18
CHAPTER
2
Benchmarking the
Performance of CTAs
Lionel Martellini and Mathieu Vaissié
T
he bursting of the Internet bubble in March 2000 plunged traditional
market indices (stocks, bonds, etc.) into deep turmoil, leaving most insti-
tutional investors with the impression that portfolio diversification tends to
fail at the exact moment that investors have a need for it, namely in peri-
ods when the markets drop significantly.
1
At the same time, most alterna-
tive investments (e.g., hedge funds, CTAs, real estate, etc.) posted attractive
returns. They benefited from large capital inflows from high-net-worth
individuals (HNWI) and institutional investors, who were both looking for
investment vehicles that would improve the diversification of their portfo-
lios. At the same time, many recent academic and practitioner studies have
documented 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 Gupta
2003a; Schneeweis, Karavas, and Georgiev 2003).
Nevertheless, due to the “natural” (survivorship/selection) and “spuri-
ous” (backfilling/weighting scheme) biases that are present in hedge fund
databases (see Fung and Hsieh 2000, 2002a), it remains challenging to come
up with an accurate estimate of returns on hedge funds. The challenging
nature of hedge fund return measurement has been exemplified by the het-
erogeneity in hedge fund index returns, which is now a well-documented
problem (cf. Amenc and Martellini 2003; Vaissié 2004). As evidenced by

from January 1998 through September 2003 is 0.94, the difference
between the monthly returns on two of these indices can be as high as 7.50
percent, the return difference between the S&P Index (+13.50 percent) and
the Barclay CTA Index in December 2000. The corresponding average
monthly difference amounts to 2.90 percent. This gives clear evidence that
managed futures indices are not free from “natural” and/or “spurious”
biases. As evidenced in Posthuma and Van der Sluis (2003), the backfilling
bias is even higher for commodity trading advisers (CTAs) than for hedge
funds (3.30 percent versus 2.23 percent). Liang (2003), perhaps surpris-
ingly, drew the same conclusion with respect to survivorship bias, which
turns out to be significantly higher in the case of CTAs (5.85 percent versus
2.32 percent).
Table 2.1 illustrates the consequences of the heterogeneity of index con-
struction methodologies and fund selection in terms of risk factor expo-
2
For example, CSFB/Tremont Managed Futures Index, the CISDM Trading Advisor
Qualified Universe Index, the HF Net CTA/Managed Futures Average, the Barclay
CTA Index, and the S&P Managed Futures Index.
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20 PERFORMANCE
sures. To come up with a limited set of risk factors, we selected 16 factors
known to be related to the strategies implemented by managed futures,
namely stocks, bonds, interest rates, currency, and commodities factors. We
then used stepwise regression with the backward entry procedure to avoid
any multicollinearity problems and keep a sufficient number of degrees of
freedom. While four factors are common to all indices (Lehman Global U.S.
Treasury, U.S. dollar [USD] versus major currency, USD versus Japanese
yen, and Goldman Sachs Commodity Index [GSCI], the corresponding
exposures turn out to be very different. The S&P index yields a beta of 1.49
with the Lehman Global U.S. Treasury while the beta is 0.67 for the Bar-

T-stats −1.4
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Benchmarking the Performance of CTAs 21
tion and attribution), investors should be aware of and tackle those differ-
ences in factor exposures. In what follows, we present an index construc-
tion methodology aimed at addressing this issue. Note that this methodology
was first introduced in Amenc and Martellini (2003) and is now imple-
mented to construct the Edhec Alternative Indices.
3
Given that it is impossible to be objective on what is the best existing
index, a natural idea consists of using some combination of competing
indices (i.e., CTA indices available on the market) to extract any common
information they might share. One straightforward method would involve
computing an equally weighted portfolio of all competing indices. Because
competing indices are based on different sets of CTAs, the resulting port-
folio of indices would be more exhaustive than any of the competing indices
it is extracted from. We push the logic one step further and suggest using
factor analysis to generate a set of hedge fund indices that are the best pos-
sible one-dimensional summaries of information conveyed by competing
indices for a given style, in the sense of the largest fraction of variance
explained. Technically speaking, this amounts to using the first component
of a Principal Component Analysis of competing indices. The Edhec CTA
Index is thus able to capture a very large fraction of the information con-
tained in the competing indices.
On one hand, the Edhec CTA Index generated as the first component
in a factor analysis has a built-in element of optimality, since there is no
other linear combination of competing indices that implies a lower infor-
mation loss. On the other hand, since competing indices are affected differ-
ently by measurement biases, searching for the linear combination of
competing indices that implies a maximization of the variance explained

