollar-neutral strategy
documenting return differentials and create a modified S&P 500
Index that overweights and underweights cyclical and defensive
sectors systematically based on VIX levels. Absolute and relative
returns for a sector allocation strategy that uses VIX levels
significantly outperforms a passive buy and hold approach byusing mean reversion to generate alpha. We postulate that theapproach likely works because of behavioral biases related toloss aversion and the disposition effect creating mispricingsthat are repeatable and exploitable during periods of extreme
market stress.
All rights are reserved. This publication is the sole propertyof Lead-Lag Publishing, LLC. You may not copy, reproduce,
distribute, publish, display, perform, modify, create derivative
works, transmit (in any form of by any means), or in any way
exploit any such publication. Further, you may not distribute,sell, or offer to sell, or store this publication. You may notalter or remove any copyright or other notice from copies ofthis publication. Copying or storing this publication except asprovided above is expressly prohibited without prior written
permission of the Lead- Lag Publishing, LLC. For permission
to use the publication, please contact michaelgayed@
leadlagreport.com.

Introduction

The Efficient Market Hypothesis is at the core of all
traditional arguments for buy and hold investing. Because
this theory postulates that all information is known andfactored immediately into price, active asset allocators andtraders cannot possibly outperform or have any analyticaledge.1 A major assumption for the Efficient Market Hypothesis
to hold, however, is that market participants are on average
rational and do not exhibit behavioral biases that cause overor underreactions in current price. We know from numerous
academic studies that this simply is not true.2 Market
participants exhibit clear patterns of irrational responses toalready known data, allowing for exploitable opportunities
and alpha generation through the identification of near-term
PAGE 54 IFTA.ORG

c/o NAAIM Founders Award
6732 W. Coal Mine Avenue #446
Littleton, CO 80123+1 (888) 261-0787
michaelgayed@leadlagreport.com
www.naaim.org

activity driven by emotion.
Active traders and asset allocators inherently attempt
to exploit repeatable human behavior to create a betterrisk-adjusted return profile for their portfolios. One welldocumented anomaly traders often focus on is momentum.
Underreaction to positive news is often cited as the reason
for why the momentum anomaly exists. Investors may be
exposed to all data points that impact valuation, but the gradual
diffusion of information, and hesitation to aggressively positionbullishly into a particular segment of the market creates
persistence in price movement and ultimately forms trends.
Conversely, overreactions to all available information tend
to present themselves during periods of heightened fear andrisk of loss. Prospect theory3 argues that individuals do not
act rationally and value gains and losses differently, creating abias toward loss aversion and a stronger emotional response to
declining stock prices than advancing ones. Put simply, a dollar
of loss is felt more strongly than a dollar of gain.
Fear of loss, rather than hope for gain, is where the mostaggressive mispricing occurs when it comes to investing andis most felt during periods of heightened volatility for thestock market. Perceived risk during corrections and crashes
often results in panic selling, usually at the wrong time, asloss aversion dictates actions more than any Efficient Market
Hypothesis ever could. While it may be cliché to say that mostinvestors tend to “sell bottoms,” the reality is that there is ample
evidence proving that market participants often act defensively
after a decline in asset values has already taken place, sellingwinners and holding on to losers.4
Buy and hold index investors will argue that this is exactly
why buy and hold works. If you don’t care about near-term
volatility, you don’t risk selling at the wrong time, and as such,are better off in the long run. As investing legend Peter Lynch
once said, “far more money has been lost by investors preparing
for corrections, or trying to anticipate corrections, than has
been lost in corrections themselves.” However, this is only
correct if the execution for preparing for a correction is wrong.
It is the “preparation for a correction” that must be definedproperly. If Black Swans5 are considered unpredictable and are
the catalyst for severe losses in markets, then the objective foractive managers shouldn’t be to try to anticipate exactly whena correction or crash is set to take place. Rather, it would makemore sense to position oneself defensively in case there is avolatility spike and collapse in markets while still maintaining
beta exposure, and then increase that beta exposure atlower prices when overreactions create discounted buying
opportunities.

IFTA JOURNAL

Sector Momentum and Crashes

One of the most studied and well-known anomalies thatcounters the Efficient Market Hypothesis is the existence of
momentum and autocorrelation in asset prices. Moskowitz andGrinblatt in 1999 documented the persistence of returns at the
one-month interval6 across stocks and notably on the sector andindustry level, while other studies show that other asset classes
also exhibit such patterns.7 As sectors and industries advance,
they tend to continue to advance because they already have,allowing active traders to take advantage of trends and pricedrift.
While momentum continues to be an observable andexploitable phenomenon, it certainly is not guaranteed nor
risk-free. Momentum as a factor for generating alpha is prone
to periodic “momentum crashes,” which can create “infrequentand persistent strings of negative returns. These momentum
crashes are partially forecastable. They occur in panic states,
following market declines when market volatility is high, andare contemporaneous with market rebounds. The low exante expected returns in panic states are consistent with aconditional high premium attached to the option like payoffs
of past losers.”8 Momentum studies when evaluating sector
allocation strategies tend to not put the anomaly in the context
of volatility and environments of heightening uncertainty forthe stock market. The objective is not to buy low and sell high,but instead buy high and sell higher. Continuously chasing thebest-performing sectors works until the inevitable volatility
spike and crash takes place.
A different approach to sector positioning is to not consider
momentum at all when over or underweighting against abenchmark’s passive positioning. Sectors and industries may
explain why momentum exists, but behavior explains why
sectors get mispriced after volatility spikes. These volatility
spikes may be unpredictable, but the mispricing that occurs
in cyclical sectors following severe panic states for the stock
market is the exact opportunity active traders should befocused on. Positioning defensively in advance of high volatility
periods through lower beta sectors like Utilities, Consumer
Staples, and Healthcare allows for protection prior to whenunpredictable losses occur. As losses and volatility increase tounsustainable levels, the positioning out of defensive sectors
into cyclical ones presents an opportunity to buy into panic andbenefit from a return to normalcy, until the pattern repeats
and defensive positioning during excessively low periods ofvolatility is warranted again.

Deconstructing the VIX

The CBOE Volatility Index, better known as the VIX, isan index designed to measure the market’s expectations
for volatility over the following 30 days. It does this using
the CBOE’s S&P 500 index derivatives contracts. Originallyenvisioned as a means of simply measuring volatility
expectations using the S&P 100 index, the VIX has become thepremier benchmark for U.S. stock market volatility. It is citedby numerous financial media outlets as the “fear index” andhas spawned a number of tradable products using it as theunderlying index, including exchange-traded funds (ETFs),
exchange-traded notes (ETNs), and options contracts.92022 EDITION

Many traders and investment managers use the VIX as part oftheir decision-making processes. Historically, there has been astrong negative correlation between stock market performanceand the VIX (see Chart 1). This is demonstrated by looking at
daily returns in the S&P 500 index in relation to daily changes inthe VIX.10
Chart 1. Daily VIX and stock market correlation

From 1990 through 2018, significant daily losses in the S&P
500 have been strongly linked to short-term spikes in the VIX.
The same correlation also exists when viewing S&P 500 returns
and VIX changes on a monthly basis (see Chart 2).
Chart 2. Monthly VIX and stock market correlation

Which of the two factors is more causal in this relationshipis unclear, but loss aversion could be explanatory. Investors
have a tendency to want to avoid losses more than generate
gains. In practice, investors seeing sharp declines in financial
markets often rush to sell before any further losses occur. The
disposition effect11 argues that investors sell their winners
before their losers, and often times the winners before a VIX
spike and decline in stocks are high beta/cyclical areas of thestock market. The overreaction takes place and brings with
it an anomaly to exploit, but not often. Volatility spikes andcorrective environments for stocks, while painful, are relatively
infrequent. VIX levels more often than not stay in a range of
12 to 24 and experience extremes at tails that are few and far
between (see Chart 3).

IFTA.ORG PAGE 55

IFTA JOURNAL

2022 EDITION

Chart 3. Range of VIX levels historically

Sector Returns and VIX Levels

Since high levels of market volatility, using the VIX as the benchmark, are closely tied to negative equity returns, we theorizethat spikes in volatility could produce “buy low” opportunities in certain segments of the market. In Benjamin Graham’s book The
Intelligent Investor, the author discusses how investors should expect volatility when investing in equities and to use volatility to theiradvantage. He uses the example of “Mr. Market,” a hypothetical investor who is overly emotional and reactive to prevailing sentimentinstead of relying on the underlying fundamentals of any given security. Graham argues that during periods such as these, securities
can become either overbought or oversold, thus creating an opportunity for outperformance.12
We test this theory by examining the forward-looking returns of specific sectors of the market during various periods of market
volatility, as measured by the VIX. In Tables 1 and 2, we use a rolling 14-trading day average for the VIX to smooth out some of the daily
fluctuations and examine sector-level forward returns both 200 trading days and 500 trading days out into the future.13
Table 1. Sector performance following VIX levels 200 days forward

We find that cyclical sectors, such as Technology, Industrials, Materials, and Consumer Discretionary, tend to outperform wheninvesting during periods of high volatility, while defensive sectors, such as Utilities, Consumer Staples, and Healthcare tend tounderperform. Conversely, there is a much less discernible trend when examining the starting points of low volatility.

PAGE 56 IFTA.ORG

IFTA JOURNAL

2022 EDITIONIn Table 2, we find similar results when examining 500-day forward returns.
Table 2. Sector performance following VIX levels 500 days forward

Again, the traditionally cyclical sectors deliver above-average performance during high volatility starting points while defensive
sectors underperform. Forward-looking returns in low- to moderate-volatility periods yield only modest differences across sectors.
Given the more notable performance differences in high-volatility periods, we theorize that by overweighting cyclical sectors andunderweighting defensive sectors in these high-volatility periods, we can achieve significant alpha in comparison to the S&P 500 index
by waiting for such periods to take place and acting afterwards.

Sector Returns During Market Corrections

There is a generally held belief among investors that defensive and safe-haven assets, such as Treasury Bonds, Utilities, and Gold,tend to outperform during times of market turmoil. We find that regardless of whether the economy is in recession, if there is asignificant correction in equity prices and levels of volatility are elevated, this flight to quality into traditionally defensive sectors
and out of cyclical areas does indeed occur. However, different sectors can experience greater impacts depending on the nature of themarket environment at the time.

