## Abstract

The authors propose the use of short and long portfolios to analyze the risk and return characteristics of trend-following strategies. They present evidence for the asymmetric profitability of trend-following strategies, showing that returns to the long side are more profitable. They also find that the exposure of CTAs to the long and short sides of trend-following strategies have become more biased toward long positions. The main lesson of the study is that the long and short sides should be differentiated in an analysis of dynamic investment strategies.

**TOPICS:** Portfolio construction, commodities, statistical methods, performance measurement

One important top-down investment asset allocation decision investors must make is how to allocate money between low-risk government bonds and higher-risk portfolios of stocks and other investments. While the latter offer the expectation of higher return, a benefit of the former is not only their lower expected risk but also their attractive diversification properties in crisis situations. Connolly, Stivers, and Sun (2009), for example, showed that the correlation of bond returns with stock returns tends to be low in times of market turbulence. While investments in bonds offer low risk and equities offer high returns, the temptation to capture both gives rise to systematic directional trading that exploits the best of two worlds by following trends in equities, bonds, and other asset classes, typically through the use of futures contracts.

Directional trading, as a component of an investor portfolio, is often entrusted to Commodity Trading Advisors (CTAs) or macro funds, which implement futures trading strategies on market trends. This trend-following behavior lends support to Samuelson’s dictum (see Jung and Shiller [2005]) that the stock market is “macro inefficient,” relating the investigation of CTA performance to the Efficient Market Hypothesis (EMH). Research in the field by Cutler, Poterba, and Summers (1991); Szakmary et al. (2012); Moskowitz, Ooi, and Pedersen (2012); and DeMiguel, Nogales, and Uppal (2014) supports macro inefficency by presenting evidence of the positive time-series predictability of a security’s own past returns, the “trend” effect, backing the credibility of trend followers. If this trend effect exists, a successful trend follower may be profitable in both bearish and bullish markets, but may also deliver equity-like returns.

Unfortunately, the problem with trend-following strategies is that their performance and simultaneous exposure to different market trends can be difficult to assess in the long run. The existing conception of the characteristics of trend followers is that they aim to follow market trends by following both bullish and bearish market trends to profit from large positive and negative price movements. However, the existing literature makes no clear distinction between the actual trading of the two different market trends. Fung and Hsieh (2001) modeled the returns of trend followers using lookback straddles. Moskowitz, Ooi, and Pedersen (2012) documented the trend effect, which takes into consideration both the long and short positions in futures contracts as an asset pricing anomaly, but they did not distinguish between them. While Baltas and Kosowski (2013) found that CTAs follow time-series momentum strategies, Baltas and Kosowski (2015) investigated the performance of a long-only constant volatility strategy of the time-series momentum strategy. Thus, none of these studies explicitly differentiated between the long and short sides of trend-following strategies or reflected the performance of CTAs on both sides.

The purpose of our study is to investigate the synthesis of the long and short positions of trend-following investment strategies in various assets. Our approach is to use established and common trend-following trading rules on futures markets to explore the risk accompanying the long and short positions of trend-following strategies. We begin by examining whether the profitability of the long and short positions differs. We then examine whether the replicated trend-following returns are representative of actual CTA returns. Our analysis includes combined trend-following strategies on 60 equity index, bond, commodity, and FX futures, and we investigate their performance during the period January 1984 to February 2015.

We argue that the long and short sides of trend followers are not uniform; what matters is how trend followers establish their short and long positions in different markets, and how these affect CTAs differentially. This aspect is as empirically relevant as the seminal evidence by Brock, Lakonishok, and LeBaron (1992) on the profitability of simple technical trading rules suggested that the long side of technical trading rules is more profitable than the short side. In addition, trend followers may overweight their exposure to the long or short side of a trend effect, as some investors may be less willing or able to short positions in some markets. For example, trading frictions and the asymmetry of the risks of the long and short legs of an investment strategy could be reasons for this overweighting, as noted by Stambaugh, Yu, and Yuan (2015). Also, according to Lo’s (2004) Adaptive Market Hypothesis (AMH), weaker profitability of the short side and matters related to the survival of trend followers by overweighting long positions could lead to asymmetry in the long and short positions. This matter is especially important for investors who invest in trend-following futures strategies.

