
50.0047.4244.7141.9939.3436.6734.0931.5529.0626.6124.25
0.004.999.9414.8219.6724.4529.2233.9838.7543.5448.50
0.005.489.9513.6016.5518.9120.8022.3323.3224.0424.40
0.00−5.30−9.30−12.40−14.90−16.70−18.20−19.40−20.20−20.80−21.40
Gain Mean Changeper annum Kurtosis0.000.661.151.531.832.052.232.372.462.532.60
0.00−0.18−0.34−0.50−0.66−0.82−0.98−1.15−1.31−1.46−1.59
Looking at the change in expected return, we see that as a result of theaddition of managed futures and the subsequent leverage, the expectedreturn actually increases instead of drops. From the last column we also seethat this rise in expected return is accompanied by a significant drop in kurtosis. This compares very favorably with the results in Kat (2003, 2004),where it is shown that the costs of skewness reduction through stock indexor hedge fund puts can be quite significant.TABLE 1.6 Allocations and Change in Mean and Kurtosis 33/66 Portfolios ofStocks, Bonds, Hedge Funds, Managed Futures, and Cash with 0.03 Skewnessand Standard Deviations as in Third Column of Table 1.3Initial% HF
%Stocks
%Bonds
%HF
%MF
%Cash
05101520253035404550
33.3332.0830.5428.8326.9925.1123.2121.3219.4717.6515.85
66.6764.1661.0757.6653.9950.2246.4142.6338.9435.2931.71
0.005.0710.1815.2620.2525.1129.8434.4438.9443.3147.56
0.006.7012.7117.9622.3726.0629.0431.4133.1534.3535.18
0.00−8.00−14.50−19.70−23.60−26.50−28.50−29.80−30.50−30.60−30.30
Gain Mean Changeper annum Kurtosis0.000.981.792.442.933.293.533.693.763.763.70
0.00−0.07−0.15−0.22−0.31−0.42−0.56−0.73−0.93−1.15−1.38
Managed Futures and Hedge Funds
17
ConclusionIn this chapter we have studied the possible role of managed futures in portfolios of stocks, bonds, and hedge funds. We have found that allocating tomanaged futures allows investors to achieve a very substantial degree ofoverall risk reduction at limited costs. Despite their lower expected return,managed futures appear to be more effective diversifiers than hedge funds.Adding managed futures to a portfolio of stocks and bonds will reduce thatportfolio’s standard deviation more effectively than hedge funds alone, andwithout the undesirable impact on skewness and kurtosis. This does notmean that hedge funds are superfluous. Overall portfolio standard deviation can be reduced further by combining both hedge funds and managedfutures with stocks and bonds. As long as at least 45 to 50 percent of thealternatives allocation is allocated to managed futures, there will be no negative side effects on portfolio skewness and kurtosis. Assuming that hedgefunds will continue to provide higher returns than managed futures, theinclusion of hedge funds also will boost the portfolio’s expected returnsomewhat.
CHAPTER
2
Benchmarking thePerformance of CTAsLionel Martellini and Mathieu Vaissié
he bursting of the Internet bubble in March 2000 plunged traditionalmarket indices (stocks, bonds, etc.) into deep turmoil, leaving most institutional investors with the impression that portfolio diversification tends tofail at the exact moment that investors have a need for it, namely in periods when the markets drop significantly.1 At the same time, most alternative investments (e.g., hedge funds, CTAs, real estate, etc.) posted attractivereturns. They benefited from large capital inflows from high-net-worthindividuals (HNWI) and institutional investors, who were both looking forinvestment vehicles that would improve the diversification of their portfolios. At the same time, many recent academic and practitioner studies havedocumented the benefits of investing in alternative investments in general,and hedge funds in particular (see Amenc, Martellini, and Vaissié 2003;Amin and Kat 2002, 2003b; Anjilvel Boudreau, Urias, and Peskin 2000;Brooks and Kat 2002; Cerrahoglu and Pancholi 2003; Daglioglu and Gupta2003a; Schneeweis, Karavas, and Georgiev 2003).Nevertheless, due to the “natural” (survivorship/selection) and “spurious” (backfilling/weighting scheme) biases that are present in hedge funddatabases (see Fung and Hsieh 2000, 2002a), it remains challenging to comeup with an accurate estimate of returns on hedge funds. The challengingnature of hedge fund return measurement has been exemplified by the heterogeneity in hedge fund index returns, which is now a well-documentedproblem (cf. Amenc and Martellini 2003; Vaissié 2004). As evidenced byAmenc and Martellini (2003), the correlation between indices representing
T
1Longin and Solnik (1995) provide evidence that the correlation between the stock
markets in different countries converges toward 1 when there is a sharp drop in U.S.stock markets.
