theworld.What makes CTAs special? They are different from hedge fund andlong-only portfolio managers because they do not follow trends in stock orbond markets, but rather attempt to seize opportunities in a variety of commodity and financial futures markets. Many accredited investors todayhave understood the benefits of diversification by including CTAs in pension fund and institutional portfolios. The performance of CTAs can provide a better reward-to-risk ratio than equity mutual fund managers.Recent academic studies have examined the benefits of adding CTAs totraditional stock and bond portfolios and have concluded that CTAs canreduce the standard deviation and increase the risk-adjusted returns of portfolios. Furthermore, in months where stocks markets have done poorly,CTAs have often returned positive numbers, offering a cushion in thesedown months.Whether stock markets go up or down, CTAs can provide positivereturns in both environments. Academic studies also have demonstratedthat CTAs perform better than hedge funds in down markets. This is ofparamount importance because over the last few years, volatility in stockmarkets has been very high and finding protection only with hedge fundsmay not yield an optimal investment portfolio.
xxiii
PART
One
Performance
Chapter 1 demonstrates how adding managed futures to a portfolio ofstocks and bonds can reduce that portfolio’s standard deviation more andmore quickly than hedge funds can, and without the undesirable consequences that often accompany hedge fund allocations. Portfolios consistingof both hedge funds and managed futures are shown to exhibit even moredesirable diversification properties.Chapter 2 presents an original methodology for constructing a representative and pure commodity trading advisor (CTA) index that addressessome of the crucial issues investors can face during the allocation process.Using this index as a reference, the chapter also analyzes CTAs’ return characteristics and the extent to which investors would be better off integratingCTAs in their global allocation.Chapter 3 examines the many benefits to investing in CTAs. Past studies have found little evidence of performance persistence in the returns toCTAs. But these studies have used small data sets and methods with low statistical power. Larger data sets and a variety of statistical methods are usedhere to investigate whether some advisors or funds consistently outperformothers. The analysis uses data from public funds, private funds, and CTAsand applies four distinct methods to evaluate performance persistence.
1
2
PERFORMANCE
A small amount of performance persistence was found. It was strongerwhen a return/risk measure was used as the measure of performance. Thepersistence found was small relative to the noise in the data, and, therefore,precise methods and long time series had to be used to properly select fundsor CTAs. Results also indicated that CTAs using long- or medium-run systemshad higher returns than CTAs using short-term trading systems and thatCTAs with higher historical returns tend to charge higher fees. Returns werenegatively correlated with the most recent past returns, but were positive inthe long run. Yet, when deciding whether to invest or withdraw funds,investors put more weight on the most recent returns.Chapter 4 examines CTA performance, which has been analyzed bymany academic and practioners. However, few studies attempt to determinewhether there are significant differences in their performance over time.The study presented in this chapter investigates CTA performance using oneof the biggest databases ever employed in performance analysis studies todetermine if some funds consistently and significantly over- or underperform. The chapter also analyzes the survivorship bias present in CTAs aswell as the dissolution frequencies of these funds.Chapter 5 applies data envelopment analysis (DEA) to a performanceevaluation framework for CTAs. The DEA methodology allows the authorsto integrate several performance measures into one efficiency score byestablishing a multidimensional efficient frontier. Two dimensions of thefrontier are consistent with the standard Markowitz mean-variance framework. Additional risk and return dimensions include skewness and kurtosis. The chapter also illustrates a method of analyzing determinants ofefficiency scores. Tobit regressions of efficiency scores on equity betas, betasquared, fund size, length of manager track record, investment style (market focus), and strategy (discretionary versus systematic) are performed forCTA returns over two time frames representing different market environments. The authors find the efficiency scores to be negatively related tobeta-squared in both time periods. Results also indicate that emerging CTAs(those with shorter manager track records) tend to have better DEA efficiency scores. This relationship is strongest during the period from 1998 to2000, but not statistically significant during the period from 2000 to 2002.For both time periods, fund size is not related to efficiency scores.Chapter 6 examines the performance of six CTA indices from 1990 to2003, during which time four distinct market trends are identified as wellas three extreme events. The authors show that traditional multifactor aswell as multimoment asset pricing models do not adequately describe CTAreturns. However, with a proper choice of risk factors, a significant proportion of CTA returns can be explained and the abnormal performance ofeach strategy can be assessed properly.
