Commodity Trading Advisors: Risk, Performance Analysis, and Selection Chapter 21 pdf

Joe Moffitt using ARMA models to the case of CTAs.. We show that for the period 1996 to 2003, the return series of the largest CTAs are stationary and that ARMA models in certain cases

ARMA Modeling

of CTA Returns

Vassilios N Karavas and L Joe Moffitt

using ARMA models to the case of CTAs We show that for the period

1996 to 2003, the return series of the largest CTAs are stationary and that ARMA models in certain cases provide adequate representation of the return series Comparing to the hedge fund case, we see that a higher order

of ARMA model usually is required We also test for structural changes in the return processes, and we fit similar models for the period 2000 to 2003 Results appear to be no drastically different from those reported in previ-ous studies for hedge funds

INTRODUCTION

The period 1996 to 2003 offered a number of surprises to investors, with the excellent performance of the equity market during the first four years of the period and the subsequent drawdown for three consecutive years until

2003, when the long-expected economic recovery finally appeared Com-modity trading advisors (CTAs) did not suffer many years of losses, and definitely not at the magnitude of the equity markets’ losses The CTA indices showed that all years (included in this study) were profitable for the CTAs with the exception of 1999, when small losses were reported CTAs offered investors a safe harbor for the years during which control was lost

in the equity markets In the next section we show pieces of historical evi-dence that CTAs were more stable over time, from a performance point of view, not only when compared to equity markets but also when compared

to hedge funds

Over the past few years, a large number of hedge fund managers were dragged toward an increased equity exposure, which in several cases

Nasdaq Annual Return CSFB MF Annual Return CSFB Composite CSFB CA CSFB Short Bias CSFB Em.M CSFB EMN CSFB ED

–100%

–80%

–60%

–40%

–20%

20%

40%

60%

80%

100%

appeared to be rather catalytic for their existence, as the expected economic recovery, after the tech boom, did not arrive until 2003 In Figures 21.1 to 21.3, it is obvious that CTAs (as proxied by Credit Suisse First Boston Man-aged Futures Index [CSFB MF]) have strongly resisted the downward trend

in equity markets At the same time they have offered positive returns except in 1999, when they suffered mild losses Figure 21.1 shows the annual correlation of each of the hedge fund strategies and CTAs relative to S&P 500 It also shows how the changes in the correlation with the S&P

1996 1997 1998 1999 2000 2001 2002 2003

S&P 500 Annual Return CSFB MF Annual Return CSFB Composite CSFB CA CSFB Short Bias CSFB Em.M CSFB EMN CSFB ED CSFB DS CSFB ED Multi CSFB MA CSFB FIA

–100%

–80%

–60%

–40%

–20%

0%

20%

40%

60%

80%

100%

have affected the annual returns of the CSFB MF Figures 21.2 and 21.3 show the corresponding results for Nasdaq and Lehman Aggregate Bond Index respectively

These historical performance comparative results indicate that CTAs are an investment vehicle worth exploring and can offer unique risk/return characteristics in a stock/bond portfolio as well as in a stock/bond hedge funds portfolio A number of studies have explored the benefits of managed futures (CISDM 2002), so we limit the analysis of managed futures to showing the importance of modeling their return series

In the next section we examine whether CTAs generate stationary return time series, and we attempt to fit auto-regressive moving average (ARMA) models

METHODOLOGY

We test for second-order (weak) stationarity in our return time series

In other words, we test whether its first and second moments and its auto-correlations are invariant in time For comparison purposes, we carry out all the tests that appeared in Gregoriou and Rouah (2003a) for hedge funds, among others However, we examine a more complete set of CTAs that sat-isfy certain track record and assets under management requirements, as we have included all the CTAs that report their performance in the database from the Center for International Securities and Derivatives Markets (CISDM) We also extend the analysis to the manager’s excess returns as a proxy for deter-mining stationarity of manager’s alpha We use the Augmented Dickey-Fuller

{ } =

∞ 1

–100%

–80%

–60%

–40%

–20%

0%

20%

40%

60%

80%

100%

Lehman Agg Annual Return CSFB MF Annual Return CSFB Composite CSFB CA

Aggregate

(ADF) test to test for the presence of a unit root in the series In our exam-ples, intercept and time trend have been taken into account

(21.1)

After we test for stationarity, we model the return series using

ARMA(p,q) processes of different orders using correlograms for each series

as a guide Finally we perform stability tests using the Chow test to investi-gate possible structural changes in the parameters of the specified ARMA processes

DATA

For this study we have chosen the 10 largest CTAs from the CISDM data-base that have complete data series (monthly) for the period from January

1996 to December 2003 Their average assets under management were over

$100 million during the fourth quarter of 2003 For comparison purposes,

we required that the return series are complete, and we wanted to examine CTAs with relatively long historical track records and that are of significant size (based on the most recent information available) The effects of length

of track record as well as fund size have been extensively examined by Schneeweis, Kazemi, and Karavas (2003a, b) for hedge funds Although similar analysis for CTAs, to the best of our knowledge, is not available, we anticipate that the benefits of larger hedge funds with long track records apply to CTAs, too Briefly, a long track record provides evidence of man-ager performance under different market conditions, while high assets under management indicate that the strategy followed can be replicable at larger scale The latter is important especially for CTAs because of the impact on prices due to trade of high volumes of specific futures; managers with low assets under management impact the prices to a lesser extent For the calculation of the excess returns used in the tests, we calculated the excess CTA monthly return from the CISDM Equally Weighted Trading Advisor Qualified Universe Index (CISDM CTA) The CISDM CTA Index

is the median return of all CTAs and commodity pool operators (CPOs) reporting to the CISDM CTA database At the end of 2003, there existed approximately 600 CTAs and CPOs each having approximately an equal share in the database

