Commodity Trading Advisors: Risk, Performance Analysis, and Selection Chapter 19 doc

336
CHAPTER
19
CTA Strategies for Returns-
Enhancing Diversification
David Kuo Chuen Lee, Francis Koh, and Kok Fai Phoon
I
n this chapter, we analyze the risk and performance characteristics of
different strategies involving the trading of commodity futures, financial
futures, and options on futures employed by CTAs. Differing from previous
studies, we employ full and split samples to examine the correlations, and
compute risk and performance measures for various CTA strategies. We rank
the returns of the S&P 500 and MSCI Global Indices from the worst to the
best months, and partition the sample into 10 deciles. For each decile, we
compute the relationship between the CTA indices and the equity indices and
compare their risk and return characteristics. We find that CTA strategies
have higher Sharpe and Sortino ratios compared to other asset classes for the
entire sample period under study. Further, unlike hedge funds, the correlation
coefficients between CTA and equity portfolios for the first decile (worst per-
formance of the equity indices) are mostly negative. The volatility (measured
by downside deviation) of CTA strategies is lower compared to equity indices.
And, for the up-market months, CTA strategies are associated with high
Sortino ratios.
Our results are consistent with previous findings that returns from CTA
strategies are less correlated with equity market indices during down markets
than hedge fund strategies. One possible explanation is that CTAs, unlike
hedge funds, are exposed to lower liquidity risk in down markets and there-
fore do not suffer any severe “liquidity” squeeze. Our findings suggest that
the negative correlations of CTAs with equity indices during periods of equity
downturns can provide an effective hedge against catastrophic event risks.
Although hedge funds may provide diversification, they have positive corre-

lation with equity indices in down markets, especially when extreme events
occur. Hence, our findings suggest that adding CTA investments to an equity
portfolio can improve the risk-return profile of a portfolio. Such strategies not
only provide the usual portfolio diversification effects, but, given the negative
correlation in down markets, the CTAs are returns-enhancing diversifiers.
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CTA Strategies for Returns-Enhancing Diversification 337
INTRODUCTION
In recent years, there has been a marked change in the asset allocation strategy
in institutional investors, especially endowment funds. In 2002 and 2003, it
was reported that many university endowment funds allocated, on average,
about 5 percent and 7 percent, respectively, of their total investable funds to
alternative investments. Recently some endowments have increased their allo-
cations to alternative investments significantly, to a figure as high as 40 percent
of their assets under management (Lee 2003). In particular, Vanderbilt Uni-
versity (2002) has used alternatives since the 1970s and allocates just under
half of its $2 billion endowment to them, including nearly 30 percent in hedg-
ing and arbitrage strategies. The endowment has returned 8 percent per annum
over 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 venture
capital as well as commodity pools, also referred to as commodity trading
advisors (CTAs). In the current low-interest environment compounded by
somewhat bearish equity market sentiments, investors have been flocking to
alternative investments to enhance their returns as well as to protect their
investments. Institutional investors also have increased their demand for
alternative investments in the search for absolute positive returns (Till 2004).
Private equity and venture capital, in the main, provide “direct” invest-
ment opportunities for the astute investor. Conversely, alternative investments
like hedge funds and CTAs add value “indirectly” through the use of a wide

range of trading strategies, techniques, and instruments. In this chapter, we
focus on the risk and returns performance of CTAs.
LITERATURE REVIEW
A number of earlier researchers have analyzed CTAs, including Elton, Gruber,
and Renzler (1987), who concluded that CTAs offer neither an attractive alter-
native to bonds and stocks nor a profitable addition to a portfolio of bond and
stocks. Brorsen and Irwin (1985) and Murphy (1986), however, concluded
that commodity funds produce favorable and appropriate investment returns.
Schneeweis, Spurgin, and Potter (1996) found that a portfolio comprised
of equal investment in a managed future index outperformed a protective put
strategy consisting of the Standard & Poor’s (S&P) 500 index and a simulated
at-the-money put. They concluded that managed futures may offer some of
the hedging properties of a put option at a lower cost.
1
1
Schneeweis and Spurgin (1998b) used a dollar-weighted index of CTAs published
by Managed Account Reports (MAR).
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338 PROGRAM EVALUATION, SELECTION, AND RETURNS
Schneeweis and Spurgin (1998b) further presented evidence that hedge
funds and managed futures may improve the risk-return profiles of equity,
fixed income, as well as traditional alternative investments such as risky
debt. Their findings were based on correlation analysis between the under-
lying factors of:
■ Hedge fund indices from Hedge Fund Research and Evaluation Associ-
ates 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 Bond
indices for fixed income securities

