clean formatting:

A Century of Evidence

 

on Trend-Following Investing

 

BRIAN HURST, YAO HUA OOI, AND LASSE HEJE PEDERSEN

 

BRIAN HURST novel data on commodity futures prices that s an investment style, trend fol- A

is a principal at AQR  we hand collect and transcribe from annual lowing has existed for a very

Capital Management  5 reports of the Chicago Board of Trade. long time. Some 200 years ago,

in Greenwich, CT. We find that time-series momentum the classical economist David

Y has been consistently profitable throughout AO  H UA  O OI Ricardo’s imperative to “cut short your

is a principal at AQR  losses” and “let your profits run on” sug- the past 137 years. We examine the strategy’s

Capital Management  gests an attention to trends. A century later, decade-by-decade performance, its correla-

in Greenwich, CT. the legendary trader Jesse Livermore stated tion to major asset classes, and its performance

 

L explicitly that the “big money was not in the in historical equity bull and bear markets.  ASSE  H EJE  P EDERSEN individual fluctuations but in…sizing up the This wealth of data also provides context for is a principal at AQR  1 Capital Management in  entire market and its trend.” evaluating how the strategy performs across

Greenwich, CT, and a  The most basic trend-following strategy various macroeconomic environments—

professor at Copenhagen  is time-series momentum—going long such as recessions versus booms, war versus

Business School in  markets with recent positive returns and peacetime, high- versus low-interest-rate

Frederiksberg, Denmark,  shorting those with recent negative returns. regimes, high- versus low-volatility periods, and New York University

in New York, NY. The literature shows that since 1985, time- high- versus low-inflation periods, and high-

series momentum has been profitable, on versus low-correlation periods. Although

average, for nearly all equity index futures, the strategy has historically performed well

fixed-income futures, commodity futures, across most of these economic environments,

and currency forwards.2 The strategy explains the characteristic that appears to have affected

the strong performance of managed futures the performance the most is correlation—the

funds from the late 1980s, when fund returns strategy has performed the best during low-

and index data first become available,3 and correlation environments. We also estimate

captures most forms of trend-following the effects of fees and transaction costs and

investing.4 evaluate the benefits of allocating to a trend-

In this article, we seek to establish following strategy from a traditional stock/

whether the strong performance of trend bond portfolio.

following is a statistical fluke of the last few

decades or a more robust phenomenon that DATA

exists over a wide range of economic condi-

tions. We construct a time-series momentum In our analysis, we use monthly returns

strategy all the way back to 1880 using histor- for 67 markets across four major asset classes:

ical data from a number of sources, including 29 commodities, 11 equity indices, 15 bond

 

FALL 2017 THE JOURNAL OF PORTFOLIO MANAGEMENT markets, and 12 currency pairs. To study the broadest thus be viewed as an out-of-sample test of those papers.

set of markets over the longest time series in which we These studies find that time-series momentum captures

can find data, we combine a large number of existing well the performance of the managed futures indices and

datasets and hand collect new data that have not been manager returns, including the largest funds, over the

studied previously, to our knowledge. In particular, we past few decades when data on such funds exist.

construct a novel dataset of daily commodities futures Specifically, we construct an equal-weighted com-

prices by manually transcribing the “Annual Report bination of 1-month, 3-month, and 12-month time-

of the Trade and Commerce of the Chicago Board of series momentum strategies for the 67 markets cited

Trade” going back as early as 1877. The hand-collected above—from as far back as January 1880 to December

data extends to 1951, when electronic datasets became 2016. The strategy is rebalanced each month as follows.

available. For the study, we use a monthly sample based For each of the three time-series momentum strate-

on end-of-month prices and returns. gies, the position taken in each market is determined

We construct a monthly time series of futures by assessing the past excess return in that market over

returns by simulating that we hold, and “roll,” one of the relevant look-back horizon. A positive past excess

the most liquid futures contracts. In particular, we “roll” return is considered an “up” trend and leads to a long

by simultaneously performing two trades: (1) selling the position; a negative past excess return is considered a

futures contract that we held and (2) buying the next “down” trend and leads to a short position.

