CTA performance persistence: 1994-2010.

Molyboga, Marat ; Baek, Seungho ; Bilson, John F.O. 等

In the wake of financial disasters, such as the Asian Financial crisis of 1997 and the global financial crisis of 2008, the benefits of investing in commodity trading advisors (CTAs) during turbulent times as strong diversifiers of traditional portfolios of stocks and bonds, as well as hedge funds, have been clearly highlighted. The difficult task of quantitative CTA selection is complicated, however, by low persistence in returns as well as by biases in the data that might invalidate empirical research findings that do not appropriately account for such bias.

Interest in studies of CTA performance has increased since the late 1980s. From the analysis of CTA and hedge fund performance, Schneeweis et al. [1991], Schneeweis [1996], Billingsley and Chance [1996], and Edwards and Park [1996] show that managed futures add more value to traditional portfolios of stocks and bonds than hedge funds do. Considering market events, Schneeweis and Georgiev [2002] identify that CTAs add value to traditional portfolios, especially during bear markets, whereas Georgiev [2001] reports that CTA performance during bull markets is typically inferior to that of hedge funds. Fung and Hsieh [2002] show that CTA impact on a traditional portfolio is similar to that of a lookback call and lookback put. Edwards and Caglayan [2001] find that CTAs generate higher returns than hedge funds during bear markets, along with negative correlation to stocks, providing better downside protection.

Schneeweis et al. [1996] examine survivorship bias in CTA returns. Schneeweis and Spurgin [1999] further analyze the performance of dissolved CTAs and conclude that dissolved CTAs begin underperforming 18 to 24 months before dissolution. Diz 119991 concludes that ignoring survival issues in the selection of managed futures programs results in significant .reduction of performance in the range of 4.2% to 4.7% per year. Capocci [2004] reports that dissolution frequencies can reach 60%. Gregoriou et al. [2005] discover that CTA survivorship is highly contingent on the fund strategy and that low assets under management (AUM), poor returns, and high risk exposure hasten CTA mortality.

A number of researchers have used various approaches to evaluate persistence in CTA returns and report mixed results. Schwager [1996] finds little evidence of predictability for top-performing funds when funds are ranked by return/risk. McCarthy et al. [1997] report that there is persistence in performance if CTA returns are adjusted for market risk. Brorsen and Townsend [2002] suggest that performance persistence is still weak relative to the noise in the data, although persistence is stronger if return/risk measures of performance and long time series of data are used. Capocci [2004] detects significant persistence in badly performing CTAs and weak persistence in well-performing CTAs by adopting Carhart's decile methodology (Carhart [1997]).

Although the aforementioned research finds low persistence in returns, particularly among top funds, and a number of studies estimate the magnitude .of backfill bias, little work has been done on investigating the impact of issues in the CTA data on detected performance persistence. This study explicitly considers the potential impact of the incubation and backfill biases on detected persistence in returns by first performing persistence tests without accounting for the incubation and backfill biases and then repeating the analysis after excluding the first 12 and 24 months of data for each fund.

We find that the incubation and backfill biases have little impact on the average relationship between previous rankings and future unleveraged returns and on persistence of the worst-performing funds. The detected strong persistence of the best-performing funds, however, is primarily driven by the incubation and backfill biases.

We recognize that previous studies examined CTA returns without explicitly accounting for leverage in returns. They applied various approaches, including variations of the Sharpe ratio and return, to test for persistence in returns. In contrast, we suggest a simple explicit approach to "un-leverage" CTA returns.

Our first CTA performance persistence test uses Fama--MacBeth (FM) regression (see iFama and Macbeth [1973]), which is known as a good measurement to estimate longitudinal time series data, also called panel data. As Goyal [2012] points out, there are several significant advantages of FM regression when using panel data. First, the approach is flexible enough to allow for time-varying betas. 'Second, it can handle unbalanced data, which is particularly useful in our study because the number of CTAs varies substantially over time.

FM regression has been used in analyzing CTA performance. Sapp and Tiwari [2006] use FM regression to study the "smart money effect" in CTAs. They find some evidence of a smart money effect and report that investors tend to invest in funds with recent outperformance rather than in funds with high loadings to momentum style. Do et al. [2011] find that top-performing CTAs are rewarded with high fund inflows, thus indicating performance-chasing rather than a smart money .effect. Likewise, they use FM regression to investigate the relationship between previous funds' performance and new investment inflows.