Kat (2002) studied the possible role of managed futures in portfolios of
stocks, bonds, and hedge funds. He found that managed futures appear to
be more effective diversifiers than hedge funds. He found that adding man-
aged futures to a portfolio of stocks and bonds will reduce a portfolio’s
standard deviation much more and quicker than hedge funds will, and
without the undesirable side effects on skewness and kurtosis.
For the period 1994 to 2001, Liang (2003) found that although CTAs
on a stand-alone basis underperformed hedge funds, returns from CTAs were
negatively correlated with other instruments, making CTAs suitable for
hedging against downside risks.
Although the performance and risk characteristics of alternative invest-
ments as stand-alone investments are interesting and informative, analysis
of the contribution of CTAs to a portfolio of traditional investments would
be instructive and functionally useful. Finance theory has espoused the con-
cept that the ability to diversify allows for a more efficient return-risk trade-
off. In the mean-variance framework, widely attributed to Markowitz
(1952), an existing portfolio becomes more diversified upon the addition of
a new asset with a relatively lower correlation.
In this chapter, we attempt to differentiate three categories of asset
diversifiers:
1. Returns-protection diversifiers have relatively high correlations in both
the up and down markets with a generic asset class (such as the S&P
500 Index).
2. Returns-enhancing diversifiers possess correlations with the same
generic asset class in an up market but are relatively less correlated in
a down market.
3. “Ineffective” diversifiers are assets that do not add value, even though
they may possess significant correlation coefficients with the generic
asset class.
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CTA Strategies for Returns-Enhancing Diversification 339
To illustrate, a hedge fund strategy that has a negative correlation coef-
ficient in an up-market regime and positive correlation coefficient in a
down-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 of
a good diversifier as it weakens the returns on an uptrend and exaggerates
the negative returns of the portfolio.
We will show that CTAs are differentiated from hedge funds and are
returns-enhancing diversifiers.
CTAs, HEDGE FUNDS, AND FUND OF FUNDS
There are many similarities between CTAs and hedge funds and hedge fund
of funds, including the management and incentive fee structures, high ini-
tial investment requirements, and the use of leverage and derivatives. How-
ever, significant differences also exist. For example, hedge funds engage a
variety of dynamic trading strategies using different financial instruments in
different markets. CTAs, however, mainly use technical trading strategies
in commodity and financial futures markets. The use of different markets
and instruments give rise to distinct differences in risk and returns profiles.
On the regulatory side, CTAs must register with the Commodity Futures
Trading Commission (CFTC); hedge funds and fund of funds are largely
exempt from government regulations. The CFTC is a federal regulatory
body established by the Commodity Exchange Act in 1974. It supervises a
self-regulatory organization called the National Futures Association and
has exclusive jurisdiction over all U.S. commodity futures trading, futures
exchanges, futures commission merchants, and their agents, floor brokers,
floor traders, commodity trading advisors, commodity pool operators, lever-
age transaction merchants, and any associated persons of any of the forego-
ing. CTAs are subject to higher standard of compliance, including disclosure
reporting, record keeping, and accounting rules. These requirements are not

required of hedge funds (which are not registered with CFTC). Many CTAs
may have been losing their assets and customers to hedge funds in recent
years partly due to restrictive regulations by the CFTC. As a consequence,
some CTAs have started emulating hedge funds, using similar trading strate-
gies and instruments and getting more involved in equities. If this trend con-
tinues, the distinction between hedge funds and CTAs may become blurred.
On the subject of returns, Liang (2003) and other past studies found
that the correlations among the returns of hedge funds employing different
styles are high. But the correlations between the returns from different CTA
strategies and hedge fund styles are almost zero or negative. This correla-
tion structure points to a need to distinguish CTAs from hedge funds (as
well as funds of funds) in academic research.
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340 PROGRAM EVALUATION, SELECTION, AND RETURNS
The work of Liang (2003) analyzing CTAs and hedge funds separately
also provided several interesting results. Table 19.1 summarizes the results.
DATA AND METHODOLOGY
The S&P 500, MSCI Global, Lehman U.S. Aggregate, and Lehman Global
data 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 of
Lehman Global, which starts from January 1990, we have 279 observations
for each series. There are only 159 observations for the Lehman Global
Index. For the same period, we used returns data over differing periods of
four CTA indices from MarHedge: Universe, Universe Equally-Weighted
(EW), Future Funds Index, and Future Funds Equally Weighted (EW). We
also conducted analysis on subindices from MarHedge covering six strate-
TABLE 19.1 Comparison between CTAs and Hedge Funds
Hedge Fund/Hedge
CTAs Fund of Funds
Risk-adjusted Lower on a stand- Hedge fund are highest followed