futures contract, while collecting the current prices of Therefore, each strategy always holds either a long

both contracts to make the analysis as realistic as possible. or short position in every market. Each position is sized

We focus on closing prices when available, but in the to target the same amount of volatility, both to pro-

early sample of commodities, we only have access to vide diversification and to limit the portfolio risk from

high and low prices; thus, we use an average of these. any one market. The positions across the three strate-

For all markets, we use futures returns when they gies are aggregated each month and scaled such that the

are available, but for asset classes other than commodi- combined portfolio has an annualized ex ante volatility

ties, futures are not available back to 1877. Hence, prior 7 target of 10% annualized. The volatility scaling proce-

to the availability of futures data, we rely on cash index dure ensures that the combined strategy targets a consis-

returns financed at local short-term interest rates for tent amount of risk over time, regardless of the number

each country. Our time-series momentum strategy of markets traded at each point in time.

requires three years of past data to estimate volatilities, Finally, we subtract transaction costs and fees. The

so our sample of simulated strategy returns runs from transaction costs are based on recent estimates of average

1880 to the end of 2016. We do not have data on each of transaction costs in each of the four asset classes, as well

the 67 markets during each month in this sample, so we as an estimate of how much higher these transaction

construct the trend-following strategies using the set of costs were historically, based on Jones [2002]. We note

assets for which return data exist at each point in time. that transaction costs are estimated with a significant

Appendix A shows the markets for which we have data amount of uncertainty, and the strategy may also be

at each point in time and the respective data sources for subject to other costs such as the costs of “rolling”

each market and each time period.6 futures contracts, which are not accounted for in our

simulations. To simulate fees, we apply a 2% manage-

 

CONSTRUCTING THE TIME-SERIES  ment fee and a 20% performance fee subject to a high- 8 water mark, as has been typical for hedge funds. Details MOMENTUM STRATEGY on transaction costs and fee simulations are given in

Trend-following investing involves going long Appendix B.

markets that have been rising and going short markets

that have been falling, betting that those trends con- PERFORMANCE OVER A CENTURY tinue. We create a time-series momentum strategy that

is simple, without many of the often arbitrary choices of Exhibit 1 shows the performance of the time-series

more complex models. Our methodology follows that of momentum strategy over the full sample since 1880, as

Moskowitz et al. [2012] and Hurst et al. [2013] and can well as for each decade over this time period. We report

 

A CENTURY OF EVIDENCE ON TREND-FOLLOWING INVESTING FALL 2017 E X H I B I T 1

Performance of Time-Series Momentum, 1880–2016

 

Note: This exhibit shows the strategy’s annualized excess returns (i.e., returns in excess of the risk-free interest rate), before and after simulated transaction costs, and gross and net of hypothetical 2-and-20 fees.

 

the results gross and net of simulated transaction costs interest rate volatility, they may slow down the rate

and consider returns both before and after fees. at which information is incorporated into prices, thus

The performance has been surprisingly consis- creating trends. The fact that trend-following strategies

tent over an extensive time horizon that includes the have performed well historically indicates that these

Great Depression, multiple recessions and expansions, behavioral biases and nonprofit-seeking market partici-

multiple wars, stagflation, the global financial crisis, and pants have likely existed for a long time.

periods of rising and falling interest rates. Our long-term To study the robustness and source of these results,

out-of-sample evidence suggests that it is unlikely that Exhibit 2 considers the performance separately for the

the existence of price trends in markets is a product of 1-month, 3-month, and 12-month signals. We see that

statistical randomness or data mining. Indeed, the first trend-following at each of these horizons has delivered

10 decades of data is out-of-sample evidence relative positive returns in each decade. To further study the

to the literature, and the performance remains strong robustness and ability to implement these strategies, we

during this period. Trends thus appear to be a pervasive consider a version in which the signal is lagged a month.

