Commodity Trading Advisors: Risk, Performance Analysis, and Selection Chapter 6 potx

Most indices display null ornegative alphas, but they seem to exhibit positive market timing abilities.The currency index reports both types of positive performance during thefirst subpe

CHAPTER 6 The Performance of CTAs

in Changing Market Conditions

Georges Hübner and Nicolas Papageorgiou

This chapter studies the performance of 6 CTA indices during the period

1990 to 2003 Four distinct phases of financial markets are isolated, aswell as three extreme events We show that traditional multifactor as well

as multimoment asset pricing models do not adequately describe CTAreturns for any of the subperiods With a proper choice of risk factors, wecan, however, explain a significant proportion of CTA returns and assessthe abnormal performance of each strategy Most indices display null ornegative alphas, but they seem to exhibit positive market timing abilities.The currency index reports both types of positive performance during thefirst subperiod Severe market crises do not seem to affect abnormal CTAreturns, except the Asian crisis, which benefited investors in the discre-tionary index The Russian crisis has a uniform, although insignificant,negative impact on CTA abnormal returns

INTRODUCTION

Since the blossoming of an extensive literature on hedge funds, commoditytrading advisors (CTAs) have profited from renewed interest amongresearchers Following the initial studies by Brorsen and Irwin (1985) andMurphy (1986), Elton, Gruber, and Rentzler (1987) ascertained that com-modity funds were not likely to provide a superior return to passively man-aged portfolios of stocks and bonds As a result of these discouragingfindings, for over a decade very little research was devoted to the analysis

of CTAs

Fung and Hsieh’s paper (1997a) on the analysis of hedge fund ance rekindled academic interest in CTAs In their paper the authors noticethat the return distributions of certain hedge funds share some important

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characteristics with those of CTAs Subsequently, Schneeweis and Spurgin(1997), Brown, Goetzmann, and Park (2001), and Edwards and Caglayan(2001) performed studies on a joint sample of CTA and hedge fund data.Fung and Hsieh (1997b) analyzed these two investment vehicles independ-ently and discovered that CTA returns exhibit optionlike dynamics that mayprovide them with a peculiar role in portfolio management Liang (2003)explicitly separated CTAs and hedge funds in his analysis and concluded thataside from the particular management rules that differentiate them fromhedge funds, CTAs exhibit very low correlation with hedge funds strategies.Although they seem to underperform hedge funds and even funds-of-fundsstrategies in bullish markets, Edwards and Caglayan (2001) and Liang(2003) discovered that their creditable behavior in bearish market conditionsindicates that CTAs could represent precious hedging instruments whenmarkets are in a downtrend This atypical behavior can be attributed at least

in part to the nonnormality of the return structure of CTAs

Although the particular return distributions of CTAs are now nized, the measurement of their performance has yet to be adapted Bymimicry with the large stream of performance studies on mutual funds, vir-tually all studies on hedge funds have adopted the classical Sharpe ratio(1966) and Jensen’s alpha (1968) as relevant performance measures Thesequestionable choices become all the more inaccurate when they are applied

recog-to CTAs [see Edwards and Liew (1999); Edwards and Caglayan (2001);Liang (2003)] because their underlying distributional properties, and, most

of all, very low correlation with traditional risk factors do not support thesemeasures Edwards and Caglayan (2001) use catastrophic loss measures toassess the hedging properties of these funds, but this type of measure isapplicable only to extremely risk-averse agents, which is not a frameworkthat corresponds to real portfolio management constraints The positiveaspect of these measures is that they do not require prior knowledge of theunderlying return-generating process, which eliminates most of the difficul-ties associated with the discovery of a proper pricing model for CTAs

In this chapter we test a joint set of pricing models and performancemeasures that aim to better capture the distributional features of CTAs Theidentification of risk premia and of the sensitivities of CTA returns tothese factors will clear the way toward the use of less utility-based per-formance measures than the Sharpe ratio and to a more proper use of sto-chastic discount factor–based performance measures, such as Jensen’salpha, the Treynor ratio, or the Treynor and Mazuy (1966) measure of mar-ket timing ability

The next section of this chapter examines the market trends and crisesover the sample period and presents the descriptive statistics of the CTAindex returns An examination of the explanatory power of market factors

as well as trading strategy factors in describing CTA returns follows Thenext section looks at different performance measures on the CTAs.

