CHAPTER 9 CHAPTER 9 Measuring the Long Volatility Strategies of Managed Futures Mark Anson and Ho Ho C ertain hedge fund strategies create investment positions that resemble a long put option. Specifically, managed futures or commodity trading advisors have significant exposure to volatility events. This exposure is pos- itively related to volatility much like a long option position. We identify and measure this long volatility exposure, which may not always be transparent from the trading positions of a commodity trading advisor. We also examine ways to apply these long volatility strategies to improve risk management. INTRODUCTION The managed futures industry has come full circle in its application over the last 15 years. In the early 1990s, global macro funds were the predominant form of the hedge fund industry. These funds were primarily managed futures funds run by commodity trading advisors (CTAs). As the 1990s pro- gressed, other types of hedge fund strategies came to the forefront, such as relative value arbitrage, event driven, merger arbitrage, and equity long/short. As these strategies grew, managed futures became a smaller part of the hedge fund industry. Now, however, managed futures have achieved a renewed interest because of their risk reducing properties relative to other hedge fund strate- gies. Specifically, most CTA strategies employ some form of trend-following strategy. These trend-following strategies pursue both up- and down-market movements in futures markets. These strategies also may be called momen- tum strategies because they follow the momentum of the market and then liquidate their positions (or reverse them) when they detect that the momen- tum is changing or about to change. 183 c09_gregoriou.qxd 7/27/04 11:15 AM Page 183 Whether we call managed futures trend-following or momentum stra- tegies, they have one important characteristic: They capitalize on the volatility in the futures market. Trend-following strategies tend to be “long-volatility” strategies; that is, they profit during volatile markets. Long-volatility strate- gies can be useful risk management tools for other active trading strategies that tend to be short volatility. We begin with a brief overview of the managed futures industry. We then measure the long-volatility exposure captured these strategies. Next we apply Monte Carlo simulation to estimate the value at risk for long- volatility strategies. Last, we demonstrate some practical risk management strategies that may be employed with managed futures. BRIEF REVIEW OF THE MANAGED FUTURES INDUSTRY Managed futures is often referred to as an absolute return strategy because their return expectations are not driven by broad market indices, such as the Standard & Poor’s (S&P) 500, but instead by the specialized trading strategy of the commodity trading advisor. More specifically, their return expectations are an absolute level of return sufficient to compensate them for the risk associated with trading in the futures markets. This absolute level is established independently of the return on the stock market. The managed futures industry is another skill-based style of investing similar to hedge fund managers. In fact, managed futures is considered a subset of the hedge fund world. Commodity trading advisors use their spe- cial knowledge and insight in buying and selling futures and forward con- tracts to extract a positive return. This skill and insight can be applied regardless of whether the stock or bond markets are rising or falling, pro- viding the absolute return benefits described above. Commodity trading advisors have one goal in mind: to capitalize on price trends in futures markets. Typically, CTAs look at various moving aver- ages of commodity prices and attempt to determine whether the price will continue to trend up or down, and then trade accordingly. Some CTAs also use volatility models such GARCH (generalized auto-regressive conditional heteroskedasticity) to forecast both price trends and volatility changes. Prior empirical studies have indicated that managed futures, or com- modity trading advisors, have investment strategies that tend to be long volatility. Fung and Hsieh (1997a) found that trend-following styles have a return profile similar to a long option straddle position—a long volatility position. Fung and Hsieh (1997b) documented that commodity trading advisors apply predominantly trend-following strategies. 