of these three conditions) can be ascertained by testingfor the presence of a unit root, using so-called unit root tests such as theADF test.We use the ADF test because of its popularity as a unit root test and dueto its simplicity, since Monte Carlo studies such as Haug (1993a, 1993b)discovered that it performs well. Some authors have suggested that unitroot tests suffer from low power and that the test does not discriminate very
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PROGRAM EVALUATION, SELECTION, AND RETURNS
well between mean reverting series and series that do not mean revert at all(Kennedy 1998). However, the robustness of the ADF test is increased whenlags are used.If a series is found to be nonstationary by the ADF test, it does not necessarily imply that it behaves like a random walk, because random walksare but one example of nonstationary time series. Fortunately, the ADF testalso can be used to test specifically for random walks. No CTA strategy thatrelies solely on historical prices can be continuously profitable if marketsare efficient and the random walk hypothesis holds true. In this case, futurepercent changes in NAVs would be entirely unrelated by the historical performance (Pindyck and Rubinfeld 1998).Recent studies have shown that a minimal amount of performance persistence is found in CTAs and there could exist some advantages in selecting CTAs based on past performance when a long time series of data isavailable and accurate methods are used (Brorsen and Townsend 2002).Schneeweis, Spurgin, and McCarthy (1996) observe that performance persistence is virtually inexistent during the 1987 to 1995 time frame.The next section of this chapter presents the data along with a brief discussion of the ADF test and random walks. Following that, we display theresults of the analyses, while the final section summarizes and concludes thefindings.
DATA AND METHODOLOGYThe data set consists of CTA subindices from the Zurich Capital Marketsdatabase/CTA database1 provided LaPorte Asset Allocation System, covering monthly percent changes in NAVs from January 1994 to December2000. The database separates CTAs into these classes: discretionary, trendfollower, currency, diversified, financial, European, systematic, and stockindex (see Table 18.1).We use the NAVs in each CTA subindex. It is well documented in themutual fund literature that daily data provide better estimates than monthlydata, and help increase the power of tests (Busse and Bollen 2001; Kothariand Warner 2001). Unfortunately, CTA database vendors only providemonthly data.
1The Zurich indices during the investigation period do not suffer from survivorship bias.
329
Random Walk Behavior of CTA Returns
TABLE 18.1
Zurich Advisor Qualified Universe Indices as of December 2000
Trading StyleSubindex
Numberof Advisors
Equity($US Billions)
Definition ofInvestment Style
Discretionary
54
9.8
Use fundamental/economic analysis tomake trading decisions
Trend Follower
68
5.5
Focus only on trendfollowing strategies
Systematic
200
17.6
Use systematic, but notpurely trend-followingstrategies
MarketSubindex
Numberof Advisors
Equity($US Billions)
Definition ofInvestment Style
Diversified
193
17.8
Limit risk by holding alarge number of positions
Currency
45
5.9
Specialize in currencytrading
European
43
3.6
Financial
57
9.1
Specialize in Europeancommodities marketsCurrency, interest rate,stock index, and preciousmetals
Stock Index
17
0.2
Specialize in stock indexfutures and options
Source: T. Schneeweis, R. Spurgin, and G. Georgiev. “Benchmarking CommodityTrading Advisor Performance with a Passive Futures-Based Index.” CISDM Working Paper, Isenberg School of Management, University of Massachusetts, Amherst,MA, 2001, p.14.
The ADF test (Dickey and Fuller 1981; Hamilton 1994) supposes thatthe monthly mean CTA return, Yt, can be described by equation 18.1:p
Yt = Yt −1 = α + βt + (ρ − 1)Yt −1 + ∑ λ j ∆Yt − j + ε t
(18.1)
j =1
where ∆Yt = Yt − Yt−1 are the first differencesthe number of lags, p, chosen is sufficiently large so that the resulting error terms et are serially independent.