returns alone basis.
a
by hedge fund of funds.
Explanation by CTA returns are Hedge fund returns cannot be
factors explained by option explained by option trading
trading factors. factors.
Attrition rate Generally higher Generally lower attrition rates.
attrition rate. Down-market conditions have
Relatively lower greater impact on attrition rates.
attrition rates
in down markets.
b
Correlation Low or negative Highly correlated with each
structure correlation with other with other during down
other instruments. markets.
Source: Bing Liang, “On the Performance of Alternative Investments: CTAs, Hedge
Funds, and Funds-of-Funds,” Case Western Reserve University, Working Paper,
2003, Cleveland, OH.
a
Liang used Sharpe ratios after adjusting for autocorrelation in returns. He
explained that the difference may be due to the fee structure as well as the risks
and autocorrelation structure.
b
Up and down markets are defined according to the S&P 500 index returns. Up
markets are periods when the monthly S&P 500 index returns are positive; down
markets are defined as periods when the index returns are negative.
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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 perform-
ance of the two equity indices, the S&P 500 and the MSCI Global. The worst-
returns month was ranked first followed by the second worst. The CTAs
indices then are matched in that same order. The ranked sample was then
divided into deciles. As we are interested only in a two-asset class situation,
we would observe the corresponding S&P 500 and CTAs returns accord-
ingly and calculate the linear correlation coefficient for each decile. For
example, analyzing the S&P 500 and Universe indices, we would compute
the correlation coefficient for each decile between the two strategies.
2
FINDINGS AND OBSERVATIONS
Table 19.2 presents the summary statistics and risk-adjusted returns. We
reported the standard summary statistics associated with the first four
moments for the whole period—mean, standard deviation, skewness, excess
kurtosis (in excess of the normal distribution)—and the “down-side devia-
tion” defined as the volatility of downside deviation below a minimum
acceptable return of zero, the Sharpe and Sortino ratios, and the matrix of
correlations between the different CTA strategies with the stock and bond
indices. There are a number of interesting observations.
Most of the CTA strategies have correlations with the equity indices
that are close to zero or negative. However, it is interesting to note that the
Discretionary Sub Index in Table 19.2 has a negative correlation with the
S&P 500 but a high positive correlation with the MSCI Global.
Most historical returns of the various CTA strategies (with the excep-
tion of Stock Index Sub) are higher than the benchmark group. Corre-
spondingly, the standard deviations are mostly higher than the benchmark
group (but comparable with equity indices with an absolute difference in
the order of less than 7 percent).
All CTA strategies have skewness greater than 1 (with the exception of
the Stock Index Sub Index strategy, which has negative skewness). Further,

all CTA strategies have positive excess kurtosis (between 0.77 and 18.61).
2
We split the sample into deciles to study the relationships of the subsamples using the
Pearson correlation coefficient. It is well known that the correlation is much higher for
hedge funds among themselves and with equity benchmarks during crisis than in normal
times. It is also known that the better-performing hedge funds have higher correlations
with equity indices. We acknowledge that there are other methods, such as Copula-based
methods, that will give a more complete picture of the associations among several assets.
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TABLE 19.2 Summary Statistics and Risk-Adjusted Measures for CTA Indices, S&P 500, MSCI Global, Lehman Global,
and Lehman U.S. Aggregate (Various Sample Periods)
Universe Index
Sample Size Mean Std. Dev. DD by MAR
a
Skewness Kurtosis Sharpe Sortino
Universe Index 279 1.19% 4.76% 4.91% 1.19 3.44 0.75 2.81
S&P 500 279 0.85% 4.52% 4.60% −0.59 2.16 0.50 2.01
MSCI Global 279 0.72% 4.31% 4.37% −0.51 1.11 0.42 1.78
Lehman Global 159 0.63% 1.44% 1.57% 0.19 −0.09 1.27 4.99
Lehman US Agg 279 0.11% 1.78% 1.78% 0.60 5.23 −0.03 0.73
Correlation Universe Index S&P 500 MSCI GlobalLehman GlobalLehman US Agg
Universe Index 1
S&P 500 −0.03 1
MSCI Global −0.05 0.84 1
Lehman Global 0.23 0.10 0.20 1
Lehman US Agg 0.06 0.23 0.20 0.73 1
Universe Index EW
Sample Size Mean Std. Dev. DD by MAR Skewness Kurtosis Sharpe Sortino
Universe EW 279 1.42% 5.19% 5.38% 1.62 4.81 0.85 3.11
S&P 500 279 0.85% 4.52% 4.60% −0.59 2.16 0.50 2.01

