Commodity Trading Advisors: Risk, Performance Analysis, and Selection Chapter 2 pptx

We then use the Edhec CTA Index to analyze CTA return characteristics and the extent to which investors would be better off integrating CTAs in their global alloca-tion.. DEALING WITH CT

Benchmarking the Performance of CTAs Lionel Martellini and Mathieu Vaissié

The bursting of the Internet bubble in March 2000 plunged traditional market indices (stocks, bonds, etc.) into deep turmoil, leaving most insti-tutional investors with the impression that portfolio diversification tends to fail at the exact moment that investors have a need for it, namely in peri-ods when the markets drop significantly.1 At the same time, most alterna-tive investments (e.g., hedge funds, CTAs, real estate, etc.) posted attracalterna-tive returns They benefited from large capital inflows from high-net-worth individuals (HNWI) and institutional investors, who were both looking for investment vehicles that would improve the diversification of their portfo-lios At the same time, many recent academic and practitioner studies have documented the benefits of investing in alternative investments in general, and hedge funds in particular (see Amenc, Martellini, and Vaissié 2003; Amin and Kat 2002, 2003b; Anjilvel Boudreau, Urias, and Peskin 2000; Brooks and Kat 2002; Cerrahoglu and Pancholi 2003; Daglioglu and Gupta 2003a; Schneeweis, Karavas, and Georgiev 2003)

Nevertheless, due to the “natural” (survivorship/selection) and “spuri-ous” (backfilling/weighting scheme) biases that are present in hedge fund databases (see Fung and Hsieh 2000, 2002a), it remains challenging to come

up with an accurate estimate of returns on hedge funds The challenging nature of hedge fund return measurement has been exemplified by the het-erogeneity in hedge fund index returns, which is now a well-documented problem (cf Amenc and Martellini 2003; Vaissié 2004) As evidenced by Amenc and Martellini (2003), the correlation between indices representing

1 Longin and Solnik (1995) provide evidence that the correlation between the stock markets in different countries converges toward 1 when there is a sharp drop in U.S stock markets.

the same investment style may turn out to be as low as 0.43 for equity mar-ket neutral or 0.46 for equity long short This fact may leave investors with

a somewhat confused picture of the performance of alternative investment strategies More surprisingly perhaps, index heterogeneity also may be of concern in the case of CTAs Dealing with CTA index heterogeneity is dis-cussed in the next sections It is crucial for investors to pay particular atten-tion to the selecatten-tion of an appropriate index to benchmark their performance and to assess their exposure to risk factors To respond to investors’ expec-tations, in this chapter we present an original methodology to construct a pure and representative CTA index (also known as the Edhec CTA Global Index; hereafter referred to as the Edhec CTA Index) We then use the Edhec CTA Index to analyze CTA return characteristics and the extent to which investors would be better off integrating CTAs in their global alloca-tion Finally, we derive a five-factor model to identify the underlying risk factors driving CTA performance

DEALING WITH CTA INDEX HETEROGENEITY

Because managed futures tend to trade more liquid assets than hedge funds and because they have to register with the Commodity Futures Trading Commission (CFTC), one would expect the different managed futures indices to exhibit negligible heterogeneity This, however, is not the case While the average correlation between the different indices available on the

between the monthly returns on two of these indices can be as high as 7.50 percent, the return difference between the S&P Index (+13.50 percent) and the Barclay CTA Index in December 2000 The corresponding average monthly difference amounts to 2.90 percent This gives clear evidence that managed futures indices are not free from “natural” and/or “spurious” biases As evidenced in Posthuma and Van der Sluis (2003), the backfilling bias is even higher for commodity trading advisers (CTAs) than for hedge funds (3.30 percent versus 2.23 percent) Liang (2003), perhaps surpris-ingly, drew the same conclusion with respect to survivorship bias, which turns out to be significantly higher in the case of CTAs (5.85 percent versus 2.32 percent)

Table 2.1 illustrates the consequences of the heterogeneity of index con-struction methodologies and fund selection in terms of risk factor

expo-2 For example, CSFB/Tremont Managed Futures Index, the CISDM Trading Advisor Qualified Universe Index, the HF Net CTA/Managed Futures Average, the Barclay CTA Index, and the S&P Managed Futures Index.