characteristic of speculative financial markets over the In other words, if the trend signal is computed at the

long term. last trading day of January, we assume that we trade

Time-series momentum strategies perform well on this signal only at the end of February (in the same

only if prices trend more often than not. A large body of year). As seen in Exhibit 2, these strategies also deliver

research suggests that price trends exist in part because of positive returns in most decades, but the performance

long-standing behavioral biases exhibited by investors,9 naturally deteriorates with the lagging, especially for the

such as anchoring and herding, as well as the trading shorter-term signals.

activity of nonprofit-seeking participants, such as central Given the consistent performance of the strategy

banks and corporate hedging programs. For instance, over time, it is also interesting to study the consis-

when central banks intervene to reduce currency and tency across markets. For this, Exhibit 3 reports the

 

FALL 2017 THE JOURNAL OF PORTFOLIO MANAGEMENT E X H I B I T 2

Performance of Time-Series Momentum by Signal

 

Notes: This exhibit shows the annualized gross Sharpe ratio (i.e., excess return before simulated transaction costs and fees divided by volatility) separately for each time-series momentum signal based on the past 1-month, 3-month, and 12-month trend, respectively. Also, the table shows the performance when each of these signals is lagged by one month.

 

risk-adjusted returns (as measured by the Sharpe ratio) large equity bull and bear markets. Exhibit 5 shows

of each of the 67 markets included in our time-series the annual simulated returns to the strategy, plotted

momentum strategy over the full sample from 1880 to against the returns to the U.S. equity market from 1880

2016. We see that the strategy has delivered positive to 2016. The “smile” shows that trend following has

average returns in each market, with an average Sharpe done particularly well in extreme up or down years for

ratio of approximately 0.4. the stock market, echoing results from recent decades

We next consider the out-of-sample evidence for (Fung and Hsieh [1997] and Moskowitz et al. [2012]).

individual markets relative to the initial time-series This strong performance in bear markets over the cen-

momentum study of Moskowitz et al. [2012], who tury extends the evidence that has been documented

used data starting in 1985. To do this, we report the since the 1980s, as exemplified most recently with the

performance of each market before 1985 in Exhibit 4, strong performance of trend following during the global

including only markets with at least 10 years of data financial crisis.

during this subsample, 1880–1984. Again, we see a As another way to evaluate the diversifying proper-

remarkably consistent performance across markets and ties of trend following during crisis periods, we consider

asset classes. the performance during peak-to-trough drawdowns for

the traditional 60/40 portfolio, which invests 60% in

PERFORMANCE DURING CRISIS PERIODS U.S. equities and 40% in U.S. bonds.10 Exhibit 6 shows

the performance of the time-series momentum strategy

The returns to the strategy have exhibited low cor- during the 10 largest drawdowns experienced by this

relations to stocks and bonds over the full time period, 60/40 portfolio over the past 137 years. We see that

as well as in each decade, as shown in Exhibit 1. Even the time-series momentum strategy experienced posi-

more impressively, the strategy has performed best in tive returns in 8 out of 10 of these stress periods and

 

A CENTURY OF EVIDENCE ON TREND-FOLLOWING INVESTING FALL 2017 E X H I B I T 3

Time-Series Momentum Performance by Individual Asset: Full Sample, 1880–2016

 

Note: This exhibit shows the Sharpe ratio of time-series momentum (gross of fee, gross of cost) by asset.

 

delivered significant positive returns during a number from sharp market movements in those environments.

of these events. Hence, the valuable diversification ben- Nevertheless, the tendency for the strategy to do well,

efits that trend-following strategies delivered during the on average, in major bear markets, while still achieving

2007–2009 Global Financial Crisis may represent a more a positive return, on average, makes it a potentially valu-

general pattern when you consider how the strategy has able diversifier for investor portfolios.

behaved in other deep bear markets over the century. Given the attractive returns and diversifying char-

Why have trend-following strategies tended to do acteristics of a time-series momentum strategy, allo-

well in bear markets? The intuition is that most bear cating to this strategy would have improved a traditional

markets have historically occurred gradually over several portfolio’s performance over the past 137 years. Spe-

months, rather than abruptly over a few days, giving cifically, Exhibit 7 shows the simulated effect of allo-

trend followers an opportunity to position themselves cating 20% of the capital from a 60/40 portfolio to the

short after the initial market decline and profit from time-series momentum strategy. We see that such an

continued market declines. In fact, the average peak- allocation reduced the maximum portfolio drawdown,

to-trough drawdown length of the 10 largest 60/40 lowered portfolio volatility, and increased portfolio

drawdowns between 1880 and 2016 was approximately returns.