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PROGRAM EVALUATION, SELECTION, AND RETURNS
This condition can be verified by examining the resulting Durbin-Watsonstatistic; a value near 2, indicating serial independence. The ADF test worksby running a regression on model 18.1 and calculating a t-statistic (calledthe tau-statistic) to test whether the regression parameter r − 1 = 0 (orequivalently, r = 1). Failure to reject this test indicates the presence of a unitroot and that nonstationarity cannot be rejected. In that case, one often performs the test using first differences: denote these as Wt = Yt = Yt − 1, replaceYt by Wt in equation 18.1, and repeat the analysis.As explained by Pindyck and Rubinfeld (1998), to test for randomwalks, one must suppose that Yt in equation 18.1 can be described withoutlagged first differences,Yt = Yt − 1 = a + bt + (r − 1)Yt − 1 + et
(18.2)
and test whether b = 0 and r = 1 simultaneously. This determines whetherYt instead follows a random walk with drift parameter a, sometimesreferred to as a difference-stationary process (DSP) (Gujarati 1995)Yt = a + Yt − 1 + et
(18.3)
One then runs the ADF test with p = 1, so that equation 18.1 becomes the“unrestricted” modelYt − Yt − 1 = a + bt + (r − 1)Yt − 1 + l1∆Yt − 1 + et
(18.4)
while the “restricted” model (b = 0 and r = 1) isYt − Yt − 1 = a + l1∆Yt − 1 + et
(18.5)
The error sums of squares from models 18.4 and 18.5 are used to construct an F-statistic for the test of (a, b, r) = (a, 0, 1). Large values of theF-statistic will lead to the rejection of this hypothesis and to the conclusionthat the model with trend 18.4, rather than the random walk model withdrift 18.5, is the model of choice. Failure to reject this hypothesis providesevidence toward random walk behavior. Under the null hypothesis (whenthe series are nonstationary), neither test statistic just described follows anF- or a t-distribution, even in large samples, so to assess significance, thestatistics must be compared to critical values tabulated by MacKinnon(1991), who updated those from Dickey and Fuller (1981).
331
Random Walk Behavior of CTA Returns
EMPIRICAL ANALYSISWe used up to four lags in the eight CTA subindices but realized that in eachcase one lag was sufficient for the et to be serially independent. Table 18.2contains results of the ADF tests (equation 18.1 with p = 1), on the originalseries and on their first differences, along with values of the Durbin-Watsonstatistic. We find that none of the CTA subindices is stationary, as evidencedby the small values of the ADF statistics, ranging from −4.17 to −1.58, noneof which is large enough (in absolute value) to reject the hypothesis of nonstationarity at the 1, 5, or 10 percent significance level. However, when firstdifferences are employed, the ADF statistics are all large enough (inabsolute value) to reject nonstationarity at the 1 percent level in all classes.Durbin-Watson statistics from the original and differenced series are allnear 2, providing evidence of serial independence among the errors and vindicating our choice of p = 1 in equation 18.1.Thus, it appears that further analyses of these data need only considerfirst differences to achieve stationarity and that these analyses would likelynot be exposed to dangers associated with overdifferencing.Results of the random walk test are found in Table 18.3, which presents parameter estimates for models 18.4 and 18.5 for the original series Yt,along with corresponding standard errors in parentheses. The F-statistic fortesting (a, b, r) = (a, 0, 1) is presented in the last column. We find evidence
TABLE 18.2 ADF Test Statistics of Nonstationarity and Durbin-Watson Statisticsof Serial Correlation (Equation 18.1 with p = 1), for Monthly CTA Mean Returns,(1994 to 2000)ADF Statistic (DW Statistic)CTA Trading AdvisorSubindexes
OriginalSeries Yt
FirstDifferenced Series Wt
Discretionary AdvisorTrend FollowerFinancial ProgramDiversified AdvisorCurrency ProgramEuropean AdvisorSystematicStock Index
–3.48 (1.98)–2.76 (1.95)–2.62 (1.96)–4.17 (1.94)–2.73 (1.96)–2.74 (1.87)–2.69 (1.92)–1.58 (2.03)
–6.44* (2.00)–6.08* (1.94)–5.74* (1.94)–6.82* (1.91)–7.79* (1.96)–6.48* (1.78)–6.40* (1.90)–5.95* (2.07)
*Significance of ADF statistic at the 1 percent level, from MacKinnon (1991).