DATA AND SAMPLE PERIOD

The data set that we use is the Barclay’s Trading group CTA data for theperiod from January 1990 to November 2003 The data set is composed

of end-of-month returns for the CTA index as well as for five subindices1:the Barclay Currency Traders Index, the Barclay Financial and MetalTraders Index, the Barclay Systematic Traders Index, the Barclay Diversi-fied Traders Index, and the Barclay Discretionary Traders Index

We divide the sample period into subperiods to investigate the ior of the CTA indices under specific market conditions (see Table 6.1)

TABLE 6.1 Summary of Subperiods

Panel A: Bull and Bear Markets

Market Trend Start Finish Ann Return # Obs Weak Bull 01:1990 12:1993 +10.0% 48 Moderate Bull 01:1994 09:1998 +19.0% 57 Strong Bull 09:1998 03:2000 +29.5% 18

Panel B: Financial Crises

Extreme Event Start Finish Magnitude # Obs Russian Crisis 10:1997 11:1997 −13.0% 2 Asian Crisis 08:1998 09:1998 −14.7% 2 Terrorist Crisis 09:2001 10:2001 −18.2% 2 For both panels, start and finish dates are identified as the end-of-month trading days surrounding the subperiod under study In Panel A, annualized returns are computed using closing values of the S&P 500 index In Panel B, the magnitude of the crisis is computed by taking the minimum and maximum values of the S&P 500 index during the event month.

1 We do not include the Barclay Agricultural Traders Index in this study as the cial variables used for the return-generating model would not explain a significant proportion of the return variance.

finan-The bull market that lasted from the early 1990s until the end of the com bubble in March 2000 is broken down into three subperiods We refer

dot-to the final 18 months prior dot-to the market crash as “Strong Bull”; duringthis time the annualized return on the Standard & Poor’s (S&P) 500 was29.5 percent We call the period from January 1990 to December 1993

“Weak Bull” and the period from January 1994 to September 1998 erate Bull.” Not only do the annualized returns nearly double from 10 per-cent to 19 percent over these two subperiods, the return distributions areconsiderably different over the two periods The fourth and final subpe-riod that we investigate is the “Bear Market” that lasted from March 2000

“Mod-to September 2002, during which time the annualized return on the S&P

500 was −22.6 percent

Three significant market crises occur during our sample period, each ofwhich caused a significant short-term drop in the market Predictably, thesethree crises are the Russian default, the Asian currency crisis, and Septem-ber 11 terrorist attacks Interestingly, the magnitude and duration of thesethree shocks on the S&P 500 is very similar Each event triggered a drop inthe S&P 500 of about 15 percent, and the time required for the index toreturn to its preevent level was generally two to three months The threecrises occur in two different subperiods: “Moderate Bull” and “Bear.”Table 6.2 presents the descriptive statistics for the excess returns onthe CTA indices for the entire period as well as for the four subperiods.Although each individual CTA index has certain intrinsic characteristics,certain general properties appear to be common to all the CTAs in our sam-ple More specifically, the Jarque-Bera tests over the entire sample periodillustrate that all the CTA indices, with the sole exception of the diversifiedindex, exhibit nonnormality in their excess returns Another common trait

is the very poor results during the “Strong Bull” period: all the CTA indicesdisplay negative excess returns for this period of very high returns in thestock markets As a matter of fact, this is unanimously the worst subperiod

in terms of performance for all the CTA indices These results are in dance with previous findings by Edwards and Caglayan (2001) and Liang(2003), who identified the poor performance of CTAs in bull markets Afurther examination of the mean excess returns over the four subperiodsreveals that for all the CTA indices, the highest excess returns are achieved

accor-in “Weak Bull,” which accor-includes the recession of the early 1990s, and

“Bear,” which followed the collapse of the dot-com bubble This wouldseem to concur with the notion that CTAs possess valuable return charac-teristics during down markets

The descriptive statistics for the excess returns of the CTA indices seem

to indicate that there exist similar return dynamics across the different types

of CTAs The two subindices that exhibit marginally different return

over the same period *

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terns are the Discretionary Traders Index and the Currency Traders Index.These two indices display the highest skewness and kurtosis; the former isthe only index to exhibit negative returns over the entire sample.

Table 6.3 examines the correlation coefficients between the differentCTA indices as well as between the CTA indices and the first two returnmoments of the Russell 3000 (Russell squared) The results for the entiresample as well as the subsamples confirm our earlier findings The correla-tion coefficient between the CTA index, the Financial and Metal TradersIndex, the Systematic Traders Index, and the Diversified Traders Index arepositive and close to 1 for all the different periods The Currency TraderIndex and the Discretionary Index have the lowest correlation coefficientwith the other CTA indices The coefficients are still positive between all theindices and for all the subperiods, but the correlation coefficient is muchsmaller Over the entire period, all of the CTA indices have a small and neg-ative correlation coefficient with the Russell 3000 index and a positive rela-tion with the square of the Russell 3000 returns These results are consistentduring the four subperiods with the exception of the Currency and Discre-tionary indices, which have a positive relation with the Russell 3000 in cer-tain subperiods These correlations remain nonetheless small in magnitude

EXPLAINING CTA RETURNS

Here we introduce three types of return-generating processes that may behelpful in understanding monthly CTA returns over the period We first per-form a classical multifactor analysis using risk premia similar to the Famaand French (1993) and Carhart (1997) models, with an additional factorrelated to stock dividend yields, in a similar spirit to Kunkel, Ehrhardt, andKuhlemeyer (1999) We then use a simple specification aimed at capturingthe exposure to skewness and kurtosis Finally, we select several other fac-tors that have been applied to performance studies of hedge funds and/orCTAs to identify the best linear asset-pricing model for each particular sub-period under study