sures To come up with a limited set of risk factors, we selected 16 factors known to be related to the strategies implemented by managed futures, namely stocks, bonds, interest rates, currency, and commodities factors We then used stepwise regression with the backward entry procedure to avoid any multicollinearity problems and keep a sufficient number of degrees of freedom While four factors are common to all indices (Lehman Global U.S Treasury, U.S dollar [USD] versus major currency, USD versus Japanese yen, and Goldman Sachs Commodity Index [GSCI], the corresponding exposures turn out to be very different The S&P index yields a beta of 1.49 with the Lehman Global U.S Treasury while the beta is 0.67 for the

versus major currency while the beta is 0.18 for the Barclay index Only two indices (CSFB and HF Net) appear to exhibit significant exposure to the S&P 500 and only one (HF Net) to the evolution of the VIX (implied volatility on the S&P 500)

Since the choice of index may have a significant impact on the whole investment process (from strategic allocation through performance

evalua-TABLE 2.1 The Heterogeneity of CTA Indices’ Risk Factor Exposure,

September 1999 to September 2003

Constant 4.52E−03 6.78E−03 2.93E−03 8.04E−03 4.27E−03

US TREASURY

YIELD CORP

CURRENCY

US $ TO JAPANESE −0.54 −0.55 −0.20 −0.40 −0.39 YEN

Commodity Index

tion and attribution), investors should be aware of and tackle those differ-ences in factor exposures In what follows, we present an index construc-tion methodology aimed at addressing this issue Note that this methodology was first introduced in Amenc and Martellini (2003) and is now

Given that it is impossible to be objective on what is the best existing index, a natural idea consists of using some combination of competing indices (i.e., CTA indices available on the market) to extract any common information they might share One straightforward method would involve computing an equally weighted portfolio of all competing indices Because competing indices are based on different sets of CTAs, the resulting port-folio of indices would be more exhaustive than any of the competing indices

it is extracted from We push the logic one step further and suggest using factor analysis to generate a set of hedge fund indices that are the best pos-sible one-dimensional summaries of information conveyed by competing indices for a given style, in the sense of the largest fraction of variance explained Technically speaking, this amounts to using the first component

of a Principal Component Analysis of competing indices The Edhec CTA Index is thus able to capture a very large fraction of the information con-tained in the competing indices

On one hand, the Edhec CTA Index generated as the first component

in a factor analysis has a built-in element of optimality, since there is no other linear combination of competing indices that implies a lower infor-mation loss On the other hand, since competing indices are affected differ-ently by measurement biases, searching for the linear combination of competing indices that implies a maximization of the variance explained leads implicitly to a minimization of the bias As a result, the Edhec CTA Index tends to be very stable over time and easily replicable

CTA PERFORMANCE AT A GLANCE

Table 2.2 gives a comparative overview of the Edhec CTA Index, the S&P

500, and the Lehman Global Bond Index Due to an average return that is slightly superior to the S&P 500 (0.73 percent versus 0.50 percent) and variance that is close to that of the Lehman Global Bond Index (0.84 per-cent versus 0.14 perper-cent), the Edhec CTA Index obtains a Sharpe ratio that

is significantly higher than stock and bond indices (0.72 versus 0.21 and

−0.39, respectively) Its superiority in terms of risk-adjusted performance is even more marked when considering the Sortino ratio (11.01 versus 1.05

3 Further details on the construction methodology of the Edhec Alternative Indices may be found at www.edhec-risk.com.

4 cf Favre and Galeano (2002b) for more details on the Modified VaR and its application to hedge funds.

percent for the S&P 500) The Edhec CTA Index posts positive returns in about 57 percent of months, with an average gain of 2.52 percent versus an

not-ing that the Edhec index presents a smaller maximum uninterrupted loss than both the stock and bond indices

Concerning extreme risks, the Edhec CTA Index is closer to the bond index than to the stock index with a modified value at risk (VaR) (also

TABLE 2.2 Basic Statistical Properties of the Edhec CTA Global Index,

January 1997 to September 2003

Global Index S&P 500 Bond Index

Maximum Uninterrupted Loss −5.43% −20.55% −6.75%

Monthly Std Deviation Ann’d 9.17% 17.94% 3.75%

Monthly Downside Risk (MAR = Rf*)** 0.49% 1.85% 0.12%

* *The risk-free rate is calculated as the 3-month LIBOR average over the period January 1997 to September 2003, namely 4.35 percent.