332
Diversified
Financial
Trend Follower
Discretionary
Equation (18.5)
Equation (18.4)
Equation (18.5)
Equation (18.4)
Equation (18.5)
Equation (18.4)
Equation (18.5)
Equation (18.4)
Zurich CTA Trading AdvisorSubindex147.790(41.350)6.100(1.757)91.602(31.958)5.033(3.147)50.749(18.449)3.430(1.979)86.360(20.243)2.758(1.205)
A
R−10.1895(0.1060)——0.1420(0.1160)——0.2120(0.1170)——0.2070(0.1150)——
B−0.2319(0.0660)——−0.1690(0.0610)——−0.1420(0.0540)——−0.3620(0.0870)——1.6662(0.4690)0.1120(0.1100)0.8580(0.3350)0.0530(0.1150)0.5890(0.2410)0.1270(0.1160)0.9040(0.2200)0.0220(0.1160)
L1
8.69*
3.43
3.82
6.34
F-statistic for test of(A, B, R) = (A, 0, 1)
Parameter Estimates from Dickey-Fuller Unit Root Tests of Monthly CTA Class Mean Returns, (1994 to 2000),on Original Series
TABLE 18.3
333
Equation (18.5)
Equation (18.4)
Equation (18.5)
Equation (18.4)
Equation (18.5)
Equation (18.4)
Equation (18.5)
Equation (18.4)
31.6000(11.2540)1.2250(0.5520)17.9540(6.4550)0.4730(0.1777)19.2490(6.8070)0.9520(0.4780)6.5060(4.1210)0.0890(0.3480)
A
R-10.088(0.111)——0.066(0.121)——0.122(0.120)——−0.005(0.011)——
B−0.161(0.059)——−0.164(0.060)——−0.166(0.062)——−0.065(0.041)——0.247(0.091)0.018(0.112)0.087(0.031)−0.020(0.121)0.162(0.064)0.025(0.118)0.004(0.015)−0.036(0.110)
L1
1.26
3.64
3.90
3.76
F-statistic for test of(A, B, R) = (A, 0, 1)
*Significant at the 5 percent level.Values in parentheses are standard errors of parameter estimates. Critical values for the F-test with n = 75 are 6.61 at the 5 percentlevel and 9.02 at the 1 percent level, from Dickey and Fuller (1981), Table VI.
Stock Index
Systematic
European
Currency
Zurich CTA Trading AdvisorSubindex
TABLE 18.3 (continued)
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PROGRAM EVALUATION, SELECTION, AND RETURNS
of random walk behavior in all CTA subindices except for diversified, whoseF-statistic of 8.69 attains significance at the 5 percent level. It is thereforepossible that a trend representation exists for this series. None of theF-statistics for the other series are large enough to attain significance. Thus,all classes are better represented by equation 18.5 except diversified, forwhich equation 18.4 is the model of choice.Large estimated values of the drift parameter coupled with small standard errors (usually defined as less than one-half of the drift parameter inabsolute value) would suggest that a drift could be present in the series.Table 18.3 thus provides evidence of positive drift (a > 0) in the discretionary, diversified, currency, and European classes. Only the stock indexclass appears to behave as a pure random walk.
CONCLUSIONThe nonstationarity observed in most CTA subindices implies that portfolio managers wishing to include CTAs within a traditional stock andbond portfolio cannot be assured that their NAVs will be mean reverting.Yet evidence of positive drift in some of the CTA subindices under consideration leaves open the possibility that these NAVs will contain increasingtrends. Portfolio managers wishing to obtain reliable predictions of CTApercent changes in NAVs therefore must be careful when using historicaldata to design future trading strategies. CTAs assume both long and shortmarket positions, and realize profits when there are persistent trends inmarkets and when those trends can be identified early enough. Thus, theperformance of CTAs depends not only on price movements, but also onthe managers’ ability to identify them.One possible explanation for random walk behavior during the examination period is due to the fact that traditional CTAs make large profitsduring extreme market movements, themselves random events. Their correlations may be more accurate and stable if they are used as a hedge againstshort volatility exposure. The discretionary, currency, and European traderstrade in periods of high liquidity, which has been the case since 1995. Wefound that only one class, diversified, did not behave as a random walk,likely since trends in a diversified portfolio are stable, although they may notproduce sufficient profits to satisfy the expectations of all investors. Due totheir very low or negative correlation to stock markets, CTAs are usually lessaffected by severe market shocks, such as those caused by the Asian crisis of1997 and the collapse of the Russian currency in August 1998. By allocating assets into CTAs whose returns are not pure random walks, portfoliomanagers can, in times of increased volatility, add value to traditional stock,
Random Walk Behavior of CTA Returns
335
bond, and currency portfolios by providing returns that are more readilypredictable. Inclusion of CTAs therefore will provide portfolios with immunization against extreme stock market movements.This study has attempted to characterize some of the time series properties of CTA classes. Using subindices does not provide information on anyparticular CTA, only on the overall behavior of CTAs within each classification. Thus, our results are especially useful for investors wishing to allocate holdings into all CTAs within a particular class—in that case thesubindex would represent an adequate measure of monthly performance.However, investors wishing to invest in a small number of CTAs wouldlikely benefit from an analysis similar to this one but that targets individual CTAs. Further investigation into the returns of CTAs is warranted, asincreased volatility in stock markets is likely to spur additional interestin these alternative investments on the part of investors, academics, andpractitioners.
