Commodity Trading Advisors: Risk, Performance Analysis, and Selection Chapter 10 pps

CHAPTER
10
CHAPTER 10
The Interdependence of Managed
Futures Risk Measures
Bhaswar Gupta and Manolis Chatiras
P
ractitioners today are faced with a wide choice of methods to measure
return and risk in portfolios, either in absolute or relative terms. The
Sharpe ratio, maximum drawdown, and semideviation are common exam-
ples. We classify 24 such measures into six groups and attempt to gauge
how the measures interact, by using data on five different CTA strategies.
For each measure, two groups of portfolios are created, containing CTAs
with the lowest and highest values of the measure. We find evidence of
high correlation between the measures in some of the CTA strategies,
pointing to information overlaps and suggesting that some of these meas-
ures may be redundant.
INTRODUCTION AND REVIEW OF THE LITERATURE
The managed futures industry has grown from just under $1 billion in 1985
to more than $40 billion as of June 2003. This growth has led to closer
scrutiny of the diversification properties as well as risk management of man-
aged futures. The term “managed futures” represents an industry composed
of professional money managers known as commodity trading advisors
(CTAs) who manage client assets on a discretionary basis using global
futures and options markets (CISDM 2002). The risks in managed futures
are inherently more complex than traditional investments as they undergo
rapid change over time. Hence a thorough understanding of the risks of the
different market segments CTAs trade in is essential to effectively manage
these risks. This chapter examines risk surrogates for certain CTA portfolios.
The risks in the different market segments have been explored in sev-
eral articles. Tomek and Peterson (2001) have reviewed risk management

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practices in agricultural markets. Their review highlights gaps between con-
cepts and implementation and notes that even though many well-developed
models of price behavior exist, appropriate characterization and estimation
of probability distributions of commodity prices remain elusive. Their con-
clusions discuss what academic research can and cannot accomplish in
assisting producers with risk management decisions.
Risk surrogates also have been explored in several articles. Cooley,
Roenfeldt, and Modani (1977), using returns of a sample of 943 firms hav-
ing data for the period January 1966 to January 1974, calculate 11 risk
measures to indicate the wide range of risk surrogates. Daglioglu and Gupta
(2003b) study the interdependence of hedge fund risk measures. Using 330
hedge funds that had complete data for the period January 1996 to Sep-
tember 2002, they construct 48 portfolios (24 top 50 percent and 24 bot-
tom 50 percent) based on 24 risk measures. The 330 funds belonged to
seven strategies. Their results had several implications:
■ Although certain risk measures are relevant for some strategies, they
are not relevant for others.
■ Certain risk measures for some strategies are perfectly correlated for
both the top and bottom portfolios. This suggests that there is strong
information overlap and the use of any one would suffice.
■ For some strategies (e.g., equity hedge and fund of funds), the risk
measures are not perfectly correlated.
■ The occurrence of low correlations is much greater for the market-
neutral strategy than for any other strategy.
Daglioglu and Gupta (2003b) note that these results point to an important
conclusion: Risk measures should be chosen carefully for inclusion in per-
formance reports so that redundancy is avoided.
Gordon (2003) also examines several risk measures, such as historical

standard deviation, downside deviation, semideviation, and maximum
drawdown. Using data from a large hedge fund of funds over the period
December 1991 to December 2000, he analyzes out-of-sample performance
to predict results in the nonoverlapping subsequent period of investment in
each hedge fund. He finds that historical standard deviation tends to be
somewhat helpful in predicting future risk. He also finds that correlation
between preinvestment standard deviation, downside deviation, and maxi-
mum drawdown is significant. Gordon concludes that standard deviation
appears to be a better predictor of future losses than downside risk measures
such as historical downside deviation and maximum drawdown. Although
this advantage is not statistically significant for some of the downside risk
measures, he notes that standard deviation should probably be favored over
all other downside risk measures because it is simple and well understood.
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In this chapter we analyze the significance of the same 24 risk measures
used in Daglioglu and Gupta (2003b) for certain CTA portfolios. The 24
measures are used as much in CTA performance reports as they are in hedge
fund reports. Our results shed greater light on the implications of these
measures for particular CTA strategies. They also provide a clearer under-
standing of the interdependence of these two measures for certain CTA
portfolios. We provide empirical evidence on the redundancy of certain risk
surrogates, to help investors determine the relevance and applicability of
these risk measures when evaluating CTA portfolios.
In the next section we describe the methodology used for this study.
Then we describe the data, present the empirical results, and conclude.
METHODOLOGY
We study the 24 risk measures that were analyzed in Daglioglu and Gupta
(2003b) to ascertain the degree of informational overlap among them. We
use correlation analysis in our study. We divide the degree of correlation