**This indicator is also referred to as the lower partial moment of order 2.

percent for the S&P 500 and −3.31 percent for the Lehman Global Bond Index This is a very interesting property as low volatility strategies often present large exposures to extreme risks due to a transfer of the risk from second- to third- and fourth-order moments Our analysis suggests that it is not the case with CTAs

To account for the presence of extreme risks in the evaluation of risk-adjusted performance, we suggest computing the Omega ratio (cf Keating and Shadwick 2002) of the CTA index:

where F(x) = cumulative distribution function,

MAR (minimum acceptable return) = gain/loss threshold,

[a,b] = interval for which the distribution of asset returns is defined.

This performance measurement indicator has appealing properties because it does not require the distribution function of the underlying asset

to be specified or any assumption to be made with respect to investors’ pref-erences It can thus account for the presence of fat tails in the case of non-normal distribution functions Figure 2.1 compares the Omega ratios obtained by the Edhec index to those of the stock and bond indices Again,

[ ( )]

MAR

F x dx

F x dx MAR

b

a MAR

=

−

∫

∫

1

Threshold %

Omega Ratio

Lehman Global Bond Index S&P 500

Edhec CTA Global Index

1.80 1.60 1.40 1.20 1.00 0.80 0.60 0.40 0.20 0.00

FIGURE 2.1 Omega Ratio as a Function of the Gain/Loss Threshold

up to an improbable loss threshold of roughly 18 percent per year, the Edhec index offers a better gain/loss ratio than both the S&P 500 and the Lehman Global Bond Index, which confirms the superiority of CTA risk-adjusted performance on a stand-alone basis

MANAGED FUTURES IN THE ASSET ALLOCATION

PROCESS: RETURN ENHANCERS, RISK REDUCERS,

OR BOTH?

On a stand-alone basis, CTAs offer better risk-adjusted performance than traditional asset classes and thus may be used as return enhancers How-ever, investors expect alternative investments in general, and CTAs in par-ticular, to be efficient in a portfolio context To assess the extent to which CTAs may be used to improve investors’ portfolio diversification, we will study the conditional correlation of the Edhec CTA Index with eight indices (S&P 500, S&P 500 Growth, S&P 500 Value, S&P Small Cap, Lehman Global Treasury/High Yield/Investment Grade/Global Bond Index) and a balanced portfolio made up of 50 percent stocks (i.e., S&P 500) and 50 per-cent bonds (i.e., Lehman Global Bond Index) We divide our sample (monthly returns from 09/99 through 09/03) into three subsamples (Low, Medium, High) The Low subsample corresponds to the most bearish months of the filtering index, and the High subsample to its most bullish months We then computed the correlation of the Edhec CTA Index with the other indices for each of the three subsamples As can be seen from Table 2.3, the Edhec CTA Index is systematically higher in the High sub-sample than in the Low subsub-sample with both the stock and bond indices The only exception is the correlation with the S&P Growth 500, which is slightly lower in market declines A first striking feature is the propensity of the correlation with the Lehman Global Bond Index to remain stable through all market conditions It is also worth noting that the Edhec CTA Index is systematically negatively correlated with stock indices during large down market trends On top of that, as shown in the Table, correlations with stock and bond indices tend to be either “Good” or “Stable.” No sin-gle correlation is significantly lower in the Low subsample than in the High subsample This leads the CTA index to exhibit put option-like payoffs with respect to equity oriented indices (i.e., negative correlation during market declines, resulting in high positive returns, and low negative correlation during increasing markets, resulting in slightly negative returns) and strad-dlelike behavior with respect to most bond-oriented indices In other words, CTAs may play the role of portfolio insurers This interesting profile cou-pled with relatively low volatility suggests that CTAs are not only return enhancers but also risk reducers

If CTAs offer good diversification potential while posting attractive risk-adjusted performance, this should be reflected with a translation of efficient frontiers to the top-left corner of the graph in Figure 2.2 Note that

to take extreme risks into account, we defined the risk dimension as the modified VaR with 99 percent confidence level Comparing the efficient

repre-sented by dashed lines in Figure 2.2, it is clear that CTAs can both reduce the risk and enhance the performance of the balanced portfolio This fact should encourage investors to reconsider their strategic allocation to CTAs However, to tap the diversification potential of CTAs in an optimal manner, investors need to have a better understanding of the extent to which CTAs differ from traditional asset classes Such an understanding naturally implies better knowledge of the risk factors that drive their performance

TABLE 2.3 Edhec CTA Global Index Conditional Correlations with Stock

and Bond Indices, 1999 to 2003

Correlation with Edhec CTA Global Index

S&P 500 Value −49.55% 6.56% −11.77% Good (0.96) S&P Small Cap −46.37% 13.03% 12.29% Good (1.26) Lehman High −62.96% 29.75% −17.31% Good ( −0.19) Yield Index

