Commodity Trading Advisors: Risk, Performance Analysis, and Selection Chapter 18 pps

Monthly data from January 1994 to December 2000 are tested for nonstationarity and random walk with drift, using the Augmented Dickey-Fuller test.. The effectiveness of CTAs in enhancing

Random Walk Behavior

of CTA Returns Greg N Gregoriou and Fabrice Rouah

This chapter examines whether CTA percent changes in NAVs follow ran-dom walks with drift Monthly data from January 1994 to December

2000 are tested for nonstationarity and random walk with drift, using the Augmented Dickey-Fuller test All classifications (except the diversified subindex) are found to behave like random walks, but many of the series show evidence of a positive drift parameter, an indication that trends could

be present in the series The effectiveness of CTAs in enhancing risk-return characteristics of portfolios could be compromised when pure random walk behavior is identified

INTRODUCTION

This chapter investigates whether monthly percent changes in net asset val-ues (NAVs) of commodity trading advisor (CTA) classifications follow ran-dom walks Previous econometric studies of financial time series have employed unit root tests, such as the Augmented Dickey-Fuller test (ADF),

to identify random walk behavior in stock prices and market indices, for example The characteristics of CTAs are such that investment into this alternative investment class can enhance portfolio returns, but these char-acteristics are likely to be mitigated if pure random walk behavior is pres-ent because that would imply a lack of evidence of value added to the portfolio (differential manager skill)

Research into the performance persistence of CTAs is sparse, so there

is little information on the long-term diligence of these managers (Edwards

This article previously appeared in Journal of Alternative Investments, No 2, 2003.

Reprinted by permission of the publisher.

and Ma 1988; Irwin, Krukemeyer, and Zulauf 1992; Irwin, Zulauf, and Ward 1994; Kazemi 1996) However, it is generally agreed that during bear markets, CTAs provide greater downside protection than hedge funds, and have higher returns along with an inverse correlation with stock returns in bear markets (Edwards and Caglayan 2001) The benefits of CTAs are sim-ilar to those of hedge funds, in that they improve and can offer a superior risk-adjusted return trade-off to stock and bond indices while acting as diversifiers in investment portfolios (Schneeweis, Savayana, and McCarthy 1991; Schneeweis 1996)

During the 1990 to 1998 period the correlation of managed futures to the Standard & Poor’s (S&P) 500 during its best 30 months was 0.33 and

−0.25 during its worst 30 months (Worthington 2001) The benefit of low correlation cannot be easily replicated through other investment alterna-tives According to Schneeweis, Spurgin, and Georgiev (2001), CTAs are known to short stock markets regularly One drawback, however, is that during bull markets their performance is generally inferior to those of hedge funds (Georgiev 2001)

Investors who choose to include CTAs in their portfolios usually allo-cate only a small portion of their assets (Georgiev 2001) Others are un-aware that during increased periods of stock market volatility, careful inclusion of CTA managers into investment portfolios can enhance their return characteristics, especially during severe bear markets (Schneeweis and Georgiev 2002) Moreover, international financial markets in times of extreme volatility this past decade, such as the Asian currency crisis of 1997 and the Russian ruble crisis of August 1998, did not really affect CTAs In fact, CTAs make their money and produce superior returns during such periods of high volatility One must consider the possibility that CTA per-cent changes in NAVs follow random walks, for that would indicate that temporary shocks in the NAVs are persistent and not reverting to the mean level Such behavior would likely affect the timing of CTA allocation in and out of investment portfolios

Time series that are “mean reverting” are usually defined as second-order stationary, weak stationary, or simply stationary in the statistical lit-erature These are characterized by a constant mean and variance and by autocorrelations that depend only on the time lag Nonstationarity (the vio-lation at least one of these three conditions) can be ascertained by testing for the presence of a unit root, using so-called unit root tests such as the ADF test

We use the ADF test because of its popularity as a unit root test and due

to its simplicity, since Monte Carlo studies such as Haug (1993a, 1993b) discovered that it performs well Some authors have suggested that unit root tests suffer from low power and that the test does not discriminate very

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 when lags are used

If a series is found to be nonstationary by the ADF test, it does not nec-essarily imply that it behaves like a random walk, because random walks are but one example of nonstationary time series Fortunately, the ADF test also can be used to test specifically for random walks No CTA strategy that relies solely on historical prices can be continuously profitable if markets are efficient and the random walk hypothesis holds true In this case, future percent changes in NAVs would be entirely unrelated by the historical per-formance (Pindyck and Rubinfeld 1998)

Recent studies have shown that a minimal amount of performance per-sistence is found in CTAs and there could exist some advantages in select-ing CTAs based on past performance when a long time series of data is available and accurate methods are used (Brorsen and Townsend 2002) Schneeweis, Spurgin, and McCarthy (1996) observe that performance per-sistence is virtually inexistent during the 1987 to 1995 time frame The next section of this chapter presents the data along with a brief dis-cussion of the ADF test and random walks Following that, we display the results of the analyses, while the final section summarizes and concludes the findings

DATA AND METHODOLOGY

The data set consists of CTA subindices from the Zurich Capital Markets

cover-ing monthly percent changes in NAVs from January 1994 to December

2000 The database separates CTAs into these classes: discretionary, trend follower, currency, diversified, financial, European, systematic, and stock index (see Table 18.1)

We use the NAVs in each CTA subindex It is well documented in the mutual fund literature that daily data provide better estimates than monthly data, and help increase the power of tests (Busse and Bollen 2001; Kothari and Warner 2001) Unfortunately, CTA database vendors only provide monthly data

1 The Zurich indices during the investigation period do not suffer from survivor-ship bias

The ADF test (Dickey and Fuller 1981; Hamilton 1994) supposes that

(18.1)

the number of lags, p, chosen is sufficiently large so that the

j

p

∑

1

1

TABLE 18.1 Zurich Advisor Qualified Universe Indices as of December 2000

Trading Style Number Equity Definition of

Subindex of Advisors ($US Billions) Investment Style

economic analysis to make trading decisions

trend-following strategies

purely trend-following strategies

Market Number Equity Definition of Subindex of Advisors ($US Billions) Investment Style

large number of positions

trading

commodities markets

stock index, and precious metals

futures and options

Source: T Schneeweis, R Spurgin, and G Georgiev “Benchmarking Commodity

Trading Advisor Performance with a Passive Futures-Based Index.” CISDM Work-ing Paper, Isenberg School of Management, University of Massachusetts, Amherst,

MA, 2001, p.14.