The remainder of this study is organized as follows. In the next section, we present our hypothesis and the trend-following systems for the replication of the returns of trend followers. We describe the methodology and data used in our study in the third section. We present and discuss our results in the fourth section, and the final section contains the conclusion of our study.

## MODELING TREND-FOLLOWING STRATEGIES

### Trend-Following Systems

The replication of trend-following returns using a set of trend-following systems should be plausible, as CTAs appear to use relatively little discretion and follow common investment styles (Schneeweis and Spurgin [1998]). We argue that technical trading rules correspond to real-life trend-following strategies, which frequently take positions on upcoming buy and sell signals. We model the returns of the trend-following universe by employing two distinct approaches: one, a slower reacting moving average cross-over method, and, two, a faster reacting moving average breakout method. Szakmary and Lancaster (2015) employed channel and dual moving average rules that are conceptually similar to the moving average cross-over and moving average breakout methods. The purpose behind employing the two reaction speeds is to cover as much style variation as possible, albeit with simple modeling, to capture the market timing of CTAs at different frequencies, as shown in Hayes (2011).

An additional benefit of using a set of trading rules is that market participants are likely to adapt and employ adjusted trading rules. For example, Urquhart, Gebka, and Hudson (2015) presented evidence on how investors learn to react to signals from technical trading rules, and found that anticipating the signals would have yielded superior returns. Thus, a set of trading rules based on commonly used technical trading methods enables us to optimally capture the behavior of trend followers.^{1}

The moving average breakout model builds on a band breakout strategy, where a long-term moving average acts as the initial calculation point, from which the price will fluctuate and diverge.^{2} The upper and lower bands for the band breakout strategy are defined by Welles Wilder’s Average True Range (ATR) multiplied by *n*. Using the multiplier *n*, the model gives an indication of establishing a trading position when the price deviates by the product of *n* and ATR from the moving average. If the price reverts and trades back through the moving average, the position is closed. As price action occurs during the session, it is assumed that the positions are opened (closed) at pre-defined values as per the moving averages and bands. For the moving average breakout model, we use a 20-day ATR and a 100-day moving average. The multiplier *n* takes values of 5, 6, 7, or 8, yielding four trading portfolios.

For the moving average cross-over model, we follow a strategy that utilizes the Simple Moving Average (SMA). We assume that the positions are opened (closed) at the opening of the next trading session. As with the moving average breakout model, we form four portfolios by using the following pairs of short-term (fast) and long-term (slow) moving averages: 75 and 225, 100 and 300, 125 and 375, or 150 and 450. The long position is opened when SMA (fast) > SMA (slow) and Previous Close > SMA (slow), and it is closed when Previous Close < SMA (fast) and (slow). The short position is opened when SMA (fast) < SMA (slow) and Previous Close < SMA (slow), and it is closed when Previous Close > SMA (fast) and (slow).

When comparing the trading rules for the models based on the SMA and ATR, it is important to note that their trading rules for the opening and closing positions are different in both cases, allowing for more price fluctuation before a position is opened and requiring a significant change in trend before a position is closed. Also, our methodology permits the establishment of positions at different market timing frequencies simultaneously (i.e., fast and slow reactions) and an indefinite holding period; it also permits zero-positioning in a contract, as signals from the trading systems may indicate that the trends are long, flat, or short, thereby implying the possibility of not trading every contract. None of these features are considered for the time-series momentum strategy in Moskowitz, Ooi, and Pedersen (2012), nor in the trend-following strategy by Baltas and Kosowski (2013). In relation to these earlier studies and the study by Fung and Hsieh (2001), our return factors capture more of the heterogeneity among trend followers given the use of different trading systems. Our factors are also notably different from the time-series momentum strategy in Moskowitz, Ooi, and Pedersen (2012), as the positions are established on a daily rather than a monthly basis.

We also adjust for trading costs, where we allow 0.015 basis points per contract traded for slippage and execution. As noted earlier, once the trading positions have been triggered, we require a change in the prevailing price direction to close them, thereby reducing the trading costs that would arise due to noise.^{3} Thus we also benefit from employing the two trading models, because they do not generate buy and sell signals based solely on the sign of the past returns, thereby enabling more effective timing of significant trend-effects. Baltas and Kosowski (2015) also stressed this consideration in improving the performance of trend-following strategies. We reduce the possibility of curve fitting whereby the parameters are chosen because of their historical success by choosing a fixed number of four parameters for the moving average breakout model and a range of four combinations for the moving average cross-over model. This approach yields eight trend-following systems.