Performance
3
Chapter 7 applies the basic, cross-evaluation, and superefficiency DEAmodels to evaluate the performance of CTA classifications. With the everincreasing number of CTAs, there is an urgency to provide money managers, pension funds, and high-net-worth individuals with a trustworthyappraisal method for ranking CTA efficiency. Data envelopment analysiscan achieve this, with the important benefit that benchmarks are notrequired, thereby alleviating the problem of using traditional benchmarksto examine nonnormal returns.
CHAPTER
1
Managed Futuresand Hedge Funds:A Match Made in HeavenHarry M. Kat
n this chapter we study the possible role of managed futures in portfoliosof stocks, bonds, and hedge funds. We find that allocating to managedfutures allows investors to achieve a very substantial degree of overall riskreduction at, in terms of expected return, relatively limited costs. Apartfrom their lower expected return, managed futures appear to be more effective diversifiers than hedge funds. Adding managed futures to a portfolio ofstocks and bonds will reduce that portfolio’s standard deviation more andmore quickly than hedge funds will, and without the undesirable side effectson skewness and kurtosis. Overall portfolio standard deviation can bereduced further by combining both hedge funds and managed futures withstocks and bonds. As long as at least 45 to 50 percent of the alternativesallocation is to managed futures, this will have no negative side effects onskewness and kurtosis.
I
INTRODUCTIONHedge funds are often said to provide investors with the best of both worlds:an expected return similar to equity combined with a risk similar to bonds.When past returns are simply extrapolated and risk is defined as the standard deviation of the fund return, this is indeed true. Recent research, however, has shown that the risk and dependence characteristics of hedge fundsare substantially more complex than those of stocks and bonds. Amin andKat (2003), for example, show that although including hedge funds in a traditional investment portfolio may significantly improve that portfolio’smean-variance characteristics, it can also be expected to lead to significantly
5
6
PERFORMANCE
lower skewness. The additional negative skewness that arises when hedgefunds are introduced in a portfolio of stocks and bonds forms a major risk,as one large negative return can destroy years of careful compounding. Tohedge this risk, investors need to expand their horizon beyond stocks andbonds. Kat (2003) showed how stock index put options may be used to hedgeagainst the unwanted skewness effect of hedge funds. Kat (2004) showedthat put options on (baskets of) hedge funds may perform a similar task.Of course, the list of possible remedies does not end here. Any asset orasset class that has suitable (co-)skewness characteristics can be used. Oneobvious candidate is managed futures. Managed futures programs are oftentrend-following in nature. In essence, what these programs do is somewhatsimilar to how option traders hedge a short call position. When the marketmoves up, they increase exposure, and vice versa. By moving out of the market when it comes down, managed futures programs avoid being pulled in.As a result, the (co-)skewness characteristics of managed futures programscan be expected to be more or less opposite to those of many hedge funds.In this chapter we investigate how managed futures mix with stocks,bonds, and hedge funds and how they can be used to control the undesirableskewness effects that arise when hedge funds are added to portfolios of stocksand bonds. We find that managed futures combine extremely well withstocks, bonds, and hedge funds and that the combination allows investors tosignificantly improve the overall risk characteristics of their portfolio without,under the assumptions made, giving up much in terms of expected return.
MANAGED FUTURESThe asset class “managed futures” refers to professional money managersknown as commodity trading advisors (CTAs) who manage assets using theglobal futures and options markets as their investment universe. Managedfutures have been available for investment since 1948, when the first public futures fund started trading. The industry did not take off until the late1970s. Since then the sector has seen a fair amount of growth with currentlyan estimated $40 to $45 billion under management.There are three ways in which investors can get into managed futures.1. Investors can buy shares in a public commodity (or futures) fund, inmuch the same way as they would invest in stock or bond mutualfunds.2. They can place funds privately with a commodity pool operator (CPO)who pools investors’ money and employs one or more CTAs to managethe pooled funds.