IFTA.ORG PAGE 57

IFTA JOURNAL

2022 EDITIONIn Table 3, we detail broad market and sector returns during five periods of significant equity market declines.14
Table 3. Sector returns in major market declines

The two recessionary periods were marked by severe underperformance in the sectors largely attributed to causing the recession.
During the dot-com bubble, Technology was a massive underperformer. During the financial crisis, it was Financials that were thebiggest losers. Outside of those two sectors in those recessions, we can conclude that defensive sectors, such as Utilities and Consumer
Staples, outperformed the S&P 500, but the remaining sectors were inconsistent in their returns.
In the three non-recessionary periods measured, however, there are more distinct patterns of defensive and cyclical sector
performance. We note that Utilities and Consumer Staples were strong outperformers and beat the S&P 500 by at least 9% in
all measured periods. The more traditional economically cyclical sectors, such as Financials, Materials, Energy, and Industrials,
underperformed in 11 of the 12 instances. The consumer-cyclical sectors, including Consumer Discretionary and Technology, produced
mixed results but demonstrated the ability to beat the S&P 500 despite heightened market volatility. From these results, we canestablish that investors do tend to rotate into more conservative market sectors during periods of above-average market volatility
that often
From these results, we can establish that investors do tend to rotate into more conservative market sectors during periods ofabove-average market volatility that often correlate with meaningful declines in the value of equities. The clear beneficiaries of thisdefensive rotation are the Utilities and Consumer Staples sectors.

PAGE 58 IFTA.ORG

IFTA JOURNAL

The Trigger

The above shows that when the VIX is at a particular level,
certain sectors outperform in the subsequent 12 months.
With this in mind, an optimal trigger level needs to be
defined for when cyclical sectors are expected to outperformdefensive sectors in the subsequent periods. An additional
trigger is required for when one should switch positions fromcyclical sectors to defensive sectors. To do this, Nelder-Mead
optimization is performed over a learning period.
There are two methods used to determine the learning
periods applied. The first is a static period between January
1, 1999, and December 31, 2004. The second is a rolling fiveyear period with the first period between January 1, 1999, andDecember 31, 2004. Subsequently, the oldest month is dropped
and a new month is added, with the final rolling period being
September 1, 2014, to August 31, 2019. This means that thetrigger level will vary through time.
In addition to this, one could equally weight their investment
in cyclical and defensive sectors to create a cyclical anddefensive index, or one could use the sector weightings of apassive benchmark such as the S&P 500 to reconstruct an index.
Both possibilities were used in generating the optimal trigger.
In Table 4 and Charts 4 and 5, the results of the static and therolling trigger levels for equally and sector-weighted indices areshown.
Table 4. VIX trigger levels

2022 EDITION

For both equally-weighted and sector-weighted indices, thedifference between the initial entry trigger and exit trigger isvery high. This gap closes through time, although it has widened
again since 2018. This could be an indication that a more volatile
market climate may lead to a greater differential in the trigger
levels.

Trading Strategies

To determine whether one could use the VIX as a sector
allocation tool, three different trading strategies are created.
The first, dollar-neutral, is where, when the entry trigger level isreached, one goes 100% long the cyclical index and 100% shortthe defensive index, with this reversed when the exit trigger
level is reached. The second, sector-rotation, is where, when theentry trigger level is reached, one rotates fully into the cyclicalindex and out of the defensive index, with this reversed whenthe exit trigger level is reached. Finally, the sector overweight
and underweight strategy increases the cyclical index weightby 5% of its respective S&P level when the entry trigger level ismet, reducing the defensive index weight by 5%, and inverting
this when the exit level is met. These trading strategies are
implemented using both equally and sector-weighted cyclicaland defensive indices and using a static and rolling training
period for optimization. To mirror the actual returns that one
would generate, the SPDR sector ETFs are used.
Dollar-Neutral Strategy
The dollar-neutral strategy is one where the pure alphaof differential returns based on a VIX trigger level can bediscerned. Because it is dollar-neutral, the returns would be
expected to be lower, but this should also be met with lower risk,
meaning higher risk-adjusted returns are possible. The different
performance metrics for the four variants of the strategy arecalculated in Table 5.

Charts 4 and 5. Range of VIX triggers

IFTA.ORG PAGE 59

IFTA JOURNAL

2022 EDITION

Table 5. Dollar neutral returns
Equally-Weighted(Static Training)

Sector-Weighted (Static
Training)

Equally-Weighted(Rolling Training)

Sector-Weighted(Rolling Training)

S&P 500

Return (Annualized)

3.34%

3.89%

5.82%

5.54%

8.92%

Risk (Annualized)

11.25%

10.40%

11.23%

10.39%

16.47%

Risk-Adjusted Return

0.30

0.37

0.52

0.53

0.54

Maximum Drawdown-33.94%-31.98%-31.84%-30.81%- 55.25%

Upside Capture (%)

9.71%

10.29%-7.43%-2.49%

Downside Capture (%)

7.21%

7.29%

-14.11%-8.40%

There are two clear findings that can be drawn from theabove. The first is that the dollar-neutral strategy has lower
risk compared to the S&P 500. The second is that the choiceof learning method to generate the VIX trigger levels leads tosignificantly different return.
Across all variants, the portfolio is long the defensive index
and short the cyclical index until mid-2008, when there is aswitch across to cyclical stocks. There is also a move towards
Across all variants, the portfolio is long the defensive index
and short the cyclical index until mid-2008, when there is aswitch across to cyclical stocks.There is also a move toward
the defensive index in 2012 lasting to 2016 across all variants.
However, there are clear differences between the different
training methods used and the sector plays. In the equallyweighted trading strategy using a static training period, there
are fewer switches across indices compared to the rollingtraining period. This lack of switching is most likely the reason
for the relative underperformance, as the cyclical or defensive
indices are held on for too long a period. The opposite occurs
with the sector-weighted indices, with a static training periodleading to many more switches. In this case, this would leadto underperformance, as the defensive or cyclical index istraded out before the returns have been fully realized. This
also explains the upside capture being negative and downside
capture being more negative, as the strategy is more often
exposed to shorting high beta cyclical sectors that perform
strongly in bull markets until the VIX spike occurs.
Finally, the performances through time are decomposed todetermine the times where the strategy performs and the times
it does not. These performances are graphed in Charts 6 and 7.15

PAGE 60 IFTA.ORG

Charts 6 and 7. Dollar-neutral versus S&P 500 (static)

Using a static training period to optimize the VIX levels leads
to fairly flat performance through time, irrespective of theweighting methodology used. There is clear alpha generated
in 2008, as the strategies are long defensive stocks and shortcyclical stocks, and again in 2016. However, that alpha is slowly
eroded through time. One anomaly is that the equally weighted
portfolio, using this training method, is long cyclical stocks
and short defensive stocks from 2019—the only variant of thestrategy that is. As such, it is receiving some negative alpha due
to market conditions during that evaluation period.
Unlike the returns created using the static-training-periodgenerated VIX trigger levels, the returns created using the rollingtraining-period-generated VIX trigger levels show a clear upward
trend (see Charts 8 and 9). Both variants remain flat through thesubprime crisis and then generate alpha as cyclical stocks rebound.
The performance then flattens from 2012 to 2015 as a defensive
play is held; however, this then yields positive performance during
the volatility of the 2015 market. This erodes during the subsequent
market run but is made up during the changed market conditions
where defensive stocks are outperforming.

IFTA JOURNAL

2022 EDITION

Charts 8 and 9. Dollar-neutral versus S&P 500 (rolling)

All-In Sector Rotation Strategy
The sector rotation strategy allocates 100% to either the cyclical index or the defensive index. Unlike the dollar-neutral strategy,
the performance of the strategy is also dependent on the movement of the market, as it always has beta exposure (see Table 6). The
performances of the four variants of the strategy are tabulated below.
Table 6. All-in rotation strategy returns
Equally-Weighted(Static Training)

Sector-Weighted (Static
Training)

Equally-Weighted(Rolling Training)

Sector-Weighted(Rolling Training)

S&P 500

Return (Annualized)

10.63%

11.06%

12.04%

12.00%

8.92%

Risk (Annualized)

17.60%

17.65%

16.96%

17.12%

16.47%

Risk-Adjusted Return

0.60

0.63

0.71

0.70

0.54

Maximum Drawdown-54.54%-52.51%-54.54%-52.51%-55.25%Upside Capture (%)

96.07%

97.77%

88.24%

91.53%

Downside Capture (%)

94.14%

95.54%

84.34%

87.91%

The absolute and risk-adjusted returns for all four variants exceeds that of buying and holding the S&P 500. The annualized risks
are greater than the buy-and-hold strategy, but the maximum drawdowns are roughly the same. Across the variants, using a rollingtraining period to optimize the VIX trigger levels yields greater absolute and risk-adjusted returns. While no strategy is able to “keepup” with the S&P 500 fully, given upside capture ratios that are less than 100%, this is countered by downside captures being less thanupside capture. Alpha, it appears, comes not from being up more with the strategy, but rather by being down less prior to the volatility
spike and decline in equities.
Charts 10 through 13 show the rotation across cyclical and defensive indices through time. As the triggers are the same as thedollar-neutral strategy, the rotations occur at the same time. However, because it is a full sector rotation, these weights remain 100%
until the next switch.

IFTA.ORG PAGE 61

IFTA JOURNAL

2022 EDITION

Charts 10 and 11. Sector rotation allocation (equallyweighted)

Finally, the performances through time are decomposed
to determine the times where the strategy performs and thetimes it does not. These performances are graphed in Charts 14
through 17.
Charts 14 and 15: All-in sector rotation strategy versus
S&P 500 (static)

Charts 12 and 13. Sector rotation allocation (sectorweighted)

Using the static-training-period-generated VIX trigger
levels, the equally-weighted and sector-weighted strategies
outperform the S&P 500 buy-and-hold strategy across mosttime periods (see Charts 14 and 15). As defensive stocks are held
until mid-2008, the strategies outperform the buy-and-holdstrategy before they switch into cyclical stocks and have similar
negative returns. However, in the period after, they recoverquicker, leading to outperformance compared to the buy-andhold strategy. This outperformance continues across time, withthere being particularly strong performances in 2019.

