-based style of investingsimilar to hedge fund managers. In fact, managed futures is considered asubset of the hedge fund world. Commodity trading advisors use their special knowledge and insight in buying and selling futures and forward contracts to extract a positive return. This skill and insight can be appliedregardless of whether the stock or bond markets are rising or falling, providing the absolute return benefits described above.Commodity trading advisors have one goal in mind: to capitalize onprice trends in futures markets. Typically, CTAs look at various moving averages of commodity prices and attempt to determine whether the price willcontinue to trend up or down, and then trade accordingly. Some CTAs alsouse volatility models such GARCH (generalized auto-regressive conditionalheteroskedasticity) to forecast both price trends and volatility changes.Prior empirical studies have indicated that managed futures, or commodity trading advisors, have investment strategies that tend to be longvolatility. Fung and Hsieh (1997a) found that trend-following styles have areturn profile similar to a long option straddle position—a long volatilityposition. Fung and Hsieh (1997b) documented that commodity tradingadvisors apply predominantly trend-following strategies.
Measuring the Long Volatility Strategies of Managed Futures
185
In our research we use three Barclay Commodity Trading Advisorindices to capture the trading dynamics of the CTA market: CommodityTrading Index, Diversified Commodity Trading Advisor Index, and Systematic Trading Index. These indices are an equally weighted average of a groupof CTAs who identify themselves as belonging to one of the three strategies.There are alternative ways to gain exposure to the futures marketswithout 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 pricetrends in several futures markets. It uses a 12-month look-back window tocalculate the moving average unit asset value for each futures market inwhich it invests. Once a month, on the day prior to the last trading day ofthe month, the algorithm examines the current unit asset value in eachfutures market compared to the average value for the prior 12-monthperiod. If the current unit asset value is above the 12-month average, theMLMI purchases the futures contract. If the current unit asset value isbelow the 12-month moving average, the MLMI takes a short position inthe futures contract.The MLMI invests in and is equally weighted across 25 futures contracts in seven major commodity futures categories: grains, livestock,energy, metals, food and fiber, financials, and currencies. The purpose of itsconstruction is to capture the pricing trend of each commodity futures contract without regard to its production value or trading volume in the market.Our next step is to document the long volatility strategy of the managed futures industry.
DEMONSTRATION OF A LONG VOLATILITY STRATEGYIn this section we use the direction of the stock market to demonstrate theasymmetric payout associated with managed futures. That is, we expectthat large downward movements in the stock market will result in largegains from managed futures. Conversely, we expect that large positivemovements in the stock market will result in a constant return to managedfutures. This type of return pattern is consistent with a long put optionexposure. Therefore, this section plots the direction of the stock market versus the returns earned by managed futures. In the “Mimicking Portfolios”section we specifically incorporate a measure of volatility to determine itsimpact on these hedge fund strategies.We start by producing a scatter plot of the excess return to the BarclayCommodity Trading Index returns versus the excess returns to the Standard
186
RISK AND MANAGED FUTURES INVESTING
CTA Excess Returns
12.00%10.00%8.00%6.00%4.00%2.00%0.00%–2.00%–4.00%–6.00%–8.00%–20.00%
–15.00%
–10.00%
–5.00%
0.00%
5.00%
10.00%
15.00%
S&P 100 Excess ReturnsCTARegression Line
FIGURE 9.1
Barclay Commodity Trading Index
& Poor’s (S&P) 100.1 We use the S&P 100 because this is the underlyingindex for which the VIX volatility index is calculated. We use the VIX indexin the next section. Figure 9.1 presents this scatter plot.On the scatter plot in Figure 9.1, we overlay a regression line of theexcess return to the Barclay Commodity Trading Index on the excessreturn to the S&P 100. Note that the fitted regression line is “kinked.” Thekink indicates that there are really two different relationships between theexcess returns to the stock market and the excess returns to managedfutures.To the right of the kink, the relationship between the returns earned bythe CTAs and the stock market appears orthogonal. That is, there is noapparent relationship between the returns to CTAs who pursue a diversifiedtrading program and the returns to the stock market, when the returns tothe stock market are positive.When the stock market earns positive returns, the Commodity TradingIndex earns a consistent return regardless of how positive the stock market
1Excess return is simply the total return minus the current risk-free rate.