MSCI Global 279 0.72% 4.31% 4.37% −0.51 1.11 0.42 1.78
Lehman Global 159 0.63% 1.44% 1.57% 0.19 −0.09 1.27 4.99
Lehman US Agg 279 0.11% 1.78% 1.78% 0.60 5.23 −0.03 0.73
342
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TABLE 19.2 (continued)
Universe Index EW (continued)
Correlation Universe EW S&P 500 MSCI Global Lehman Global Lehman US Agg
Universe EW 1
S&P 500 −0.11 1
MSCI Global −0.13 0.84 1
Global 0.20 0.10 0.20 1
Lehman US Agg 0.10 0.23 0.20 0.73 1
Currency Subindex
Sample Size Mean Std. Dev. DD by MAR Skewness Kurtosis Sharpe Sortino
Currency Sub 159 0.81% 3.55% 3.64% 1.53 4.72 0.64 2.58
S&P 500 159 0.65% 4.37% 4.41% −0.44 0.45 0.35 1.55
MSCI Global 159 0.27% 4.34% 4.33% −0.39 0.25 0.04 0.49
Lehman Global 159 0.63% 1.44% 1.57% 0.19 −0.09 1.27 4.99
Lehman US Agg 159 0.09% 1.08% 1.08% −0.27 0.05 −0.13 0.93
Correlation Currency Sub S&P 500 MSCI Global Lehman Global Lehman US Agg
Currency Sub 1
S&P 500 0.03 1
MSCI Global 0.03 0.86 1
Lehman Global 0.09 0.10 0.20 1
Lehman US Agg 0.10 0.18 0.14 0.73 1
343
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TABLE 19.2 (continued)
Diversified Sub Index

Sample Size Mean Std. Dev. DD by MAR Skewness Kurtosis Sharpe Sortino
Diversified Sub 195 0.97% 4.06% 4.17% 1.28 4.45 0.69 2.68
S&P 500 195 0.75% 4.61% 4.68% −0.83 2.76 0.41 1.71
MSCI Global 195 0.48% 4.45% 4.48% −0.53 1.18 0.21 1.04
Lehman Global 159 0.63% 1.44% 1.57% 0.19 −0.09 1.27 4.99
Lehman US Agg 195 0.06% 1.18% 1.18% −0.24 0.03 −0.21 0.54
Correlation Diversified Sub S&P 500 MSCI Global Lehman Global Lehman US Agg
Diversified Sub 1
S&P 500 −0.02 1
MSCI Global −0.03 0.84 1
Lehman Global 0.23 0.10 0.20 1
Lehman US Agg 0.18 0.14 0.05 0.73 1
Discretionary Sub Index
Sample Size Mean Std. Dev. DD by MAR Skewness Kurtosis Sharpe Sortino
Discretionary Sub 195 1.44% 3.23% 3.54% 3.28 18.61 1.48 5.10
S&P 500 195 0.75% 4.61% 4.68% −0.83 2.76 0.41 1.71
MSCI Global 195 0.48% 4.45% 4.48% −0.53 1.18 0.21 1.04
Lehman Global 159 0.63% 1.44% 1.57% 0.19 −0.09 1.27 4.99
Lehman US Agg 195 0.06% 1.18% 1.18% −0.24 0.03 −0.21 0.54
344
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TABLE 19.2 (continued)
Discretionary Sub Index (continued)
Correlation Discretionary Sub S&P 500 MSCI Global Lehman Global Lehman US Agg
Discretionary Sub 1.00
S&P 500 −0.17 1.00
MSCI Global 0.84 −0.13 1.00
Lehman Global 0.10 0.08 0.20 1.00
Lehman US Agg 0.14 0.22 0.05 0.73 1.00
Stock Index Sub Index

Sample Size Mean Std. Dev. DD by MAR Skewness Kurtosis Sharpe Sortino
Stock Index Sub 111 0.31% 3.00% 3.02% −0.44 1.09 0.17 1.07
S&P 500 111 0.65% 4.63% 4.68% −0.55 0.19 0.32 1.43
MSCI Global 111 0.29% 4.25% 4.47% −0.56 0.35 0.06 0.55
Lehman Global 111 0.52% 1.41% 1.50% 0.30 0.21 0.99 4.22
Lehman US Agg 111 0.05% 1.09% 1.09% −0.21 0.18 −0.27 0.44
Correlation Stock Index Sub S&P 500 MSCI Global Lehman Global Lehman US Agg
Stock Index Sub 1.00
S&P 500 −0.11 1.00
MSCI Global −0.11 0.94 1.00
Lehman Global −0.04 −0.01 0.02 1.00
Lehman US Agg −0.04 0.04 −0.04 0.68 1.00
345
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TABLE 19.2 (continued)
Systematic Subindex
Sample Size Mean Std. Dev. DD by MAR Skewness Kurtosis Sharpe Sortino
Systematic Sub 135 0.63% 3.16% 3.22% 0.37 0.77 0.51 2.21
S&P 500 135 0.62% 4.27% 4.31% −0.56 −0.65 0.34 1.51
MSCI Global 135 0.33% 4.06% 4.07% −0.56 0.43 0.11 0.74
Lehman Global 135 0.55% 1.39% 1.49% 0.19 0.08 1.08 4.49
Lehman US Agg 135 0.06% 1.07% 1.07% −0.26 0.10 −0.23 0.59
Correlation Systematic Sub S&P 500 MSCI Global Lehman Global Lehman US Agg
Systematic Sub 1.00
S&P 500 −0.11 1.00
MSCI Global −0.06 0.90 1.00
Lehman Global 0.31 0.00 0.08 1.00
Lehman US Agg 0.31 0.06 0.01 0.71 1.00
Trend Follower
Sample Size Mean Std. Dev. DD by MAR Skewness Kurtosis Sharpe Sortino