Although FM regression has been used to investigate CTA performance, we specifically use it to detect persistence in performance. We find that ranking funds using the t-statistics of alpha with respect to a CTA benchmark is predictive of future unleveraged returns. (1) In addition, we use the quintile methodology to test the performance persistence hypothesis for the top and bottom funds, as well as the predictability of attrition rates.

After we have introduced the research background and the purpose of this research, the second section discusses the CTA data and data-cleaning procedures. The third section describes the methodology, including the FM regression and quintile methodology. The fourth section presents our empirical test results. The last section provides the conclusion and summary of the research findings and suggests future research directions.

DATA DESCRIPTION

There are six commonly used CTA databases: Barclay Trading Group, the Center for International Securities and Derivatives Markets (CISDM, formerly the MAR database), Lipper's Trading Advisor Selection System (TASS), International Traders Research (ITR), Stark, and Autumn Gold. The CISDM database was one of the first databases that began tracking CTA data in 1979. It currently includes data for more than 500 active CTAs. ITR has been providing CTA data since 1996; it -currently includes more than 500 active programs and. approximately 90.0 defunct funds. Autumn Gold currently includes 428 active programs. The Stark CTA database contains around 500 CTA programs. The TASS database reports data for 628 active CTAs and 1,842 defunct funds. Barclay Trading Group has the largest list of active and defunct traders. The current study uses the Barclay database containing 3,912 funds, including 1,126 active CTAs and 2,786 defunct funds, for the most accurate and representative results.

To obtain reliable results on CTA performance persistence, we examine the database for data errors and biases. First, we exclude all data prior to 1994, when the number of available CTAs was too small for drawing statistically significant conclusions. Then we eliminate all multi-advisors and benchmarks, because the scope of this study is limited to individual funds. We take out all funds that reported only gross returns, to preserve comparability. We remove all funds with AUM below US$1 million, because they would be too small for institutional investors., and their returns tend to contain the most noise. Furthermore, we eliminate all funds with abnormal monthly returns in excess of 100% and remove zero returns at the end of defunct fund return streams.

We make additional data corrections for attrition. rate research. Managers voluntarily report to a database because they are actively marketing their funds and looking to attract new investors. Consequently. CTAs tend to stop reporting when they are not looking to attract new investors. Appendix A describes our approach to classifying the defunct funds into three categories: "liquidated funds," "closed funds," and "unknown."

Only traders from the first category should be considered defunct in the attrition rate research. Because the second and third categories contain successful traders, including them in the dissolution analysis as defunct funds artificially 'increases the attrition rate of the well-performing funds. Capocci 120041 defines dissolved CTAs as all funds that stop reporting and, therefore, considers traders from all three categories as defunct CTAs. Consequently, he reported that the 10th decile funds (containing top CTAs) have a higher dissolution probability than CTAs from the 6th, 7th, 8th, and 9th deciles. To identify traders from the second and third categories, we examine each CTA's returns, AUM, and fund status. Appendix A contains the full description of the classification procedure. The filtered dataset contains 2,595 funds, including 835 active CTAs and 1,760 defunct funds (1,41.7 liquidated, 134 closed, and 209 with unknown status).

It is well known that CTA databases contain incubation and backfill biases resulting from the voluntary nature of self-reporting. To mitigate these biases, we perform our analysis excluding the first 12 months of the data for each fund, as suggested in Kosowski et al. [2007]. To investigate potential impact of the incubation and backfill biases on the detected persistence, we repeat the analysis after excluding the first 24 months of the data and then once again without excluding any data. Inclusion of defunct funds mitigates the survivorship bias.

We use three CTA benchmarks commonly used in the literature: TASS, Barclay, and CISDM. Exhibit 1. contains information about these benchmarks' performance during the 1994-2010 period.

EXHIBIT 1

Performance of the TASS, Barclay, and CISDM CTA Indexes,
1994-2010

 TASS Barclay CISDM

Annualized Return (in %) 3.77 2.86 5.56

Annualized Std Dcv (in %) 9.66 7.61 8.66

Sharpe ratio 0.39 0.38 0.64

Note: This exhibit displays annualized excess returns, annualized
standard deviation of excess returns, and the Sharpe ratio calculated
for each benchmark over the 1994-2010 period.