The eight trading systems operate independently of one another. This creates a portfolio that is the sum of the trading systems, where one trading system may establish a position that will be aggregated on the portfolio level. The use of these eight different trading systems and aggregating them into one portfolio reduces the impact of any given specific strategy. For position sizing, we use a position sizing algorithm that assigns the weight of the position of a trading system in a contract each day *t* as follows:^{4}

where *U* is the number of contracts (i.e., unit size) per trade; *A* is the assigned risk of five basis points of the assumed account size for every trading system; *S* is the assumed account size of 20 million; *N* is the volatility of the contract measured using a 20-day ATR; and *V* is the value of the contract per big point (see Exhibit A1 in the Appendix).^{5} As we employ eight trading systems for 60 contracts, we use position sizing for trading 480 different combinations of strategies and contracts. According to Equation 1, the position sizing decreases when the volatility increases, which is in line with the volatility scaling of the time-series momentum strategies (e.g., Moskowitz, Ooi, and Pedersen 2012).

The combined portfolios constructed on the two different trend-following trading models should be good candidates for real-life CTA strategies.^{6} All in all, we get 3 × 4 combined portfolios (four symmetric, four short, and four long) of the trading systems, and we refer to the returns of these portfolios as Combined Trend-Following Factors (CTFFs). In order to make these 12 return streams more comparable with how they contribute to the volatility of a trend follower, we form an equal-weighted portfolio of the four symmetric portfolios to represent the total CTFF return. As we apply the position sizing algorithm to each of the four symmetric portfolios, the total CTFF portfolio allocates risk equally among the four sectors, equities, bonds, FX, and commodities to simulate the trend-following industry.^{7}

### Hypothesis

As both market timers and trend followers attempt to profit from price movements, Fung and Hsieh (2001) modeled a trend follower using an approach related to the analysis of market timing, using the concept of the Primitive Trend-Following Strategy (PTFS). The results of Fung and Hsieh (2001) showed that, although the PTFSs replicate the key features of trend-following funds, the PTFS factor on stock indexes does not explain trend-following fund returns in relation to the PTFSs, which are symmetric factors to the long and short sides. It is worth noting that the evidence of Brock, Lakonishok, and LeBaron (1992) on simple technical trading rules on the Dow Jones Index suggests that buy signals generate higher and less volatile returns than sell signals.

This finding has at least two plausible explanations. First, it is a stylized fact that the drawdowns of assets returns are larger than their upward movements (see Cont 2001). Thus, it may be possible that it is easier to follow a slow upward price movement than a sudden price decline, making the trading of upward price trends more profitable. Second, considering Hong and Stein’s (1999) gradual information diffusion model, it is possible that information diffusion is different in up and down markets, affecting the profitability of trend-following strategies that can depend on sluggish price adjustment, similar to momentum strategies. For example, Cooper, Gutierrez, and Hameed (2004) presented evidence that the profitability of the momentum strategy depends on the state of the market, and found that momentum returns are lower following negative market returns. Therefore, we devote our hypothesis to the difference in the profitability of the long and short strategies of trend followers as follows:

H:Long CTFFs are more profitable than short CTFFs.

After testing this hypothesis, we investigate the relationship between the returns on CTA indexes and CTFFs. This part of our study assesses the performance attribution of CTAs to the replicated trend-following returns in order to reveal how representative they are of actual CTA returns.

## DATA AND METHODOLOGY

We collected our study data from several sources: First, we accessed the end-of-the-month index values of the DJ CS Managed Futures and SG CTA Trend Indexes via DataStream. The purpose of the DJ CS Managed Futures Index is to represent the overall return performance of the CTA industry. The SG CTA Trend Index, which is a sub-index of the SG CTA Index, is particularly suited for this study because it tracks the 10 largest trend-following CTAs. Secondly, we obtained the risk-free rate from the Kenneth R. French Data Library at http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/index.html. Finally, we formed our trend-following systems on the futures price data from CSI Unfair Advantage, as described above. These 60 futures contracts span currencies (6 contracts), commodities (17 contracts), equities (22 contracts), and bonds (15 contracts). For currencies, long positions in USD are considered to be long positions for the long FX CTFF (see Exhibit A1 in the Appendix showing the markets).