This condition can be verified by examining the resulting Durbin-Watson statistic; a value near 2, indicating serial independence The ADF test works

by running a regression on model 18.1 and calculating a t-statistic (called

root and that nonstationarity cannot be rejected In that case, one often

As explained by Pindyck and Rubinfeld (1998), to test for random

lagged first differences,

referred to as a difference-stationary process (DSP) (Gujarati 1995)

“unrestricted” model

The error sums of squares from models 18.4 and 18.5 are used to

F-statistic will lead to the rejection of this hypothesis and to the conclusion

that the model with trend 18.4, rather than the random walk model with drift 18.5, is the model of choice Failure to reject this hypothesis provides evidence toward random walk behavior Under the null hypothesis (when the series are nonstationary), neither test statistic just described follows an

F- or a t-distribution, even in large samples, so to assess significance, the

statistics must be compared to critical values tabulated by MacKinnon (1991), who updated those from Dickey and Fuller (1981)

EMPIRICAL ANALYSIS

We used up to four lags in the eight CTA subindices but realized that in each

series and on their first differences, along with values of the Durbin-Watson statistic We find that none of the CTA subindices is stationary, as evidenced

of which is large enough (in absolute value) to reject the hypothesis of non-stationarity at the 1, 5, or 10 percent significance level However, when first differences are employed, the ADF statistics are all large enough (in absolute value) to reject nonstationarity at the 1 percent level in all classes Durbin-Watson statistics from the original and differenced series are all near 2, providing evidence of serial independence among the errors and

Thus, it appears that further analyses of these data need only consider first differences to achieve stationarity and that these analyses would likely not be exposed to dangers associated with overdifferencing

Results of the random walk test are found in Table 18.3, which

along with corresponding standard errors in parentheses The F-statistic for

of Serial Correlation (Equation 18.1 with p= 1), for Monthly CTA Mean Returns,

(1994 to 2000)

ADF Statistic (DW Statistic) CTA Trading Advisor Original First

Subindexes Series Y t Differenced Series W t

Discretionary Advisor –3.48 (1.98) –6.44* (2.00)

*Significance of ADF statistic at the 1 percent level, from MacKinnon (1991).

TABLE 18.3

on Original Series Zurich CT

332

TABLE 18.3

L1

*Significant at the 5 percent level V

333

of random walk behavior in all CTA subindices except for diversified, whose

F-statistic of 8.69 attains significance at the 5 percent level It is therefore

possible that a trend representation exists for this series None of the

F-statistics for the other series are large enough to attain significance Thus,

all classes are better represented by equation 18.5 except diversified, for which equation 18.4 is the model of choice

Large estimated values of the drift parameter coupled with small stan-dard errors (usually defined as less than one-half of the drift parameter in absolute value) would suggest that a drift could be present in the series

discre-tionary, diversified, currency, and European classes Only the stock index class appears to behave as a pure random walk

CONCLUSION

The nonstationarity observed in most CTA subindices implies that port-folio managers wishing to include CTAs within a traditional stock and bond portfolio cannot be assured that their NAVs will be mean reverting Yet evidence of positive drift in some of the CTA subindices under consid-eration leaves open the possibility that these NAVs will contain increasing trends Portfolio managers wishing to obtain reliable predictions of CTA percent changes in NAVs therefore must be careful when using historical data to design future trading strategies CTAs assume both long and short market positions, and realize profits when there are persistent trends in markets and when those trends can be identified early enough Thus, the performance of CTAs depends not only on price movements, but also on the managers’ ability to identify them

One possible explanation for random walk behavior during the exami-nation period is due to the fact that traditional CTAs make large profits during extreme market movements, themselves random events Their corre-lations may be more accurate and stable if they are used as a hedge against short volatility exposure The discretionary, currency, and European traders trade in periods of high liquidity, which has been the case since 1995 We found that only one class, diversified, did not behave as a random walk, likely since trends in a diversified portfolio are stable, although they may not produce sufficient profits to satisfy the expectations of all investors Due to their very low or negative correlation to stock markets, CTAs are usually less affected by severe market shocks, such as those caused by the Asian crisis of

1997 and the collapse of the Russian currency in August 1998 By allocat-ing assets into CTAs whose returns are not pure random walks, portfolio managers can, in times of increased volatility, add value to traditional stock,

bond, and currency portfolios by providing returns that are more readily predictable Inclusion of CTAs therefore will provide portfolios with immu-nization against extreme stock market movements

This study has attempted to characterize some of the time series prop-erties of CTA classes Using subindices does not provide information on any particular CTA, only on the overall behavior of CTAs within each classi-fication Thus, our results are especially useful for investors wishing to allo-cate holdings into all CTAs within a particular class—in that case the subindex would represent an adequate measure of monthly performance However, investors wishing to invest in a small number of CTAs would likely benefit from an analysis similar to this one but that targets individ-ual CTAs Further investigation into the returns of CTAs is warranted, as increased volatility in stock markets is likely to spur additional interest

in these alternative investments on the part of investors, academics, and practitioners