Schn.eeweis and Spurgin [1996], Schneeweis et al. [2007] reported results of comparative analysis of various CTA benchmarks along with their descriptions. We repeat our analysis for each benchmark to ensure robustness of the results to the choice of a benchmark. The three-month T-bill rate is used For calculating excess returns.

METHODOLOGY

This study uses two methodologies: FM regression and quintile analysis. Both techniques use rolling CTA rankings based on the t-statistics of alpha. To calculate it at time t, we run regression of the last k net-of-fee excess returns of a CTA [r.sub.[tau].sup.i] on the corresponding excess returns of a CTA benchmark, [I.sub.[tau]]:

[r.sub.[tau].sup.i] = [[alpha].sub.t.sup.i](k) + [[beta].sub.[tau].sup.i](k)[I.sub.[tau]] + [[epsilon].sub.[tau].sup.i] (1)

Then we estimate the standard error of alpha, [sigma][[alpha].sub.t.sup.i], and define standard t-statistics of alpha as [T.sub.l.sup.i](k) = [a.sub.l.sup.i](k) /[sigma]([T.sub.l.sup.i](k) )

FM Regression

Fama and MacBeth [1973] suggested FM regression, which is recognized as a standard methodology used in asset pricing. This study uses FM regression because of its superior benefits when working with panel data. At each point in time t, the t-statistics of alpha, [T.sub.l.sup.i](k) is calculated for each fund that has complete data during that period and meets minimum AUM requirements. Then future unleveraged returns over the next 1 months (as defined in Appendix B), [R.sub.t+l.sup.i](k), are regressed against the corresponding values of the t-statistics of alpha:

[R.sub.t+l.sup.i](k) = [[delta].sub.t] + [[beta].sub.t.][T.sub.t.sup.i](k) + [[epsilon].sub.t.sup.i] (2)

Values of [[delta].sub.t.] and [[beta].sub.t.] are recorded. Then the data window is shifted by l months and the estimation procedure is repeated. Finally, the slope coefficient [^.[beta]] is estimated as the average of all slope coefficients

[^.[beta]] = 1/S [s.summation over (m=1)][[beta].sub.m] (3)

along with the corresponding standard error s([beta]) and its t-statistics:

t([^.[beta]] )=[^.[beta]] /s([beta])/[square root of (s)] (4)

The value of [^.[beta]] represents the average impact of the past t-statistics of alpha of a fund on its future unleveraged returns. The corresponding t-statistic t([beta]) shows the statistical significance of that relationship.

Although FM regression indicates the average relationship between past rankings of funds with their future unleveraged returns, that relationship can be potentially driven by a relatively small group of funds. Therefore, we complement our study with quintile analysis that explicitly focuses on persistence of funds within quintiles.

Quintile Analysis

Although in this study we calculate FM regression for a wide range of parameters k and. 1 for all three CTA benchmarks, the scope of our quintile analysis is limited to using the Barclay CTA Index for ranking funds and applying one set of parameters .commonly used in the industry. The window length k, used for ranking funds, is equal to 24 months, and the frequency of rebalancing l is equal to 12 months.

The quintile analysis is performed similarly to the octile methodology of Hendricks et al. [1993] and the decile methodology of Carhart [1997]. On December of each year, the t-statistic of alpha [T.sub.t.sup.i](k) is calculated for each fund that has complete data during the most recent 24 months and meets minimum AUM requirements. Quintiles are formed based on the ranking, and their equally weighted unleveraged portfolios are built and tracked for the next 12 months. At that point, the process of re-ranking funds, forming portfolios, and tracking their performance is repeated. If a fund stops reporting during that period, its allocation is assumed to be reinvested in the risk-free asset with zero excess return until the end of the year. Performance of each portfolio and transition probabilities are recorded.

Because database reporting is voluntary, most likely a liquidated fund does not record its last losing month, thus introducing liquidation bias. Therefore, the above .assumption of reinvestment in the risk-free asset results in the upward bias in portfolio performance for each quintile. The difference of returns between the top and bottom quintiles, however, would be understated if the bottom portfolio contains more liquidated funds than the top portfolio.