15 months. In contrast, the strategy may not perform We can also consider the stress periods for time-

well in bear markets that occur very rapidly, such as series momentum (rather than the stress periods for

the 1987 stock market crash, because the strategy may the overall market), which tend to be associated with

not be able to take positions quickly enough to benefit periods of sharp reversals across multiple markets or

 

FALL 2017 THE JOURNAL OF PORTFOLIO MANAGEMENT E X H I B I T 4

Time-Series Momentum Performance by Individual Asset: Before 1985 (new evidence)

Notes: This exhibit shows the Sharpe ratio of time-series momentum (gross of fee, gross of cost) by asset, 1880–1984. We include only assets that have at least 10 years of data before 1985. This evidence is out of sample relative to the study of Moskowitz et al. [2012].

 

E prolonged periods in which many markets exhibit a X H I B I T  5

Time-Series Momentum “Smile,” 1880–2016 lack of clear trends. Specifically, Exhibit 8 shows the

10 largest drawdowns of the time-series momentum

strategy, including the amount of time the strategy

took to realize and recover from each drawdown. The

drawdown is computed as the percentage loss since the

strategy reached its highest-ever cumulative return (its

high-water mark). Naturally, the strategy has experi-

enced significant drawdowns, losing up to 25%, over

extended time periods.

 

PERFORMANCE ACROSS ECONOMIC

ENVIRONMENTS

 

We next consider the performance across different

economic environments. This is interesting both to under-

stand the nature of the strategy and to further analyze its

Note: This exhibit shows the annual returns of time-series momentum  potential diversification benefits. Indeed, investors ben-

(gross of fee, net of cost) vs. U.S. equity market returns, as well  efit most from strategies that deliver high returns during

as the fitted second-order polynomial.

 

A CENTURY OF EVIDENCE ON TREND-FOLLOWING INVESTING FALL 2017 E X H I B I T 6

Time-Series Momentum during the 10 Worst Drawdowns for 60/40

Note: This exhibit shows the returns of time-series momentum (gross of fee, net of cost) and return of the portfolio that invested 60% in U.S. stocks and 40% in U.S. bonds over the 10 time periods selected as the largest drawdowns for the latter portfolio.

 

E X H I B I T 7

Combining 60/40 with an Allocation to Time-Series Momentum, January 1880 to December 2016

 

Notes: This exhibit reports the historical performance characteristics of the 60/40 portfolio that invested 60% in U.S. equities and 40% in U.S. bonds. Also, the table reports the performance of a portfolio with 80% invested in the 60/40 portfolio (gross of fees and transaction costs) and 20% invested in the time-series momentum strategy (net of fees and transaction costs).

 

“tough times” when their marginal utility of wealth is and, again we find very similar performance for time-

high. We have already considered the performance during series momentum. The strong performance during reces-

crisis periods as defined by drawdowns by 60/40, but sions and different inflation regimes is evidence of the

several other economic environments are of interest. historical diversifying properties of the strategy.