187
Measuring the Long Volatility Strategies of Managed Futures
Diversified Excess Returns
performs. This part of the graphed line is flat, indicating a constant, consistent return to managed futures when the stock market earns positivereturns. In this part of the graph, the excess return provided by the Commodity Trading Index is almost zero. That is, after taking into account theopportunity cost of capital (investing cash in treasury bills), the return tothis style of managed futures is effectively zero, when there is no volatilityevent. This result highlights a point about the managed futures industry: Itis 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 relationship between the returns to managed futures and the S&P 100. Declines inthe stock market driven by volatility events result in large, positive returnsfor the Barclay Commodity Trading Index. In fact, the fitted regression linein Figure 9.1 mirrors the payoff function for a long put option.Figures 9.2 through 9.4 demonstrate a similar “kinked” relationshipfor the Barclay Diversified Trading Index, Systematic Trading Index, andthe MLMI. Each figure demonstrates a long put optionlike exposure. In thenext section, we examine how this kinked relationship can be quantified.
15.00%
10.00%
5.00%
0.00%
–5.00%
–10.00%–20.00%
–15.00%
–10.00%
–5.00%
0.00%
5.00%
10.00%
15.00%
S&P 100 Excess ReturnsDiversified TradingRegression Line
FIGURE 9.2
Barclay Diversified Trading Index
Systematic Excess Returns
188
RISK AND MANAGED FUTURES INVESTING
0.200
0.150
0.100
0.050
0.000
–0.050
–0.100–0.175
–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 ReturnsSystematic TradingRegression Line
FIGURE 9.3
Barclay Systematic Trading Index
MLMI Excess Returns
0.0600.040
0.0200.000–0.020–0.040
–0.060
–0.080–0.175 –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 ReturnsMLM IndexRegression Line
FIGURE 9.4
MLM Index
Measuring the Long Volatility Strategies of Managed Futures
189
FITTING THE REGRESSION LINEThe previous discussion provides a general framework in which to describeempirically the long volatility exposure embedded within CTA trendfollowing strategies. To fit the kinked regression demonstrated in Figures9.1 through 9.4, we use a piecewise linear capital asset pricing model(CAPM)–type model. The model can be described as:Rtf − Rf = (1 − D)[a low + b low(ROEX − Rf)] +D[a high + b high(ROEX − Rf)]
(9.1)
whereRtf = return to the trend-following strategyRf = risk-free rateROEX = return to the S&P 100a low, b low= regression coefficients to the left-hand side of the kinka high, b high= regression coefficients to the right-hand side of the kinkD = 1 if ROEX − Rf > the thresholdD = 0 if ROEX − Rf < or equal to the threshold.In essence we plot two regression lines that have different alpha andbeta coefficients depending on which side of the kink the market returnsfall. The trick is to maintain continuity at the kink in the fitted regressionline. 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:Rtf − Rf = (1 − D)[a low + b low(ROEX − Rf )] +D[a low + (b low − b high)(Threshold) + b high(ROEX − Rf)]
(9.3)
We express our regression equation in this fashion to demonstrate how thethreshold value is explicitly incorporated into the solution. Table 9.1 presents the results for our fitted regression lines.For the Barclay Commodity Trading Index, the threshold value (thekink) is −5.2 percent.2 Several observations can be made from the regresion
2We found the threshold value through a recursive method that minimizes the
residual sum of squares in equation 9.3.