Trend Follower 243 1.27% 6.41% 6.54% 1.05 2.42 0.55 2.09
S&P 500 243 0.84% 4.48% 4.56% −0.74 2.59 0.50 2.04
MSCI Global 243 0.74% 4.31% 4.37% −0.51 1.31 0.44 1.85
Lehman Global 159 0.63% 1.44% 1.57% 0.19 −0.09 1.25 4.91
Lehman US Agg 243 0.11% 1.33% 1.33% −0.16 0.42 −0.07 0.89
346
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TABLE 19.2 (continued)
Trend Follower (continued)
Correlation Trend Follower S&P 500 MSCI Global Lehman Global Lehman US Agg
Trend Follower 1.00
S&P 500 −0.04 1.00
MSCI Global −0.07 0.83 1.00
Lehman Global 0.24 0.10 0.20 1.00
Lehman US Agg 0.17 0.21 0.16 0.73 1.00
Futures Fund Index
Sample Size Mean Std. Dev. DD by MAR Skewness Kurtosis Sharpe Sortino
Futures Fund 279 0.93% 4.43% 4.54% 0.78 2.39 0.63 2.47
S&P 500 279 0.85% 4.52% 4.60% −0.59 2.16 0.50 2.01
MSCI Global 279 0.72% 4.31% 4.37% −0.51 1.11 0.42 1.78
Lehman Global 159 0.63% 1.44% 1.57% 0.19 −0.09 1.27 4.99
Lehman US Agg 279 0.11% 1.78% 1.78% 0.60 5.23 −0.03 0.73
Correlation Futures Fund S&P 500 MSCI Global Lehman Global Lehman US Agg
Futures Fund 1.00
S&P 500 −0.01 1.00
MSCI Global −0.01 0.84 1.00
Lehman Global −0.18 0.10 0.20 1.00
Lehman US Agg 0.06 0.23 0.20 0.73 1.00
347
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TABLE 19.2 (continued)
Futures Fund EW
Sample Size Mean Std. Dev. DD by MAR Skewness Kurtosis Sharpe Sortino
Futures Fund EW 279 0.93% 4.73% 4.82% 1.10 2.93 0.54 2.14
S&P 500 279 0.85% 4.52% 4.60% −0.59 2.16 0.50 2.01
MSCI Global 279 0.72% 4.31% 4.37% −0.51 1.11 0.42 1.78
Lehman Global 159 0.63% 1.44% 1.57% 0.19 −0.09 1.27 4.99
Lehman US Agg 279 0.11% 1.78% 1.78% 0.60 5.23 −0.03 0.73
Correlation Futures Fund EW S&P 500 MSCI Global Lehman Global Lehman US Agg
Futures
Fund EW 1.00
S&P 500 −0.01 1.00
MSCI Global −0.03 0.84 1.00
Lehman Global 0.24 0.10 0.20 1.00
Lehman US Agg 0.07 0.23 0.20 0.73 1.00
a
DD by MAR measures the volatility of monthly returns below the minimal acceptable return (MAR) as established by the investor
(in our case, the MAR is taken as 0 percent).
348
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CTA Strategies for Returns-Enhancing Diversification 349
The Sharpe and Sortino ratios in most cases were higher for the full
sample period, suggesting that the return per unit risk is almost always
higher than the benchmark group.
In Table 19.3, we take a closer look at the correlation coefficients at
different deciles. The ranking of the deciles is in accordance to the performance of
S&P 500 or MSCI Global. In other words, what we are attempting to do is to see
how correlated the strategies are with S&P at different times, the up mar-
kets (bullish period) and the down markets (bearish period) and the times
in between. We also have computed the numbers for the up period as well