Managed Futures and Hedge Funds
7
3. Investors can retain one or more CTAs directly to manage their moneyon an individual basis or hire a manager of managers (MOM) to selectCTAs for them.The minimum investment required by funds, pools, and CTAs variesconsiderably, with the direct CTA route open only to investors who want tomake a substantial investment. CTAs charge management and incentive feescomparable to those charged by hedge funds (i.e., 2 percent managementfee plus 20 percent incentive fee). Like funds of hedge funds, funds andpools charge an additional fee on top of that.Initially, CTAs were limited to trading commodity futures (whichexplains terms such as “public commodity fund,” “CTA,” and “CPO”).With the introduction of futures on currencies, interest rates, bonds, andstock indices in the 1980s, however, the trading spectrum widened substantially. Nowadays CTAs trade both commodity and financial futures.Many take a very technical, systematic approach to trading, but others optfor a more fundamental, discretionary approach. Some concentrate on particular futures markets, such as agricultural, currencies, or metals, but mostdiversify over different types of markets.For our purposes, one of the most important features of managed futuresis their trend-following nature. That CTA returns have a strong trendfollowing component can be shown by calculating the correlation betweenmanaged futures returns and the returns on a purely mechanical trendfollowing strategy. One such strategy underlies the Mount Lucas Management(MLM) index, which reflects the results of a purely mechanical, movingaverage-based, trading strategy in 25 different commodity and financialfutures markets. Estimates of the correlation between the MLM index andCTA returns are typically positive and highly significant.
DATAWe distinguish between four different asset classes: stocks, bonds, hedgefunds, and managed futures. Stocks are represented by the Standard &Poor’s (S&P) 500 index and bonds by the 10-year Salomon Brothers Government Bond index. Hedge fund return data were obtained from TremontTASS, one of the largest hedge fund databases currently available. Aftereliminating funds with incomplete and ambiguous data as well as funds offunds, the database at our disposal as of May 2001 contained monthly netof-fee returns on 1,195 live and 526 dead funds. To avoid survivorship bias,we created 455 seven-year monthly return series by, beginning with the 455
8
PERFORMANCE
funds that were alive in June 1994, replacing every fund that closed downduring the sample period by a fund randomly selected from the set of fundsalive at the time of closure, following the same type of strategy and of similar age and size. Next we used random sampling to create 500 differentequally weighted portfolios containing 20 hedge funds each. From themonthly returns on these portfolios we calculated the mean, standard deviation, skewness, and kurtosis and determined the median value of each ofthese statistics. Subsequently we selected the portfolio whose sample statistics came closest to the latter median values. We use this “median portfolio”to represent hedge funds.Managed futures are represented by the Stark 300 index. This assetweighted index is compiled using the top 300 trading programs from theDaniel B. Stark & Co. database.1 The top 300 trading programs are determined quarterly based on assets under management. When a trading program closes down, the index does not get adjusted backward, which takescare of survivorship bias issues. All 300 of the CTAs in the index are classified by their trading approach and market category. Currently the indexcontains 248 systematic and 52 discretionary traders, which split up in 169diversified, 111 financial only, 9 financial and metals, and 11 nonfinancialtrading programs.Throughout we use monthly return data over the period June 1994 toMay 2001. For bonds, hedge funds, and managed futures we use the sample mean as our estimate of the expected future return. For stocks, however,we assume an expected return of 1 percent per month, as it would be unrealistic to assume an immediate repeat of the 1990s bull market. Under theseassumptions, the basic return statistics for our four asset classes are shownin Table 1.1 The table shows that managed futures returns have a lowermean and a higher standard deviation than hedge fund returns. However,managed futures also exhibit positive instead of negative skewness andmuch lower kurtosis.2 From the correlation matrix we see that the correlation of managed futures with stocks and hedge funds is very low. Thismeans that, as long as there are no negative side effects, such as lower skewness or higher kurtosis, managed futures will make very good diversifiers.This is what we investigate in more detail next.