Exhibit 9, Panel A, considers the performance of It is also interesting to consider the performance

time-series momentum across different regimes, starting during “tough times” in the sense of wartime. There have

with the two classic macroeconomic characteristics (or been so many conflicts around the world that defining

themes), growth and inflation. To analyze macroeconomic wartime and peacetime is not straightforward. To have

growth, we separate the months into recessions and a clear-cut definition, we focus on the largest wars—

booms as defined by the NBER Business Cycle Dating defined as those with more than 1 million casualties with

Committee. We see that the performance is similar across at least three nations at war—which are World War 1,

these environments. The average excess return has been World War 2, the Vietnam War, and the Korean War,

slightly higher during booms, but the difference is not with “peace” being all other time periods (again, despite

statistically significant. Next, the exhibit reports the per- the numerous other conflicts). We see that the strategy

formance across low- versus high-inflation environments, has performed similarly across both samples. If anything,

 

FALL 2017 THE JOURNAL OF PORTFOLIO MANAGEMENT E X H I B I T 8

The 10 Largest Drawdowns of Time-Series Momentum, 1880–2016

 

Note: This exhibit reports the 10 largest peak-to-trough drawdowns of the time-series momentum strategy, calculated using gross of fee, net of cost returns.

 

the performance has been better during major wars, but Such a prospective analysis could be used to time a

the difference is not statistically significant. trading strategy, in principle, but we note several caveats.

Lastly, the table in Exhibit 9, Panel B, considers First, certain variables are not known in real time (e.g.,

bull markets versus bear markets; bear markets are the dating of recessions), and second, the classification

définies comme des périodes au cours desquelles le tirage au sort du pic au creux de l'inflation basse par rapport à l'inflation élevée est effectué ex post.

baisse du marché boursier américain est supérieure à 20 %, en tout état de cause, le panneau B montre que la performance de la tendance

and bull markets are all other times. The strategy has following was similar across groups. Hence, whereas

performed better in bear markets, but the difference is Panel B shows the apparent difficulty of improving the

only marginally significant, and perhaps the more robust strategy via timing decisions, Panel A shows the good

result is the smile curve in Exhibit 5. news that the strategy appears to be relatively robust

Exhibit 9, Panel B, considers the same economic across various economic environments.

environments, but now the economic environment is In Exhibit 10, we consider different economic

lagged by one month. For example, this panel considers indicators, while separating the time periods into quin-

the performance of trend-following investing during the tiles (because each of these indicators are numerical,

month after a recession month (so the month in which rather than binary variables such as war/peace or reces-

the return is calculated might, or might not, continue sion/boom). In particular, we consider the S&P vola-

to be a recession). tility (estimated over the most recent 36 months), the

Panels A and B thus address different issues: 3-month change in the estimated volatility, the average

Panel A takes the perspective of an investor who stands absolute pairwise correlations across the markets traded

at the end of each month, looking back at the perfor- in the portfolio, and the T-bill yield. Panel A reports the

mance of trend following in relation to the economic contemporaneous time-series momentum performance,

environment experienced during the same month. This while Panel B reports the performance in the following

perspective cannot be used to make timing decisions in month (or, said differently, the economic indicator is

the portfolio because the economic environment was lagged one month, as in Exhibit 9, Panel B).

not known ahead of time. In contrast, Panel B takes the Starting with the first row of Exhibit 10, Panel A,

perspective of an investor who stands at the beginning of we see that time-series momentum has performed best in

each month, looking at the performance of trend fol- quintiles 3 and 2, where the contemporaneous S&P 500

lowing in the coming month in relation to the economic volatility was average or just below average, although this

environment experience in the previous month. result could also simply reflect randomness in the data.

 

A CENTURY OF EVIDENCE ON TREND-FOLLOWING INVESTING FALL 2017 E X H I B I T 9

Time-Series Momentum across Economic Regimes: Binary Indicators

 

Notes: This exhibit shows the performance of the time-series momentum strategy before fees and after simulated transaction costs. For each economic regime, we report the strategy’s annualized excess return, its t-statistic, volatility, and Sharpe ratio. The regimes are “recession vs. boom” indicators as defined by NBER Business Cycle Dating Committee; “inflation: low vs. high” based on U.S. CPI from 1913 to 2016 and before 1913, based on Shiller [2000] who uses the Warren and Pearson [1935] price index; “war vs. peace,” where war periods are World War 1, World War 2, the Vietnam War, and the Korean War and peace are other time periods; “stock market: bull vs. bear,” where bear markets are defined as periods where peak to trough drawdown of U.S. equity market is greater than 20% and bull market is all other times. In Panel A, we consider the contemporaneous effect—for example, for “war,” we compute the return during each recession month of war even if the war started midmonth. In Panel B, we lag the indicator of the economic environ-ment—for example, for “war,” we compute the return each month following a war month.