190
ThresholdAlpha_lowBeta_lowAlpha_highBeta_highS.E.RegressionR squareAdj R square
0.05550.0437
−0.0526−0.0158−0.39620.0014−0.06760.0264
Coefficient
−1.1759
−1.2699−2.1083
t-statistic
Commodity Trading
TABLE 9.1 Two-Step Regression Coefficients
0.07450.0629
−0.0868−0.0793−1.10180.0043−0.13840.0353
Coefficient
−2.0820
−1.7150−2.1911
t-statistic
Diversified Trading
0.05200.0402
−0.0485−0.0175−0.49230.0029−0.07170.0343
Coefficient
−0.9365
−1.2127−2.1703
t-statistic
Systematic Trading
0.12030.1094
−0.0926−0.0437−0.58930.0022−0.09290.0155
Coefficient
−3.2138
−1.7743−2.3223
t-statistic
MLM Index
Measuring the Long Volatility Strategies of Managed Futures
191
coefficients. First, the value of b low is negative and significant at the 5 percent level, with a t-statistic of −2.11. This demonstrates that when thereturns to the S&P 100 are negative, the commodity trading strategies earnpositive excess returns. In particular, the value of b low is −0.396, indicatingthat CTAs earn, on average, about a 0.4 percent excess return for every 1percent decline in the S&P 100 below the threshold value.This is similar to a put option being exercised by the CTA managerwhen the returns to the stock market are negative, but created syntheticallyas a consequence of the trend-following strategy. As long as stock marketreturns remain positive, CTAs earn a constant return equal to a cash (treasury bill) rate. However, when the stock market suffers a negative volatilityevent that drives market returns into negative territory, the synthetic putoption is exercised, leading to large positive returns.The coefficient for b high is close to zero (−0.067). It is neither economically nor statistically significant.3 Trend-following CTAs do not earn excessreturns when the returns to the stock market are positive. When the returnsto the S&P 100 are positive, there is no need to exercise the put option. Inaddition, ahigh is also close to zero, indicating a lack of excess returns overthis part of the graph. Managed futures earn a treasury bill rate of returnwhen the returns to the stock market are positive. The lack of any excessreturn over this part of the graph can be considered the payment for the putoption premium. That is, trend-following CTAs forgo excess returns whenthe returns to the stock market are positive in return for a long put optionexposure to be exercised when the returns to the stock market are negative.Similar results are presented in Table 9.1 for diversified trading managed futures, systematic trading, and the passive MLMI index. In each case,b low is economically and statistically significant. In addition, b low alwayshas a negative sign, indicating positive returns to managed futures when thestock market earns negative returns. Also, ahigh is close to zero for each category of managed futures. Once again, this indicates that managed futuresdo not generate any excess returns when the returns to the stock market arepositive. All that is received is a cash return equal to treasury bills.b high is statistically significant in two categories: diversified trading andthe MLMI. The sign of the b high is negative, indicating a downward sloping curve. However, the coefficient is small and lacks economic significance.Still, this indicates that managed futures can be countercyclical when thestock market has positive returns.
ahigh because this coefficient is a linear combination ofthe other regression coefficients (see equation 9.2).
3There is no t-statistic for
192
RISK AND MANAGED FUTURES INVESTING
MIMICKING PORTFOLIOHere we specifically incorporate the long volatility exposure trend-followingstrategies to build mimicking portfolios of the strategies. The idea is that ifwe can build portfolios of securities that mimic the returns to CTAs, we canthen simulate how trend-following strategies should perform under variousmarket 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 optionis used to capture the synthetic long put option exposure. The long S&P 100index is used to capture any residual market risk that exists when the market performs positively. Last, we use the risk-free rate to measure the optionpremium that must be paid by CTAs to the right-hand side of the thresholdvalue (when the stock market performs positively). We use the coefficientestimates from equation 9.3 to construct the mimicking portfolio.
Long OEX Put OptionStrike = OEX index × (1 + Threshold + risk-free rate)Volatility = VIX indexThe number of options bought = (blow − bhigh)Short the S&P 100 4The number of S&P 100 to buy is = bhighLong Risk-Free SecurityThe number of risk-free securities to buy = 1 − blow
Figures 9.5 through 9.8 present the results from our mimicking portfolios. Similar to Figure 9.1, Figure 9.5 contains the scatter plot of the excessreturns earned by the Barclay Commodity Trading Index plotted against theexcess returns of the S&P 100. In addition, it contains the return of ourmimicking portfolio.
4Since the beta (high) is negative, a short amount of a negative number is equal to
a long position in the stock market.
193
Measuring the Long Volatility Strategies of Managed Futures
CTA Excess Returns
12.00%10.00%8.00%6.00%4.00%2.00%0.00%–2.00%–4.00%–6.00%–8.00%–20.00%
–15.00%
–10.00%
–5.00%
0.00%
5.00%
10.00%
15.00%
S&P 100 Excess ReturnsCTAMimicking Portfolio
FIGURE 9.5
Mimicking Portfolio Returns for the Barclay Commodity Trading
Index
Our mimicking portfolio performs relatively well and has the samecharacteristics of the fitted regression line in Figure 9.1. First, the mimicking portfolio has a distinct “kink” in its shape. Additionally, the slope of themimicking 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 trendfollowing strategies. We can see in each case that to the right of the kink,there is a negative slope to our mimicking portfolio, just as there was forthe fitted regression lines. Each mimicking portfolio demonstrates a longput option exposure.In summary, we are able to build mimicking portfolios using traditionalsecurities that mimic the return patterns of trend-following CTA strategies.Specifically, these mimicking portfolios capture both the long volatilityexposure of a long put option as well as the premium payment when all performs well. Our next step is to provide some Value at Risk analysis.