184 RISK AND MANAGED FUTURES INVESTING c09_gregoriou.qxd 7/27/04 11:15 AM Page 184 In our research we use three Barclay Commodity Trading Advisor indices to capture the trading dynamics of the CTA market: Commodity Trading Index, Diversified Commodity Trading Advisor Index, and System- atic Trading Index. These indices are an equally weighted average of a group of CTAs who identify themselves as belonging to one of the three strategies. There are alternative ways to gain exposure to the futures markets without the use of a CTA. One way is a passive managed futures index, such as the Mount Lucas Management Index (MLMI). The MLMI applies a mechanical trading rule for following the price trends in several futures markets. It uses a 12-month look-back window to calculate the moving average unit asset value for each futures market in which it invests. Once a month, on the day prior to the last trading day of the month, the algorithm examines the current unit asset value in each futures market compared to the average value for the prior 12-month period. If the current unit asset value is above the 12-month average, the MLMI purchases the futures contract. If the current unit asset value is below the 12-month moving average, the MLMI takes a short position in the futures contract. The MLMI invests in and is equally weighted across 25 futures con- tracts in seven major commodity futures categories: grains, livestock, energy, metals, food and fiber, financials, and currencies. The purpose of its construction is to capture the pricing trend of each commodity futures con- tract without regard to its production value or trading volume in the market. Our next step is to document the long volatility strategy of the man- aged futures industry. DEMONSTRATION OF A LONG VOLATILITY STRATEGY In this section we use the direction of the stock market to demonstrate the asymmetric payout associated with managed futures. That is, we expect that large downward movements in the stock market will result in large gains from managed futures. Conversely, we expect that large positive movements in the stock market will result in a constant return to managed futures. This type of return pattern is consistent with a long put option exposure. Therefore, this section plots the direction of the stock market ver- sus the returns earned by managed futures. In the “Mimicking Portfolios” section we specifically incorporate a measure of volatility to determine its impact on these hedge fund strategies. We start by producing a scatter plot of the excess return to the Barclay Commodity Trading Index returns versus the excess returns to the Standard Measuring the Long Volatility Strategies of Managed Futures 185 c09_gregoriou.qxd 7/27/04 11:15 AM Page 185 & Poor’s (S&P) 100. 1 We use the S&P 100 because this is the underlying index for which the VIX volatility index is calculated. We use the VIX index in the next section. Figure 9.1 presents this scatter plot. On the scatter plot in Figure 9.1, we overlay a regression line of the excess return to the Barclay Commodity Trading Index on the excess return to the S&P 100. Note that the fitted regression line is “kinked.” The kink indicates that there are really two different relationships between the excess returns to the stock market and the excess returns to managed futures. To the right of the kink, the relationship between the returns earned by the CTAs and the stock market appears orthogonal. That is, there is no apparent relationship between the returns to CTAs who pursue a diversified trading program and the returns to the stock market, when the returns to the stock market are positive. When the stock market earns positive returns, the Commodity Trading Index earns a consistent return regardless of how positive the stock market 186 RISK AND MANAGED FUTURES INVESTING –8.00% –6.00% –4.00% –2.00% 0.00% 2.00% 4.00% 6.00% 8.00% 10.00% 12.00% –20.00% –15.00% –10.00% –5.00% 0.00% 5.00% 10.00% 15.00% S&P 100 Excess Returns CTA Excess Returns CTA Regression Line FIGURE 9.1 Barclay Commodity Trading Index 1 Excess return is simply the total return minus the current risk-free rate. c09_gregoriou.qxd 7/27/04 11:15 AM Page 186 performs. This part of the graphed line is flat, indicating a constant, con- sistent return to managed futures when the stock market earns positive returns. In this part of the graph, the excess return provided by the Com- modity Trading Index is almost zero. That is, after taking into account the opportunity cost of capital (investing cash in treasury bills), the return to this style of managed futures is effectively zero, when there is no volatility event. This result highlights a point about the managed futures industry: It is a zero-sum