In addition, the analysis assumes an FX neutral strategy where exchange rates are fixed for the duration of the testing period. The basis of this assumption is that when a trader holds a diversified futures portfolio with contracts denominated in several currencies, there is a daily marking-to-market where all profit and loss is calculated in the trader’s base currency. The time of the daily mark-to-market is the settlement time for each individual market. It is not worth hedging the exchange rate risk following this assumption, which reflects actual portfolio management.

For calculating the returns for our trend-following strategies, we back-adjusted the futures contract prices. This adjustment leaves the most recent contract prices intact while adjusting the historical contracts by the roll spread, which cannot be captured by investors. Contract rollovers are triggered by volume and open interest after the notice day according to the CSI Unfair Advantage procedures.

We test our hypothesis by performing a univariate analysis of the mean returns of the DJ CS Managed Futures and SG CTA Trend Indexes and CTFFs. We then continue our analysis by performing a multivariate analysis using an empirical model, which is devoted to analyzing the CTA performance attribution as presented in Equation 2:

2where *R*_{CTA,t} is the excess return over the risk-free rate for the CTA universe (we use the DJ CS Managed Futures and SG CTA Trend Indexes as the proxies for the performance of the CTA universe) in month *t*; and *CTFF*_{i,t} is a combined trend-following factor *i* in month *t*. The purpose of Equation 2 is to attribute the performance of the CTA investment universe to CTFFs, which take into account the long and short positions of trend followers in different asset classes. The composition of the performance attribution then shows evidence of the exposure of CTAs in their long and short positions in different asset classes. The set of long and short CTFFs enables us to assess the exposure of the composite CTA indexes to the short and long legs of the trend-following investment strategies. Since CTA styles may be time-varying and dependent on market states, we carry out the analysis of Equation 2 for the pre- and post-2008 Financial Crisis periods.

Exhibit 1 presents the summary statistics of the variables used in our study. The statistics for the CTFFs in Exhibit 1 show that the range of the average returns of the trend-following strategies is considerable. For the CTFFs, the average monthly return is highest, (1.49%) for the long bond CTFF, and lowest (−0.33%) for the short bond CTFF. Considering the low average return for the short equity CTFF (−0.05%) and the high average return for the long equity CTFF (1.35%), it can be clearly seen that the gap in the average returns for the long and short sides of the trend-following strategies in these assets is considerable. This higher return for the long side of the equity trend-following strategy is in line with the evidence of Brock, Lakonishok, and LeBaron (1992) on technical trading rules that suggests buy signals are more profitable than short signals.

Exhibit 2 presents the Pearson correlation statistics of the variables in our study. The returns on the SG CTA Trend Index show their highest correlation, 0.82, with the total CTFF return. The same applies to the DJ CS Managed Futures Index, which shows a correlation of 0.78 with the total CTFF return. The high correlation between the total CTFF and the return of the DJ CS Managed Futures Index provides irrefutable evidence that CTFFs can be used to replicate CTA returns. Even more importantly, as the SG CTA Trend Index tracks the performance of trend-following CTAs, the high level of correlation between the return of this index and the total CTFF shows that our methodology of tracking trend-following strategies is associated with the strategies of funds considered to be trend followers.

## RESULTS

### Returns of the Trend-Following Strategies

We begin our empirical analysis by addressing the differences in the profitability of the long and short CTFFs. Exhibit 3 presents the results for testing Hypothesis 1 that *the long only CTFFs are more profitable than the short only CTFFs*. The exhibit shows the average returns, the long-short difference in the average returns, and the *t*-test statistics of the long and short CTFFs by asset. While the results show that all the long CTFF factors have statistically significant and positive mean returns, the results for the short CTFF factors are mixed. Specifically, the mean returns of the short CTFFs for equities and commodities are not statistically significant, but the mean returns of the short CTFFs for bonds and FX are negative and positive, respectively, and are statistically significant. These results highlight in particular how the short positions of trend-following strategies can generate very different returns that can be either negative or positive. The results for the differences in the means between the long and short strategies confirm that the profitability of the long and short sides is not symmetric for equities, bonds, and commodities.