18
Benchmarking the Performance of CTAs
19
the same investment style may turn out to be as low as 0.43 for equity market neutral or 0.46 for equity long short. This fact may leave investors witha somewhat confused picture of the performance of alternative investmentstrategies. More surprisingly perhaps, index heterogeneity also may be ofconcern in the case of CTAs. Dealing with CTA index heterogeneity is discussed in the next sections. It is crucial for investors to pay particular attention to the selection of an appropriate index to benchmark their performanceand to assess their exposure to risk factors. To respond to investors’ expectations, in this chapter we present an original methodology to construct apure and representative CTA index (also known as the Edhec CTA GlobalIndex; hereafter referred to as the Edhec CTA Index). We then use theEdhec CTA Index to analyze CTA return characteristics and the extent towhich investors would be better off integrating CTAs in their global allocation. Finally, we derive a five-factor model to identify the underlying riskfactors driving CTA performance.
DEALING WITH CTA INDEX HETEROGENEITYBecause managed futures tend to trade more liquid assets than hedge fundsand because they have to register with the Commodity Futures TradingCommission (CFTC), one would expect the different managed futuresindices to exhibit negligible heterogeneity. This, however, is not the case.While the average correlation between the different indices available on themarket2 from January 1998 through September 2003 is 0.94, the differencebetween the monthly returns on two of these indices can be as high as 7.50percent, the return difference between the S&P Index (+13.50 percent) andthe Barclay CTA Index in December 2000. The corresponding averagemonthly difference amounts to 2.90 percent. This gives clear evidence thatmanaged futures indices are not free from “natural” and/or “spurious”biases. As evidenced in Posthuma and Van der Sluis (2003), the backfillingbias is even higher for commodity trading advisers (CTAs) than for hedgefunds (3.30 percent versus 2.23 percent). Liang (2003), perhaps surprisingly, drew the same conclusion with respect to survivorship bias, whichturns out to be significantly higher in the case of CTAs (5.85 percent versus2.32 percent).Table 2.1 illustrates the consequences of the heterogeneity of index construction methodologies and fund selection in terms of risk factor expo-
2For example, CSFB/Tremont Managed Futures Index, the CISDM Trading Advisor
Qualified Universe Index, the HF Net CTA/Managed Futures Average, the BarclayCTA Index, and the S&P Managed Futures Index.