1Note that contrary to the Mount Lucas Management index, the Stark 300 is a trueCTA index.2Over the sample period the MLM index has a mean of 0.89 percent, a standarddeviation of 1.63 percent, a skewness of −0.81 and a kurtosis of 3.42. The Stark 300index has fundamentally different skewness and kurtosis properties than the MLMindex.
9
Managed Futures and Hedge Funds
TABLE 1.1 Basic Monthly Statistics S&P 500, Bonds, Hedge Funds,and Managed Futures
MeanStandard deviationSkewnessExcess kurtosis
S&P 500
Bonds
Hedge Funds
Managed Fut.
1.004.39−0.821.05
0.451.770.581.45
0.992.44−0.472.67
0.702.890.450.21
Correlations
S&P 500BondsHFMF
S&P 500
Bonds
Hedge Fund
Managed Fut.
10.150.63−0.07
1−0.050.20
1−0.14
1
STOCKS, BONDS, PLUS HEDGE FUNDSOR MANAGED FUTURESGiven the complexity of the relationship between hedge fund and equityreturns, we study the impact of hedge funds and managed futures for twodifferent types of investors. The first are what we refer to as 50/50investors—investors who always invest an equal amount in stocks andbonds. When adding hedge funds and/or managed futures to their portfolio, 50/50 investors will reduce their stock and bond holdings by the sameamount. This gives rise to portfolios consisting of 45 percent stocks, 45 percent bonds, and 10 percent hedge funds or 40 percent stocks, 40 percentbonds, and 20 percent managed futures. The second type of investors, whatwe call 33/66 investors, always divide the money invested in stocks andbonds in such a way that one-third is invested in stocks and two-thirds isinvested in bonds.The first step in our analysis is to see whether there are any significantdifferences in the way in which hedge funds and managed futures combinewith stocks and bonds. We therefore form portfolios of stocks, bonds, andhedge funds, as well as portfolios of stocks, bonds, and managed futures.Table 1.2 shows the basic return statistics for 50/50 investors. Table 1.3shows the same for 33/66 investors. From Table 1.2 we see that if the hedgefund allocation increases, both the standard deviation and the skewness ofthe portfolio return distribution drop substantially, while at the same timethe return distribution’s kurtosis increases. A similar picture emerges from
10
PERFORMANCE
TABLE 1.2 Return Statistics 50/50 Portfolios of Stocks, Bonds, and Hedge Fundsor Managed FuturesHedge Funds
Managed Futures
% HF
Mean
SD
Skewness
Kurtosis
% MF
Mean
SD
Skewness Kurtosis
05101520253035404550
0.720.730.740.760.770.780.800.810.820.840.85
2.492.432.382.332.292.252.222.202.182.172.16
−0.33−0.40−0.46−0.53−0.60−0.66−0.72−0.78−0.82−0.85−0.87
−0.030.020.080.170.280.420.580.770.971.191.41
05101520253035404550
0.720.710.710.710.710.710.710.710.710.710.71
2.492.372.262.162.082.001.951.911.891.891.91
−0.33−0.28−0.21−0.14−0.060.020.100.180.240.300.34
−0.03−0.18−0.30−0.39−0.42−0.40−0.32−0.20−0.060.080.19
Table 1.3 for 33/66 investors, except that the drop in skewness is much morepronounced. With managed futures the picture is different. If the managedfutures allocation increases, the standard deviation drops faster than withhedge funds. More remarkably, skewness rises instead of drops while kurtosis drops instead of rises. Although (under the assumptions made) hedgefunds offer a somewhat higher expected return, from an overall risk perspective managed futures appear to be better diversifiers than hedge funds.TABLE 1.3 Return Statistics 33/66 Portfolios of Stocks, Bonds, and Hedge Fundsor Managed FuturesHedge Funds
Managed Futures
% HF
Mean
SD
Skewness
Kurtosis
% MF
Mean
SD
05101520253035404550
0.620.640.660.680.690.710.730.750.770.790.80
2.011.971.931.901.871.861.851.841.851.861.89
0.03−0.05−0.14−0.24−0.34−0.43−0.52−0.60−0.66−0.71−0.75
0.210.130.080.040.040.090.170.310.490.700.94
05101520253035404550
0.620.620.630.630.640.640.650.650.650.660.66
2.011.931.851.791.751.711.701.701.721.761.81
Skewness Kurtosis
