A Century Of Evidence On Trend-Following Investing

Transcription

A Century of Evidence onTrend-Following InvestingBrian HurstFall 2014PrincipalExecutive SummaryYao Hua OoiPrincipalWe study the performance of 80,Lasse H. Pedersen, Ph.D.*extending the existing evidence by more than 100Principalyears. We find that trend following has deliveredstrong positive returns and realized a low correlationto traditional asset classes for more than a century.We analyze trend-following returns through ication benefits the strategy has historicallyprovided in equity bear markets. Finally, weevaluate the recent environment for the strategy inthecontextof*Brian Hurst and Yao Hua Ooi are at AQR Capital Management,and Lasse Heje Pedersen is at New York University, CopenhagenBusiness School and AQR Capital Management. We are gratefulto Cliff Asness, John Liew, and Antti Ilmanen for helpfulcomments, and to Ari Levine, Haitao Fu, Vineet Patil, JusvinDhillon, and David McDiarmid for excellent research assistance.AQR Capital Management, LLCTwo Greenwich PlazaGreenwich, CT 068301We originally published this paper in Fall 2012, and are nowreleasing an update due to the availability of additional historicalp: 1.203.742.3600data, which have allowed us to extend the backtest to 1880 andf: 1.203.742.3100increase the number of assets in the sample at every point in time.w: aqr.comtheselong-termresults.1

A Century of Evidence on Trend-Following InvestingSection 1: Introduction1context for evaluating the recent environment forthe strategy. We consider the effect of increasedAs an investment style, trend following has existedassets in the strategy as well as the increasedfor a very long time. Some 200 years ago, thecorrelations across markets since the 2008 Globalclassical economist David Ricardo’s imperative toFinancial Crisis. We also review a number of“cut short your losses” and “let your profits run on”developments that are potentially favorable for thesuggests an attention to trends. A century later, thestrategy going forward, such as lower trading costs,legendary trader Jesse Livermore stated explicitlylower fees and an increasing number of tradablethat the “big money was not in the individualmarkets.fluctuations but in . sizing up the entire market andits trend.”2Section 2: Constructing the Time Series MomentumStrategyThe most basic trend-following strategy is timeseries momentum — going long markets with recentTrend-followingpositive returns and shorting those with recentmarkets that have been rising and going shortnegative returns. Time series momentum has beenmarkets that have been falling, betting that thoseprofitable on average since 1985 for nearly all equitytrends continue. We create a time series momentumindex futures, fixed income futures, commoditystrategy that is simple, without many of the oftenfutures andcurrency3forwards.The uallongmodels.Specifically,Futures funds from the late 1980s, when fundcombination of 1-month, 3-month and 12-monthreturns and index data first becomes available.constructgoingexplains the strong performance of Managed4weinvolvesweightedtime series momentum strategies for 67 marketsacross four major asset classes — 29 commodities, 11This paper seeks to establish whether the strongequity indices, 15 bond markets and 12 currencyperformance of trend following is a statistical flukepairs — from as far back as January 1880 toofrobustDecember 2013. Since not all markets have returnphenomenon that exists over a wide range ofdata going back to 1880, we construct the strategieseconomic conditions. Using historical data from ausing the set of assets for which return data exist atnumber of sources, we construct a time serieseach point in time. We use futures returns whenmomentum strategy all the way back to 1880 andthey are available. Prior to the availability of futuresfindconsistentlydata, we rely on cash index returns financed at localprofitable throughout the past 135 years.5 Weshort-term interest rates for each country. AppendixexamineA lists the markets that we consider and the sourcethelastthatfewdecadesthe strategytheorahas beenstrategy’smoredecade-by-decadeperformance, its correlation to major asset classesand length of historical return data used.6and its performance in historical equity bull andbear markets. The wealth of data also providesFor each of the three time series momentumstrategies, the position taken in each market is2Ricardo's trading rules are discussed by Grant (1838) and the quoteattributed to Livermore is from Lefèvre (1923).3Moskowitz, Ooi and Pedersen (2012).4Hurst, Ooi and Pedersen (2012).5Our century of evidence for time series momentum complements theevidence that cross-sectional momentum (a closely related strategybased on a security’s performance relative to its peers) has deliveredpositive returns in individual equities back to 1866 (Chabot, Ghysels andJagannathan, 2009) and has worked across asset classes (Asness,Moskowitz and Pedersen, 2012).6While we have attempted to create as realistic a simulation as possible,we are not claiming that this strategy would have been implementable asdescribed back in the 1880s. Modern day financing markets didn’t existthen, nor did equity index and bond futures markets which are simulatedin this study. The commodities data throughout is based on tradedcommodities futures prices and is therefore the most realistic, and by the1980s most of the returns are based on futures prices. The main point ofthe study is to show that markets have exhibited statistically significanttrends for well over a century.