20
PERFORMANCE
TABLE 2.1 The Heterogeneity of CTA Indices’ Risk Factor Exposure,September 1999 to September 2003Risk Factors
CSFB
S&P
Barclay
HF Net
CISDM
Constant4.52E−03 6.78E−03 2.93E−03 8.04E−03 4.27E−03T-stats1.11.11.02.51.5S&P 500−0.21−0.09T-stats−2.8−1.3LEHMAN GLB.0.891.490.670.760.71US TREASURYT-stats2.93.63.33.33.5LEHMAN HIGH−0.39−0.13−0.21−0.12YIELD CORPT-stats−2.0−1.4−1.7−1.3US $ MAJOR−0.69−0.540.18−0.46−0.44CURRENCYT-stats−2.2−1.21.7−2.0−2.1US $ TO JAPANESE−0.54−0.55−0.20−0.40−0.39YENT-stats−2.8−2.0−1.9−2.7−2.9Goldman Sachs0.210.260.140.160.13Commodity IndexT-stats3.32.73.03.22.8Chg in VIX−0.03T-stats−1.4
sures. To come up with a limited set of risk factors, we selected 16 factorsknown to be related to the strategies implemented by managed futures,namely stocks, bonds, interest rates, currency, and commodities factors. Wethen used stepwise regression with the backward entry procedure to avoidany multicollinearity problems and keep a sufficient number of degrees offreedom. While four factors are common to all indices (Lehman Global U.S.Treasury, U.S. dollar [USD] versus major currency, USD versus Japaneseyen, and Goldman Sachs Commodity Index [GSCI], the correspondingexposures turn out to be very different. The S&P index yields a beta of 1.49with the Lehman Global U.S. Treasury while the beta is 0.67 for the Barclay index. In the same vein, the CSFB index has a −0.69 beta with the USDversus major currency while the beta is 0.18 for the Barclay index. Onlytwo indices (CSFB and HF Net) appear to exhibit significant exposure tothe S&P 500 and only one (HF Net) to the evolution of the VIX (impliedvolatility on the S&P 500).Since the choice of index may have a significant impact on the wholeinvestment process (from strategic allocation through performance evalua-
Benchmarking the Performance of CTAs
21
tion and attribution), investors should be aware of and tackle those differences in factor exposures. In what follows, we present an index construction methodology aimed at addressing this issue. Note that this methodologywas first introduced in Amenc and Martellini (2003) and is now implemented to construct the Edhec Alternative Indices.3Given that it is impossible to be objective on what is the best existingindex, a natural idea consists of using some combination of competingindices (i.e., CTA indices available on the market) to extract any commoninformation they might share. One straightforward method would involvecomputing an equally weighted portfolio of all competing indices. Becausecompeting indices are based on different sets of CTAs, the resulting portfolio of indices would be more exhaustive than any of the competing indicesit is extracted from. We push the logic one step further and suggest usingfactor analysis to generate a set of hedge fund indices that are the best possible one-dimensional summaries of information conveyed by competingindices for a given style, in the sense of the largest fraction of varianceexplained. Technically speaking, this amounts to using the first componentof a Principal Component Analysis of competing indices. The Edhec CTAIndex is thus able to capture a very large fraction of the information contained in the competing indices.On one hand, the Edhec CTA Index generated as the first componentin a factor analysis has a built-in element of optimality, since there is noother linear combination of competing indices that implies a lower information loss. On the other hand, since competing indices are affected differently by measurement biases, searching for the linear combination ofcompeting indices that implies a maximization of the variance explainedleads implicitly to a minimization of the bias. As a result, the Edhec CTAIndex tends to be very stable over time and easily replicable.
CTA PERFORMANCE AT A GLANCETable 2.2 gives a comparative overview of the Edhec CTA Index, the S&P500, and the Lehman Global Bond Index. Due to an average return that isslightly superior to the S&P 500 (0.73 percent versus 0.50 percent) andvariance that is close to that of the Lehman Global Bond Index (0.84 percent versus 0.14 percent), the Edhec CTA Index obtains a Sharpe ratio thatis significantly higher than stock and bond indices (0.72 versus 0.21 and−0.39, respectively). Its superiority in terms of risk-adjusted performance iseven more marked when considering the Sortino ratio (11.01 versus 1.05
3Further details on the construction methodology of the Edhec Alternative Indices
may be found at www.edhec-risk.com.