0.030.090.150.220.280.340.390.420.450.470.48
0.210.170.140.150.180.240.300.360.410.430.42
11
Managed Futures and Hedge Funds
HEDGE FUNDS PLUS MANAGED FUTURESThe next step is to study how hedge funds and managed futures combine witheach other. This is shown in Table 1.4. Adding managed futures to a hedgefund portfolio will put downward pressure on the portfolio’s expected returnas the expected return on managed futures is lower than that of hedge funds.From a risk perspective, however, the benefits of managed futures are againvery substantial. From the table we see that adding managed futures to aportfolio of hedge funds will lead to a very significant drop in the portfolioreturn’s standard deviation. With 40 percent invested in managed futures,the standard deviation falls from 2.44 percent to 1.74 percent. When 45 percent is invested in managed futures, skewness rises quickly—from −0.47 to0.39, and kurtosis exhibits a strong drop—from 2.67 to −0.17. Giving up 10to 15 basis points per month in expected return does not seem an unrealistic price to pay for such a substantial improvement in overall risk profile.
STOCKS, BONDS, HEDGE FUNDS,AND MANAGED FUTURESThe final step in our analysis is to bring all four asset classes together in oneportfolio. We do so in two steps. First, we combine hedge funds and managedfutures into what we will call the alternatives portfolio. Then we combine thealternatives portfolio with stocks and bonds. We vary the managed futuresallocation in the alternatives portfolio as well as the alternatives allocation inthe overall portfolio from 0 percent to 100 percent in 5 percent steps.Without managed futures, increasing the alternatives allocation willsignificantly raise the expected return. When the managed futures alloca-
TABLE 1.4 Return Statistics Portfolios of Hedge Funds and Managed Futures% MF
Mean
SD
Skewness
Kurtosis
05101520253035404550
0.990.970.960.940.930.920.900.890.870.860.85
2.442.312.182.061.961.881.811.761.741.741.76
−0.47−0.37−0.27−0.15−0.030.090.200.290.360.390.39
2.672.311.911.461.010.590.23−0.01−0.14−0.17−0.15
12
PERFORMANCE
2.902.702.502.302.101.901.701.50
% in AlternativesPortfolio
0
20
40
60
80
100
20
40
60
80 100
% in Managed Futures
FIGURE 1.1 Standard Deviation 50/50 Portfolios of Stocks, Bonds, Hedge Funds,and Managed Futurestion increases, however, the expected return will drop. This follows directlyfrom the result that the expected return on hedge funds is 0.99 percent, butit is only 0.70 percent on managed futures (Table 1.1). On the risk front thepicture is much more interesting. Figures 1.1 and 1.2 show that investing inalternatives can substantially reduce the overall portfolio return’s standarddeviation, for 50/50 as well as 33/66 investors. The drop, however, is heavily dependent on the percentage of managed futures in the alternatives portfolio. Surprisingly, for allocations to alternatives between 0 percent and 20percent, the lowest standard deviations are obtained without hedge funds,
2.902.702.502.302.101.901.701.500
% in AlternativesPortfolio
20
40
6060
4080
20
80
100
% in Managed Futures
100
FIGURE 1.2 Standard Deviation 33/66 Portfolios of Stocks, Bonds, Hedge Funds,and Managed Futures
13
Managed Futures and Hedge Funds
0.600.400.200.00–0.20–0.40–0.60–0.80100
80
60
% in Managed Futures
40
20
20
40
60
80
–1.00100
% in Alternatives Portfolio
0
FIGURE 1.3 Skewness 50/50 Portfolios of Stocks, Bonds, Hedge Funds,and Managed Futuresthat is, when 100 percent is invested in managed futures. For higher alternatives allocations, however, it pays also to include some hedge funds in thealternatives portfolio. This makes sense, because for the alternatives portfolio, the lowest standard deviation is found when 40 to 45 percent isinvested in managed futures. We saw that before in Table 1.4.Figures 1.3 and 1.4 show the impact of allocation on skewness, for50/50 and 33/66 investors respectively. From these graphs we see once more