Balanced Portfolio −45.04% 18.04% 11.90% Good (1.00) (50% Stocks +

50% Bonds)

S&P 500 Growth −28.47% 6.61% −29.54% Stable (1.95)* Lehman Global 23.59% 20.52% 25.60% Stable ( −3.50)* Bond Index

Lehman Global 26.31% −7.71% 36.30% Stable ( −4.40)* Treasury Index

Lehman Investment 18.79% −41.99% 39.83% Stable ( −3.93)* Grade Index

When the correlation differential between high and low subsamples is greater (lower) than 25 percent ( −25 percent), the correlation of the Edhec index with the benchmark is regarded as a good (bad) correlation When the correlation differen-tial is between −25 percent and 25 percent, the correlation is regarded as Stable.

*Denotes significance at 5 percent level.

OVERVIEW OF KEY PERFORMANCE DRIVERS OF CTAS

CTAs offer very attractive properties on a stand-alone basis as well as in a portfolio To best allocate them, however, investors need to know which risk factors drive their performance To do so, one may want to carry out a factor analysis with dozens of risk factors on a randomly selected CTA

robustness of the results would certainly be low Because the different CTA indices rely on different databases and are constructed according to diverse methodologies, it is highly probable that their returns are driven by differ-ent risk factor exposures (see Table 2.1) To circumvdiffer-ent the data snooping issue, we focused on the same 16 factors selected for the factor analysis pre-sented in Table 2.1 We then applied stepwise regression with the backward entry procedure To circumvent the index heterogeneity issue, we ran the analysis on the Edhec CTA Index The advantage is twofold: First, the index

is, by construction, more representative of the investment universe Second,

it is less prone to measurement biases such as survivorship, backfilling, or stale price bias This second point is crucial because, as evidenced in Asness, Krail, and Liew (2001) and Okunev and White (2002), biases, and especially stale prices, may entail a significant downward bias with respect to risk fac-tor exposure measurement We should thus be able to identify purer risk factor exposures with the Edhec CTA Index

As can be seen from Table 2.4, the Edhec CTA Index is exposed to five main factors: one stock market factor (S&P 500), one bond market factor

0.00%

1.00%

2.00%

3.00%

4.00%

5.00%

6.00%

7.00%

8.00%

9.00%

10.00%

0.00% 10.00% 20.00% 30.00% 40.00% 50.00% 60.00%

Modified VaR

Balanced Portfolio + Edhec CTA Global S&P 500 +

Edhec CTA Global

Lehman Global Bond+ Edhec CTA Global

S&P 500 + LGBI

FIGURE 2.2 Efficient Frontiers, January 1997 to September 2003

(Lehman Global Treasury), two currency factors (USD vs major currency and USD vs Japanese yen) and one commodity factor (Goldman Sachs Commodity Index [GSCI]) The most important factor turns out to be the GSCI, which stresses the still-prevalent exposure of CTAs to the commod-ity market CTAs also appear to be strongly exposed to interest rates, with

a long position on the Lehman U.S Treasury Index The other statistically significant factors are ones related to the foreign exchange market, with coefficients indicating that CTAs held long net positions on the USD over the analysis period (especially against the Japanese yen) Not surprisingly, the index return is negatively correlated with the S&P 500 return, which is consistent with the fact that CTAs post their best performance in large mar-ket declines

To validate the influence of the aforementioned risk factors, we study the average performance of the Edhec CTA Index conditioned on the per-formance level of the risk factors We again divide our sample into three sub-samples corresponding to the most bearish (Low), stable (Medium), and most bullish (High) months for the five factors selected The results are summarized in Table 2.5 The T-stats in the last column correspond to tests

of the differences between Low/Med, Med/High, and Low/High subsample averages, respectively Statistically significant differences at the 5 percent level are followed by an asterisk Interestingly, the difference in mean returns

is significant four out of five times between Low and Medium subsamples

In the same vein, it is worth noting that the average return obtained by the Edhec CTA Index in the Low subsample is particularly high in three out of four cases This is especially true when considering the equity risk factor (i.e., S&P 500), which confirms the fact that CTAs are akin to portfolio insurance (i.e., long position on a put option on the S&P 500) Also, it is worth

not-TABLE 2.4 Edhec CTA Index Risk Factors Exposure, September 1999

to September 2003