The results in Exhibit 3 show that the long side is significantly more profitable for equities, bonds, and commodities, thus providing support for Hypothesis 1. It is notable, however, that this finding does not apply to FX, for which the profitability between the long versus the short sides in terms of US dollar positions appears not to be significantly different. This different result for FX may be related to the fact that FX positions are not long or short by nature. In addition, the result may be explained by the different empirical characteristics of asset returns. For example, Cont (2001) lists gain/loss asymmetry, i.e., larger drawdowns than upward movements, as a stylized statistical property of asset returns, but explicitly notes that this is not true for exchange rates. The gain/loss asymmetry could be a potential driver of trend-following returns.

In relation to the previous literature, the results in Exhibit 3 provide even further evidence that buy signals are more profitable than short signals not just for equities but also for bonds and commodities. This finding is in line with the evidence of Brock, Lakonishok, and LeBaron (1992) and adds to their evidence on equities. The finding that the short and long sides of trend-following strategies for several assets can generate such different returns is a novel one and not documented in the extant literature on trend-following strategies (e.g., Baltas and Kosowski [2013]; Urquhart, Gebka, and Hudson [2015]; Szakmary and Lancaster [2015]).

Overall, the results in Exhibit 3 show that the discretion in the trading of long and short sides has a considerable effect on the risk and return characteristics of trend followers. In relation to Samuelson’s dictum regarding the macro efficiency of the stock market, an explanation for the better profitability of the trend-following strategy in bull markets could be that the market is more macro-efficient in bear markets. Alternatively, the symmetric design of our trend-following system may be unable to capture the gain/loss asymmetry explaining the result.

### CTA Performance Attribution

The results in Exhibit 4 show the parameter estimates obtained from two alternative regression specifications from Equations 2 that utilize different sets of trend-following factors. The purpose of this analysis is to address how CTAs are exposed to different trend-following strategy factors by analyzing the exposure of CTAs to the different CTFFs.

The regression results in Exhibit 4 lend support to the view that CTA returns can be replicated and demystified to a large extent using the CTFFs, which are simple trend-following strategies, as the adjusted R-squared is as high as 67% in these factor models indicates. The adjusted R-squared of the analysis of CTA returns is higher than the maximum level of 51% obtained in a similar analysis by Ahmerkamp and Grant (2013), or the maximum level of 51.65% obtained by Baltas and Kosowski (2013). In addition, the adjusted R-squared for the analysis of CTA returns is higher using the long and short CTFFs than using the symmetric CTFFs, thus showing that it is important to distinguish between the long and short positions of trend followers when explaining their returns.

The results for the symmetric factors show that the four symmetric CTFFs for the four different assets are statistically significant determinants of CTA returns and have a positive association with the returns of the two different CTA indexes. Comparing the regression coefficients for these same CTFFs shows that the symmetric bond and FX CTFFs obtain the highest values, indicating that the performance of CTAs is more exposed to bond and FX trend-following strategies than to equity and commodity trend-following strategies.

The only factor among the CTFFs that obtains statistically insignificant values for the SG CTA Trend Index in Exhibit 4 is the short FX CTFF. These results indicate that the FX strategies of CTAs may be less popular and/or different from common trend-following strategies, thus making their exposure to common trend-following factors weaker. Insignificant exposure to the short FX CTFF indicates that CTAs do not maintain consistent short exposure to USD. The results utilizing the long and short CTFFs continue to show evidence that the CTFFs explain CTA returns. Excluding the short FX CTFF, these results suggest that all the long and short CTFFs significantly explain CTA returns in the full sample of our study. When comparing the different regression results in Exhibit 4, it is worth noting that they both yield negative alphas, indicating that an average CTA underperforms the returns of common trend-following strategies.

It is also possible that CTAs change their exposures with the market environment. In fact, Getmansky, Lee, and Lo (2015) suggested that the average volatility of hedge fund returns decreased after the crisis due to the less aggressive use of leverage in the hedge fund industry. Considering the evidence of Szakmary and Lancaster (2015) that the profitability of trend-following trading strategies in US stocks vanished after 2007, it is even more crucial to analyze the sub-sample performance of CTAs before and after the crisis. Exhibit 5 presents the results from the analysis of Equation 2 for the periods before and after the 2008 Financial Crisis.