TABLE 2.2 Basic Statistical Properties of the Edhec CTA Global Index,
January 1997 to September 2003
Edhec CTA Lehman Global
Global Index S&P 500 Bond Index
Monthly Average Return 0.73% 0.50% 0.06%
Monthly Median Return 0.65% 0.76% 0.12%
Monthly Max. Return 6.91% 9.67% 2.15%
Monthly Min. Return −5.43% −14.58% −3.94%
Maximum Uninterrupted Loss −5.43% −20.55% −6.75%
Excess Kurtosis −0.10 −0.28 1.44
Skewness 0.15 −0.43 −0.76
% of Winning Months 56.79% 55.56% 54.32%
Average Winning Return 2.52% 4.32% 0.83%
% of Losing Months 43.21% 44.44% 45.68%
Average Losing Return −1.62% −4.27% −0.85%
Monthly Std Deviation Ann’d 9.17% 17.94% 3.75%
Monthly Variance Ann’d 0.84% 3.22% 0.14%
Monthly Semivariance Ann’d 0.39% 1.76% 0.08%
Monthly Downside Risk (MAR = Rf*)** 0.49% 1.85% 0.12%
VaR (99%) −6.89% −12.55% −2.58%
Modified VaR (99%) −6.52% −13.49% −3.31%
Sharpe Ratio 0.72 0.21 −0.39
Sortino Ratio (MAR = Rf*) 11.01 1.05 −8.11
**The risk-free rate is calculated as the 3-month LIBOR average over the period
January 1997 to September 2003, namely 4.35 percent.
**This indicator is also referred to as the lower partial moment of order 2.
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Benchmarking the Performance of CTAs 23
percent for the S&P 500 and −3.31 percent for the Lehman Global Bond
Index. This is a very interesting property as low volatility strategies often

1
Threshold %
Omega
Ratio
0
5
10
15
20
Lehman Global Bond Index
S&P 500
Edhec CTA Global Index
1.80
1.60
1.40
1.20
1.00
0.80
0.60
0.40
0.20
0.00
FIGURE 2.1 Omega Ratio as a Function of the Gain/Loss Threshold
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24 PERFORMANCE
up to an improbable loss threshold of roughly 18 percent per year, the
Edhec index offers a better gain/loss ratio than both the S&P 500 and the
Lehman Global Bond Index, which confirms the superiority of CTA risk-
adjusted performance on a stand-alone basis.
MANAGED FUTURES IN THE ASSET ALLOCATION

during increasing markets, resulting in slightly negative returns) and strad-
dlelike behavior with respect to most bond-oriented indices. In other words,
CTAs may play the role of portfolio insurers. This interesting profile cou-
pled with relatively low volatility suggests that CTAs are not only return
enhancers but also risk reducers.
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Benchmarking the Performance of CTAs 25
If CTAs offer good diversification potential while posting attractive
risk-adjusted performance, this should be reflected with a translation of
efficient frontiers to the top-left corner of the graph in Figure 2.2. Note that
to take extreme risks into account, we defined the risk dimension as the
modified VaR with 99 percent confidence level. Comparing the efficient
frontier of stocks and bonds (S&P 500 + LGBI) and that of a balanced port-
folio with CTAs (Balanced Portfolio + Edhec CTA Global), both repre-
sented by dashed lines in Figure 2.2, it is clear that CTAs can both reduce
the risk and enhance the performance of the balanced portfolio. This fact
should 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 CTAs
differ from traditional asset classes. Such an understanding naturally
implies better knowledge of the risk factors that drive their performance.
TABLE 2.3 Edhec CTA Global Index Conditional Correlations with Stock
and Bond Indices, 1999 to 2003
Correlation with Edhec CTA Global Index
Low Med High High–Low T-stats
S&P 500 −52.92% 0.53% −24.79% Good (1.16)
S&P 500 Value −49.55% 6.56% −11.77% Good (0.96)
S&P Small Cap −46.37% 13.03% 12.29% Good (1.26)
Lehman High −62.96% 29.75% −17.31% Good (−0.19)
Yield Index

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

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. R
2
0.42
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28 PERFORMANCE
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

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
a
Above average
b
Below average but positive
c
Below average and negative
*Significant at 5% level
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Benchmarking the Performance of CTAs 29
major currencies. Investors must obviously be aware of such time-varying

S&P 500
USD to Major Currency
FIGURE 2.3 Edhec CTA Index Factor Exposure Evolution, September 1999 to
September 2003
Source: Edhec Risk.
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CONCLUSION
Like hedge funds, CTAs are destined to play an important role in the diver-
sification strategy of institutional investors. As evidenced in this chapter,
they may be considered both risk reducers and return enhancers, due to
their specific exposure to a variety of risk factors (e.g., stock markets, inter-
est rates, commodity markets, foreign exchange markets, etc.). This chap-
ter has presented an original method for constructing a representative and
pure CTA index that addresses some of the crucial issues investors are fac-
ing in the allocation process. It also has analyzed CTA return characteris-
tics and the extent to which investors would be better off integrating CTAs
in their global allocation. Further research should now focus on identifying
a conditional model with potentially nonlinear risk factors to replicate the
Edhec CTA Global Index and measure CTA performance.
30 PERFORMANCE
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