CHAPTER
19
CTA Strategies for ReturnsEnhancing DiversificationDavid Kuo Chuen Lee, Francis Koh, and Kok Fai Phoon
n this chapter, we analyze the risk and performance characteristics ofdifferent strategies involving the trading of commodity futures, financialfutures, and options on futures employed by CTAs. Differing from previousstudies, we employ full and split samples to examine the correlations, andcompute risk and performance measures for various CTA strategies. We rankthe returns of the S&P 500 and MSCI Global Indices from the worst to thebest months, and partition the sample into 10 deciles. For each decile, wecompute the relationship between the CTA indices and the equity indices andcompare their risk and return characteristics. We find that CTA strategieshave higher Sharpe and Sortino ratios compared to other asset classes for theentire sample period under study. Further, unlike hedge funds, the correlationcoefficients between CTA and equity portfolios for the first decile (worst performance of the equity indices) are mostly negative. The volatility (measuredby downside deviation) of CTA strategies is lower compared to equity indices.And, for the up-market months, CTA strategies are associated with highSortino ratios.Our results are consistent with previous findings that returns from CTAstrategies are less correlated with equity market indices during down marketsthan hedge fund strategies. One possible explanation is that CTAs, unlikehedge funds, are exposed to lower liquidity risk in down markets and therefore do not suffer any severe “liquidity” squeeze. Our findings suggest thatthe negative correlations of CTAs with equity indices during periods of equitydownturns can provide an effective hedge against catastrophic event risks.Although hedge funds may provide diversification, they have positive correlation with equity indices in down markets, especially when extreme eventsoccur. Hence, our findings suggest that adding CTA investments to an equityportfolio can improve the risk-return profile of a portfolio. Such strategies notonly provide the usual portfolio diversification effects, but, given the negativecorrelation in down markets, the CTAs are returns-enhancing diversifiers.
I
336
CTA Strategies for Returns-Enhancing Diversification
337
INTRODUCTIONIn recent years, there has been a marked change in the asset allocation strategyin institutional investors, especially endowment funds. In 2002 and 2003, itwas reported that many university endowment funds allocated, on average,about 5 percent and 7 percent, respectively, of their total investable funds toalternative investments. Recently some endowments have increased their allocations to alternative investments significantly, to a figure as high as 40 percentof their assets under management (Lee 2003). In particular, Vanderbilt University (2002) has used alternatives since the 1970s and allocates just underhalf of its $2 billion endowment to them, including nearly 30 percent in hedging and arbitrage strategies. The endowment has returned 8 percent per annumover the past five years and 15 percent per annum over the past nine years(Vanderbilt University Endowment Review, “2002 Financial Report,” 2003).Alternative investments include hedge funds, private equity, and venturecapital as well as commodity pools, also referred to as commodity tradingadvisors (CTAs). In the current low-interest environment compounded bysomewhat bearish equity market sentiments, investors have been flocking toalternative investments to enhance their returns as well as to protect theirinvestments. Institutional investors also have increased their demand foralternative investments in the search for absolute positive returns (Till 2004).Private equity and venture capital, in the main, provide “direct” investment opportunities for the astute investor. Conversely, alternative investmentslike hedge funds and CTAs add value “indirectly” through the use of a widerange of trading strategies, techniques, and instruments. In this chapter, wefocus on the risk and returns performance of CTAs.