The CTA returns, as well the returns of the CSFB/Tremont and CISDM indices, used in this analysis have not been adjusted to eliminate biases

i

N

=

∑

1

ent in them A description of potential biases in the indices, some of which apply to the databases as well, can be found in Karavas and Siokos (2004) The following tables provide descriptive statistics for the data set used

in the simulations as well as for the corresponding excess returns As we see

in Table 21.1, CTAs offer a wide range of performance characteristics It is noteworthy to see that the risk-adjusted return as proxied by the informa-tion ratio varies significantly relative to the informainforma-tion ratio of the CISDM CTA index This means that across the 10 largest CTAs in existence for at least eight years, the majority of them offer returns that are not justified for the amount of risk they undertake (see Table 21.2) Information ratios in bold denote values below the information ratio of the CISDM CTA index

RESULTS

The ADF tests showed that for all CTAs included in this study, the error terms were white noise; thus all series were stationary With the exception of one CTA (#3), we could reject the null hypothesis of unit root for all CTAs at 99 percent confidence level (#3: at 90 percent) All the ADF tests were run for four lags; the results are shown in Table 21.3 Similar tests were performed

on CTAs’ excess returns and are shown in Table 21.4 The results using CTA returns were consistent with those in Gregoriou and Rouah (2003a) for hedge funds Those authors did not examine excess returns, however, this study shows that the added alpha relative to the strategy (as proxied by the CISDM CTA index) for the 10 largest funds is indeed stationary

Using the correlograms, we determined that in several cases the auto-correlations did not fade after the first lag, so more lags needed to be included in the models As we see in Table 21.3, the CTA returns studied carry the effect of previous months return levels The table shows the dif-ferent orders of ARMA models that have been utilized to better represent the corresponding return series In certain cases (CTA: 2, 5, 10) the

repre-sentation is adequate, evidenced by relatively high R2values and significant

coefficients For CTA #9, although there is a relatively high R2, the MA process is noninvertible For CTA #3, although we have not rejected the existence of unit root at 95 percent, we have used an ARMA (2,2) model

with a low R2 We note that CTAs #2 and #3 are the only ones that are low negatively correlated with the CTA Index

Table 21.4 presents similar results to Table 21.3 using excess returns The benefit of studying CTAs’ excess returns is it allows us to see whether and how individual CTAs outperform the strategy to which they belong It

is rather useful when managers of specific strategies are evaluated for

inclu-TABLE 21.1

bin

a CT

b Assets under management.

372

sion in portfolios of CTAs (CPOs) or in portfolio of mixed strategies and the objective is to maximize alpha

Table 21.2 shows that CTA #2 has underperformed the CISDM CTA Index, but Table 21.4 shows its series (excess returns) appears to be sta-tionary Excess returns of CTA #9 and #10 are adequately represented by

the ARMA models shown in Table 21.4, as evidenced by high R2and sig-nificant coefficients Both CTAs have outperformed the CISDM CTA Index, but they were the most volatile of the 10 CTAs and the index

We then performed a stability test on the ARMA model parameters to investigate possible structural changes For this purpose we utilized the Chow test before and after January 2000 The justification for this break-point is that 1999 was a very profitable year for the equity indices; CTAs did not perform as well afterward

Chow test statistics appear in Table 21.3 The F-statistics for three

CTAs are relatively high, indicating structural changes For CTA #9, we did not test for structural changes as the MA process was noninvertible, and the model did not fit better even for the period 2000 to 2003

For the three CTAs with relatively high F-statistics, we fitted the

corre-sponding ARMA models for the period 2000 to 2003 As shown in Table 21.5,

TABLE 21.2 Statistics for the Excess Returns of the 10 Largest CTAs, January

1996 to December 2003

Months Months with with

374

TABLE 21.4

375

there is a significant improvement for CTA #3 and #8 (evidenced by the

increased R2) For CTA #4, ARMA (1,1) (results not shown) appear to bet-ter model the return series during 2000 to 2003 than the ARMA (2,1) model utilized for 1996 to 2003 and 2000 to 2003

CONCLUSION

In this study, we investigated the return series behavior of the 10 largest CTAs in the CISDM database and utilized a number of ARMA models Results showed that the series are in general stationary (using ADF tests),

as are the excess returns of the same CTAs relative to the CISDM CTA Index ARMA models for the largest CTAs tended to be of higher orders than those in the case of hedge funds (Gregoriou and Rouah 2003b) In spite of the significant parameters in most cases, very few of these CTA

models were accompanied by substantial R2 Unfortunately, this implies that the models have little forecasting power A few indicated possible struc-tural changes, evidenced by Chow tests For two CTAs the same models offered a better representation for the period after the breakpoint (January 2000), while for the third CTA a different ARMA model appears to offer better results

CTA3 0.0123 −0.8042 −0.6546 0.9994 0.9800

0.16

CTA3: p-value 0.0895 0.0000 0.0000 0.0000 0.0000

0.04

CTA4: p-value 0.0288 0.0126 0.5748 0.0000

CTA8 0.0120 −0.7018 −0.1482 0.9529

0.09

CTA8: p-value 0.0831 0.0000 0.3521 0.0000