EMPIRICAL RESULTS

Test Results of FM Regression

The results of the FM regression methodology are robust to the choice of the benchmark. Exhibit 2 presents values of the slope coefficients and their t-statistics as defined in Equations (3) and (4), calculated using our standard parameter set with the window length K, used for ranking funds, equal to 24 months and the frequency of rebalancing l equal to 12 months.

EXHIBIT 2

Betas for FM Regression with k=24, l=12

 TASS Barclay CISDM

Beta (in %) 1.27 1.28 1.17
 (3.23) (3.39) (3.17)

Notes: This exhibit presents values of betas calcuated in the FM
regression using the TASS, Barclay, and CISDM CTA indexes for CTA
ranking. The t-statistics are in parentheses.

To get a sense of the economic significance of the result, let us consider two hypothetical funds with the t-statistics of alpha, calculated with respect to the TASS CTA Index over the most recent 24 months, equal to +2 and -2. The difference in their next year's expected unleveraged returns would be equal to 5.08% = [2 -(-2)] x 1.27%, which is economically significant given the expected future volatility of 15%.

We repeat analysis for the range of the ranking window k between. 12 and 60 months as well as the range of the rebalancing frequency l between 1 and 12 months. Our results are summarized in Exhibit 3 for the case of the Barclay CTA Index used as the benchmark for calculation of the t-statistics of alpha.

Exhibit 3 shows that the relationship between the past values of the t-statistics of alpha and future values of unleveraged returns is robust across a wide range of parameters of the ranking window and the rebalancing frequency. When ranking is performed using the TASS and CISDM CTA indexes, results are very similar.

EXHIBIT 3

Values of Betas for FM Regression Using Barclay CTA Index
for CTA Ranking

 Rebalancing
 Frequency (months)

Ranking Window (months) 1 3 6 12

12 1.52 1.40 1.31 1.32

 (4.53) (3.96) (5.23) (4.03)

18 1.76 1.56 1.46 1.20

 (5.99) (5.56) (5.46) (4.89)

24 1.40 1.20 1.22 1.27

 (4.66) (4.02) (3.48) (3.23)

30 1.35 1.05 1.12 1.09

 (4.19) (3.40) (3.34) (3.58)

36 1.17 1.03 1.04 1.04

 (3.49) (3.23) (2.84) (2.77)

42 1.02 0.88 0.88 0.83

 (3.02) (2.69) (2.40) (2.03)

48 0.94 0.73 0.90 0.88

 (2.73) (2.16) (2.27) (2.40)

54 0.95 0.75 0.83 0.86

 (2.77) (2.30) (1.92) (1.96)

60 0.83 0.64 0.71 0.73

 (2.33) (1.69) (1.27) (1.48)

Notes: This exhibit presents values of betas calcuated in the FM
regression using the TASS, Barclay, and CISDM CTA indexes
for CTA ranking. The t-statistics are in parentheses.

To investigate the potential impact of the incubation and backfill biases on the persistence result, we repeat our analysis by excluding the first 24 months of the data and then once again without excluding any data. Although the results seem slightly weaker when the first 24 months of data are excluded and slightly stronger when no data are excluded, the overall impact of the incubation and backfill biases on persistence results as measured by the FM slope coefficients and their corresponding t-statistics is insignificant.

Our empirical results confirm that performance is persistent on average for a wide range of parameters, with negligible impact of the backfill and incubation biases or the choice of a benchmark. We further investigate whether that relationship is driven by the top-performing funds, worst-performing funds, or average performers by applying quintile methodology.

Test Results of Quintile Analysis

Each December, all funds that have at least 24 months of data and at least US$ 1 million in AUM are ranked using the t-statistics of alpha with respect to the Barclay CTA index. Exhibit 4 displays the values of the t-statistics of alpha that serve as the breakpoints of the quintiles. On average, funds have positive alphas, which can be explained by the choice of the Barclay CTA Index composition.

[ILLUSTRATION OMITTED]

Exhibit 5 presents the number of funds in each quintile. The number of funds in each quintile is sufficiently large and more than doubled during the period covered in the study.