into four groups:
1. (P) means Perfectly Correlated, correlation = 1.00.
2. (H) means Highly Correlated, 0.90 < correlation < 1.00.
3. (M) means Moderately Correlated, 0.65 < correlation < 0.90.
4. (L) means Low Correlated, correlation < 0.65.
The 24 risk measures are:
1. Average Monthly Gain 13. Gain/Loss Ratio
2. Average Monthly Loss 14. Beta
3. Standard Deviation 15. Annualized Alpha
4. Gain Standard Deviation 16. Treynor Ratio
5. Loss Standard Deviation 17. Jensen Alpha
6. Semideviation 18. Information Ratio
7. Skewness 19. Up Capture
8. Kurtosis 20. Down Capture
9. Coskewness 21. Up Number Ratio
10. Sharpe ratio 22. Down Number Ratio
11. Calmar ratio 23. Up Percentage Ratio
12. Maximum Drawdown 24. Down Percentage Ratio.
These measures can be classified into six groups:
1. Absolute return measures
2. Absolute risk measures
3. Absolute risk-adjusted return measures
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4. Relative return measures
5. Relative risk measures
6. Relative risk-adjusted return measures
DATA
The data for this study came from the Center for International Securities
and Derivatives Markets (CISDM) database. We selected a sample of 200

CTA managers who had complete return data for the period from January
1998 to July 2003. The CTAs covered five strategies:
1. Agriculture
2. Currencies
3. Diversified
4. Financials
5. Stocks
Using these monthly rates of return, we calculated the 24 risk measures
for the overall period, January 1998 to July 2003. These risk measures are
indicative of the wide range of risk surrogates suggested in the literature on
CTA analysis and portfolio management.
We then ranked all of the CTAs by these 24 risk measures for the five
different CTA strategies. Next, we took the first half and second half to
construct bottom 50 percent and top 50 percent portfolios for these strate-
gies. In other words, we created 48 portfolios (24 portfolios for bottom 50
percent, 24 portfolios for top 50 percent) for each CTA strategy. Tables
10.1, 10.3, 10.5, 10.7, and 10.9. present annualized returns, standard devi-
ations, and Sharpe ratios of these portfolios and Tables 10.2, 10.4, 10.6,
10.8, and 10.10 present the correlations between the portfolios.
EMPIRICAL RESULTS
Agriculture
Table 10.1 presents summary statistics for the agriculture portfolios, and
Table 10.2 presents the correlation matrix. The top 50 percent monthly
standard deviation, top 50 percent gain standard deviation, top 50 percent
loss standard deviation, and top 50 percent semideviation yield exactly the
same results as do the bottom 50 percent portfolios for the four risk meas-
ures. Similarly the top 50 percent portfolio of the up percentage ratio yields
the same results as the top 50 percent portfolio of the down percentage ratio,
and the bottom 50 percent portfolio of the up percentage ratio yields the
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TABLE 10.1 Summary Statistics for Agriculture Portfolios
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TABLE 10.2 Correlation Matrix for Agriculture Portfolios
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same results as the bottom 50 percent portfolio of the down percentage
ratio. The top 50 percent up capture portfolio yields exactly the same results
as the top 50 percent average monthly gain portfolio, and the bottom 50 per-
cent up capture portfolio yields exactly the same results as the bottom 50
percent average monthly gain portfolio. As expected, these portfolios are
perfectly correlated with each other. There are also several high and moder-
ate correlations and many low correlations. The low correlations can be
explained by the characteristics of our sample. Seven funds have complete
data over the period of our study. Three are trend followers and four are
not. If the risk measures split the sample in a way that trend followers were
in one sample and non-trend followers in the other for the top and bottom
50 percent portfolios, then one would expect low correlations among the
portfolios. However, if the portfolios were split in such a way that they
contain equal numbers of trend-following and non-trend-following funds,
then one would expect moderate to high correlations.
We also examined the sectors traded by these trading advisors. All seven
indicated that they traded grains; three said they traded meats; and three
said they traded softs. One indicated that he traded currencies and interest
rates, and another indicated that he traded energy and metals. Given the
diverse characteristics of these portfolios, the low correlation between cer-
tain risk measures is a natural consequence.
Currencies
Twenty-seven currency CTAs had complete data for the period of our

