CTAs offer very attractive properties on a stand-alone basis as well as in a portfolio. To best allocate them, however, investors need to know which risk factors drive their performance. To do so, one may want to carry out a factor analysis with dozens of risk factors on a randomly selected CTA index. This would obviously lead to a high in-sample adjusted R2, but the robustness of the results would certainly be low. Because the different CTA indices rely on different databases and are constructed according to diverse methodologies, it is highly probable that their returns are driven by differ- ent risk factor exposures (see Table 2.1). To circumvent the data snooping issue, we focused on the same 16 factors selected for the factor analysis pre- sented in Table 2.1. We then applied stepwise regression with the backward entry procedure. To circumvent the index heterogeneity issue, we ran the analysis on the Edhec CTA Index. The advantage is twofold: First, the index is, by construction, more representative of the investment universe. Second, it is less prone to measurement biases such as survivorship, backfilling, or stale price bias. This second point is crucial because, as evidenced in Asness, Krail, and Liew (2001) and Okunev and White (2002), biases, and especially stale prices, may entail a significant downward bias with respect to risk fac- tor exposure measurement. We should thus be able to identify purer risk factor exposures with the Edhec CTA Index.
As can be seen from Table 2.4, the Edhec CTA Index is exposed to five main factors: one stock market factor (S&P 500), one bond market factor
0.00%
1.00%
2.00%
3.00%
4.00%
5.00%
6.00%
7.00%
8.00%
9.00%
10.00%
0.00% 10.00% 20.00% 30.00% 40.00% 50.00% 60.00%
Modified VaR
Expected Return
Balanced Portfolio +
Edhec CTA Global S&P 500 +
Edhec CTA Global
Lehman Global Bond+ Edhec CTA Global
S&P 500 + LGBI
FIGURE 2.2 Efficient Frontiers, January 1997 to September 2003
Benchmarking the Performance of CTAs 27
(Lehman Global Treasury), two currency factors (USD vs. major currency and USD vs. Japanese yen) and one commodity factor (Goldman Sachs Commodity Index [GSCI]). The most important factor turns out to be the GSCI, which stresses the still-prevalent exposure of CTAs to the commod- ity market. CTAs also appear to be strongly exposed to interest rates, with a long position on the Lehman U.S. Treasury Index. The other statistically significant factors are ones related to the foreign exchange market, with coefficients indicating that CTAs held long net positions on the USD over the analysis period (especially against the Japanese yen). Not surprisingly, the index return is negatively correlated with the S&P 500 return, which is consistent with the fact that CTAs post their best performance in large mar- ket declines.
To validate the influence of the aforementioned risk factors, we study the average performance of the Edhec CTA Index conditioned on the per- formance level of the risk factors. We again divide our sample into three sub- samples corresponding to the most bearish (Low), stable (Medium), and most bullish (High) months for the five factors selected. The results are summarized in Table 2.5. The T-stats in the last column correspond to tests of the differences between Low/Med, Med/High, and Low/High subsample averages, respectively. Statistically significant differences at the 5 percent level are followed by an asterisk. Interestingly, the difference in mean returns is 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 the Edhec CTA Index in the Low subsample is particularly high in three out of four 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- TABLE 2.4 Edhec CTA Index Risk Factors Exposure, September 1999
to September 2003
Risk Factors Edhec T-stats
Constant 4.54E-03 1.5
S&P 500 −0.11 −2.0
LEHMAN GLB. U.S. TREASURY 0.69 3.1
US $ MAJOR CURRENCY −0.47 −2.0
US $ TO JAPANESE YEN −0.41 −2.8
Goldman Sachs Commodity Index 0.17 3.5
Adj.R2 0.42
ing that the Edhec CTA Index payoff resembles a long position on a put option on currency risk factors and a long position on a call option on the GSCI. We can thus conclude that the performance of the Edhec CTA Index is clearly affected by the evolution of the risk factors selected.
A word of caution is in order. Even if CTA managers generally continue to invest in the same markets and follow the same investment strategies, they may engage in various factor timing strategies to take advantage of macroeconomic trends. In other words, they tend to increase or decrease their exposure to specific markets according to their expectations, which may in turn lead to a change in factor exposures. To illustrate this phe- nomenon we ran regressions using two-year rolling windows starting from September 1999 through August 2001, each time with one nonoverlapping observation. We thus obtained betas from September 2001 through Sep- tember 2003. Results are presented in Figure 2.3. It is interesting to note that the exposure to the Lehman Global U.S. Treasury Index, although evolving through time, remains high (around 1.00) during the whole period. This is in contrast with the beta with respect to the S&P 500 index, which remains relatively low (around 0) with a steady down trend until April 2003. The exposure to the GSCI is symmetrical to that of the S&P 500, showing an up trend from January 2003 though September 2003. In the same vein, over the period of analysis CTA managers progressively increased their bet on the rise of the USD against the yen while taking opposing bets on the USD versus TABLE 2.5 Edhec CTA Index Conditional Performance, September 1999
to September 2003
Low Med High T-stats
S&P 500 2.40%a −0.86% 0.49%b 5.30* / −1.81* / 1.92*
LEHMAN GLB. −1.09%c 0.59%b 2.44%a −1.79* / −2.34* / −3.97*
U.S. TREASURY
US $ MAJOR 1.78%a −0.38%c 0.59%b 2.55* / −1.47 / 1.19 CURRENCY
US $ TO 1.39%a −0.26%c 0.86%a 2.02* / −1.17 / 0.69 JAPANESE YEN
Goldman Sachs 0.02%b 0.34%b 1.59%a −0.25 / −1.71 / −1.39 Commodity Index
aAbove average
bBelow average but positive
cBelow average and negative
*Significant at 5% level
Benchmarking the Performance of CTAs 29
major currencies. Investors must obviously be aware of such time-varying effects when considering investment in CTAs.
Three conclusions may be drawn from this analysis.
1. The five risk factors selected can explain a significant part of the Edhec CTA Index variance.
2. The exposure of the Edhec CTA Index to these risk factors appears to be nonlinear.
3. Risk factor exposures evolve through time, suggesting that multifactor models such as the one we use may not be suited for performance meas- urement purposes.
As largely documented in the literature, it would be interesting to integrate conditional factor models (Gregoriou 2003b; Gupta, Cerrahoglu, and Daglioglu 2003; Kat and Miffre 2002; Kazemi and Schneeweis 2003) and/or models including nonlinear risk factors (see Agarwal and Nạk 2004; Fung and Hsieh 1997a, 2002b, 2003; Schneeweis, Spurgin, and Georgiev 2001) to better benchmark CTA performance.
Sep-01 Mar-02 Sep-02 Mar-03 Sep-03
1 .50
1.00
0.50
0.00
–0.50
–-1.00
Lehman Global U.S. Treasury
USD to Yen GSCI
S&P 500
USD to Major Currency
FIGURE 2.3 Edhec CTA Index Factor Exposure Evolution, September 1999 to September 2003
Source:Edhec Risk.