as the down period.
ANALYSIS OF THE FINDINGS
Our results show that all the CTA Indices and subindices generally have
negative correlation coefficients for the first decile with the S&P 500 Index.
This means that these CTA strategies have negative association with the
S&P 500 during the worst periods of the down markets. During the peri-
ods that the S&P 500 was doing extremely badly, the CTA strategies were
doing much better. In other words, these CTA strategies enhanced portfolio
returns during the worst periods of the down market (when the S&P was
experiencing negative returns). Thus, inclusion of CTA strategies in equity
portfolios would not only reduce portfolio volatility (as good diversifiers)
but would also enhance the portfolio returns when times are “bad.”
The results are almost similar with MSCI Global. However, 3 out of 10
strategies exhibited positive correlation coefficients. The highest correlation
coefficient was only 0.2, indicating that these 3 strategies were still very
good diversifiers.
Our results are consistent with previous findings that returns from CTA
strategies are less correlated with equity market indices during down mar-
kets than hedge fund strategies. One possible explanation is that CTAs,
unlike hedge funds, are exposed to lower liquidity risk in down markets and
therefore do not suffer any severe “liquidity” squeeze.
Table 19.4 presents the deciles analysis and points to the usefulness of the
Futures Fund Index Strategy as a returns enhancing diversifier. For the first
decile of both the S&P 500 and MSCI Global indices, the returns of the
Futures Fund Index were both positive. This means that portfolio returns
would be enhanced in the “bad” period if a Futures Fund Index was included.
We examine the relative advantage of including different percentages of
the CTA Futures Index in an equity portfolio (using the MSCI Global) in
Table 19.5. The results suggest that several combinations will provide pos-
itive absolute returns. For example, a combination of 60/40 of CTA Futures

Index/MSCI Global had the highest return, of 10.22 percent. However, this
combination did not provide the least number of negative returns. If one
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TABLE 19.3 Sample Correlation Coefficients for CTA Indices with S&P and MSCI Global
Correlation with S&P
Universe Futures Futures
Universe Index Currency Diversified Discretionary Stock Index Systematic Trend Fund Fund
Index EW Subindex Subindex Subindex Subindex Subindex Follower Index EW
1st Decile −0.21 −0.21 −0.05 −0.03 0.27 −0.30 −0.50 −0.17 −0.15 −0.15
2nd Decile −0.12 −0.25 −0.04 0.11 −0.01 −0.27 0.39 0.10 −0.14 −0.14
3rd Decile 0.22 0.23 −0.01 0.25 −0.34 −0.57 0.16 0.18 0.02 0.18
4th Decile −0.34 −0.32 0.35 −0.31 0.03 −0.35 0.02 −0.06 −0.31 −0.37
5th Decile −0.22 −0.15 −0.52 −0.54 −0.15 −0.35 −0.48 −0.41 −0.21 −0.29
6th Decile −0.23 −0.23 0.07 −0.17 0.20 −0.36 0.29 −0.24 −0.26 −0.25
7th Decile −0.20 0.07 −0.02 −0.19 −0.31 −0.33 0.33 −0.21 −0.13 −0.25
8th Decile −0.27 0.02 0.20 −0.20 0.25 0.35 0.41 −0.32 −0.21 −0.26
9th Decile −0.08 −0.14 0.14 −0.18 0.18 −0.24 0.21 −0.41 −0.14 −0.14
10th Decile −0.02 0.04 0.60 0.40 −0.48 0.33 −0.19 0.08 0.02 0.00
Down Half −0.14 −0.26 0.26 −0.19 −0.51 −0.11 −0.18 −0.15 −0.10 −0.12
Up Half 0.10 0.11 0.08 0.12 0.06 0.02 −0.07 0.12 0.13 0.12
Overall −0.03 −0.11 0.03 −0.02 −0.17 −0.11 −0.11 −0.04 0.01 −0.01
350
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TABLE 19.3 (continued)
Correlation with MSCI Global
Universe Futures Futures
Universe Index Currency Diversified Discretionary Stock Index Systematic Trend Fund Fund
Index EW Subindex Subindex Subindex Subindex Subindex Follower Index EW
1st Decile −0.23 −0.54 0.14 −0.09 −0.67 −0.51 0.20 −0.28 −0.13 0.15
2nd Decile 0.11 0.20 0.45 −0.05 0.40 −0.28 −0.07 0.06 0.10 −0.44