study. Table 10.3 presents the summary statistics for the currency portfo-
lios; Table 10.4 presents the correlations among the portfolios. There were
only two instances of perfect correlations, the top and bottom 50 percent
monthly standard deviation portfolios with the top and bottom 50 percent
average monthly gain portfolios, and the top and bottom 50 percent semi-
deviation portfolios with the top and bottom 50 percent loss standard
deviation portfolios. There were several instances of high, moderate, and
low correlations. Of the 27 funds, three indicated that their trades had a
short-term time horizon; four indicated that their trades had short-,
medium-, and long-term horizons. Eight of the funds indicated that their
trades had a medium-term horizon; four indicated that they had a long-
term horizon. Two indicated that they traded intraday. Seven of the funds
were classified as discretionary, 15 as systematic, 2 as trend-based, and
3 as trend-identifier.
There is considerable variety even within the strategies. For example, a
certain fund that was classified as systematic and short term had a correla-
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tion of only 0.19 with another fund that was classified as systematic and
medium term for the time period studied. Another pair where both were
classified as systematic and medium term had a correlation of 0.25. Sys-
tematic funds can be either trend followers or contrarian; in this case one
was a systematic trend follower and the other was a systematic non-trend
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TABLE 10.3 Summary Statistics for Currency Portfolios
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TABLE 10.4 Correlations for Currency Portfolios
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follower. However, a pair where both funds were classified as systematic

trend followers had a correlation of 0.47. As expected, the discretionary
funds had low correlations. Given the diversity of the funds classified as
currency, the correlation patterns of risk measures are along expected lines.
Diversified Portfolios
Table 10.5 presents the summary statistics for the diversified portfolios;
Table 10.6 presents the correlations among the portfolios. For the period
of our study, 107 diversified CTAs had complete data. One interesting
result in the case of diversified CTAs is that no portfolios are perfectly cor-
related with each other. However, a majority of portfolios had high corre-
lations, a few had moderate correlations, and none had low correlations.
Of the 107 funds, 10 were classified as discretionary, 69 as systematic, 24
as trend based, and 4 as trend identifier. Clearly since more than half of the
funds were systematic, these funds dominated the portfolios in all cases.
Another reason why the portfolios exhibited high correlations is that many
of the funds had high correlations before analysis. Although there were
pairs—for example, two funds classified as long-term systematic with a
correlation of 0.46—these did not impact the rankings enough to show
that the risk measures are not interdependent. Another reason for these
results is the markets diversified CTAs trade in. Diversified CTAs encom-
pass agriculture, currencies, financials, and stocks. Because most diversi-
fied CTAs trade in a majority of these markets, their return patterns
showed similar risk characteristics.
Financial Portfolios
Table 10.7 presents the summary statistics of the financial portfolios and
Table 10.8 presents the correlations. In this case the portfolios were mostly
highly or moderately correlated with only one perfectly correlated portfo-
lio pair. The top 50 percent and bottom 50 percent information ratio port-
folios were perfectly correlated with the top and bottom 50 percent Sharpe
ratio portfolios. Thirty-nine CTAs had complete data for the period of our
study. Of these 5 were discretionary, 21 were systematic, 10 were trend

based, and 3 were trend identifiers. Clearly the systematic or trend-based
funds dominated the portfolios. The return patterns of these portfolios sug-
gest that they have similar risk characteristics.
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TABLE 10.5 Summary Statistics for Diversified Portfolios
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TABLE 10.6 Correlations for Diversified Portfolios
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TABLE 10.7 Summary Statistics for Financial Portfolios
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TABLE 10.8 Correlations for Financial Portfolios
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TABLE 10.9 Summary Statistics for Stock Portfolios
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TABLE 10.10 Correlations for Stock Portfolios
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Stock Portfolios
Table 10.9 presents the summary characteristics of the stock portfolios;
Table 10.10 presents the correlations. Several portfolios were perfectly
correlated. For example, the top and bottom 50 percent gain standard
deviation portfolios were perfectly correlated with the top and bottom
50 percent average monthly gain portfolios, and the top and bottom 50
percent information ratio portfolios were perfectly correlated with the

top and bottom 50 percent compounded monthly rate of return portfo-
lios. There were several instances of weakly correlated portfolios. Of
the 15 funds that were analyzed, 3 were discretionary, 9 were systematic,
and 3 were trend-based. The return patterns of stock futures can vary
depending on the stock index; that is one explanation of the weakly cor-
related portfolios.
Implications
One immediate application of the results of this analysis is in due diligence.
Because the measures analyzed in this study are commonly used by
investors to evaluate the performance of CTAs, perfect or high correlations
can lead to redundancy. Our results are also important for performance
reporting. Investors may want to examine correlations between ranked
portfolios of these risk measures to avoid redundancy.
CONCLUSION
This research can be extended in many ways. For managed futures, we
could further classify the CTAs as systematic trend following, systematic
non-trend following, or discretionary. It would be interesting to attempt to
identify similar correlation patterns for discretionary and systematic CTAs
in the different market segments. We also could explore performance char-
acteristics of these portfolios to verify whether the top portfolios always
performed better than the bottom portfolios for the whole period. In addi-
tion, we could perform out-of-sample testing to see whether the rankings
had any significance in other periods.
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