0.600.400.200.00–0.20–0.40–0.60–0.80100
80
% in Managed Futures
60
40
20
0
20
40
60
80
–1.00100
% in Alternatives Portfolio
FIGURE 1.4 Skewness 33/66 Portfolios of Stocks, Bonds, Hedge Funds,and Managed Futures
14
PERFORMANCE
that without managed futures, increasing the alternatives allocation will leadto a substantial reduction in skewness. The higher the managed futures allocation, however, the more this effect is neutralized. When more than 50 percent is invested in managed futures, the skewness effect of hedge funds is(more than) fully eliminated and the skewness of the overall portfolio returnactually rises when alternatives are introduced. Finally, Figures 1.5 and 1.6show the impact on kurtosis. With 0 percent allocated to managed futures,kurtosis rises substantially when the alternatives allocation is increased.With a sizable managed futures allocation, however, this is no longer thecase, and kurtosis actually drops when more weight is given to alternatives.To summarize, Figures 1.1 to 1.6 show that investing in managedfutures can improve the overall risk profile of a portfolio far beyond whatcan be achieved with hedge funds alone. Making an allocation to managedfutures not only neutralizes the unwanted side effects of hedge funds butalso leads to further risk reduction. Assuming managed futures offer anacceptable expected return, all of this comes at quite a low price in terms ofexpected return forgone.To make sure that these findings have general validity—that they arenot simply due to the particular choice of index—we repeated the procedure with a number of other CTA indices, including various indices calculated by the Barclay Group. In all cases the results were very similar, which
3.002.502.001.501.000.500.00–0.50–1.00100
80
2060
% in Alternatives Portfolio
0
4060
4020
100
80
% in Managed Futures
FIGURE 1.5 Kurtosis 50/50 Portfolios of Stocks, Bonds, Hedge Funds,and Managed Futures
15
Managed Futures and Hedge Funds
3.002.502.001.501.000.500.00–0.50–1.00100
80
2060
% in Alternatives Portfolio
0
4060
4020
100
80
% in Managed Futures
FIGURE 1.6 Kurtosis 33/66 Portfolios of Stocks, Bonds, Hedge Funds,and Managed Futuressuggests that our results are robust with respect to the choice of managedfutures index.
SKEWNESS REDUCTION WITH MANAGED FUTURESOur findings lead us to question what the exact costs are of using managedfutures to eliminate the negative skewness that arises when hedge funds areintroduced in a traditional portfolio of stocks and bonds. To answer thisquestion we follow the same procedure as in Kat (2003). First, we determine the managed futures allocation required to bring the overall portfolioskewness back to its level before the addition of hedge funds, which is −0.33for 50/50 investors and 0.03 for 33/66 investors. Next, we leverage (assuming 4 percent interest) the resulting portfolio to restore the standard deviation. Tables 1.5 and 1.6 show the resulting overall portfolio allocations andthe accompanying changes in expected return (on a per annum basis) andkurtosis. From Table 1.6 we see that the optimal portfolios are quitestraightforward. In essence, the bulk of the managed futures holdings isfinanced by borrowing, without changing much about the stock, bond, andhedge fund allocations. It is interesting to see that for smaller initial hedgefund allocations, the optimal hedge fund and managed futures allocationare more or less equal. This is true for 50/50 as well as 33/66 investors.
16
PERFORMANCE
TABLE 1.5 Allocations and Change in Mean and Kurtosis 50/50 Portfolios ofStocks, Bonds, Hedge Funds, Managed Futures, and Cash with −0.33 Skewnessand Standard Deviations as in Third Column of Table 1.2Initial% HF
%Stocks
%Bonds
%HF
%MF
%Cash
05101520253035404550
50.0047.4244.7141.9939.3436.6734.0931.5529.0626.6124.25