2A Century of Evidence on Trend-Following Investingdetermined by assessing the past return in thatmuch higher transaction costs were historicallymarket over the relevant look-back horizon. Acompared with the present, based on Jones (2002).positive past return is considered an “up” trend andTo simulate fees, we apply a 2% management feeleads to a long position; a negative past return isand a 20% performance fee subject to a high-waterconsidered a “down” trend and leads to a shortmark, as is typical for Managed Futures managers.8position. Therefore, each strategy always holdsDetails on transaction costs and fee simulations areeither a long or short position in every market. Eachgiven in Appendix B. Our methodology follows thatposition is sized to target the same amount ofof Moskowitz, Ooi and Pedersen (2012) and Hurst,volatility, both to provide diversification and to limitOoi and Pedersen (2012). These authors find thatthe portfolio risk from any one market. Thetimepositions across the three strategies are aggregatedperformance of the Managed Futures indices andeach month and scaled such that the combinedmanager returns, including the largest funds, overportfolio has an annualized ex ante volatility targetthe past few decades when data on such fundsof 10%.7 The volatility scaling procedure ensuresexists.seriesmomentumcaptureswellthethat the combined strategy targets a consistentamount of risk over time, regardless of the numberof markets that are traded at each point in time.Section 3: Performance Over a CenturyExhibit 1 shows the performance of the time seriesFinally, we subtract transaction costs and fees. Ourmomentum strategy over the full sample since 1880transaction cost estimates are based on currentas well as for each decade over this time period. Weestimates of average transaction costs in each of thereport the results net of simulated transaction costs,four asset classes, as well as an estimate of howand consider returns both before and after fees.Exhibit 1 — Hypothetical Performance of Time Series MomentumStrategy performance after simulated transaction costs both gross and net of hypothetical 2-and-20 fees.Time PeriodFull SampleJan 1880-Dec 2013By DecadeJan 1880-Dec 1889Jan 1890-Dec 1899Jan 1900-Dec 1909Jan 1910-Dec 1919Jan 1920-Dec 1929Jan 1930-Dec 1939Jan 1940-Dec 1949Jan 1950-Dec 1959Jan 1960-Dec 1969Jan 1970-Dec 1979Jan 1980-Dec 1989Jan 1990-Dec 1999Jan 2000-Dec 2013Gross of FeeReturns(Annualized)Net of 2/20 FeeReturns(Annualized)Realized Volatility(Annualized)Sharpe Ratio, Netof FeesCorrelation to U.S.Equity MarketCorrelation to US10-year 0.200.31-0.19-0.37-0.25-0.160.210.25Source: AQR. Time Series performance is hypothetical as described above. Hypothetical data has inherent limitations, some of which are disclosed in the Appendix.Past performance is not a guarantee of future performance. U.S. Equity Market: (Prior to 1926, the U.S. Equity series was constructed by adding price-weightedcapital appreciation returns of NYSE stocks collected by Goetzmann, Ibbotson, and Peng to U.S. equity dividend returns recorded by the Cowles commission. Theseries consists of returns of the S&P 90 from 1926 to 1957 and returns of the S&P 500 from 1957 onwards.)87A simple covariance matrix estimated using rolling 3-year (equallyweighted) monthly returns is used in the portfolio volatility scalingprocess.While a 2/20 fee structure has been commonplace in the industry, somemanagers charged higher management and performance fees in earliertime periods. On the other hand, there are also managers that chargelower fees for the strategy today.