22
PERFORMANCE
TABLE 2.2 Basic Statistical Properties of the Edhec CTA Global Index,January 1997 to September 2003Edhec CTAGlobal Index
S&P 500
Lehman GlobalBond Index
0.73%0.65%6.91%−5.43%−5.43%−0.100.1556.79%2.52%43.21%−1.62%
0.50%0.76%9.67%−14.58%−20.55%−0.28−0.4355.56%4.32%44.44%−4.27%
0.06%0.12%2.15%−3.94%−6.75%1.44−0.7654.32%0.83%45.68%−0.85%
Monthly Std Deviation Ann’d9.17%Monthly Variance Ann’d0.84%Monthly Semivariance Ann’d0.39%Monthly Downside Risk (MAR = Rf*)** 0.49%
17.94%3.22%1.76%1.85%
3.75%0.14%0.08%0.12%
VaR (99%)Modified VaR (99%)
−6.89%−6.52%
−12.55%−13.49%
−2.58%−3.31%
Sharpe RatioSortino Ratio (MAR = Rf*)
0.7211.01
0.211.05
−0.39−8.11
Monthly Average ReturnMonthly Median ReturnMonthly Max. ReturnMonthly Min. ReturnMaximum Uninterrupted LossExcess KurtosisSkewness% of Winning MonthsAverage Winning Return% of Losing MonthsAverage Losing Return
**The risk-free rate is calculated as the 3-month LIBOR average over the periodJanuary 1997 to September 2003, namely 4.35 percent.**This indicator is also referred to as the lower partial moment of order 2.
and −8.11) due to a limited downside risk (i.e., 0.49 percent versus 1.85percent for the S&P 500). The Edhec CTA Index posts positive returns inabout 57 percent of months, with an average gain of 2.52 percent versus anaverage loss of −1.62 percent in 43 percent of the cases. It is also worth noting that the Edhec index presents a smaller maximum uninterrupted lossthan both the stock and bond indices.Concerning extreme risks, the Edhec CTA Index is closer to the bondindex than to the stock index with a modified value at risk (VaR) (alsoreferred to as Cornish Fisher VaR4) of −6.52 percent as opposed to −13.494cf. Favre and Galeano (2002b) for more details on the Modified VaR and its
application to hedge funds.
23
Benchmarking the Performance of CTAs
percent for the S&P 500 and −3.31 percent for the Lehman Global BondIndex. This is a very interesting property as low volatility strategies oftenpresent large exposures to extreme risks due to a transfer of the risk fromsecond- to third- and fourth-order moments. Our analysis suggests that it isnot the case with CTAs.To account for the presence of extreme risks in the evaluation of riskadjusted performance, we suggest computing the Omega ratio (cf. Keatingand Shadwick 2002) of the CTA index:b
∫ [1 − F(x)]dx
Ω (MAR) = MARMAR
∫ [ F(x)]dxa
where F(x) = cumulative distribution function,MAR (minimum acceptable return) = gain/loss threshold,[a,b] = interval for which the distribution of asset returns is defined.This performance measurement indicator has appealing propertiesbecause it does not require the distribution function of the underlying assetto be specified or any assumption to be made with respect to investors’ preferences. It can thus account for the presence of fat tails in the case of nonnormal distribution functions. Figure 2.1 compares the Omega ratiosobtained by the Edhec index to those of the stock and bond indices. Again,
1.801.60Edhec CTA Global Index1.40
OmegaRatio
1.20S&P 500
1.000.800.600.40
Lehman Global Bond Index
0.200.000
5
10
15
Threshold %
FIGURE 2.1
Omega Ratio as a Function of the Gain/Loss Threshold
20
24
PERFORMANCE
up to an improbable loss threshold of roughly 18 percent per year, theEdhec index offers a better gain/loss ratio than both the S&P 500 and theLehman Global Bond Index, which confirms the superiority of CTA riskadjusted performance on a stand-alone basis.