 

Further, the performance has been similar across quin- lagged correlations are associated with higher average

tiles based on changes in equity market volatility and the future returns, while high correlations are associated

level of Treasury bill yields. While some practitioners with low returns. To understand this finding, note first

have described trend following as a strategy that is “long that for given notional exposures, a higher correlation

volatility,” the quintile sorts on changes in equity vola- implies a higher risk at the portfolio level. However,

tility show that the strategy’s performance has historically because our portfolio construction methodology seeks

been relatively consistent across periods of increasing and to target a constant volatility, this effect is “undone” by

decreasing market volatility. Looking at the pairwise cor- reducing all position sizes when correlations are high.

relations across markets, we see that lower correlations These lower position sizes in turn may lead to lower

appear to have been associated with better performance. average returns, which can help explain why the strategy

Turning to Panel B, we see a similar pattern, which performs worse during times of high correlations. Said

could be related to the persistence of the economic differently, when correlations are high, there are fewer

indicators. Again, the only indicator with a monotonic truly different trends to bet on.

relation to the performance of time-series momentum is Exhibit 11 plots the time series of the average abso-

the pairwise correlation across markets. We see that low lute pairwise correlation across all the markets used in

FALL 2017 THE JOURNAL OF PORTFOLIO MANAGEMENT E X H I B I T 1 0

Time-Series Momentum across Economic Regimes: Quintiles

 

Notes: This exhibit shows the performance of the time-series momentum strategy before fees and after simulated transaction costs. For each economic regime, we report the strategy’s annualized excess return, its t-statistic, volatility, and Sharpe ratio. We consider the economic indicators: S&P volatility (estimated over the most recent 36 months), the 3-month change in the estimated volatility, the average absolute pairwise correlations across the markets, and the T-bill yield. For each indicator, we sort the data into quintiles. Panel A reports the contemporaneous time-series momentum performance, and Panel B reports the time-series momentum performance in the following month.

 

our strategy. We see that the average correlations have CONCLUSION

been relatively stable over time, but increased meaning-

fully from late 2008 until the middle of 2014. During Trend-following investing has performed well in

this period, the many markets moved together based on each decade for more than a century, as far back as we

“risk-on/risk-off,” leading to higher correlations both can get reliable return data for several markets. Our

within and across asset classes. analysis provides significant out-of-sample evidence

across markets and asset classes beyond the substantial

 

A CENTURY OF EVIDENCE ON TREND-FOLLOWING INVESTING FALL 2017 E X H I B I T 1 1

Average Absolute Pairwise Asset Correlations

 

Note: This exhibit shows the absolute pairwise correlations across all assets available at each time, estimated over 36 months.

 

evidence already in the literature. Further, we find that long bond. Futures returns are obtained from Morgan Markets

a trend-following strategy performed relatively simi- and Bloomberg. We use country-level cash bond returns from

larly across a variety of economic environments and Datastream, Ibbotson, and Global Financial Data (GFD) prior

 

tional allocation. This consistent long-term evidence from GFD and Ibbotson to a constant duration of 4 years,  assuming a duration of 2 years for the U.S. 2-year note, 4 years  suggests that trends are pervasive features of global provided significant diversification benefits to a tradi- to the availability of futures returns. We scale monthly returns

markets. for the U.S. 5-year note and German REX Index, 20 years for

the U.S. long bond, and 7 years for all other bonds.