194
RISK AND MANAGED FUTURES INVESTING
Diversified Excess Returns
15.00%
10.00%
5.00%
0.00%
–5.00%
–10.00%–20.00%
–15.00%
–10.00%
–5.00%
0.00%
5.00%
10.00%
15.00%
S&P 100 Excess ReturnsDiversified TradingMimicking Portfolio
Systematic Excess Returns
FIGURE 9.6
Mimicking Portfolio Returns for the Barclay Diversified Trading Index
0.200
0.150
0.100
0.050
0.000
–0.050
–0.100–0.175
–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 ReturnsSystematic TradingMimicking Portfolio
FIGURE 9.7
Mimicking Portfolio Returns for the Barclay Systematic Trading Index
195
MLMI Excess Returns
Measuring the Long Volatility Strategies of Managed Futures
0.080
0.060
0.040
0.020
0.000
–0.020
–0.040
–0.060
–0.080–0.175 –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 ReturnsMLM IndexMimicking Portfolio
FIGURE 9.8
Mimicking Portfolio Returns for the MLM Index
VALUE AT RISK FOR MANAGED FUTURESThe main reason for building mimicking portfolios is to simulate thereturns to trend-following strategies for developing risk estimates. Specifically, we can run Monte Carlo simulations with our mimicking portfoliosand estimate value at risk (VaR). Armed with these data, we can estimatethe probability of the risk of loss associated with long volatility strategies.This is important to help us understand the off-balance sheet risks associated with trend-following strategies.In addition, we can use Monte Carlo simulations to graph the frequency distribution of returns. Doing so allows us to demonstrate pictorially the return patterns associated with long volatility strategies. A reviewof these return patterns can provide some sense of the downside risk of loss.Using the mimicking portfolios we run 10,000 simulations for the managedfutures strategies. Table 9.2 presents the results.For example, the one-month VaR for the Barclay Commodity TradingIndex is −0.93 percent at a 1 percent confidence level and −0.69 percent ata 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 RiskCTA
Diversified
Systematic
MLM
1 Month VaR@ 1% Confidence Level1 Month VaR@ 5% Confidence LevelMaximum 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 bya diversified CTA manager will not exceed 0.93 percent (0.69 percent) inany given month. Table 9.2 also contains the VaR for the other trend-following strategies.Figures 9.9 to 9.12 present the frequency distributions for the fourtrend-following strategies based on our Monte Carlo simulations. Forexample, for the Barclay Diversified CTA Index, the return distributiondemonstrates a positive skewness of 2.64 and a large positive kurtosis of11.35. 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
0.0539
Return
FIGURE 9.9
Simulated Commodity Trading Index Return Distribution
More
197
Measuring the Long Volatility Strategies of Managed Futures
10,0009,0008,000
Frequency
7,0006,0005,0004,0003,0002,0001,0000–0.0199
0.0208
0.0615
0.1022
0.1429
0.1836
0.2243
0.2649
More
Return
FIGURE 9.10
Simulated Diversified Trading Index Return Distribution
trend-following strategies tend to provide a large upside tail—the same riskexposure as a long put option.The positive skew indicates that these return distributions tend to havemore large positive returns than large negative returns. Additionally, thelarge value of kurtosis indicates that these return distributions have fat tails.
5,0004,5004,000
Frequency
3,5003,0002,5002,0001,5001,0005000−0.0135
−0.0033
0.0070
0.0172
0.0274
0.0377
0.0479
Return
FIGURE 9.11
Simulated Systematic Trading Return Distribution
0.0581
More
198
RISK AND MANAGED FUTURES INVESTING
8,0007,0006,000
Frequency
5,0004,0003,0002,0001,0000–0.0164
0.0154
0.0473
0.0792
0.1110
0.1429
0.1748
0.2066
More
Return
FIGURE 9.12
Simulated MLM Index Return Distribution
That is, the returns to managed futures are exposed to outlier events compared to a normal, bell-curve distribution. Together, a positive value ofskew and a large value of kurtosis indicate that managed futures have significant exposure to large positive returns. This return profile is very similar to a long options position.