3rd Decile −0.08 −0.17 −0.39 −0.29 −0.43 −0.54 0.10 0.15 0.00 0.60
4th Decile −0.01 0.02 −0.01 0.31 0.20 −0.33 0.20 0.17 0.13 0.10
5th Decile −0.34 −0.30 −0.10 −0.02 −0.28 0.31 0.40 −0.31 −0.34 −0.21
6th Decile 0.20 0.13 −0.04 0.18 0.03 0.00 −0.19 0.15 0.21 0.38
7th Decile −0.09 −0.04 0.01 −0.02 0.20 0.24 −0.07 −0.25 −0.01 −0.05
8th Decile 0.31 0.30 0.13 0.30 −0.06 0.44 −0.36 0.25 0.31 0.51
9th Decile 0.39 0.30 −0.04 0.15 −0.10 −0.37 −0.19 −0.05 0.38 −0.37
10th Decile 0.25 0.15 0.32 0.28 0.37 −0.06 −0.44 0.08 0.26 −0.54
Down Half −0.18 −0.23 0.04 −0.14 −0.26 −0.06 −0.30 −0.23 −0.20 −0.18
Up Half 0.10 0.12 0.02 −0.01 0.10 0.02 −0.26 0.07 0.13 0.12
Overall −0.05 −0.13 0.03 −0.03 0.84 −0.11 −0.06 −0.07 −0.01 −0.03
351
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TABLE 19.4 Summary Statistics, Correlation Coefficients, and Risk-Adjusted Measures for Futures Fund Index with S&P
and MSCI Global
0–10% 10–20% 20–30% 30–40% 40–50%
Futures Futures Futures Futures Futures
Fund S&P Fund S&P Fund S&P Fund S&P Fund S&P
Index 500 Index 500 Index 500 Index 500 Index 500
Futures Sample Size 28 28 28 28 28 28 28 28 27 27
Fund Mean 2.08% −7.74% −0.43% −3.32% 0.54% −1.84% 1.90% −0.59% 0.57% 0.63%
Index Std. Dev. 3.69% 3.53% 3.58% 0.64% 5.46% 0.39% 4.43% 0.34% 3.09% 0.29%
vs. DD by
S&P 500 MAR 4.26% 8.63% 3.60% 3.44% 5.49% 1.92% 4.84% 0.69% 3.15% 0.70%
Skewness −1.44 −2.70 −0.83 −0.63 0.96 0.12 1.07 0.17 0.58 −0.49
Kurtosis 3.53 9.00 1.57 −0.67 3.70 −0.99 0.70 −0.86 −0.17 −0.90
Sharpe 2.00 −5.22 −0.59 −15.76 0.18 −15.82 1.47 −7.13 0.47 6.30
Sortino 6.35 −7.22 −1.60 −9.69 0.89 −10.44 4.97 −9.95 2.08 11.11
Correlation −0.15 −0.14 0.02 −0.31 −0.21
352

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TABLE 19.4 (continued)
50–60% 60–70% 70–80% 80–90% 90–100%
Futures Futures Futures Futures Futures
Fund S&P Fund S&P Fund S&P Fund S&P Fund S&P
Index 500 Index 500 Index 500 Index 500 Index 500
Futures Sample Size 28 28 28 28 28 28 28 28 28 28
Fund Mean 0.13% 1.48% 0.72% 2.57% 0.29% 3.79% 1.75% 5.20% 2.29% 8.27%
Index Std. Dev. 3.78% 0.30% 3.01% 0.41% 4.37% 0.25% 5.61% 0.57% 5.93% 1.88%
vs. DD by
S&P 500 MAR 3.79% 1.54% 3.10% 2.64% 4.38% 3.87% 5.89% 5.32% 6.37% 8.63%
Skewness 0.03 0.00 0.71 0.49 0.62 −0.05 1.71 −0.16 0.43 1.05
Kurtosis 0.41 −1.34 −0.10 −0.88 0.77 −1.21 4.18 −1.30 −0.49 0.26
Sharpe −0.06 17.10 0.67 24.23 0.06 63.18 1.01 41.48 1.33 24.23
Sortino 0.18 12.54 2.73 13.43 0.56 14.55 3.58 15.71 4.51 18.43
Correlation −0.26 −0.13 −0.21 −0.14 0.02
353
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TABLE 19.4 (continued)
0–10% 10–20% 20–30% 30–40% 40–50%
Futures Futures Futures Futures Futures
Fund MSCI Fund MSCI Fund MSCI Fund MSCI Fund MSCI
Index Global Index Global Index Global Index Global Index Global
Futures Sample Size 28 28 28 28 28 28 28 28 27 27
Fund Mean 2.44% −7.57% 1.67% −3.36% −0.38% −1.86% 0.31% −0.58% 0.50% 0.43%
Index Std. Dev. 2.86% 2.94% 5.41% 0.67% 3.67% 0.29% 4.77% 0.36% 4.23% 0.29%
vs. DD by
MSCI MAR 3.79% 8.25% 5.67% 3.49% 3.69% 1.92% 4.78% 0.69% 4.26% 0.52%
Global Skewness −0.12 −1.66 0.92 −0.54 −0.43 −0.06 1.03 −0.47 −0.25 −0.30
Kurtosis −0.33 3.01 2.89 −0.95 0.06 −0.61 3.10 −0.79 0.97 −1.37