MANAGED FUTURES IN THE ASSET ALLOCATIONPROCESS: RETURN ENHANCERS, RISK REDUCERS,OR BOTH?On a stand-alone basis, CTAs offer better risk-adjusted performance thantraditional asset classes and thus may be used as return enhancers. However, investors expect alternative investments in general, and CTAs in particular, to be efficient in a portfolio context. To assess the extent to whichCTAs may be used to improve investors’ portfolio diversification, we willstudy the conditional correlation of the Edhec CTA Index with eight indices(S&P 500, S&P 500 Growth, S&P 500 Value, S&P Small Cap, LehmanGlobal Treasury/High Yield/Investment Grade/Global Bond Index) and abalanced portfolio made up of 50 percent stocks (i.e., S&P 500) and 50 percent bonds (i.e., Lehman Global Bond Index). We divide our sample(monthly returns from 09/99 through 09/03) into three subsamples (Low,Medium, High). The Low subsample corresponds to the most bearishmonths of the filtering index, and the High subsample to its most bullishmonths. We then computed the correlation of the Edhec CTA Index withthe other indices for each of the three subsamples. As can be seen fromTable 2.3, the Edhec CTA Index is systematically higher in the High subsample than in the Low subsample with both the stock and bond indices.The only exception is the correlation with the S&P Growth 500, which isslightly lower in market declines. A first striking feature is the propensity ofthe correlation with the Lehman Global Bond Index to remain stablethrough all market conditions. It is also worth noting that the Edhec CTAIndex is systematically negatively correlated with stock indices during largedown market trends. On top of that, as shown in the Table, correlationswith stock and bond indices tend to be either “Good” or “Stable.” No single correlation is significantly lower in the Low subsample than in the Highsubsample. This leads the CTA index to exhibit put option-like payoffs withrespect to equity oriented indices (i.e., negative correlation during marketdeclines, resulting in high positive returns, and low negative correlationduring increasing markets, resulting in slightly negative returns) and straddlelike behavior with respect to most bond-oriented indices. In other words,CTAs may play the role of portfolio insurers. This interesting profile coupled with relatively low volatility suggests that CTAs are not only returnenhancers but also risk reducers.
25
Benchmarking the Performance of CTAs
TABLE 2.3 Edhec CTA Global Index Conditional Correlations with Stockand Bond Indices, 1999 to 2003Correlation with Edhec CTA Global Index
S&P 500S&P 500 ValueS&P Small CapLehman HighYield IndexBalanced Portfolio(50% Stocks +50% Bonds)S&P 500 GrowthLehman GlobalBond IndexLehman GlobalTreasury IndexLehman InvestmentGrade Index
Low
Med
High
High–Low
T-stats
−52.92%−49.55%−46.37%−62.96%
0.53%6.56%13.03%29.75%
−24.79%−11.77%12.29%−17.31%
GoodGoodGoodGood
(1.16)(0.96)(1.26)(−0.19)
−45.04%
18.04%
11.90%
Good
(1.00)
−28.47%23.59%
6.61%20.52%
−29.54%25.60%
StableStable
(1.95)*(−3.50)*
26.31%
−7.71%
36.30%
Stable
(−4.40)*
18.79%
−41.99%
39.83%
Stable
(−3.93)*
When the correlation differential between high and low subsamples is greater(lower) than 25 percent (−25 percent), the correlation of the Edhec index with thebenchmark is regarded as a good (bad) correlation. When the correlation differential is between −25 percent and 25 percent, the correlation is regarded as Stable.*Denotes significance at 5 percent level.
If CTAs offer good diversification potential while posting attractiverisk-adjusted performance, this should be reflected with a translation ofefficient frontiers to the top-left corner of the graph in Figure 2.2. Note thatto take extreme risks into account, we defined the risk dimension as themodified VaR with 99 percent confidence level. Comparing the efficientfrontier of stocks and bonds (S&P 500 + LGBI) and that of a balanced portfolio with CTAs (Balanced Portfolio + Edhec CTA Global), both represented by dashed lines in Figure 2.2, it is clear that CTAs can both reducethe risk and enhance the performance of the balanced portfolio. This factshould encourage investors to reconsider their strategic allocation to CTAs.However, to tap the diversification potential of CTAs in an optimal manner,investors need to have a better understanding of the extent to which CTAsdiffer from traditional asset classes. Such an understanding naturallyimplies better knowledge of the risk factors that drive their performance.