A Century of Evidence on Trend-Following Investing3The performance has been remarkably consistentExhibit 1. Even more impressively, the strategy hasover an extensive time horizon that includes theperformed best in large equity bull and bearGreatandmarkets. Exhibit 2 shows the annual hypotheticalexpansions, multiple wars, stagflation, the GlobalDepression,multiplerecessionsreturns to the strategy, plotted against the returns toFinancial Crisis and periods of rising and fallingthe U.S. equity market from 1880–2013. The “smile”interest rates. Some skeptics argue that managedshows that trend following has done particularlyfutures has benefited mainly from a long secularwell in extreme up or down years for the stockdecline in interest rates. While the strategy didmarket. This strong performance in bear marketsperform well over the past 30 years, the best-over the century extends the evidence that has beenperforming decade for the strategy was the 1970s,documented since the 1980s, as exemplified mostwhen U.S. 10-year Treasury yields rose from 7.8% torecently with the strong performance of trend11.1% with extreme volatility in between.following during the Global Financial Crisis.Our long-term out-of-sample evidence suggests thatExhibit 2 — Time Series Momentum “Smile”it is unlikely that such price trends are a product ofThe annual net of fee returns of a time series momentum strategy versusU.S. Equity Market Returns, 1880-2013statistical randomness or data mining. Indeed, the80%first 10 decades of data is out-of-sample evidencerelative to the literature, and the performanceTime Series Momentum Returnsremains strong during this period. Trends appear tobe a pervasive characteristic of speculative ategies perform well only if prices trend moreoften than not. A large body of research9 has shownthat price trends exist in part due to long-standingbehavioral biases exhibited by investors, such asanchoring and herding, as well as the trading60%40%20%0%-20%activity of non-profit-seeking participants, such ascentral banks and corporate hedging programs. For-40%-60%instance, when central banks intervene to reduceprices, thus creating trends. The fact that trend--20%0%20%40%60%U.S. Equity Market Returnscurrency and interest-rate volatility, they slow downthe rate at which information is incorporated into-40%Source: AQR. Time Series performance is hypothetical as described above.Hypothetical data has inherent limitations, some of which are disclosed in theAppendix. Past performance is not a guarantee of future performance.following strategies have performed well historicallyindicates that these behavioral biases and non-As another way to evaluate the diversifyingprofit-seekingproperties of trend following during extreme events,marketparticipantshavelikelyexisted for a long time.we consider the performance during peak-to-troughdrawdowns for the typical 60/40 portfolio.10 ExhibitThe returns to the strategy have exhibited low3 shows the performance of the time seriescorrelations to stocks and bonds over the full timemomentumstrategyduringthe10largestperiod, as well as in most subperiods, as shown in109Barberis, Shleifer and Vishny (1998), Daniel, Hirshleifer, Subrahmanyam(1998), De Long et al. (1990), Hong and Stein (1999) and Frazzini (2006)discuss a number of behavioral tendencies that lead to the existence ofprice trends.The 60/40 portfolio has 60% of the portfolio invested in the U.S.Equity Market and 40% invested in U.S. 10-year government bonds. Theportfolio is rebalanced to the 60/40 weights at the end of each month,and no fees or transaction costs are subtracted from the portfolioreturns.

4A Century of Evidence on Trend-Following InvestingExhibit 3 — Total Returns of U.S. 60/40 Stock/Bond Portfolio and Time Series Momentum in the 10 WorstDrawdowns for 60/40 between 1880 and 2013150%60-40Trend-Following100%50%Panic 1987Crash0%Panic of1907-50%-100%Feb 1893Aug 1893Oct 1906Dec 19071937RecessionDec 1916Dec 1917Sep 1929Jun 1932Mar 1937Mar 1938End of DotCom BubbleOil CrisisDec 1968Jun 1970Jan 1973Sep 1974Sep 1987Nov 1987Sep 2000Sep 2002Nov 2007Feb 2009Source: AQR. Time Series performance is hypothetical as described above. Hypothetical data has inherent limitations, some of which are disclosed in the Appendix.The 6

Trend-Following Investing Brian Hurst Principal Yao Hua Ooi Principal Lasse H. Pedersen, Ph.D.* Principal Fall 2014 Executive Summary We study the performance of trend-following investing across global markets since 1880, extending the existing evidence by more than 100 years. We find that trend following has delivered strong positive returns and realized a low correlation to traditional asset .