LITERATURE REVIEWA number of earlier researchers have analyzed CTAs, including Elton, Gruber,and Renzler (1987), who concluded that CTAs offer neither an attractive alternative to bonds and stocks nor a profitable addition to a portfolio of bond andstocks. Brorsen and Irwin (1985) and Murphy (1986), however, concludedthat commodity funds produce favorable and appropriate investment returns.Schneeweis, Spurgin, and Potter (1996) found that a portfolio comprisedof equal investment in a managed future index outperformed a protective putstrategy consisting of the Standard & Poor’s (S&P) 500 index and a simulatedat-the-money put. They concluded that managed futures may offer some ofthe hedging properties of a put option at a lower cost.11Schneeweis and Spurgin (1998b) used a dollar-weighted index of CTAs published
by Managed Account Reports (MAR).
338
PROGRAM EVALUATION, SELECTION, AND RETURNS
Schneeweis and Spurgin (1998b) further presented evidence that hedgefunds and managed futures may improve the risk-return profiles of equity,fixed income, as well as traditional alternative investments such as riskydebt. Their findings were based on correlation analysis between the underlying factors of:Hedge fund indices from Hedge Fund Research and Evaluation Associates Capital Management (EACM)■ CTA indices (from MarHedge, Barclay Trading, and EACM)■ S&P 500 and MSCI World indices for equities■ Salomon Brothers Government Bond and World Government Bondindices for fixed income securities■
Kat (2002) studied the possible role of managed futures in portfolios ofstocks, bonds, and hedge funds. He found that managed futures appear tobe more effective diversifiers than hedge funds. He found that adding managed futures to a portfolio of stocks and bonds will reduce a portfolio’sstandard deviation much more and quicker than hedge funds will, andwithout the undesirable side effects on skewness and kurtosis.For the period 1994 to 2001, Liang (2003) found that although CTAson a stand-alone basis underperformed hedge funds, returns from CTAs werenegatively correlated with other instruments, making CTAs suitable forhedging against downside risks.Although the performance and risk characteristics of alternative investments as stand-alone investments are interesting and informative, analysisof the contribution of CTAs to a portfolio of traditional investments wouldbe instructive and functionally useful. Finance theory has espoused the concept that the ability to diversify allows for a more efficient return-risk tradeoff. In the mean-variance framework, widely attributed to Markowitz(1952), an existing portfolio becomes more diversified upon the addition ofa new asset with a relatively lower correlation.In this chapter, we attempt to differentiate three categories of assetdiversifiers:1. Returns-protection diversifiers have relatively high correlations in boththe up and down markets with a generic asset class (such as the S&P500 Index).2. Returns-enhancing diversifiers possess correlations with the samegeneric asset class in an up market but are relatively less correlated ina down market.3. “Ineffective” diversifiers are assets that do not add value, even thoughthey may possess significant correlation coefficients with the genericasset class.
CTA Strategies for Returns-Enhancing Diversification
339
To illustrate, a hedge fund strategy that has a negative correlation coefficient in an up-market regime and positive correlation coefficient in adown-market regime provides diversification with no incremental returns.We classify this in the third category, that is, as an ineffective diversifier.Indeed, a strategy with such a characteristic will have the opposite effect ofa good diversifier as it weakens the returns on an uptrend and exaggeratesthe negative returns of the portfolio.We will show that CTAs are differentiated from hedge funds and arereturns-enhancing diversifiers.