game, similar to Newton’s law of physics: For every action, there is an equal and opposite reaction. However, to the left side of the kink, there is a distinct linear relation- ship between the returns to managed futures and the S&P 100. Declines in the stock market driven by volatility events result in large, positive returns for the Barclay Commodity Trading Index. In fact, the fitted regression line in Figure 9.1 mirrors the payoff function for a long put option. Figures 9.2 through 9.4 demonstrate a similar “kinked” relationship for the Barclay Diversified Trading Index, Systematic Trading Index, and the MLMI. Each figure demonstrates a long put optionlike exposure. In the next section, we examine how this kinked relationship can be quantified. Measuring the Long Volatility Strategies of Managed Futures 187 –10.00% –5.00% 0.00% 5.00% 10.00% 15.00% –20.00% –15.00% –10.00% –5.00% 0.00% 5.00% 10.00% 15.00% S&P 100 Excess Returns Diversified Excess Returns Diversified Trading Re g ression Line FIGURE 9.2 Barclay Diversified Trading Index c09_gregoriou.qxd 7/27/04 11:15 AM Page 187 188 RISK AND MANAGED FUTURES INVESTING –0.100 –0.050 0.000 0.050 0.100 0.150 0.200 –0.175 –0.150 –0.125 –0.100 –0.075 –0.050 –0.025 0.000 0.025 0.050 0.075 0.100 0.125 S&P 100 Excess Returns Systematic Excess Returns Systematic Trading Re g ression Line FIGURE 9.3 Barclay Systematic Trading Index –0.080 –0.060 –0.040 –0.020 0.000 0.020 0.040 0.060 –0.175 –0.150 –0.125 –0.100 –0.075 –0.050 –0.025 0.000 0.025 0.050 0.075 0.100 0.125 S&P 100 Excess Returns MLMI Excess Returns MLM Index Regression Line FIGURE 9.4 MLM Index c09_gregoriou.qxd 7/27/04 11:15 AM Page 188 FITTING THE REGRESSION LINE The previous discussion provides a general framework in which to describe empirically the long volatility exposure embedded within CTA trend- following strategies. To fit the kinked regression demonstrated in Figures 9.1 through 9.4, we use a piecewise linear capital asset pricing model (CAPM)–type model. The model can be described as: R tf − R f = (1 − D)[a low + b low (R OEX − R f )] + D[a high + b high (R OEX − R f )] (9.1) where R tf = return to the trend-following strategy R f = risk-free rate R OEX = return to the S&P 100 a low , b low = regression coefficients to the left-hand side of the kink a high , b high = regression coefficients to the right-hand side of the kink D = 1 if R OEX − R f > the threshold D = 0 if R OEX − R f < or equal to the threshold. In essence we plot two regression lines that have different alpha and beta coefficients depending on which side of the kink the market returns fall. The trick is to maintain continuity at the kink in the fitted regression line. To insure this, we impose this following condition: a low + b low (Threshold) = a high + b high (Threshold) (9.2) Our regression equation then becomes: R tf − R f = (1 − D)[a low + b low (R OEX − R f )] + D[a low + (b low − b high )(Threshold) + b high (R OEX − R f )] (9.3) We express our regression equation in this fashion to demonstrate how the threshold value is explicitly incorporated into the solution. Table 9.1 pres- ents the results for our fitted regression lines. For the Barclay Commodity Trading Index, the threshold value (the kink) is −5.2 percent. 2 Several observations can be made from the regresion Measuring the Long Volatility Strategies of Managed Futures 189 2 We found the threshold value through a recursive method that minimizes the residual sum of squares in equation 9.3. c09_gregoriou.qxd 7/27/04 11:15 AM Page 189 TABLE 9.1 Two-Step Regression Coefficients Commodity Trading Diversified Trading Systematic Trading MLM Index Coefficient t-statistic Coefficient t-statistic Coefficient t-statistic Coefficient t-statistic Threshold −0.0526 −0.0868 −0.0485 −0.0926 Alpha_low −0.0158 −1.2699 −0.0793 −1.7150 −0.0175 −1.2127 −0.0437 −1.7743 Beta_low −0.3962 −2.1083 −1.1018 −2.1911 −0.4923 −2.1703 −0.5893 −2.3223 Alpha_high 0.0014 0.0043 0.0029 0.0022 Beta_high −0.0676 −1.1759 −0.1384 −2.0820 −0.0717 −0.9365 −0.0929 −3.2138 S.E. 0.0264 0.0353 0.0343 0.0155 Regression R square 0.0555 0.0745 0.0520 0.1203 Adj R square 0.0437 0.0629 0.0402 0.1094 190 c09_gregoriou.qxd 7/27/04 11:15 AM Page 190 coefficients. First, the value of b low is negative and significant at the 5 per- cent level, with a t-statistic of −2.11. This demonstrates that when the returns to the S&P 100 are negative, the commodity trading strategies earn positive excess returns. In particular, the value of b low is −0.396, indicating that CTAs earn, on average, about a 0.4 percent excess return for every 1 percent decline in the S&P 100 below the threshold value. This is similar to a put option being exercised by the CTA manager when the returns to the stock market are negative, but created synthetically as a consequence of the trend-following strategy. As long as stock market returns remain positive, CTAs earn a constant return equal to a cash (treas- ury bill) rate. However, when the stock market suffers a negative volatility event that drives market returns into negative territory, the synthetic put option is exercised, leading to large positive returns. The coefficient for b high is close to zero (−0.067). It is neither econom- ically nor statistically significant. 