Currencies. The universe of currency forwards covers

 

A the following 10 currencies: Australian dollar, Canadian  P P E N D I X  A dollar, German mark spliced with the euro, Japanese yen,

 

MARKETS AND DATA SOURCES Swiss franc, British pound, and U.S. dollar. We use spot and  New Zealand dollar, Norwegian krone, Swedish krona,

forward interest rates from Citigroup to calculate currency

We use historical return data from 67 markets, as seen

returns going back to 1989 for all the currencies except for

in Exhibit A1. Our data sources are as follows:

CAD and NZD, which go back to 1992 and 1996. To cal-

Indices boursiers. L'univers des contrats à terme sur indices boursiers

Pour calculer les rendements avant cela, nous utilisons les taux de change au comptant de

se compose des 11 marchés boursiers développés suivants : SPI

Datastream and LIBOR short rates from Bloomberg.

200 (Australia), S&P/TSE 60 (Canada), CAC 40 (France),

Commodities. We use a dataset of 29 different com-

DAX (Germany), FTSE/MIB (Italy), TOPIX (Japan), AEX

modity futures that is significantly longer than those previ-

(Netherlands), IBEX 35 (Spain), FTSE 100 (U.K.), Russell

ously used in the literature. Where available, we use futures

2000 (U.S.) and S&P 500 (U.S.). Futures returns are obtained

price data from Bloomberg. For periods before Bloomberg

from Datastream and Bloomberg. We use MSCI country-

data is available, we use futures prices from Commodity

level index returns and returns from Ibbotson, Global Finan-

Systems Inc. and a dataset constructed from the historical

cial Data (GFD), and the Yale School of Management prior

records of the Chicago Board of Trade. In particular, the data

to the availability of futures returns.

from 1877 to 1951 was manually transcribed from the Annual

Bond indices. The universe of bond index futures

Report of the Trade and Commerce of the Chicago Board

consists of the following 15 developed bond markets:

of Trade (CBOT). To ensure accuracy, we had two inde-

Australia 3-year bond, Australia 10-year bond, Euro Schatz

pendent data vendors transcribe the same dataset, and their

(2-year), Euro Bobl (5-year), Euro Bund (10-year), Euro Buxl

transcriptions were cross-verified to be mutually consistent.

(30-year), Canada 10-year bond, Japan 10-year bond (TSE),

We note that opening and closing prices were not recorded

long gilt, U.S. 2-year note, Italian 10-year bond, French

in the early part of the sample, so we use the average of high

10-year bond, U.S. 5-year note, U.S. 10-year note, and U.S.

and low prices before closing prices are available. Finally,

 

FALL 2017 THE JOURNAL OF PORTFOLIO MANAGEMENT E X H I B I T A 1

Data Sources by Market and Time Period

 

A CENTURY OF EVIDENCE ON TREND-FOLLOWING INVESTING FALL 2017 the roll schedule seeks to hold one of the most liquid futures  that the transaction costs are estimated with a significant

contracts across maturities. For example, each month in the  amount of uncertainty and do not include potential other

hand-collected data, we hold the nearest of the contracts  costs, such as the costs of rolling futures contracts. whose delivery month is at least two months away.

ENDNOTES

 

A P P E N D I X B We are grateful to Cliff Asness and John Liew for

helpful discussions, and to Ari Levine, Abhilash Babu,

SIMULATION OF FEES AND  David McDiarmid, Haitao Fu, and Vineet Patil for excellent

TRANSACTION COSTS research assistance.

1 Ricardo’s trading rules are discussed by Grant [1838]

To calculate net-of-fee returns for the time-series  and the quote attributed to Livermore is from Lefèvre [1923].

momentum strategy, we subtracted a 2% annual manage- 2 The original work on trend-following investing ment fee and a 20% performance fee from the gross-of-fee  and hedge funds was due to Fung and Hsieh [1997, 2001].

returns to the strategy. The performance fee is calculated and  We follow the time-series momentum methodology of

accrued on a monthly basis but is subject to an annual high- Moskowitz et al. [2012]. Research on trends also includes

water mark. In other words, a performance fee is subtracted  Cutler et al. [1991], Silber [1994], Erb and Harvey [2006],

from the gross returns in a given year only if the fund returns  Menkhoff et al. [2012], Baltas and Kosowski [2013, 2015],

are large enough that the fund’s end-of-year NAV exceeds  and Georgopoulou and Wang [2017]. The original evidence

every previous end-of-year NAV. on cross-sectional momentum (a strategy closely related to

