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 203 c10_gregoriou.qxd 7/27/04 11:22 AM Page 203 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. 204 RISK AND MANAGED FUTURES INVESTING c10_gregoriou.qxd 7/27/04 11:22 AM Page 204 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 The Interdependence of Managed Futures Risk Measures 205 c10_gregoriou.qxd 7/27/04 11:22 AM Page 205 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 206 RISK AND MANAGED FUTURES INVESTING c10_gregoriou.qxd 7/27/04 11:22 AM Page 206 The Interdependence of Managed Futures Risk Measures 207 TABLE 10.1 Summary Statistics for Agriculture Portfolios c10_gregoriou.qxd 7/27/04 11:22 AM Page 207 208 TABLE 10.2 Correlation Matrix for Agriculture Portfolios c10_gregoriou.qxd 7/27/04 11:22 AM Page 208 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- The Interdependence of Managed Futures Risk Measures 209 c10_gregoriou.qxd 7/27/04 11:22 AM Page 209 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 210 RISK AND MANAGED FUTURES INVESTING TABLE 10.3 Summary Statistics for Currency Portfolios c10_gregoriou.qxd 7/27/04 11:22 AM Page 210 TABLE 10.4 Correlations for Currency Portfolios 211 c10_gregoriou.qxd 7/27/04 11:22 AM Page 211 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. 212 RISK AND MANAGED FUTURES INVESTING c10_gregoriou.qxd 7/27/04 11:22 AM Page 212 [...]... Measures 219 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... TABLE 10. 5 Summary Statistics for Diversified Portfolios 213 214 TABLE 10. 6 Correlations for Diversified Portfolios The Interdependence of Managed Futures Risk Measures TABLE 10. 7 Summary Statistics for Financial Portfolios 215 216 TABLE 10. 8 Correlations for Financial Portfolios The Interdependence of Managed Futures Risk Measures TABLE 10. 9 Summary Statistics for Stock Portfolios 217 218 TABLE 10. 10... the top and bottom 50 percent information ratio portfolios were perfectly correlated with the top and bottom 50 percent compounded monthly rate of return portfolios 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;... 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... 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 characteristics of these portfolios to verify whether the top portfolios always performed better than the bottom portfolios for the whole period In addition, . 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. non-trend 210 RISK AND MANAGED FUTURES INVESTING TABLE 10. 3 Summary Statistics for Currency Portfolios c10_gregoriou.qxd 7/27/04 11:22 AM Page 210 TABLE 10. 4 Correlations for Currency Portfolios 211 c10_gregoriou.qxd. 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