Multifactor Model

We start with the four-factor model proposed by Carhart (1997), butexclude the factor mimicking the value premium, namely the “High minusLow” (HML) book-to-market value of equity, that yields significant resultsfor none of our regressions This factor is replaced by an additional factorrelated to the risk premium associated with high-yield dividend-payingstocks Although there is only limited and controversial evidence of theactual value added of this factor in the explanation of empirical returns,Kunkel et al (1999) find that there is a significant empirical return compo-

TABLE 6.3

nent associated with high-yield dividend-paying stocks, which is explained

in Martin and van Zijl (2003) by a tax differential argument The equationfor the market model is:

r t = a + b1Mkt t + b2SMB t + b3UMD t + b4HDMZD t + e t (6.1)

where r t= CTA index return in excess of the 13-week T-Bill rate,

Mkt t = excess return on the portfolio obtained by averaging the

returns of the Fama and French (1993) size and market portfolios

book-to-SMB t = the factor-mimicking portfolio for size (“Small Minus Big”)

UMD t = the factor-mimicking portfolio for the momentum effect

(“Up Minus Down”)

the top 30 percent quantile stocks ranked by dividend

yields and of the zero-dividend yield stocks (“High

Dividend Minus Low Dividend”).

Factors are extracted from French’s web site (http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html) Table 6.4 summarizes theresults of this regression over the entire period and the four subperiods

For all but one subperiod (Weak Bull), the adjusted R-squared

coeffi-cients are extremely low and often negative The only statistically cant linear relationship is observed for the Weak Bull subperiod, while themodel is unable to explain anything during the Strong Bull subperiod Thesignificance of the regressions is especially poor for the Discretionary andCurrency strategies, whose different pattern of returns had already beenobserved through their correlation structure During the period from 1990

signifi-to 1993, it appears that only the coefficient of the dividend facsignifi-tor is icantly positive for all indices except the Discretionary Index.2

signif-These rather weak results confirm the inaccuracy of classical tor models for the assessment of required returns of commodity tradingadvisors This is in contrast with pervasive evidence of the ability of theCarhart (1997) model to explain up to an average of 60 percent of the vari-ance of hedge funds strategies (see Capocci, Corhay, and Hübner, 2003;Capocci and Hübner, 2004), providing further evidence of the completelydifferent return dynamics of these financial instruments

multifac-2 Of course, the replacement of this risk premium, the only one that seems to have explanatory power, by the traditional HML factor would have yielded even lower

adjusted R-squared.

TABLE 6.4 Regression Results Using Modified Fama-French Factors

b 1 −0.061 −0.031 0.014 −0.090 −0.223

b2 0.001 0.373 −0.437 ** 0.062 0.011 CTA Index b 3 0.077 * 0.217 * −0.119 −0.040 0.051

b4 0.122 ** 0.915 ** −0.071 −0.005 0.020

R2

* The values are significant at the 10 percent level.

** The values are significant at the 5 percent level.

Multi-Moment Model

It is natural to suspect that the positive skewness and high kurtosis of CTAreturns reported in Table 6.2 could render our index returns sensitive to amultimoment asset pricing specification Such a framework also may cap-ture a significant proportion of the optionlike dynamics of CTAs reported

by Fung and Hsieh (1997b) and Liang (2003), because the nonlinear off structure of option contracts generates fat-tailed, asymmetric optionreturn distributions

pay-We choose to adopt a simple specification for the characterization of amultimoment return-generating model, in a similar vein to the study ofFang and Lai (1997), who report significant prices of risk for systematiccoskewness and cokurtosis of stock returns with the market portfolio Theirfirst-pass cubic regression resembles:

(6.2)

where r m,t= excess return on the market index

Unlike the prêt-à-porter specification proposed in equation 6.1, wherethe market factor chosen had to be neutral with respect to size considera-tions, the index chosen in equation 6.2 is the one whose influence on CTAreturns is likely to be highest In accordance with previous studies, we usethe Russell 3000 index as a proxy for the market portfolio

Table 6.5 summarizes the results of regression equation 6.2 over theentire period as well as the four subperiods

The regressions still explain, on average, a very low proportion of theCTA returns variance Yet four extremely interesting patterns can be noticed

1 The multimoment regression seems to provide a slightly better fit than

the multifactor model presented in equation 6.1, with the exception

of the “Weak Bull” period, where the multifactor dominates for all butthe Discretionary strategy

2 The most significant regression coefficient appears to be b2, which isthe loading on the squared market return It is positive for the globalperiod as well as for the “Weak Bull” subperiod for most CTA indices

3 The patterns of the Discretionary and Currency indices exhibit major

differences with respect to the rest of CTA indices, which behave in verysimilar ways For these indices, closely related to the behavior of finan-cial markets, the coefficient of the Russell 3000 index is negative for thewhole period, but only because it is significantly negative during the first

r t = α β+ 1r m t, + β2r m t2, + β3r m t3, +εt