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. c19_gregoriou.qxd 7/27/04 12:01 PM Page 336 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). c19_gregoriou.qxd 7/27/04 12:01 PM Page 337 338 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. c19_gregoriou.qxd 7/27/04 12:01 PM Page 338 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. c19_gregoriou.qxd 7/27/04 12:01 PM Page 339 340 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. c19_gregoriou.qxd 7/27/04 12:01 PM Page 340 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. c19_gregoriou.qxd 7/27/04 12:01 PM Page 341 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 c19_gregoriou.qxd 7/27/04 12:01 PM Page 342 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 c19_gregoriou.qxd 7/27/04 12:01 PM Page 343 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 c19_gregoriou.qxd 7/27/04 12:01 PM Page 344 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 c19_gregoriou.qxd 7/27/04 12:01 PM Page 345 [...]... US Agg TABLE 19. 2 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. .. 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... Statistics, Correlation Coefficients, and Risk-Adjusted Measures for Futures Fund Index with S&P and MSCI Global TABLE 19. 4 353 Sample Size Mean Std Dev DD by MAR Futures Fund Index vs S&P 500 1.54% 3.79% 0.00 −1.34 17.10 12.54 −0.26 1.48% 0.30% 28 S&P 500 0.13% 3.78% 28 Futures Fund Index 50–60% Skewness 0.03 Kurtosis 0.41 Sharpe −0.06 Sortino 0.18 Correlation (continued) TABLE 19. 4 0.71 −0.10 0.67 2.73 3.10%... 10th Decile Down Half Up Half Overall TABLE 19. 3 Universe Index EW −0.21 −0.25 0.23 −0.32 −0.15 −0.23 0.07 0.02 −0.14 0.04 −0.26 0.11 −0.11 Universe Index −0.21 −0.12 0.22 −0.34 −0.22 −0.23 −0.20 −0.27 −0.08 −0.02 −0.14 0.10 −0.03 −0.05 −0.04 −0.01 0.35 −0.52 0.07 −0.02 0.20 0.14 0.60 0.26 0.08 0.03 −0.03 0.11 0.25 −0.31 −0.54 −0.17 −0 .19 −0.20 −0.18 0.40 −0 .19 0.12 −0.02 0.27 −0.01 −0.34 0.03 −0.15... see how correlated the strategies are with S&P at different times, the up markets (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... TABLE 19. 5 Combining Futures and Equity Indices in Different Proportions 2.42% 2.22% 2.02% 1.82% 1.62% 1.42% 1.70% 1.01% 0.81% 0.61% 0.41% Returns 60– 70% 3.57% 3.18% 2.79% 2.41% 2.02% 1.64% 1.96% 0.87% 0.48% 0.09% −0.29% Returns 70– 80% 90– 100% 4.94% 4.72% 4.50% 4.29% 4.07% 3.85% 4.62% 3.42% 3.20% 2.99% 2.77% 7.71% 7.06% 6.41% 5.77% 5.12% 4.48% 5.37% 3.18% 2.54% 1.89% 1.25% Returns Returns 80– 90% 7 .19% ... −0.11 −0.50 0.39 0.16 0.02 −0.48 0.29 0.33 0.41 0.21 −0 .19 −0.18 −0.07 −0.11 −0.17 0.10 0.18 −0.06 −0.41 −0.24 −0.21 −0.32 −0.41 0.08 −0.15 0.12 −0.04 Currency Diversified Discretionary Stock Index Systematic Trend Subindex Subindex Subindex Subindex Subindex Follower Correlation with S&P Sample Correlation Coefficients for CTA Indices with S&P and MSCI Global −0.15 −0.14 0.02 −0.31 −0.21 −0.26 −0.13... −0.14 −0.01 −0.03 −0.67 0.40 −0.43 0.20 −0.28 0.03 0.20 −0.06 −0.10 0.37 −0.26 0.10 0.84 −0.51 −0.28 −0.54 −0.33 0.31 0.00 0.24 0.44 −0.37 −0.06 −0.06 0.02 −0.11 0.20 −0.07 0.10 0.20 0.40 −0 .19 −0.07 −0.36 −0 .19 −0.44 −0.30 −0.26 −0.06 −0.28 0.06 0.15 0.17 −0.31 0.15 −0.25 0.25 −0.05 0.08 −0.23 0.07 −0.07 Currency Diversified Discretionary Stock Index Systematic Trend Subindex Subindex Subindex Subindex... 4.06% 1.39% 1.07% Std Dev 3.22% 4.31% 4.07% 1.49% 1.07% DD by MAR Systematic Subindex 0.37 −0.56 −0.56 0 .19 −0.26 Skewness 0.77 −0.65 0.43 0.08 0.10 Kurtosis 1.00 0.71 6.41% 4.48% 4.31% 1.44% 1.33% Std Dev 6.54% 4.56% 4.37% 1.57% 1.33% DD by MAR Trend Follower 1.00 0.08 0.01 1.05 −0.74 −0.51 0 .19 −0.16 Skewness 1.00 2.42 2.59 1.31 −0.09 0.42 Kurtosis S&P 500 MSCI Global Lehman Global Lehman US Agg... Global 40–50% 355 (continued) Sample Size Mean Std Dev DD by MAR Skewness Kurtosis Sharpe Sortino Correlation TABLE 19. 4 Futures Fund Index vs MSCI Global −0.52 −1.25 17.23 12.56 0.21 1.57% 4.32% 0.63 0.82 0.87 3.24 1.51% 0.30% 28 MSCI Global 1.18% 4.15% 28 Futures Fund Index 50–60% 0.64 2.07 0 .19 1.05 3.90% 0.41% 3.88% 28 Futures Fund Index −0.30 −1.32 28.80 13.37 −0.01 2.49% 2.42% 0.32% 28 MSCI Global . 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. 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. Gruber, and Renzler (198 7), 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 (198 5)