The results in Exhibit 5 show that CTA returns had more exposure to the CTFFs after the 2008 Financial Crisis. This can be seen, for example, in the increase in the explanatory power of the CTFFs from 54% to 75%. This result could be an indication that there is an increasing lack of diversity between the strategies of different CTAs, causing the CTA composite returns to be more closely associated with appropriate systematic trend-following factors. The possibility that different trend-following strategies could track the CTFFs more closely after the 2008 Financial Crisis is a non-indigenous reason for this increased association. In addition, the crowded state of the CTA industry may also result in the explanation that an increasing amount of money results in more exposure to common trend-following strategies.

Regarding the specific changes in the factor exposures in Exhibit 5, the results lend support to the view that CTAs have a biased exposure to the long CTFFs when the sub-periods are considered. For bond trend-following strategies, the exposure and statistical significance of CTA returns to the short bond CTFF decreases dramatically for the post-2008 crisis period; the coefficient value decreased from 0.227 to 0.113, and the *t*-statistics decreased from 6.22 to 1.89. As the coefficient value for the long bond CTFF did not simultaneously decrease and did, in fact, increase, our findings reveal that CTAs established a marked bias toward long bond strategies during the post-2008 crisis period. This evidence also means that CTAs have changed their style of implementing trend-following strategies.

The results for the CTFFs for equities also reveal notable changes in the factor exposures of CTAs after the 2008 Financial Crisis. Specifically, the coefficient value for the short equity CTFF is statistically insignificant for the post-crisis period, and the coefficient value for the long equity CTFF increases from 0.080 for the pre-crisis period to 0.201 for the post-crisis period. If one considers the test statistics in Exhibit 3 showing that the long CTFFs obtain higher average returns than the short CTFFs, the weaker profitability of the short side of the trend-following strategies may be the reason CTA managers appear to overweight long positions in trend-following strategies.

An explanation for the long bias during the post-2008 crisis era could be that competition among and screening of CTA programs increased, putting more pressure on CTA managers to overweight more profitable long-positions. Thus, the same long bias finding applies to the results for the equity CTFFs, and shows that trend followers accommodate their strategies in line with the adaptive market hypothesis (AMH). These findings continue to show that it is important to differentiate between short and long positions in the analysis of trend-following strategies, although the long bias of CTAs toward trend-following strategies can only be seen in the post-crisis sample.

Taken together, the findings in Exhibit 5 indicate that the performance and diversification benefits of CTAs depend on their factor-exposure mix to the long and short sides of the strategy in addition to the underlying factor returns. The evidence for the long bias of CTAs suggests that investors in CTAs may experience unbalanced exposure, which could arise due to homogenous discretionary trading among CTAs. Further, considering the weak exposure of CTA returns to the short equity CTFF, the performance of CTAs and the associated diversification benefit in portfolio construction depend strongly on alternative long exposure to other asset classes.

This evidence is relevant in relation to studies relating trend-following studies to long volatility investing. For example, Moskowitz, Ooi, and Pedersen (2012) reflected on their results in a way that can be related to long volatility investing: “Hence, time series momentum may be a hedge for extreme events, making its large return premium even more puzzling from a risk-based perspective.” Our results sugges that the favorable exposure of CTAs, interpreted as “long volatility,” may originate from a nonfactual exposure to increases in equity market volatility. For example, trend followers may generate high returns through their long exposure in bonds when the volatility of equity returns is high and equity prices are declining, but this is not a short exposure to equity prices.

### Further Analysis

To further assess the exposure of CTAs to trend-following strategies, we ran additional quantile regressions of the returns of the DJ CS Managed Futures Index on the full model in Equation 2. The most notable finding from the untabulated results of this analysis is that the short equity CTFF does not affect good CTA returns (quantiles 0.9 and 0.75), but does affect poor CTA returns (quantiles 0.1 and 0.25). This evidence shows that the short positions of CTAs in equity futures do not lead to good performance over time.