3 Trend-following CTAs do not earn excess returns when the returns to the stock market are positive. When the returns to the S&P 100 are positive, there is no need to exercise the put option. In addition, a high is also close to zero, indicating a lack of excess returns over this part of the graph. Managed futures earn a treasury bill rate of return when the returns to the stock market are positive. The lack of any excess return over this part of the graph can be considered the payment for the put option premium. That is, trend-following CTAs forgo excess returns when the returns to the stock market are positive in return for a long put option exposure to be exercised when the returns to the stock market are negative. Similar results are presented in Table 9.1 for diversified trading man- aged futures, systematic trading, and the passive MLMI index. In each case, b low is economically and statistically significant. In addition, b low always has a negative sign, indicating positive returns to managed futures when the stock market earns negative returns. Also, a high is close to zero for each cat- egory of managed futures. Once again, this indicates that managed futures do not generate any excess returns when the returns to the stock market are positive. All that is received is a cash return equal to treasury bills. b high is statistically significant in two categories: diversified trading and the MLMI. The sign of the b high is negative, indicating a downward slop- ing curve. However, the coefficient is small and lacks economic significance. Still, this indicates that managed futures can be countercyclical when the stock market has positive returns. Measuring the Long Volatility Strategies of Managed Futures 191 3 There is no t-statistic for a high because this coefficient is a linear combination of the other regression coefficients (see equation 9.2). c09_gregoriou.qxd 7/27/04 11:15 AM Page 191 MIMICKING PORTFOLIO Here we specifically incorporate the long volatility exposure trend-following strategies to build mimicking portfolios of the strategies. The idea is that if we can build portfolios of securities that mimic the returns to CTAs, we can then simulate how trend-following strategies should perform under various market conditions. We use three components to build the mimicking portfolios: long OEX (options ticker symbol for S&P 100) put options, long the S&P 100 index, and long the one-month risk-free treasury security. The long OEX put option is used to capture the synthetic long put option exposure. The long S&P 100 index is used to capture any residual market risk that exists when the mar- ket performs positively. Last, we use the risk-free rate to measure the option premium that must be paid by CTAs to the right-hand side of the threshold value (when the stock market performs positively). We use the coefficient estimates from equation 9.3 to construct the mimicking portfolio. Long OEX Put Option Strike = OEX index × (1 + Threshold + risk-free rate) Volatility = VIX index The number of options bought = (b low − b high ) Short the S&P 100 4 The number of S&P 100 to buy is = b high Long Risk-Free Security The number of risk-free securities to buy = 1 − b low Figures 9.5 through 9.8 present the results from our mimicking portfo- lios. Similar to Figure 9.1, Figure 9.5 contains the scatter plot of the excess returns earned by the Barclay Commodity Trading Index plotted against the excess returns of the S&P 100. In addition, it contains the return of our mimicking portfolio. 192 RISK AND MANAGED FUTURES INVESTING 4 Since the beta (high) is negative, a short amount of a negative number is equal to a long position in the stock market. c09_gregoriou.qxd 7/27/04 11:15 AM Page 192 [...]... Maximum Loss −0 .93 % −1.46% −0 .97 % −1.18% −0. 69% −1.31% −1.14% −1 .99 % −0.74% −1.35% −0. 