The same underlying themes are seen here. There is
movement from defensive to cyclical sectors during thesubprime crisis. In most of the subsequent periods, defensive
stocks are held barring a few short periods where they arerotated into cyclical stocks.
PAGE 62 IFTA.ORG

IFTA JOURNAL

Charts 16 and 17: All-In Sector Rotation Strategy Versus
S&P 500 (Rolling)2022 EDITIONAs per the sector rotation strategies, the sector overweight/
underweight strategies outperform an S&P 500 buy-andhold strategy in both absolute and risk-adjusted returns. The
annualized risk is also lower, as is the maximum drawdown.
Using a rolling training period to generate the VIX trigger levels
compared to using a static training period to generate the VIX
trigger levels leads to marginally higher absolute and riskadjusted returns.
The allocations to the different sectors are derived from thesame triggers used earlier.
However, as they are cognizant of the market weightings asa whole, at most 50% of the strategy is allocated to defensive
stocks, and at most 75% is allocated to cyclical stocks (seeCharts 18 through 21). This brings them closer in line to themarket as a whole through time.
Charts 18 and 19. Defensive/cyclical weighting throughtime (equally-weighted)

Much like the strategies derived from the static training
period generated VIX trigger levels, the strategies derived fromthe rolling training period generated VIX trigger levels also
outperform a buy-and-hold strategy in most market conditions(see Charts 16 and 17).
However, the magnitude of outperformance in these variants
is greater than in the preceding variants.
Active Overweighting/Underweighting Sectors
While the sector rotation strategy is a possible trading
strategy, it is more likely that one would overweight or
underweight cyclical or defensive sectors based on the VIX
trigger level rather than do an all-in approach. In this trading
strategy (see Table 7), when the VIX entry trigger level isreached, cyclical sectors are overweighted by 5% and defensive
stocks are underweighted by 5%, with the inverse occurring
when the VIX exit trigger level is reached.
Table 7. Active overweighting/underweighting strategy returns
Equally-Weighted(Static Training)

Sector-Weighted (Static
Training)

Equally-Weighted(Rolling Training)

Sector-Weighted(Rolling Training)

S&P 500

Return (Annualized)

9.34%

9.80%

9.40%

9.81%

8.92%

Risk (Annualized)

16.07%

16.14%

16.02%

16.11%

16.47%

Risk-Adjusted Return

0.58

0.61

0.59

0.61

0.54

Maximum Drawdown-51.41%-51.82%-51.41%-51.82%-55.25%Upside Capture (%)

96.87%

97.92%

96.30%

97.49%

Downside Capture (%)

96.22%

96.91%

95.54

96.44%

IFTA.ORG PAGE 63

IFTA JOURNAL

2022 EDITION

Charts 20 and 21. Defensive/cyclical weighting throughtime (sector-weighted)

Charts 24 and 25. Active overweighting/underweighting
versus S&P 500 (rolling)

Finally, the performances through time are decomposed todetermine the times where the strategy performs and the times
it does not (see Charts 22 through 25). These performances aregraphed below.

Due to the sector allocations being more in line with the S&P
weightings, the magnitude of over or underperformance ismuch lower than in the previous strategy. However, it is clear
that, across all four variants, this trading strategy outperforms
a buy-and-hold strategy in almost all market conditions, withrelative sector weighting being between a minimal band of plus
or minus 500 basis points.

Charts 22 and 23. Active overweighting/underweighting
versus S&P 500 (static)

Why It WorksIs this simply a function of mean reversion, whereby cyclicalsectors following VIX spikes suffer steeper losses than are
justified, in turn creating an exploitable opportunity relative
to defensive stocks after the spike has occurred? Perhaps.
Volatility is inherently mean-reverting. A VIX spike can’t persist
forever and stay elevated for a particularly long period of time,as that would imply a near-permanent bear market and decline
in equities to zero.
A more behavioral explanation, however, relates to how
cyclical sectors, which tend to have higher sensitivity to bull
market factors, behave prior to a corrective environment for
stocks. If cyclical areas of the market tend to go up more andare the “winners” of investor portfolios, then the disposition
effect means that when volatility accelerates, those winners are
the first to be sold, as the relative underperformers up to thatpoint are held. The overreaction to losses and preferred methodof selling winners first creates a mispricing and misallocation
effect that can be potentially arbitraged for active investors andtraders afterwards.
The challenge of course with such an approach to sector
allocation is being defensive waiting for those levels to present
a buy low opportunity in cyclicals. This can be quite challenging
from an implementation standpoint, as it implies not being
PAGE 64 IFTA.ORG

IFTA JOURNAL

aggressively positioned in areas that could go up at a faster pacethan the averages if the positioning is defensive throughout,preparing for the unknown timing of a correction that could
take time to present itself.
The fact that all variations of the strategy have an up capturethat is less than 100% because of defensive positioning would
likely test the patience of investors implementing such an
approach. Fear of missing out on a strong bull market can bea strong reason to not be defensive throughout. Yet, that isexactly why the strategy outperforms.
This intuitively makes sense. Being defensive in advance of acorrection means the portfolio is up less during an extended bullrun when investor complacency is taking place and performance
momentum defines investor allocation decisions. When thevolatility spike occurs, it is this defensiveness that saves theportfolio from the overreaction on the downside that occurs
primarily in cyclicals.

Conclusion

While momentum is often touted as the ideal anomaly totake advantage of using sectors to express an active bet on
continued performance, we find that an approach that waits
for momentum to crash with a VIX spike allows for an ideal
setup to buy low and sell high when investor overreactions takeplace. We test various methodologies and strategies, all of whichcome to the same conclusion around using extreme VIX levels
as trigger points to determine how aggressive or defensive to
get with sector allocations. While one can never know the exact
moment an extreme period of volatility and collapse in stocks
takes place, one can be confident that it is worth being defensive
before it happens. After it does, going full speed ahead when
all is clear becomes the preferred way of positioning a portfolio
until another extreme is reached. Mean reversion using the VIX
to overweight or underweight sectors ultimately outperforms
the mean of a passive strategy.

2022 EDITION

Russell, Philip S. and Violet M. Torbey, 2002, The Efficient Market
Hypothesis: A Survey, Business Quest Journal.
Taleb, Nassim, 2007, The Black Swan, Random House Publishing.

Notes
See Malkeil (2003).
See Philip and Torbey (2002).
3
See Kahneman and Tversky (1979).
4 See Barber (2011).
5 See Taleb (2007).
6 See Moskowitz and Grinblatt (1999).
7 See Luu and Yu (2012).
8 See Daniel and Moskowitz (2015).
9 Chicago Board Options Exchange (CBOE). “CBOE Volatility Index– VIX White Paper,” CBOE, http://www.cboe.com/micro/vix/
vixwhite.pdf.
10
See Bhave (2018).
11
See Fogel and Berry (2006).
12
See Graham (2006).
13
200- and 500-trading day periods are meant to roughly approximate
one-year and two-year forward returns.
14
To define sectors, we use the SPDR Select Sector ETFs (https://us.spdrs.com/en/product/view-all-low-cost-core?cid=0). The nine
ETFs used were all launched on 12/16/98. Prior to 10/7/15, thefinancial sector included both Financials and Real Estate before
Real Estate was spun off into its own sector. Prior to 6/18/18,
the Technology and Consumer Discretionary sectors included
Communication Services companies before Communication
Services was spun off into its own sector.
15
In all backtesting that follows, we start in a defensive position at
the beginning of 2005 because the exit trigger level was reached at
12/16/2004 and it didn't hit the entry level at the point we started.
1

2

References
Barber, Brad and Terrance Odean, 2011, The Behavior of Individual
Investors, University of California, Berkeley.
Bhave, Aditya, 2018, Is VIX Predictive of Future S&P Equity Returns,
361 Capital.
Daniel, Kent and Tobias J. Moskowitz, 2015, Momentum Crashes,
Journal of Financial Economics.
Fogel, Suzanne O’Curry and Thomas Berry, 2006, The Disposition
Effect and Individual Investor Decisions: The Roles of Regret andCounterfactual Alternatives, Journal of Behavioral Finance.
Graham, Benjamin, 2006, The Intelligent Investor, Harper Business.
Kahneman, Daniel and Amos Tversky, 1979, Prospect Theory: An
Analysis of Decision Under Risk, Econometrica.
Koijen, Rodriguez, and Sbuelz, 2006, Momentum and Mean-Reversion
in Strategic Asset Allocation, Management Science 55.
Luu, Bac Van, and Peiyi Yu, 2012, Momentum in Government-Bond
Markets, Journal of Fixed Income, Vol. 22, No. 2.
Malkiel, Burton G., 2003, The Efficient Market Hypothesis and Its
Critics, Journal of Economic Perspectives, Winter 2003.
Moskowitz, Tobias J. and Mark Grinblatte, 1999, Do Industries Explain
Momentum? The Journal of Finance.
IFTA.ORG PAGE 65

IFTA JOURNAL

2022 EDITIONThe Taylor Trading Technique by George Douglas Taylor
Reviewed by Regina Meani, CFTe

George Douglas Taylor was a grain trader at the Chicago
Board of Trade in the 1950s. Through his tireless bookkeeping,hence the name “The Book Method,” Taylor found that the grainmarkets moved in a three-day cycle. The Book Method aims to
make a profit for the daily trader based on the rise and fall of thedaily movements of the markets. Taylor propounded it was not acharting method, but I tend to disagree as much of his methods
can be translated into technical analysis.
In chapter I, his references to manipulation can betransferred to read supply and demand. For example, “amovement more or less mechanical in it’s action for tactics
of manipulation do take on a mechanical action after a whileand for the simple reason of the pattern prices form throughrepetition”1
Keeping in mind that Taylor’s Book Method was introduced in
the 1950s, I took Linda Bradford Raschke’s advice and skipped
chapters II, III, and IV, and agree that manually making a book is
not really required in today’s technological world. His concepts,
however, are useful for traders and deal with identifying
objective points for buying, selling, and short selling on a daily
basis. Taylor believed that his methods trained one to rely on
their own judgements with the Book Method providing thetrader with all the tips one would require.
In the first chapter, he describes the three-day trade cyclewith the fourth and fifth days becoming the first and seconddays of the next cycle. Here Taylor advises using the first day
for buying and the second and third days for selling. This points
us to the explanation of the three-day trading method foundin chapter XIII. But before heading to this chapter one needs tounderstand how a buying day and a selling day are selected inchapters V through VII. More than one reading of these chapters
may be needed, as I must admit that on first reading, I found theconcepts a little difficult to grasp.
Clarity arrives somewhat in chapter XV where we learn about
pertinent points and we find that Taylor gives “pertinent” advice
that is beneficial to any trader. He states, “never make a tradeunless it favours your ‘play,’ it is better to pass up the entire
trading session than to buy or sell on a guess.”2 A few pages laterhe gives more advice, “a trader with any method or system of
trading must develop and have a certain amount of confidence init—with this means of trading he must believe in the occurrence
and recurrence of the past pattern of movement.”3