While our study focuses on addressing the strategies of trend followers, analyzing the other CTA-sub-categories can be used to ascertain whether CTA and Macro funds other than trend followers follow common trend-following strategies. Therefore, we performed an additional regression analysis of the returns of the SG Commodity Trading, SG Macro Discretionary, Macro Quantitative, SG Short-Term Traders, and SG Volatility Trading Indexes on the CTFFs, using data collected from the BarclayHedge CTA database. The results, presented in Exhibit 6, clearly show how several CTA subcategories that are not likely to be trend followers show very little exposure to the CTFFs. More specifically, the returns of the Macro Quantitative Trading Index show very strong exposure to the CTFFs, while the returns of the Short-Term Traders and Macro Discretionary Trading Indexes show very weak exposure to the CTFFs. For example, the adjusted R^{2} is 44% when the symmetric CTFFs are used to explain the returns of the Macro Quantitative Index, but only 1% when the symmetric CTFFs are used to explain the returns of the Macro Discretionary Index.

The results in Exhibit 6 are also in line with the view that many more CTAs and hedge funds are likely to follow the long side of a trend-following strategy than the short side. For example, the SG Commodity Index has a relatively high and statistically very significant coefficient value, 0.213, for the long commodity CTFF, but the coefficient for the short commodity CTFFs is statistically insignificant. For the Macro Quantitative Index, the short CTFFs for commodity, equity, and FX are not statistically significant, although their long CTFF counterparts are. It is also important to note how the Macro Discretionary Trading Index, in fact, has a negative exposure to the short equity CTFF. This is an interesting finding, as it would suggest that these funds could benefit from the poor profitability of the short side of the trend-following strategies.

We also address the asymmetry of the long and short trend-following returns, and the exposure of CTA returns to them in different market states; we use a market state indicator for the bull and bear markets that is constructed in a similar way to that in Asem and Tian (2011) and Cooper, Gutierrez, and Hameed (2004). The market is in a bullish (bearish) state if the prior 12-month Center for Research in Security Prices (CRSP) value-weighted (VW) return is positive (negative). The results in Exhibit 7 show that the return exposure of the DJ CS Managed Futures Index to the CTFFs is state dependent for the equity CTFFs, the short FX CTFF, and the short commodity CTFF. The insignificant exposures of CTAs to the long equity CTFF in a downward trending market, and the short equity CTFF in an upward market, can be explained by the similar design of the long and short CTFFs and the stock market state variable. The statistics for the constant terms of the four different regressions suggest that CTAs generate the lowest alpha after good stock market performance.

Since trend-following strategies are considered to be a way of exploiting the time-series momentum anomaly, we also perform our analysis using the time-series momentum factors of Moskowitz, Ooi, and Pedersen (2012) (accessed at www.aqr.com and available upon request). When compared with the symmetric CTFFs, the time-series momentum factors are approximately as volatile and have equally high average returns. The correlations coefficients for the symmetric CTFFs and the respective time-series momentum factors range from 0.74 to 0.84 and demonstrate a strong association among the variables. We find that the CTFFs perform better in explaining CTA returns in terms of the adjusted R-squared measure.

To also compare our results with the primitive trend-following strategy (PTFS) factors of Fung and Hsieh (2001), we performed our analysis in Exhibits 5 and 6 using the PTFS factors. (We accessed the data for the PTFS factors through David A. Hsieh’s Data Library at https://faculty.fuqua.duke.edu/~dah7/HFRFData.htm; the results using the PTFS factors are available on request.) This analysis yielded two notable findings: first, the explanatory power of PTFS factors in explaining the returns of the DJ SC Managed Futures and SG CTA Trend Indexes is significantly lower compared to the times-series momentum factors and the CTFFs. Second, when analyzing the periods before and after the 2008 Financial Crisis, the explanatory power of the PTFS factors decreased from 22% to 8%, which is the opposite of the results with the CTFFs. These findings will encourage future studies on CTA and hedge fund performance to use the CTFFs and other new alternative factors.