26
PERFORMANCE
10.00%9.00%8.00%
Balanced Portfolio +Edhec CTA Global
Expected Return
7.00%
S&P 500 +Edhec CTA Global
6.00%5.00%4.00%3.00%
Lehman GlobalBond + EdhecCTA Global
S&P 500 + LGBI
2.00%1.00%0.00%0.00%
10.00%
20.00%
30.00%
40.00%
50.00%
60.00%
Modified VaR
FIGURE 2.2
Efficient Frontiers, January 1997 to September 2003
OVERVIEW OF KEY PERFORMANCE DRIVERS OF CTASCTAs offer very attractive properties on a stand-alone basis as well as in aportfolio. To best allocate them, however, investors need to know whichrisk factors drive their performance. To do so, one may want to carry out afactor analysis with dozens of risk factors on a randomly selected CTAindex. This would obviously lead to a high in-sample adjusted R2, but therobustness of the results would certainly be low. Because the different CTAindices rely on different databases and are constructed according to diversemethodologies, it is highly probable that their returns are driven by different risk factor exposures (see Table 2.1). To circumvent the data snoopingissue, we focused on the same 16 factors selected for the factor analysis presented in Table 2.1. We then applied stepwise regression with the backwardentry procedure. To circumvent the index heterogeneity issue, we ran theanalysis on the Edhec CTA Index. The advantage is twofold: First, the indexis, by construction, more representative of the investment universe. Second,it is less prone to measurement biases such as survivorship, backfilling, orstale price bias. This second point is crucial because, as evidenced in Asness,Krail, and Liew (2001) and Okunev and White (2002), biases, and especiallystale prices, may entail a significant downward bias with respect to risk factor exposure measurement. We should thus be able to identify purer riskfactor exposures with the Edhec CTA Index.As can be seen from Table 2.4, the Edhec CTA Index is exposed to fivemain factors: one stock market factor (S&P 500), one bond market factor
27
Benchmarking the Performance of CTAs
TABLE 2.4 Edhec CTA Index Risk Factors Exposure, September 1999to September 2003Risk Factors
Edhec
T-stats
ConstantS&P 500LEHMAN GLB. U.S. TREASURYUS $ MAJOR CURRENCYUS $ TO JAPANESE YENGoldman Sachs Commodity IndexAdj. R2
4.54E-03−0.110.69−0.47−0.410.170.42
1.5−2.03.1−2.0−2.83.5
(Lehman Global Treasury), two currency factors (USD vs. major currencyand USD vs. Japanese yen) and one commodity factor (Goldman SachsCommodity Index [GSCI]). The most important factor turns out to be theGSCI, which stresses the still-prevalent exposure of CTAs to the commodity market. CTAs also appear to be strongly exposed to interest rates, witha long position on the Lehman U.S. Treasury Index. The other statisticallysignificant factors are ones related to the foreign exchange market, withcoefficients indicating that CTAs held long net positions on the USD overthe analysis period (especially against the Japanese yen). Not surprisingly,the index return is negatively correlated with the S&P 500 return, which isconsistent with the fact that CTAs post their best performance in large market declines.To validate the influence of the aforementioned risk factors, we studythe average performance of the Edhec CTA Index conditioned on the performance level of the risk factors. We again divide our sample into three subsamples corresponding to the most bearish (Low), stable (Medium), andmost bullish (High) months for the five factors selected. The results aresummarized in Table 2.5. The T-stats in the last column correspond to testsof the differences between Low/Med, Med/High, and Low/High subsampleaverages, respectively. Statistically significant differences at the 5 percentlevel are followed by an asterisk. Interestingly, the difference in mean returnsis significant four out of five times between Low and Medium subsamples.In the same vein, it is worth noting that the average return obtained by theEdhec CTA Index in the Low subsample is particularly high in three out offour cases. This is especially true when considering the equity risk factor (i.e.,S&P 500), which confirms the fact that CTAs are akin to portfolio insurance(i.e., long position on a put option on the S&P 500). Also, it is worth not-
28
PERFORMANCE
TABLE 2.5 Edhec CTA Index Conditional Performance, September 1999to September 2003
S&P 500LEHMAN GLB.U.S. TREASURYUS $ MAJORCURRENCYUS $ TOJAPANESE YENGoldman SachsCommodity Index
Low
Med
High
T-stats
2.40%a−1.09%c
−0.86%0.59%b
0.49%b2.44%a
5.30* / −1.81* / 1.92*−1.79* / −2.34* / −3.97*
1.78%a
−0.38%c
0.59%b