PAGE 66 IFTA.ORG

While I have been reading through the chapters, like Linda
Bradford Raschke, I have found myself visualizing candlesticks
as a representation of Taylor’s trading methods. The above quote
referring to the occurrence and recurrence of the past patternof movement seems to sanction this.
Further clarity arrives in the final section of the book, which
is an exert from George Angell’s “Winning in the Futures
Market.” Taylor describes his trading methods as on a buy
day the prices open at or fall to a low and then rise. A sell day
is identified by prices trading at, below, or slightly above theprevious day’s high. On a short sell day, prices push up and halt
in resistance to be rebuffed. The cycle then begins again. Thismethod sounds simplistic, but sometimes the simplest methods
work.
However, the unpredictability of the market can play havocwith the simple three-day cycle. George Angell tackled thisproblem and developed the LSS Three-Day Cycle Method,4creating an element of flexibility for the system. He changed
Taylor’s names to avoid confusion to “Long, Sell and Short Sale,”with the main point of the conversion that one can either buy orsell on any day.
George Angell calls Taylor’s Book Method the genesis ofa trading system, and that over the years it has become
something of an underground classic for futures traders. I findthat Taylor’s own words sum up the benefits of reading about his
system when he says “a trader must not be so rigid as to stick toa stubborn theory. Successful speculation is not based on any
set of inflexible rules and a trader must be ready to change whenconditions change, however, the trader who knows how to act
when the expected happens, is in a better position to act when
the unexpected happens.”5 Timeless advice from an experienced
trader.

Notes

1 Taylor, G.D., The Taylor Trading Technique, Steven Star Publishing,
Australia, 2016. p. 8.
2 Ibid, p. 73.
3 Ibid, p. 76.
4 Ibid, p. 109.
5 Ibid, preface.

IFTA JOURNAL

2022 EDITION

In Remembrance: J. Welles Wilder Jr.
June 11, 1935–April 18, 2021
Christchurch, New Zealand

A Farewell to One of the Greatest Technical Analysts in History
It seems like yesterday that I was given the honor andpleasure of presenting the IFTA Lifetime Achievement
Award to Welles Wilder during IFTA’s 2020 Online
Annual Conference.
It was long overdue, not only because the work andcontribution of Welles was revolutionary on many
levels, but also because his work helped countlesstechnical analysts worldwide to improve their analysis
and therefore make better investment decisions.
As technical analysts, we are all using at least one of
the indicators and systems developed by Welles, suchas the DMI System, the Relative Strength Index, theAverage True Range, or the Parabolic SAR, to get better
market insight.
But Welles was even more than that. In his personal
life, he was also a great husband, father, and friend.
While Welles could not receive the award himself, Tom
DeMark—his close friend for over 40 years—accepted
the reward on his behalf, sharing memorable stories
about their decades together as colleagues and closefriends.
I am grateful thinking of that touching moment
when Welles’ daughter, Catherine, was with us during
the conference. I still hear her loving words about
Welles being a dad and a husband. Truly a very special
moment that all who attended will never forget.
Welles leaves a big gap—as a husband, father, friend,and colleague.
We have to say farewell now, but we never will forget
Welles and the contribution he made to all of us. His
legacy continues in our charts, and this is handed downfrom one generation of technical analysts to another.
This is IFTA’s duty, and we are grateful to fulfill it.

J. Welles Wilder Jr. (June 11, 1935–April 18, 2021) wasan American mechanical engineer turned real estatedeveloper. He is best known, however, for his workin technical analysis. Wilder is the father of several
technical indicators that are now considered to be
the core tenets of technical analysis software. These
include Average True Range, the Relative Strength
Index (RSI), Average Directional Index, and theParabolic SAR.[1]John Welles Wilder was born June 11, 1935, in Norris,
Tennessee. The oldest of four children to John Welles"Jack" Wilder Sr. and Frances Green Wilder, his brotherwas former NFL Defensive Tackle and Defensive End
Albert Green "Bert" Wilder (April 14, 1939 – December
5, 2012).
After serving in the Korean War in the U.S. Navy,
Welles attended North Carolina State University
in Raleigh, graduating with a degree in mechanicalengineering in 1962. He married Eleanor Dawn
Barefoot on July 6, 1958. They had three children: John
Welles "Johnny" Wilder III (April 22, 1959–March 25,2020), Catharine Cooper, and David Wilder, settling inGreensboro, North Carolina. After a successful realestate practice, he founded Trend Research LTD and
its primary subsidiary, The Delta Society. He thenpublished New Concepts in Technical Trading Systems
in 1978.
Welles and his wife retired and relocated toChristchurch, New Zealand, in October 1999,
becoming dual citizens shortly thereafter. While inretirement, he continued with system development
until 2008. He died on April 18, 2021, in Christchurchat the age of 85.

–Wieland Arlt, 2021 IFTA President(Source: Wikipedia)

IFTA.ORG PAGE 67

IFTA JOURNAL

2022 EDITIONIFTA’s 2020 Lifetime Achievement Award
IFTA’s 2020 Lifetime Achievement Award was presented
to a man who revolutionized technical analysis. In the mid1970s, J. Welles Wilder Jr. created a set of indicators that wasconsidered revolutionary because the indicators proved optimal
during the sideways period that the market was experiencing
during those years.
His indicators, however, stood the test of time and proved
to be of great value, even when the markets witnessed strong
trends. The approach worked well in the 70s, 80s, 90s, and2000s.
Welles was a real genius and understood very well themechanics of market movements, which was obvious in his
simple but concrete definitions of upward and downward
movements in addition to the relative comparisons between
buyers and sellers that he always used in a very professionalmanner.
Welles’ DMI system is one of the most well-built systems intechnical analysis. It is a concrete system that gives you clear
information about market direction and how strong the moveis, in addition to clear overbought and oversold signals. It is
important to note the DMI system (in my opinion) is the only
system that can give you a real overbought situation during an
uptrend and a real oversold situation during a downtrend. Thisis one of the techniques that is very much underrated in thissystem.
Other great indicators include RSI, Parabolic (SAR), andAverage True Range. Professionals that used Welles’ indicators
know well that they contain real value—much more than was
actually written in his books.
Welles was 85 years old, and his achievements in technicalanalysis are endless. He will remain one of the greatest
technical analysts in history. There is no doubt about that.
Thank you, Welles, for all you have done for our industry and fortechnical analysis. We all love and respect you.
–IFTA Education Committee 2021
Tom DeMark accepted the IFTA Lifetime Achievement Award on
behalf of Welles Wilder Jr. and his family at the IFTA 2020 Virtual
Annual Meeting on Saturday, October 24, 2020.
Hello IFTA members,
It is an honor for me to be here and accept the distinguished
IFTA Lifetime Achievement Award on behalf of Welles Wilder
and his family. As you may already know, Welles’ healthprevents him from being with us at this time and, logistics are
such that his wife Dawn and children, Catherine and Ron, areunable to be here as well.
My history as a market technician spans over five decades.
Looking back over those years, I recall the two most influential
commodity industry pioneers who certainly influenced my life,and I am certain those of you who were around in the 1970s and1980s will agree, were Larry Williams and Welles Wilder. Larry’s
history and influence reverts to the 1960s and Welles to the mid
1970s.

PAGE 68 IFTA.ORG

It’s pretty common knowledge that Larry Williams’ industry
roots and influence have affected, one way or another, each andevery one of us. He has personally, unselfishly, and willingly
given his time and effort to many of us in our pursuit to share
our market timing tools and beliefs. I was one of his early
disciples. So too was Welles.
Welles’ background as an engineer and his understandingof mathematics gave him a special edge and insight into
identifying price relationships within the commodity markets.
He believed many of the theories he applied as an engineer also
had application to price patterns and number series. He became
fascinated with the commodities markets and in turn adapted
and used these concepts to develop commodity trading timing
models.
At the time when Welles was working on these timing
tools—1975 and 1976—he introduced himself to Larry and me.
We were impressed by his intellect, modesty, and passion forthe markets. What even impressed us more was his sincerity,honesty, and willingness to share. His ideas were fresh andoriginal. At the time, other than Larry Williams book How I
Made a Million Dollars Trading Commodities and his book on
seasonality, as well as his seminars, there was total absenceof any timing tools available to commodity traders. Other
than what Larry popularized, most traders relied upon thethree basic approaches to analysis: specifically, trendlines,
moving averages, and most often, guessing. Larry and Welles
changed the industry for the better. Welles created indicatorsthat enabled traders to monitor the pulse and price behaviorof the commodity markets. It was an awakening to new andvibrant methodologies designed to measure the activity of thecommodity markets. Not only did these indicators strike a chordwith commodity traders, it also attracted new traders who
previously were unwilling to effectively gamble in commodities
during the inflation riddled 1970s. They now had methods they
could use to time their trades.
Larry connected Welles with Al Schmidt and his son,
Steve, at Windsor Books, who published Welles’ book New
Concepts in Technical Trading Systems, which showcased
Welles’ contributions to the industry and for which he became
legendary.
Welles was always soft-spoken and possessed a pleasant,calming demeanor, the antithesis of the nature of mostcommodity traders. What struck me most was his patience andwillingness to share with others. He was always upbeat and had
contagious laugh.
It is an honor to accept such a distinguished award on behalfof an industry titan upon whose shoulders many of us havestood. His example as an industry professional and leader, as
well as a friend, is an inspiration to all of us.
Thank you, IFTA, for honoring such a deserved individualas Welles Wilder. I know he and his family appreciate thisrecognition and will be the highlight of his storied career.
—Tom DeMark, Creator of the DeMARK Indicators® and thefounder and CEO of DeMark Analytics, LLC

IFTA JOURNAL

2022 EDITION

I knew Welles Wilder before he was famous…
Before anyone had heard of Welles Wilder, we had become
pen-pals (back then, there were no computers, no email; people
wrote letters to one another). Welles had developed a moving
average trading system and put together a group of reallybright guys to develop market tools. In one of the think tankgroups was the very bright and gifted Gresham Northcott, who
I already knew, so I was excited to see what Welles would comeup with.
At that point, no one knew of Welles and his group. After ayear of hard work, Welles asked if I would help him spread theword of a strategy they had developed. I said, “Sure, what do you
want me to do?” Welles replied, “No one has ever heard of me,
would you do a mailing for me, and maybe Tom DeMark could
help as well.” Tom and I agreed … and the rest is history.
Welles' books broke sales records, and his indicators
shattered the traditions of how people look to trade.