## CONCLUSION

In this study, we replicate trend-following strategies and differentiate between long and short trend-following strategies on different assets, which enables us to assess the risks in trend-following strategies in a new light. We show that the profitability of the short side of trend-following strategies can be dramatically weaker than the profitability of the long side. This finding can be observed for different assets, and is relevant in relation to the stream of research that advocates limiting investors when generating returns from investment strategies due to contraints related to short selling (e.g., Stambaugh, Yu, and Yuan 2015). Thus, our study shows that even futures traders, who do not face short selling constraints as do investors in shares of stocks, may find it challenging to profitably establish and mount short positions. These results are interesting in light of the gain/loss asymmetry of asset returns (see Cont 2001) in that the difference in profitability of the long and short sides could be linked to it. Alternatively, this finding could imply stronger market efficiency when the markets are trending down.

When we use the replicated trend-following strategies to analyze the performance attribution of CTAs, we find that the returns of CTA composite indexes can be replicated by up to 67% using these strategies. Our results on CTA factor exposures show that CTAs can have an unbalanced exposure to the long and short sides of trend-following strategies. The long and short sides appear to be unbalanced for bonds and equities, for which the exposure to the short-only strategies was significatly weaker during the post-2008 crisis period.

Our findings on the asymmetry of the profitabilty of the long and short sides of trend-following strategies should be particularly important in the development of future theoretical research on trend followers (c.f., Fung and Hsieh 2001). For investors, the main result from our study is that typical CTAs should not be bought as “long volatility” investment vehicles or as certain safe havens, because this feature may originate in a misconceived performance attibution. For future studies, we propose that the exposure of individual CTAs to the long and short CTFFs should be studied. In addition, it would be interesting to examine the performance of short-, mediun-, and long-term trend signals in bull and bear markets.

## ADDITIONAL READING

**The Adaptive Markets Hypothesis**

Andrew W. Lo

*The Journal of Portfolio Management*

**https://jpm.pm-research.com/content/30/5/15**

**ABSTRACT:** *One of the most influential ideas in the past 30 years is the efficient markets hypothesis, the idea that market prices incorporate all information rationally and instantaneously. The emerging discipline of behavioral economics and finance has challenged the EMH, arguing that markets are not rational, but rather driven by fear and greed. Research in the cognitive neurosciences suggests these two perspectives are opposite sides of the same coin. An adaptive markets hypothesis that reconciles market efficiency with behavioral alternatives applies the principles of evolution? competition, adaptation, and natural selection? to financial interactions. Extending Simon’s notion of? satisficing? with evolutionary dynamics, the author argues that much of what behaviorists cite as counter-examples to economic rationality? loss aversion, overconfidence, overreaction, mental accounting, and other behavioral biases? is in fact consistent with an evolutionary model of individual adaptation to a changing environment via simple heuristics. The adaptive markets hypothesis offers a number of surprisingly concrete implications for portfolio management.*

## APPENDIX

## ENDNOTES

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^{1}Alternatively, we could model the returns of trend followers by using the time-series momentum strategy, which is empirically and theoretically closely related to moving average cross-overs (Levine and Pedersen 2016). The time-series momentum is a recently published anomaly rather than a*de facto*established trading rule, which makes the use of actual trading rules more feasible in tracking the real-life trading behavior of trend followers.↵

^{2}Practitioners know this approach as the Bollinger Band method.↵

^{3}Our approach minimizes trading costs in that our approach, rather than utilizing simple moving average rules on price cross-overs, utilizes rules that trigger signals after the price exhibits a deviation away from longer term consolidation. For example, for the 100-day moving average of the S&P 500 Index, the 100-day simple moving average crosses from above to below the price 199 times, and from below to above the price 201 times. Thus, the moving average has crossed the price about 400 times since September 1982, while the breakout from one band of the 100-day moving average has occurred 42 long and 20 short during the same period.↵

^{4}This position sizing algorithm is a volatility-based constant percentage risk position sizing algorithm available at http://www.tradingblox.com/originalturtles/originalturtlerules.htm.↵

^{5}Contract values are per big point (e.g., Crude Oil = 1,000), which is the product of tick size and minimum tick.↵

^{6}Getmansky, Lee, and Lo (2015) discussed the problem of overfitting when using a large number of explanatory factors.↵

^{7}To achieve this, the portfolio normalizes volatility across the asset classes, resulting in a scaling down effect across all asset classes. This has the effect of weighting the risks down from five basis points to approximately 1.4 basis points for equity futures, as each sector targets a volatility output of 5% annualized, resulting in a portfolio volatility of approximately 12%.

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