Exhibit B1 reports the transaction costs used to simu- time-series momentum based on a security’s performance

late the net returns of the strategy. These costs are based on  relative to its peers) is due to Jegadeesh and Titman [1993]

proprietary estimates, made in 2012, of the average transac- and Asness [1994]. tion costs for each of the four asset classes, including market  3 See Fung and Hsieh [2001] and Hurst et al. [2013]. impact and commissions. Further, the transaction costs are  4 Levine and Pedersen [2016] show that time-series assumed to be twice as high from 1993 to 2002 and six times  momentum in its most general form can capture moving-

as high from 1880 to 1992, based on Jones [2002]. We note  average crossover signals and all other linear trend filters.

5 See also Greyserman and Kaminski [2014], who

consider a very long trend-following strategy based on spot

 

E  B 1 prices. Although returns computed based on spot prices are X H I B I T not implementable (because they do not include the effects of Simulated Transaction Costs the futures “roll down,” e.g., even if spot prices exhibit trends,

trend-following investing in futures would not be profitable

if the futures prices anticipate the trend, on average), our

actual futures data allow us to construct a more realistic ver-

sion of the strategy. Our century of evidence for time-series

momentum also complements the evidence that cross-sec-

tional momentum has delivered positive returns in individual

equities back to 1866 (Chabot et al. [2009]) and has worked

across asset classes (Asness et al. [2013]).

6 Although we have attempted to create as realistic a

simulation as possible, we are not claiming that this strategy

as described would have been implementable back in the

1880s. Modern day financing markets didn’t exist then, nor

did equity index and bond futures markets simulated in this

study. The commodities data throughout are based on traded

commodities futures prices and are therefore the most real-

istic, and by the 1980s, most of the returns are based on

Note: This exhibit shows the assumed transaction costs for the time  futures prices. The main point of the study is to show that

period 2003–2016. The transaction costs are assumed to be twice as  markets have exhibited statistically significant trends for well

high from 1993 to 2002 and six times as high from 1880 to 1992,  over a century. based on Jones [2002].

 

FALL 2017 THE JOURNAL OF PORTFOLIO MANAGEMENT

7 We use a simple covariance matrix estimated using  De Long, J.B., A. Shleifer, L.H. Summers, and R.J.

rolling three-year (equally weighted) monthly returns in the  Waldmann. “Positive Feedback Investment Strategies and

portfolio volatility scaling process. Destabilizing Rational Speculation.” The Journal of Finance,

8Although a 2/20 fee structure has been commonplace  Vol. 45, No. 2 (1990). pp. 379-395. in the industry, some managers charged higher management

and performance fees in earlier time periods. On the other  Erb, C.B., and C.R. Harvey. “The Tactical and Strategic

hand, there are also managers that charge lower fees for the  Value of Commodity Futures.” Financial Analysts Journal,

strategy today. Vol. 62, No. 2 (2006), pp. 69-97.

9Barberis et al. [1998], Daniel et al. [1998], De Long et al. [1990], Hong and Stein [1999], and Frazzini [2006]  Frazzini, A. “The Disposition Effect and Underreaction

discuss a number of behavioral tendencies that lead to the  to News.” The Journal of Finance, Vol. 61, No. 4 (2006),

existence of price trends. pp. 2017-2046.

10The 60/40 portfolio has 60% of the portfolio invested in the U.S. equity market and 40% invested in U.S. 10-year  Fung, W., and D.A. Hsieh. “Empirical Characteristics of

government bonds. The portfolio is rebalanced to the 60/40  Dynamic Trading Strategies: The Case of Hedge Funds.”

weights at the end of each month, and no fees or transaction  The Review of Financial Studies, Vol. 10, No. 2 (1997),

costs are subtracted from the portfolio returns. pp. 275-302.