Most anyone can come forward with one new market
indicator or approach, but few have ever been as productive as
Welles, who brought forth a plethora of ideas—from the Adam
Theory to the wildly popular Delta Phenomena. Welles invited
me to his home to personally teach the Delta secrets to me.
What an experience that was and to see another side of Welles
and his wife.
He was as passionate about his car collection as he was about
the markets. Indeed, Welles had the Jay Leno car collection of
traders. People rave about the ideas he brought to the markets,and rightfully so. His ideas will always be remembered. What I
will remember the most is the southern kindness and courtesy
he showed me—before and after he became famous.
–Larry Williams
Larry Williams is the author of
11 books, most on stocks andcommodity trading.

Welles Wilder's Great WorkThe Directional Movement Index and the ADX
By Saleh Nasser, CMT, CFTe

Most trend-following systems that generate the best profits
are successful when a trend is underway. Usually, trend
following systems lead to very good results because it is during
trending periods that the vast majority of profits are achieved.
During sideways periods, however, these systems lead tomany losses and whipsaws, leaving the investor in agony. It is
understood that during sideways periods other overbought/
oversold oscillators should be used, like the Stochastic or RSI.
The best systems to use during trends are trend-following
systems, like moving average crossovers, breakout systems, etc.
During sideways periods, oscillators are preferred.
Fortunately, we have an indicator that tells us if the market isin a trending mood or in a trading mood. This indicator is called
the Average Directional Movement Index (ADX). It does nottell us if the market is rising or declining. It tells us only if themarket is trending (either uptrend or downtrend) or trading.
Having this information, we can use the suitable indicator in theright time.
The ADX is just one component of the Directional Movement
Index (DMI). There are two other components: the +DI and the–DI. These two lines, when used together, tell us the direction of
the market.
The DMI was invented by Welles Wilder and was described in
his 1978 book, New Concepts in Technical Trading Systems.

So the DMI consists mainly of three indicators (or three lines):+DI, –DI, and ADX.
Both +DI and –DI show us the direction of the market (up or
down), while the ADX tells us only if the market is in a trending
mood or a trading mood. This means that if a downtrend isunderway, the ADX will rise. The ADX declines when the market
is witnessing a sideways period. Obviously, when the market iswitnessing an uptrend, the ADX rises too.
Calculation
As we mentioned, the DMI has three lines: +DI, –DI, and ADX.
First we calculate the Directional Movement:
The Directional Movement is the largest part of today’s
trading range that is not included in yesterday’s range. What
does this mean?
It means that 1) if today’s bar is higher than yesterday’sbar, we will subtract yesterday’s high from today’s high:(today’s high – yesterday’s high), and 2) if today’s bar is lower
than yesterday’s bar, we will subtract the lows (today’s low– yesterday’s low). Note that we use positive values and no
negative values in the calculation.

IFTA.ORG PAGE 69

IFTA JOURNAL

2022 EDITIONIn the first case, we have +DM; in the second case the –DM iscalculated.
In other words, +DM is the largest part of today’s range which
is outside yesterday’s range during a rise.
–DM is the largest part of today’s range which is outside
yesterday’s range during a decline.

Notes:
1. An inside day will have a zero DM
Inside day, today's trading range is insideyesterday's range. DM = 0
2. During an outside day, we will have both a +DM and a –DM.
Take the largest.
Outside day occurs when today's trading
range engulfs yesterday's range. We have a+DM and a –DM. If +DM is larger than –DM,
we will take it in our calculation and neglect
the smaller –DM, and vice versa.
3. During an outside day, if +DM = –DM, then DM=0. This meansthat if the upper range is equal to the lower range, DM will beequal to zero, like the case of an inside day.
Now we calculate the +DM and –DM. +DM is the largest part oftoday’s range that is not included in yesterday’s range (during
a rise). –DM is today’s range that is not included in yesterday’s
range (during a decline). All values are positive. (+DM and –DM
refer only to movement above or below yesterday’s range.)
Next, we calculate the true range (TR):The true range is the largest of the following:
1. the distance between today’s high and today’s low.
2. The distance between today’s high and yesterday’s close.
3. The distance between today’s low and yesterday’s close.
Each day we calculate the biggest of these three values andconsider it as the true range (TR). Again, all values are positive.
Now we have calculated two things. First we calculated the
Directional Movement, which can be +DM or –DM. Then we
calculated the True Range.
Next, we calculate the Directional Indicator (DI):Now we will calculate +DI and –DI. As we mentioned before,
these are two of the three ingrediants of the Directional
Movement Index.
PAGE 70 IFTA.ORG+DI= +DM/TR–DI= –DM/TR
So we divided the positive directional movement (+DM)
by the true range to extract +DI. We also divide the negative
directional movement by the true range to extract –DI.
+DI, as Welles Wilder explains, is an expression of the percentof the true range that is UP for the day. –DI is an expression of thepercent of the true range that is DOWN for the day. Obviously, +DI
equals zero on a day that has no directional movement up; –DI
equals zero on a day that has no directional movement down.
Let us see some examples:

Example 1:
Yesterday’s range was 19–21, while the close was 21. Today’s
range was 20.5–23.
Then +DM=2 and –DM=0.
TR will be the largest of the following:
1. The distance between today’s high and low = 2.5
2. The distance between today’s high and yesterday’s close = 2
3. The distance between today’s low and yesterday’s close = 0.5
Then TR (true range) = 2.5+DI = +DM/TR = 2/2.5= 0.8
What does +DI=0.8 mean? It means that 80% of the true range
was up for this specific day.
Example 2:
Yesterday’s range was 20–21.5, while the closing price was 20.
Today’s range was 18–20
Then –DM = 2 and +DM = 0.
TR will be the largest of the following:
1. The distance between today’s high and low = 2
2. The distance between today’s high and yesterday’s close = 0
3. The distance between today’s low and yesterday’s close = 2
Then TR (true range) = 2–DI = –DM/TR = 2/2 = 1–DI = 1 in this example because today’s range was outside
yesterday’s range.
So –DI = 1 means that 100% of the true range was down thisspecific day.
Some logic is needed before we continue explaining the
calculation:
When we divide the directional movement by the true range
to identify +DI or –DI, we actually see how the market moved
in a certain direction compared to its range. This means that
if there is direction in the market, the market is in a trend; DM
will be high and might reach 1, (DM equals the true range). If themarket is not showing a trend, DM will be low compared to thetrue range. Means that the market has no direction but is morein a sideways range.
For example, if yesterday’s range was 25–27 and today’s
range was 25.5–27.25, the market rose, but there is no big moveto the upside.
+DM will be equal to 0.25, while TR will be equal to 1.75.
+DI will then be equal to 0.25/1.75 = 0.14.
This example shows that the upward direction of the market
is weak compared to the range of the day itself. (Only 14% of thetrue range was up.)

IFTA JOURNAL

We average the +DI and –DI. Wilder used a default value of 14.
The proper way to do it is to first average +DM (14-day averageof +DM) and we average TR (14-day average of TR). We thendivide the averaged +DM by the average TR to calculate +DI.
We also average –DM (14-day average of –DM) and divide itby the average of TR (14-day average of TR) to calculate –DI+DI(14) = +DM(14)/TR(14)–DI(14) = –DM(14)/TR(14)2022 EDITION

Now we calculate the ADX:
To calculate the ADX, we have to first take the absolutedifference between +DI and –DI, and then we take their sum.
Obviously we use the averaged +DI and –DI. (As we explained,
we calculate either the averaged +DI or the summed +DI. The
same holds true for –DI.)
1. Compute the difference between +DI and –DI,
DI diff = [(+DI) – (-DI)]

Averaging +DI, –DI, and TR can take different forms:
1. Welles Wilder used a summation function. He adds +DI for theprevious 14 days and does the same with –DI and TR. He thendivides the sums. He used a certain calculation to skip thetedious adding process. (Note that Wilder created this systembefore 1978, and during his days, there were no computers
like today.)
Today’s +DM14 = Previous +DM14 – (Previous +DM14/14) +Today’s +DM1
Where Previous +DM14 is the last calculation of +DM14 (adding 14
days of +DM), and +DM1 is today’s +DM
So after the first summation, he uses this formula to calculate+DM, –DM, and TR for each new day.
2. The second way is to add the last 14 values, and each new
day we drop the oldest value and add the new value. This
will obviously be done with +DM, –DM, and TR. It’s a simple
summation process. If today’s +DM=0, for example, we will
add zero to the total and subtract the oldest value.
3. The third way is to take a 14-day moving average for the threecomponents (+DM, –DM, and TR).
After the summation (averaging) process is done, we willcalculate +DI by dividing the summed +DM by the summed
TR. We will calculate –DI by dividing the summed –DM by thesummed TR.
NOW: +DI14 is the percentage of the total true range of thelast 14 days that was up. –DI14 is the percentage of the total true
range of the last 14 days that was down. Both the DI14 and –DI14
are positive numbers.
Logic: Let us say that the summed +DI = 25% and the summed–DI = 40%. This means that 25% of the true range for the past 14
days was up, while 40% of the true range during the same period
was down. If we add these two figures, then 65% of the true
range was directional (either up or down), and 35% of the true
range was nondirectional. THUS, true directional movement isthe difference between +DI and –DI. So, the more directional the
movement of a certain stock, the greater the difference between+DI and –DI. Why? Each day we have a new +DM (market goingup), +DI will increase while –DI will decline (because –DM
will be zero). We add zero to the total and subtract the oldest
value. If +DI and –DI get closer together, then the market is lessdirectional and is moving sideways.