CTAs, HEDGE FUNDS, AND FUND OF FUNDSThere are many similarities between CTAs and hedge funds and hedge fundof funds, including the management and incentive fee structures, high initial investment requirements, and the use of leverage and derivatives. However, significant differences also exist. For example, hedge funds engage avariety of dynamic trading strategies using different financial instruments indifferent markets. CTAs, however, mainly use technical trading strategiesin commodity and financial futures markets. The use of different marketsand instruments give rise to distinct differences in risk and returns profiles.On the regulatory side, CTAs must register with the Commodity FuturesTrading Commission (CFTC); hedge funds and fund of funds are largelyexempt from government regulations. The CFTC is a federal regulatorybody established by the Commodity Exchange Act in 1974. It supervises aself-regulatory organization called the National Futures Association andhas exclusive jurisdiction over all U.S. commodity futures trading, futuresexchanges, futures commission merchants, and their agents, floor brokers,floor traders, commodity trading advisors, commodity pool operators, leverage transaction merchants, and any associated persons of any of the foregoing. CTAs are subject to higher standard of compliance, including disclosurereporting, record keeping, and accounting rules. These requirements are notrequired of hedge funds (which are not registered with CFTC). Many CTAsmay have been losing their assets and customers to hedge funds in recentyears partly due to restrictive regulations by the CFTC. As a consequence,some CTAs have started emulating hedge funds, using similar trading strategies and instruments and getting more involved in equities. If this trend continues, the distinction between hedge funds and CTAs may become blurred.On the subject of returns, Liang (2003) and other past studies foundthat the correlations among the returns of hedge funds employing differentstyles are high. But the correlations between the returns from different CTAstrategies and hedge fund styles are almost zero or negative. This correlation structure points to a need to distinguish CTAs from hedge funds (aswell as funds of funds) in academic research.
340TABLE 19.1
PROGRAM EVALUATION, SELECTION, AND RETURNS
Comparison between CTAs and Hedge FundsCTAs
Hedge Fund/HedgeFund of Funds
Risk-adjustedreturns
Lower on a standalone basis.a
Hedge fund are highest followedby hedge fund of funds.
Explanation byfactors
CTA returns areexplained by optiontrading factors.
Hedge fund returns cannot beexplained by option tradingfactors.
Attrition rate
Generally higherattrition rate.Relatively lowerattrition ratesin down markets.b
Generally lower attrition rates.Down-market conditions havegreater impact on attrition rates.
Correlationstructure
Low or negativecorrelation withother instruments.
Highly correlated with eachother with other during downmarkets.
Source: Bing Liang, “On the Performance of Alternative Investments: CTAs, HedgeFunds, and Funds-of-Funds,” Case Western Reserve University, Working Paper,2003, Cleveland, OH.a Liang used Sharpe ratios after adjusting for autocorrelation in returns. Heexplained that the difference may be due to the fee structure as well as the risksand autocorrelation structure.b Up and down markets are defined according to the S&P 500 index returns. Upmarkets are periods when the monthly S&P 500 index returns are positive; downmarkets are defined as periods when the index returns are negative.
The work of Liang (2003) analyzing CTAs and hedge funds separatelyalso provided several interesting results. Table 19.1 summarizes the results.
DATA AND METHODOLOGYThe S&P 500, MSCI Global, Lehman U.S. Aggregate, and Lehman Globaldata for the period January 1980 until March 2003 were used in this study.We call these data sources as the benchmark group. With the exception ofLehman Global, which starts from January 1990, we have 279 observationsfor each series. There are only 159 observations for the Lehman GlobalIndex. For the same period, we used returns data over differing periods offour CTA indices from MarHedge: Universe, Universe Equally-Weighted(EW), Future Funds Index, and Future Funds Equally Weighted (EW). Wealso conducted analysis on subindices from MarHedge covering six strate-
CTA Strategies for Returns-Enhancing Diversification
341
gies: Currency-Sub, Diversified-Sub, Discretionary-Sub, Stock Index Sub,Systematic-Sub, and Trend Follower.The data were subsequently ranked according to the monthly performance of the two equity indices, the S&P 500 and the MSCI Global. The worstreturns month was ranked first followed by the second worst. The CTAsindices then are matched in that same order. The ranked sample was thendivided into deciles. As we are interested only in a two-asset class situation,we would observe the corresponding S&P 500 and CTAs returns accordingly and calculate the linear correlation coefficient for each decile. Forexample, analyzing the S&P 500 and Universe indices, we would computethe correlation coefficient for each decile between the two strategies.2
FINDINGS AND OBSERVATIONSTable 19.2 presents the summary statistics and risk-adjusted returns. Wereported the standard summary statistics associated with the first fourmoments for the whole period—mean, standard deviation, skewness, excesskurtosis (in excess of the normal distribution)—and the “down-side deviation” defined as the volatility of downside deviation below a minimumacceptable return of zero, the Sharpe and Sortino ratios, and the matrix ofcorrelations between the different CTA strategies with the stock and bondindices. There are a number of interesting observations.Most of the CTA strategies have correlations with the equity indicesthat are close to zero