RISK MANAGEMENT USING LONG VOLATILITYSTRATEGIESAt the beginning of this chapter we noted that managed futures can be usedfor risk management purposes with respect to other hedge fund strategies.Specifically, those hedge fund strategies that use short-volatility strategieswill benefit from the diversification benefits of adding long-volatility strategies to a portfolio of hedge fund managers. Two hedge fund styles use shortvolatility strategies: merger arbitrage and event driven.Merger arbitrage managers take a bet that the merger will be completed.They analyze antitrust regulations, consider whether the bid by the acquiringcompany is hostile or friendly, and check on potential shareholder opposition to the merger. If the merger is completed, the merger arbitrage managerearns the spread that it previously locked in through its long and short stockpositions. However, if the merger falls through, the merger arbitrage managermay incur a considerable loss that cannot be known in advance.
Measuring the Long Volatility Strategies of Managed Futures
199
From this perspective, merger arbitrage hedge funds can be viewed asmerger insurance agents. If the merger is completed successfully, the mergerarbitrage manager will collect a known premium (the spread it previouslylocked in). However, if the merger fails to be completed, the merger arbitrage manager is responsible for the loss instead of the shareholders fromwhom the shares were purchased or sold. For example, Favre and Galeano(2002a) describe relative value hedge fund strategies as selling economicdisaster insurance.This asymmetric insurance contract payoff exactly describes that of ashort put option exposure. The hedge fund manager sells the put option,collects the option premium, and increases total return. If the option expiresunexercised (the merger is successfully completed), the hedge fund managerkeeps the premium. However, if the option is exercised against the hedgefund manager (the merger deal collapses), the loss can be substantial.5The dangers of selling options has been discussed previously. Lo(2001), Weisman (2002), and Anson (2002b) all demonstrate that hedgefund 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 presentsthe scatter plot of merger arbitrage versus the S&P 100 as well as the fittedregression line and the regression statistics. Notice that a low and blow areeconomically and statistically significant.Figure 9.13 demonstrates a short put position—the mirror image of themanaged futures strategies. This analysis is reinforced in Figure 9.14, wherewe present the frequency distribution for merger arbitrage returns. We notethat merger arbitrage has a large negative skew of –2.76 and a large positivekurtosis of 11.54, indicating a fat downside tail. This profile of a distribution is consistent with a short put option position (short volatility) and themirror image of the return distributions presented in Figures 9.9 to 9.12.To prove that managed futures are an excellent diversifying agent forother hedge fund strategies, we construct a portfolio that is 50 percent managed futures and 50 percent merger arbitrage. Table 9.3 presents the MonteCarlo VaR for merger arbitrage alone and for the combined portfolio ofmerger arbitrage/managed futures. We note first that the VaR for mergerarbitrage alone are significantly larger (in absolute value) than that for thecombined portfolio. This is consistent with a short put option position—being on the hook for potential losses in a market downturn.
5See Anson and Ho (2003) for an examination of the nature of short volatility
strategies.
Merger Arbitrage Excess Returns
200
RISK AND MANAGED FUTURES INVESTING
4.00%
2.00%
0.00%
–2.00%
–4.00%
–6.00%
–8.00%–20.00%
–15.00%
–10.00%
–5.00%
0.00%
5.00%
10.00%
15.00%
S&P 100 Excess ReturnsMerger ArbRegression Line
CoefficientThresholdalowblowahighbhighS.E. RegressionAdj. R-Squared
FIGURE 9.13
−0.04510.02650.47690.00690.04100.01120.2692
t-statistic5.676.101.50
Merger Arbitrage
We also can see that the VaR at the 1 percent level and 5 percent for thecombined portfolio as well as the maximum loss are approximately onehalf of that for merger arbitrage alone. These results demonstrate the complementary behavior of managed futures with merger arbitrage. Thecombination of managed futures with merger arbitrage greatly reduces therisk of loss compared to merger arbitrage as a stand-alone investment. Ourwork supports that of Kat (2002) for blending managed futures with otherhedge fund styles to minimize and manage volatility risk.
201
Measuring the Long Volatility Strategies of Managed Futures
TABLE 9.3
Monte Carlo Value