2. Compute the sum of +DI and –DI
DI sum = [(+DI) + (-DI)]
3. Calculate the directional movement index (DX)DX = (DI diff) / (DI sum) *100
4. Calculate the ADX by taking a 14-day moving average of the DX.
ADX = 14-day moving average of DX
What did we do exactly?
We calculated the difference between +DI and –DI andcalculated the sum of +DI and –DI. We then divided thedifference by the sum to extract DX, and lastly, we calculated a
14-day moving average of the DX to calculate the ADX.
Note: This process is done with the averaged (summed) +DI
and –DI.
In other words:
ADX = 14-day moving average of ([(+DI) – (–DI)] / [(+DI) + (–DI)]*100)
What does the ADX tell us?
It tells us, as Alexander Elder explains, that when the trend
proceeds in a healthy manner, the spread between the twosmoothed directional lines increases and ADX rises (meaningthat the spread between +DI and –DI increases). ADX declines
when a trend reverses or when a market enters a trading range.
So the +DI and –DI show us the market direction, when +DI
crosses above –DI, the market is moving upwards. When –DI
crosses above +DI, the market is moving downwards. The ADX
itself does not show us the market direction. It only tells us thatthe market is in a trending period or trading period. This meansthat when the ADX is rising, there is a trend in the market(uptrend or downtrend). When the ADX declines, it tells us thatthe market is witnessing a sideways range.
WHY? Because the calculation of the ADX is based on the
movements of +DI and –DI together. When they diverge fromeach other, ADX will rise, meaning that there is directionin the market, either up or down. When both +DI and –DI
converge with each other, then the market has more horizontal
movement than direction. The greater the difference between+DI and –DI, the more directional or trending the market is(rising ADX).

IFTA.ORG PAGE 71

2022 EDITIONIFTA JOURNALMICROSOFT (27.9900, 28.7600, 27.8500, 28.4800, +0.67000)

Trending

Sideways

Trending

11.0
10.5
10.0
9.5
9.0
8.5
8.0
7.5
7.0
6.5
6.0
5.5
5.0
4.5
4.0
3.5
3.0
2.5
2.0
55

Directnl Movement ADX (15.0000)

50
45
40
35
30
25
20
15
10

N D 1994

A M J JA S O N D 1995

A M J

J A S

O N D 1996

A M J J A S O N D

The chart above shows Microsoft along with ADX. As we cansee during trending periods, ADX rises. During sideways ranges,
ADX declines.
Using ADX alone
First, it is important to know that a rising ADX means that themarket is witnessing a trend upward or downward. A declining
ADX means that there is sideways action. ADX does not tell us
the market direction. It only tells us if the market is trending or
not. ADX oscillates in a range from 0 to 100 (remember that we
multiplied the calculation by 100). In his book Computer Analysisof the Futures Market, Charles LeBeau mentions that as long as
ADX is rising, any level of the ADX above 15 indicates a trend.
He also recommends to use ADX with our favorite indicators, aseach one will find certain levels and certain patterns in the ADX
that will match our favorite indicators.
A rising ADX: A strong trend is underway and we should beusing trend-following strategies. Moving average systems
and breakout systems are preferred during these times when
ADX is rising. Obviously, we cannot use stochastic and RSI
as overbought/oversold oscillators. As we mentioned, during
trending periods, oscillators stay for long periods of times intheir overbought or oversold territories.

its calculation, while inputting the new period of strong negative
directional movement. As a result of the conflicting input, the ADX
will begin to decline for a time until the old positive directional
movement drops out of the data and the ADX begins to rise again
because of the new downtrend.”
For this reason, ADX is better at triggering uptrends thantriggering downtrends because bottoms usually take longer tobuild than tops. During a bottoming formation, prices will movesideways. The ADX will be declining. When a new trend begins,prices will move above their range, while ADX will rise. So ADX
is very useful when a long sideways period divides a trend
reversal.
ADX will work best if we go from a downtrend to sideways to
uptrend, or if we go from an uptrend to sideways to downtrend.
In either of these cases, ADX will be much better than if thetrend reversed suddenly from an uptrend to a downtrend, orfrom a downtrend to an uptrend.
NAS/NMS COMPSITE (2,125.02, 2,128.00, 2,073.15, 2,077.37, -38.6699)
2150
2100
2050
2000
1950
1900
1850

Trending Period

Trading Period

1800
1750
1700
1650

Directnl Movement ADX (47.0000)

45
40
35
30
25
20
15

28

4
11
August

18

25

2 8
15
September

22

29 6
13
October

20

27

3
10 17
November

24 1
815
December

22 29 5
12
2004

20 26

10

Using ADX along with +DI and –DI
Some useful techniques can be used using ADX, +DI, and –DI.
1. BUY when +DI and ADX are above –DI and ADX is rising. Stop
should be placed below the minor low. This shows that theuptrend is getting stronger.

A rule of thumb: When the ADX is rising, do not use overbought/
oversold oscillators to take signals contrary to the trend
direction.

27

APPLIED MATL (22.3300, 22.3900, 21.1980, 21.4100, -0.62000)

26
25
24
23
22
21
20
19
18
17

A falling ADX: We are witnessing a trendless market—
sideways range. In this case, counter-trend strategies can beused. We can use oscillators to take signals contrary to the trend
direction. We can use the stochastic and RSI as overbought/
oversold oscillators, buying on dips and selling on rallies.
Investors and fund managers who only use trend-following
strategies do not take any actions when ADX is declining. They
begin using their favorite trend-following indicators when ADX
tells them to do so.
The major problem of the ADX: When an uptrend is underway,
usually the ADX is rising. The problem lies when the trend
reverses from up to down. The ADX will begin to fall, despitethat the market is still trending. The only difference is that themarket is now witnessing a downtrend instead of an uptrend.
As we mentioned before, the ADX should be rising whether thetrend is up or down. The problem with ADX lies during market
reversals. As LeBeau explains it, “the ADX will still be including
the historical period of strong positive directional movement in
PAGE 72 IFTA.ORG

16
15
14
13
12
11
Directnl Movement ADX (17.0000), Directnl Movement +DI (14.0000), Directnl Movement -DI (30.0000)
40

+DI

ADX

35
30
25
20
15

-DI

February

March

April

May

June

10

July

AugustSeptember

October

Applied Materials (AMAT) shows a buy signal during June
2003. +DI crossed –DI to the upside. ADX began to rise andcrossed above –DI a few days later. This action is a hint that atrend began. If we look at the chart, we will find that before thisbuy signal, the stock was witnessing a sideways range. ADX,
along with +DI and –DI, work very well when the stock moves
from a trading range to a trend. Stops should be placed below
the minor low.

IFTA JOURNAL

2022 EDITION
OT (61.4900, 64.4900, 60.0000, 62.4300, +1.78000)

25
24
23
22
21
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6

2. Sell when –DI and ADX are above +DI and ADX rises. Place
your stop above the minor peak. A downtrend is underway.
26.5
26.0
25.5
25.0
24.5
24.0
23.5
23.0
22.5
22.0
21.5
21.0
20.5
20.0
19.5
19.0
18.5
18.0

APPLIED MATL (22.3300, 22.3900, 21.1980, 21.4100, -0.62000)

Directnl Movement ADX (17.0000), Directnl Movement +DI (14.0000), Directnl Movement -DI (30.0000)

Directnl Movement ADX (37.0000), Directnl Movement +DI (39.0000), Directnl Movement -DI (15.0000)

+DI

ADX

40

-DI

35
+DI

30
25

14

20

2
8
15
September

22

29
6
13
October

20

27

3
10
17
November

24

1
8
15
December

22

15

-DI

ADX

25

5
12
2004

20

21

28

4
11
November

18

25

2
9
December

16

23

30

6
2003

13

20

27

3
February

In November 2002, while Orascom Telecom was trading below
8, +DI crossed above –DI. Few days later, ADX crossed above–DI and began to rise, signaling a buy signal. ADX told us thata new trend was underway very early. As we mentioned, ADX
works beautifully with stocks that witness major bottoming
formations.

10

29

26

The first two techniques were explained by Dr. Alexander
Elder in his book Trading for a Living.
3. Another technique explained by Wilder himself is worth
mentioning. On the day that +DI crosses –DI to the upside,
use the high of this day for entry points. If this high is broken,
a buy signal is triggered. On the other hand, if –DI crosses
above +DI, use the low of the crossover day as your key point.
If this low is violated, a sell signal is triggered.

Ezz Ceramics (2.38000, 2.41000, 2.32000, 2.40000, +0.10000)

3.0

2.5

2.0

Watany Bank (11.0500, 11.7500, 10.8500, 11.2400, -0.07000)

BUY

55
50
45
40
35
30
25
20
15
10
5
0

10.0

1.5

9.5

1.0

Directnl Movement ADX (20.0000)

9.0

60
55
50
45
40
35
30
25
20
15
10

8.5

8.0

Directnl Movement +DI (42.0000), Directnl Movement -DI (6.00000)

45

+DI

40
35
30
25

-DI

20
15
10
5

20

27

3
10
November

17

24

8
December

15

22

29

5
2004

12

19

26

3
February

Watany Bank: During November 2003, +DI crossed above –DI.
The second day the price crossed the high of the crossover day.
A buy was triggered. The stock declined afterwards but did notbreak support. During mid-December, –DI crossed above +DI for
only one day, but no sell was triggered. The low of the crossover
day was safe.
4. When ADX is above both +DI and –DI, it means that the trend
is overextended. Taking profits is recommended if ADX begins
to turn down. My recommendation in this case will be to lookat other indicators to see if the market is really overbought/
oversold or not. Taking action will be better if based on priceaction (i.e., lower highs if the trend was up, or higher lows if
the trend was down). Wilder suggested that if ADX is above
both +DI and –DI, we should begin taking protective actions
as soon as it begins to turn down.
The logic of these techniques is as follows:
When +DI is above –DI, then the bulls are stronger thanthe bears. When ADX rises, it means that a trend is underway(uptrend as +DI crosses above –DI).
When –DI is above +DI, the bears are stronger. When ADX
rises, it tells us that a new trend is underway (downtrend as –DI
crosses above +DI).