89% −1.64% Number of Simulations 10,000 10,000 10,000 10,000 cent (95 percent) level of confidence that the maximum loss sustained by a diversified CTA manager will not exceed 0 .93 percent (0. 69 percent) in any given month Table 9. 2 also contains the VaR for the other trend-following strategies Figures 9. 9 to 9. 12 present... 10,000 simulations for the managed futures strategies Table 9. 2 presents the results For example, the one-month VaR for the Barclay Commodity Trading Index is −0 .93 percent at a 1 percent confidence level and −0. 69 percent at a 5 percent confidence level This means that we can state with a 99 per- 196 RISK AND MANAGED FUTURES INVESTING TABLE 9. 2 Monte Carlo Simulation of Value at Risk CTA Diversified... skewness of 2.64 and a large positive kurtosis of 11.35 The other strategies have similar distribution characteristics In short, 6,000 Frequency 5,000 4,000 3,000 2,000 1,000 0 –0.0131 –0.0035 0.0060 0.0156 0.0252 0.0348 0.0443 0.05 39 Return FIGURE 9. 9 Simulated Commodity Trading Index Return Distribution More 197 Measuring the Long Volatility Strategies of Managed Futures 10,000 9, 000 8,000 Frequency... 2,000 1,500 1,000 500 0 −0.0135 −0.0033 0.0070 0.0172 0.0274 0.0377 0.04 79 Return FIGURE 9. 11 Simulated Systematic Trading Return Distribution 0.0581 More 198 RISK AND MANAGED FUTURES INVESTING 8,000 7,000 6,000 Frequency 5,000 4,000 3,000 2,000 1,000 0 –0.0164 0.0154 0.0473 0.0 792 0.1110 0.14 29 0.1748 0.2066 More Return FIGURE 9. 12 Simulated MLM Index Return Distribution That is, the returns to managed... option position (short volatility) and the mirror image of the return distributions presented in Figures 9. 9 to 9. 12 To prove that managed futures are an excellent diversifying agent for other hedge fund strategies, we construct a portfolio that is 50 percent managed futures and 50 percent merger arbitrage Table 9. 3 presents the Monte Carlo VaR for merger arbitrage alone and for the combined portfolio... of the fitted regression line in Figure 9. 1 First, the mimicking portfolio has a distinct “kink” in its shape Additionally, the slope of the mimicking portfolio is flat to the right-hand side of the kink and has a negative slope to the left-hand side of the kink In sum, our mimicking portfolio captures the upside of a long put option exposure Figures 9. 6 to 9. 8 provide similar information for the other... Distribution More 197 Measuring the Long Volatility Strategies of Managed Futures 10,000 9, 000 8,000 Frequency 7,000 6,000 5,000 4,000 3,000 2,000 1,000 0 –0.0 199 0.0208 0.0615 0.1022 0.14 29 0.1836 0.2243 0.26 49 More Return FIGURE 9. 10 Simulated Diversified Trading Index Return Distribution trend-following strategies tend to provide a large upside tail—the same risk exposure as a long put option The positive... Maximum Loss Merger Arbitrage and Managed Futures 10,000 Finally, in Figure 9. 15, we present the distribution of returns associated with our combined portfolio managed futures and merger arbitrage As can be seen, the negative skewness has been reduced dramatically from that presented in Figure 9. 14 The distribution in Figure 9. 15 demonstrates greater symmetry than that in Figure 9. 14 4000 3500 3000 Frequency... –0. 095 –0.08 –0.065 –0.05 –0.035 –0.02 –0.005 Return FIGURE 9. 14 Distribution of Returns for Merger Arbitrage 0.01 0.025 202 RISK AND MANAGED FUTURES INVESTING 7,000 6,000 Frequency 5,000 4,000 3,000 2,000 1,000 0 –0.0552 –0.0387 –0.0223 –0.0058 0.0107 0.0272 0.0437 0.0601 Return FIGURE 9. 15 Combined Portfolio Return Distribution CONCLUSION In this chapter we demonstrate that managed futures or commodity. .. Weisman (2002), and Anson (2002b) all demonstrate that hedge fund strategies that are short volatility will be falsely accorded superior performance based on a mean-variance analysis We proceed with the same analysis as for CTAs Figure 9. 13 presents the scatter plot of merger arbitrage versus the S&P 100 as well as the fitted regression line and the regression statistics Notice that a low and blow are . three Barclay Commodity Trading Advisor indices to capture the trading dynamics of the CTA market: Commodity Trading Index, Diversified Commodity Trading Advisor Index, and System- atic Trading Index −0.0485 −0. 092 6 Alpha_low −0.0158 −1.2 699 −0.0 793 −1.7150 −0.0175 −1.2127 −0.0437 −1.7743 Beta_low −0. 396 2 −2.1083 −1.1018 −2. 191 1 −0. 492 3 −2.1703 −0.5 893 −2.3223 Alpha_high 0.0014 0.0043 0.00 29 0.0022 Beta_high. −1.17 59 −0.1384 −2.0820 −0.0717 −0 .93 65 −0. 092 9 −3.2138 S.E. 0.0264 0.0353 0.0343 0.0155 Regression R square 0.0555 0.0745 0.0520 0.1203 Adj R square 0.0437 0.06 29 0.0402 0.1 094 190 c 09_ gregoriou.qxd