Sharpe 3.17 −6.17 0.99 −15.24 −0.53 −21.49 0.06 −6.71 0.24 3.67
Sortino 8.69 −7.44 3.53 −9.66 −1.42 −10.53 0.52 −9.79 1.18 9.99
Correlation −0.13 0.10 0.00 0.13 -0.34
354
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TABLE 19.4 (continued)
50–60% 60–70% 70–80% 80–90% 90–100%
Futures Futures Futures Futures Futures
Fund MSCI Fund MSCI Fund MSCI Fund MSCI Fund MSCI
Index Global Index Global Index Global Index Global Index Global
Futures Sample Size 28 28 28 28 28 28 28 28 28 28
Fund Mean 1.18% 1.51% 0.41% 2.42% −0.29% 3.57% 2.77% 4.94% 1.25% 7.71%
Index Std. Dev. 4.15% 0.30% 3.88% 0.32% 3.31% 0.43% 5.15% 0.44% 5.56% 1.68%
vs. DD by
MSCI MAR 4.32% 1.57% 3.90% 2.49% 3.33% 3.66% 5.88% 5.04% 5.71% 8.02%
Global Skewness 0.63 −0.52 0.64 −0.30 −0.48 0.12 1.61 0.47 0.93 0.82
Kurtosis 0.82 −1.25 2.07 −1.32 0.18 −1.45 4.08 −1.16 0.44 −0.34
Sharpe 0.87 17.23 0.19 28.80 −0.49 34.47 1.98 50.82 0.65 24.41
Sortino 3.24 12.56 1.05 13.37 −1.23 14.29 6.28 15.51 2.47 17.87
Correlation 0.21 −0.01 0.31 0.38 0.26
355
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TABLE 19.5 Combining Futures and Equity Indices in Different Proportions
0– 10– 20– 30– 40– 50– 60– 70– 80– 90–
10% 20% 30% 40% 50% 60% 70% 80% 90% 100%
Portfolio
Combination Returns Returns Returns Returns Returns Returns Returns Returns Returns Returns Returns
0/100 −7.57% −3.36% −1.86% −0.58% 0.43% 1.51% 2.42% 3.57% 4.94% 7.71% 7.19%
10/90 −6.57% −2.86% −1.71% −0.49% 0.43% 1.48% 2.22% 3.18% 4.72% 7.06% 7.45%
20/80 −5.57% −2.36% −1.56% −0.40% 0.44% 1.44% 2.02% 2.79% 4.50% 6.41% 7.72%

30/70 −4.57% −1.85% −1.42% −0.31% 0.45% 1.41% 1.82% 2.41% 4.29% 5.77% 7.98%
40/60 −3.57% −1.35% −1.27% −0.22% 0.45% 1.38% 1.62% 2.02% 4.07% 5.12% 8.25%
50/50 −2.57% −0.85% −1.12% −0.14% 0.46% 1.34% 1.42% 1.64% 3.85% 4.48% 8.51%
60/40 −3.08% −1.02% −1.34% −0.16% 0.55% 1.61% 1.70% 1.96% 4.62% 5.37% 10.22%
70/30 −0.57% 0.16% −0.83% 0.04% 0.47% 1.28% 1.01% 0.87% 3.42% 3.18% 9.04%
80/20 0.43% 0.66% −0.68% 0.13% 0.48% 1.25% 0.81% 0.48% 3.20% 2.54% 9.31%
90/10 1.44% 1.16% −0.53% 0.22% 0.49% 1.21% 0.61% 0.09% 2.99% 1.89% 9.58%
100/0 2.44% 1.67% −0.38% 0.31% 0.50% 1.18% 0.41% −0.29% 2.77% 1.25% 9.84%
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were to look for the least number of negative periods, then the combination
of 90/10 would almost ensure that there would only be a 1 in 10 chance of
negative returns.
The results illustrate a useful idea: If we are concerned about event risk,
we may wish to define our objective function as one that has the least num-
ber of negative returns during the investment horizon, with the constraint
that the correlation at first decile should be the lowest. This could be a use-
ful framework to carry out constrained optimization of portfolio returns.
CONCLUSION
Our results indicate that the risk-adjusted returns as measured by Sharpe
and Sortino ratios are always higher in CTA strategies than in most tradi-
tional asset classes for the entire sample period under study. Unlike hedge
funds, the correlation coefficients of the CTAs with the equity markets are
negative during bad times (worst performance period of the equity mar-
kets). Yet the volatility (measured by downside deviation) of CTA strategies
is lower compared to equity indices. For the up-market months, CTA strate-
gies are associated with high Sortino ratios.
The negative correlations of CTAs with equity indices during periods of
marked downturns of equity markets indicate that CTAs can provide an
effective hedge against catastrophic event risks. While hedge funds also pro-

vide diversification, they have positive correlation with equity indices in
down markets, especially when extreme events occur. Hence our findings
suggest that adding more tightly regulated CTA strategies to an equity port-
folio can improve its overall risk-return profile. Such strategies not only
provide the usual portfolio diversification effects, but, given the negative
correlation in down markets, CTAs are returns-enhancing diversifiers.
Although our findings present strong reasons to use CTAs, their use may
not be without a cost. Liang (2003) found that attrition rates are higher for
CTAs when compared with hedge fund and hedge fund of funds. However,
the reasons why CTAs are return-enhancing diversifiers deserve further
investigation. The level of liquidity risk borne may be an important differ-
ence between hedge funds and CTAs.
CTA Strategies for Returns-Enhancing Diversification 357
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