2003

February

March

April

May

June

July

AugustEzz Ceramics witnessed a trading range. Before the breakof the major resistance at 1.5, ADX began to rise, hinting thata trend was underway. Look at how the ADX rose during May
2003, even before the major resistance at 1.5 was broken.
Different ADX calculation
We explained how Wilder calculated the ADX. He calculated+DM, –DM, and TR. He then took the sum of +DM, and divided itby the sum of TR to extract +DI. He also divided the sum of –DM
by the sum of TR to extract –DI.
Some technicians use a different calculation. They divide theraw +DM by TR to extract +DI, and divide –DM by TR to extract–DI. After this process, they take a 14-day moving average of+DI and a 14-day moving average of –DI. So they divide the data
first and then average the result afterwards.
Instead of averaging the components and then dividing, theyfirst divide the components and then average the result. The
numbers are probably different from Wilder’s calculation, but
we use the calculation that Wilder explained because it is themost credible one.
References
New Concepts in Technical Trading Systems: Welles Wilder.
Computer Analysis of the Futures Market: Charles LeBeau & David W.
Lucas.
Trading for a Living: Dr. Alexander Elder.
Trading Systems and Methods: Perry Kaufman.
IFTA.ORG PAGE 73

IFTA JOURNAL

2022 EDITION

Quick Comments on the ADX
By Saleh Nasser, CMT, CFTe

As we know, the ADX is an indicator that tells us whether or
not there is a trend. It is a trend identifyer. Welles Wilder wasable to construct this indicator by defining moves; he defined
an upward move and a downward move. By taking the highof today minus the high of the previous day during upward
moves and the low minus the low during the downward days, heactually was able to solve 75% of the indicator.
The key here is comparing the number of days when themarket moved up with the number of days when the market
moved down, in addition to comparing the amplitude of thesemoves. In other words, he reached the secret recipe by reaching
the conclusion that the market will be trending if the difference
between upward moves and downward moves is expanding(in either direction), and the market will be non-trending if
the difference between upward and downward movements isshrinking.
Thus, if we are rising, we will have a lot of +DMs and very few–DMs; if the market is declining, we will have a lot of –DMs andvery few +DMs; thus, the difference between +DMs and –DMs
expands either in the direction of +DM or the direction of –DM;
taking the absolute difference between +DM and –DM (or +DI
and –DI after normailizing them by the true range) will give
you an indicator that will rise during an uptrend or during adowntrend, and will decline during sideways ranges.

On the left, we have five +DMs, one –DM, and four bars with
no DMs. We can see that positive days are more than negativedays and with a higher amplitude.
On the right, we have six –DMs, two +DMs, and two bars with
no DMs. Here we have more negative directional movement.
Thus, the difference increases either to the positive side or to
the negative side if there is an upward or downward movement.
Taking the absolute difference will end up in an indicator thatwill rise whether the market is rising or falling.
We want to highlight the overbought and oversold conditionsof the ADX.
This tactic is the most underrated technique in technicalanalysis, and did not have the importance it should have taken.
When we talk about the DMI overbought and oversold (ADX
along with the +DI and –DI), we note that this system is the only
system (as an indicator or set of indicators) that can depict a
real overbought during an uptrend and a real oversold during adowntrend. What does that mean?
Overbought conditions that appear in oscillators that arein the direction of the major trend are considered as areas
PAGE 74 IFTA.ORG

of strength rather than overbought. For example, during
an uptrend, the stochastic will have most of its life in the
overbought area. This is why we use trading tactics with thestochastic oscillator that enable us to buy at overbought when
the rise is strong. We call this tactic the BOS system (buyon strength); we use both the stochastic and MACD, and we
actually buy as the stochastic approaches overbought or isactually inside overbought territory. The same goes for the RSI
and other oscillators, including the CCI and others.
The DMI system, however, is able (sometimes) to depict
overbought conditions during strong trends. This is an almost
impossible job for an indicator to do, but the DMI system cando it. The reason why the DMI system depicts overbought
situations during uptrends and oversold during downtrends is a
bit sophistcated cause it includes a thorough understanding of
crowd psychology and how peaks and bottoms form. But let us
explain it in a simple way.
When the ADX is above the +DI during an uptrend and both
the ADX and +DI are at high levels (i.e., 40 and above), thedifference between both +DM and –DM is bigger than +DM
itself, meaning not only that the market is witnessing strong
rises (i.e., buyers are getting stronger), but also that –DM isgetting much smaller (i.e., sellers are getting much weaker). Thistakes us to the extreme level of optimism when buyers get muchstronger and sellers become almost nonexistent. This what
happens when the difference between +DM and –DM is bigger
than +DM itself (because the difference takes into account –DM
too).
Having an ADX that surpasses the +DI at high levels meansthat sellers are getting weaker and weaker while buyers are
getting stronger and stronger; when the ADX begins to flatten
at these high levels, this is when we say “catch overbought!!!”because this flattening is the first sign of potential weakness
after the extreme optimism the market witnessed.

IFTA JOURNAL

2022 EDITION

Technical Analysis for the Trading Professional—”Oscillators Do Not Travel
Between 0 and 100”
By Connie Brown, CFTe, MFTA

It is always helpful to see concepts within a book applied toa current chart. It shows that the approach remains valid andtimeless. In this case study, we will look at a railway stock witha 14-period RSI to study the oscillator character described in thechapter “Oscillators Do Not Travel Between 0 and 100.” TechnicalAnalysis for the Trading Professional was first published in 1996
and then revised in 2011. The book was once required reading for
CMT III. It is now part of the IFTA CFTe syllabus.
Figure 1. CSX Corporation (Railroad) – Daily Bar Chartwith a 14-period RSI. The oscillator has a simple 9-period(red) and exponential 45-period (blue) moving average.

CSX in Figure 1 is a daily chart providing a current view asof January 11, 2021. A 14-period RSI forms bullish entry signals
when the RSI found support near 40. Focus on the range oftravel in the RSI (black line). RSI declines toward the 40 level
into the end of June 2020. The RSI creates a horizontal levelof support at 41-42 in CSX five times. Two of the five may bedifficult for you to detect for the moment.
You cannot change this chart to look at a different stock andthink the ranges created in CSX will apply to the new stock. Eachmarket creates a well-defined level that repeats but only fitsthat data set. A stock that favors RSI support at 46 is not a missbecause it does not use 41 like CSX in Figure 1.
Always study horizontal amplitude levels that repeat. We are
not looking at any diagonal lines that connect pivots as a trendline. Every stock or market will have a unique character, but therange guidelines will not change. Bear markets tend to fail near
RSI 65-68 and then fall towards 20 to 30. Bull markets hold RSI
40 to 46 and then push upwards toward 80 or 90. It is therefore
critical to read your chart and not just memorize a rule. As I
tend to keep permanent charts of stocks in like sectors, I do
not use the same chart workbooks to view multiple symbols.
Therefore, the analytics remain a fixed record. Treat eachchart’s time horizon, such as daily, weekly, or monthly charts,
as independent studies. Each will create its own clear repeatinglevel of support and resistance on a horizontal axis by RSI.

In Figure 1, each RSI test near the 40 level became an
opportunity to buy CSX stock in 2020. Figure 2 shows the firsttest near 41 in December 2019. It is marked on the far left sideof the Figure 2 chart. Such a signal is often overlooked and one
you may have missed when I stated there were five signals at
this oscillator displacement. But this first signal is extremely
important. It is important because the RSI pivot preceded the
sharp break to follow when RSI plummeted to new extreme
lows. This level of support prior to a shock is nearly always
retested after a shock extreme.
Figure 2. CSX Corporation (Railroad) – Daily

Most will overlook the strongest signal in the chart of thefive tests near the 41 level. It is the retest signal at RSI 41 that
occurs in April 2020. Not only is this the retest of the December
2019 pivot, but it occurs at the crossover of its own two averages
where the short period average is crossing up through theslower moving average. This signal is much stronger than theconventional divergences we learn about in our basic training.
These mid-range signals at support or resistance are more
subtle and often mark the true launch of a major trend or
swing. Often, the juxtaposition of RSI and its crossing averages
mark the start of wave ‘iii’ within a developing swing. This
is what differentiates the skilled technician from an averagepractitioner. It is always about attention to the details. Does
the price action cause the RSI to often form a “W” pattern at
the horizontal support or resistance zone? Or is the character
like CSX defining a sharp RSI ‘V’ pattern off support? Does theoscillator form ‘V’ bottoms but ‘M’ tops into resistance? The
market will show you how it wants to work if you look closely.
This is how to develop a probability for the signal forming. If
the market respected the horizontal level several times in thepast, it will likely be a true signal when it appears the next timewithin this target zone. If it often fails at a repeating horizontal
zone; you have your warning not to trust it this time either.
Oscillators can indicate a probability.
The price data set will give you a clear picture of how it moves
IFTA.ORG PAGE 75

IFTA JOURNAL

2022 EDITION

the RSI into a reversal signal in both tops and bottoms. Let the market guide you rather than putting yourself in a position to go out ona hunt for a preconceived expectation. The more you expect, the less you will see within your chart.
In Figure 1 a horizontal line of resistance is marked in RSI with caution arrows pointing down at the resistance zone near 68. The
65-68 level is often the retracement target for RSI in a correcting bear market. While each pullback showed support near the bullish 40
level, the repeating failures near 68-70 should raise a concern that requires further examination.
Figure 3. CSX Corporation (Railroad) – Monthly Equivolume Chart

Figure 3 is a monthly chart of CSX Corporation showing
prices up to January 11, 2021. Rather than viewing the priceaction in a bar chart, an Equivolume chart is plotted. This gives
an opportunity to show you a charting method underutilized.
On the bottom of the chart are bars displaying volume. They
are conventional, but the volume width looks odd, as they haveto mark the same time interval as the bars in prices that are
not conventional. The chart shows a steady trending decline
in volume since 2017 without much more information. An
Equivolume chart shows the price range of the period like abar chart, but the width of the bar reflects volume during thisperiod. The wider the bar, the more volume contained within the
period—in this case per month. It is easy to spot wave ‘iii’s’ andstrongest swings. The circled price action in Figure 3, containing
the current rally since the March 2020 low, shows progressively
narrowing bars of diminishing volume. Not only are the bars
narrow in the current swing, but they are compressing andshow weaker participation relative to the character within any
prior swing in the chart. The RSI range failing often near 68
is providing us with a warning. The volume within the rally is

PAGE 76 IFTA.ORG

waning as is befitting a fifth wave position.
Equivolume does not show the open and closing price, but
this is not how we are using this chart style. Compare the seriesof bar widths within the duration of each swing. The more you
study volume charting techniques with RSI, the quicker you
will realize you are reading volume within RSI itself. Volume
additions to your chart soon become unnecessary. Not that you
are ignoring volume, but you are reading volume within theoscillator position, and the ranges it is traveling carry more
information than a novice will read from the indicator.
One last takeaway for clarification as it is extremely
important: A chart that makes an extreme RSI low in a shock
environment will rise and then test the RSI amplitude of theoscillator low behind or prior to the extreme displacement. If you
study Figure 2, CSX made such a test. It is this amplitude testat the same level before and after the extreme pulse down in
RSI that is often the safest entry in a new trend after the shock.
However, be aware of the environment and range the oscillator
travels after the test. It may carry an early warning that thetrend is not as healthy as one would like to believe.

IFTA JOURNAL

2022 EDITION

Author Profiles
Michael A. Gayed, CFA
Michael A. Gayed is portfolio manager of the
ATAC Fund Family at Toroso Investments, aninvestment management company specializingin ETF focused research, investment strategies,
and services designed for financial advisors,
RIAs, family offices, and investment managers.
Prior to Toroso Investments, Michael was the co-portfolio
manager and chief investment strategist at Pension Partners,
LLC, an investment advisor managing mutual funds andseparate accounts.
Michael is the author of five award-winning research
papers on market anomalies and investing. He was an active
contributor to MarketWatch for a number of years and has
been interviewed on CNBC, Bloomberg, and Fox Business aswell as the Wall Street Journal Live for his unique approach tointerpreting market movements.
Michael earned his B.S. with a double major in finance andmanagement at New York University Stern School of Business.
He became a CFA Charterholder in 2008.
Carlos Jaureguízar, Ph.D.
Carlos Jaureguízar, Ph.D., is the CEO of Robexia
AI TechConsulting, an artificial intelligencelaboratory specialized in several sectors, with afocus on finance and advertising throughmachine learning. Carlos previously worked in
the BBVA Treasury Department and has held
positions on the IFTA board and as IEATEC chairman. He
currently participates in IEATEC’s Committee for the Transition
to Artificial Intelligence. Carlos holds a degree in economics(UAM), a master’s in financial markets (UAM), and is certified
ACI FX and MM Level I. In addition, he passed the DEA examwith a Black-Litterman inverse optimization model dissertation
and received a Ph.D. in applied economy with a merit with
distinction grade, cum laude, after the defense of the thesis: "Towhat extent do the candlestick patterns anticipate thecontinuation or turn of the previous trend of quoted prices?"
In addition to authoring numerous articles and actively
participating in forums and conferences, Carlos has written
two trading books: High Profitability in the Stock Market andOther Financial Markets and Candlestick for Traders. Carlos is thefounder of Noesis, Robexia, and Finavid and a founding partner ofContacto, an advertising agency, and Aquinas American School.
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 IFTA Journal director,
carrying the CFTe designation and the Australian AMT(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 (STA) for over 30 years.
Sandra Nieto
Sandra Nieto is COO of Robexia Tech Consulting,an artificial intelligence laboratory for thefinancial and advertising sector. Previously, she
worked first as a senior analyst and later as anaccount executive for Noesis SL, dedicated tothe design and development of financial
products, services, and projects. Sandra has a degree in masscommunication (UMA) and specialized in marketing andadvertising (UCM). Working for the financial sector, shedeveloped an interest in technical analysis, which allowed her toparticipate in several published articles dedicated to the subject.
She’s currently a member of the IEATEC’s Artificial Intelligence
Committee, dedicated to introducing new AI models andpossibilities for the study of this sector.
Shinji Okada, CMTA, CFTe, MFTA
Shinji Okada majored in political science at
Nihon University Graduate School of Law andafter graduation, started his business career atSecurities Japan Co. Ltd., Tokyo, where heengaged in the sales of various securities (e.g.,
Japanese/U.S. equities, fixed income andinvestment trusts), through which he became interested in thepractical applications of technical analysis. As his interest intechnical analysis grew, he learned that so many investors
tended to sustain losses panicking at various trend turning
points. It is this experience that has drawn him to the researchof the regression analysis of trends to find their turning
points, making the best use of famous technical analysis tools(e.g., Dow Theory, Elliot Wave Theory, Bollinger Bands). In
March 2020, he joined QUICK Corp. and has mainly been
engaged in planning and providing new and better information
services to financial institutions while continuing his researchin technical analysis.

IFTA.ORG PAGE 77

IFTA JOURNAL

2022 EDITION

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 the related IT implementations.
As a private investor, Oliver is interested in technical analysis
and due to his mathematical and programming expertise, he is
now focused on the developing and back-testing of mid-term
trading strategies based on more sophisticated algorithms.
He joined the VTAD in 2011 when he became a freelancer andcurrently Oliver serves as deputy manager of the VTAD’sregional group in Dusseldorf.
Oliver received his MFTA for his thesis on the application of
the Empirical Mode Decomposition to technical analysis, which
was rewarded with the John Brooks Memorial Award in 2019. As
a frequent attendee of IFTA’s conferences, he also presented theresults of his MFTA research at the IFTA Conference in Cairo. In
the current paper, Oliver continues his research on the Empirical
Mode Decomposition and presents its application for trading on
shorter time frames.
Christoph T. Wildensee, Ph.D., MFTA
Christoph Wildensee has a Ph.D. in businessadministration. He is a well-known auditor anddata/process analyst at enercity AG in
Hannover, Germany. Christoph’s special focus ison finding errors and optimization potential in
IT systems relevant to accounting, including, inparticular, the Energy Trade and Risk Management (ETRM)
system, which is used to handle all energy trading activities at
enercity. He was also a member of the team evaluating the new
Pioneer/Hitachi-ABB ETRM system.

PAGE 78 IFTA.ORG

IFTA JOURNAL

2022 EDITIONIFTA Staff

IFTA Board of Directors

Executive Director
Kristen LeBlanc, MPA, CAE

IFTA HEADQUARTERS
International Federation of Technical Analysts
1300 Piccard Drive, Suite LL 14
Rockville, MD 20850 USA
Phone: +1 (240) 404-6508
Fax: +1 (301) 990-9771
Email: admin@ifta.org | Web: www.ifta.org

Senior Vice President, Meetings
Grace L. Jan, CAE, CMP
Senior Member Services Manager
Linda Bernetich, CAE
Production Manager
Maryia Alenchyk
Managing Editor
Lynne Agoston
Director of Accounting Services
Dawn Rosenfeld

President
Wieland Arlt, CFTe (VTAD)
Treasurer; Website Director
Karin Roller, CFTe (VTAD)
Secretary; Membership Director
Alek Jankowski, BE, M.Eng.Sc., Grad.Dip.Mgt. (ATAA)
Vice President; Vice President, Asia-Pacific
Hiwon Yoon, Ph.D., CMTA (NTAA)
Vice President, Americas; Conference Director
Jeanette Young, CFP®, CMT, M.S. CFTe (AAPTA)
Vice President, Middle East and Africa; Immediate Past
President
Mohamed El Saiid, MFTA, CFTe (ESTA)
Vice President, Europe
Clive Lambert, MSTA, CFTe (STA)
Education Director
Saleh Nasser, CMT, CFTe (ESTA)
Examination Director
Gregor Bauer, Ph.D., CFTe (VTAD)
Marketing and Webinar Director
Ron William, MSTA, CFTe (SAMT)
Director
Giovanni Trombetta, Electronic Engineer, CFTA (SIAT)
Director
Francesco Caruso, MFTA (SIAT)
Director
Nik Ihsan Bin Raja Abdullah, MSTA, CFTe (MATA)
Director
Yukitoshi Higashino, MFTA (NTAA)IFTA.ORG PAGE 79

Certified Financial Technician (CFTe) Program
IFTA Certified Financial Technician (CFTe) consists of the CFTe I and CFTe II
examinations. Successful completion of both examinations culminates in theaward of the CFTe, an internationally recognised professional qualification intechnical analysis.

Examinations
The CFTe I exam is multiple-choice, covering a wide range of technicalknowledge and understanding of the principals of technical analysis; it isoffered 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 ofknowledge and experience in applying various methods of technical analysis.
The candidate is provided with current charts covering one specific market(often an equity) to be analysed, as though for a Fund Manager.
The CFTe II is also offered in English, French, German, Italian, Spanish, Arabic,
and Chinese, typically in April and October of each year.

Curriculum
The CFTe II program is designed for self-study, however, IFTA will
also be happy to assist in finding qualified trainers. Local societies
may offer preparatory courses to assist potential candidates.
Syllabuses, Study Guides and registration are all available on the
IFTA website at http://www.ifta.org/certifications/registration/.

To Register
Please visit our website at http://www.ifta.org/certifications/registration/ for registration details.

Cost
IFTA Member Colleagues
CFTe I $550 US
CFTe II $850* US

Non-Members
CFTe I $850 US
CFTe II $1,150* US*Additional Fees (CFTe II only):$100 US applies for non-IFTA proctored exam locations

Master of Financial Technical Analysis (MFTA) Program
IFTA’s Master of Financial Technical Analysis (MFTA) represents the highest
professional achievement in the technical analysis community, worldwide.
Achieving this level of certification requires you to submit an original body ofresearch in the discipline of international technical analysis, which should beof practical application.

Examinations
In order to complete the MFTA and receive your Diploma, you must writea research paper of no less than three thousand, and no more than five
thousand, words. Charts, Figures and Tables may be presented in addition.
Your paper must meet the following criteria:• It must be original• It must develop a reasoned and logical argument and lead to a soundconclusion, supported by the tests, studies and analysis contained in thepaper• The subject matter should be of practical application• It should add to the body of knowledge in the discipline of international
technical analysis

Timelines & Schedules
There are two MFTA sessions per year, with thefollowing deadlines:
Session 1“Alternative Path” application deadline
Application, outline and fees deadline
Paper submission deadline
Session 2“Alternative Path” application deadline
Application, outline and fees deadline
Paper submission deadline

February 28
May 2
October 15
July 31
October 2
March 15 (of thefollowing year)

To Register
Please visit our website at http://www.ifta.org/certifications/master-of-financial-technical-analysis-mfta-program/for further details and to register.

Cost$950 US (IFTA Member Colleagues);$1,200 US (Non-Members)