EXHIBIT 5

Number of Funds in Each Quintile

 Quintile Porfolios

Year I II III IV V

1997 52 54 53 53 53

1998 54 55 54 55 54

1999 59 58 59 58 59

2000 58 59 58 59 58

2001 57 57 57 57 57

2002 63 62 63 62 63

2003 67 68 67 68 67

2004 72 72 71 72 72

2005 80 81 80 81 80

2006 86 85 86 85 86

2007 90 89 90 89 90

2008 99 98 99 98 99

2009 108 107 108 107 108

2010 115 116 115 116 115

Notes: Each december, all funds that have at least 24 months of
data and at least US$1 million in assets under management are ranked
using the t-statistics of alpha with respect to the Barclay CTA index.
This exhibit displays the number of funds in each quintile by year.

Exhibit 6 shows the performance of equally weighted portfolios. We find very strong evidence that funds from the top quintile outperform funds from the bottom quintile, as represented by the difference of annualized return of 4.61% with the corresponding t-statistic of 3.61. The spreads between the top performers and the next two quintiles (1-II) and (I-III), as well as the spread between the bottom two quintiles (IV-V), also seem marginally significant as represented by the t-statistics.

EXHIBIT 6

Performance of Equally Weighted Quintile Portfolios of Funds
(12 months excluded)

 Annualized Excess Annualized
Portfolio Return (%) Std Dev (%) Sharpe
I (high) 6.44 5.99 1.08
II 4.02 6.42 0.63
III 4.62 6.80 0.68
IV 3.64 6.95 0.52
V (low) 1.84 5.61 0.33
I-V spread 4.61 4.75 0.97
 (3.63)
IV-V spread 1.80 3.46 0.52
 (1.94)
I-II spread 2.42 3.20 0.76
 (2.83)
I-III spread 1.82 3.88 0.47
 (1.75)

Notes: Each December, all funds that have at least 24 months
of data and at least US$1 million in assets under managemetn are
ranked suing the t-statistics of alpha with respect to the
Barday CTA index. Equally weighted unleveraged portfolios are formed
for each quintile and rebalanced annually. The t-statistics are in
parentheses.

To investigate the potential impact of the incubation and backfill biases on relative performance of quintile portfolios, we repeat our analysis by excluding the first 24 months of the data and then once again without excluding any data.

Exhibit 7 displays the performance of quintile portfolios when the first 24 months of data were excluded. The spread in performance between the top quintile and the other quintiles declines. The (-statistics of the spread between the first and the third quintiles (I-III) declines from 1.75 to 0.93, making outperformance statistically insignificant. On the contrary, the spread between the bottom two quintiles (IV-V) widens, with the corresponding t-statistic increasing from 1.94 to 2.45.

EXHIBIT 7

Performance of Equally Weighted Quintile Portfolios of Funds (24
months excluded)

 Annualized Excess Annualized
Portfolio Return (%) Std Dev (%) Sharpe
I (high) 5.87 6.21 0.95
II 3.87 6.93 0.56
III 4.80 7.25 0.66
IV 4.14 7.09 0.58
V (low) 1.56 5.84 0.27
l-V spread 4.31 4.88 0.88
 (3.19)
IV-V spread 2.58 3.80 0.68
 (2.45)
I-II spread 2.00 3.22 0.62
 (2.24)
I-III spread 1.07 4.16 0.26
 (0.93)

Notes: To account for incubation and backfill biases, the first
24 months of performance were excluded for each fund. Each
december, all funds that have at least 24 months of data and at
least US$1 million in assets under management are ranked using
the t-statistics of alpha with respect to the Barclay CTA index.
Equally weighted unleveraged portfolios are formed for each
quintile and rebalanced annually. The t-statistics are in
parentheses.

Exhibit 8 displays the performance of quintile portfolios when there is no exclusion of data to account for the incubation and backfill biases. The spread in performance between the top quintile and the other quintiles increases substantially. The t-statistic of the spread between the first and the third quintiles (I-III) increases from values reported in Exhibits 7 and 8, to 2.48, making outperformance statistically significant. On the contrary, the spread between the bottom two quintiles (IV--V) declines, with the corresponding t-statistic decreasing from 1.94 to 1.65.

EXHIBIT 8

Performance of Equally Weighted Quintile Portfolios of Funds
without Accounting for Incubation and Backfill Biases

 Annualized Excess Annualized
Portfolio Return (%) Std Dev (%) Sharpe
I (high) 7.05 5.88 1.20
II 4.07 6.23 0.65
III 4.56 6.39 0.71
IV 3.45 6.69 0.52
V (low) 2.10 5.60 0.37
I-V spread 4.96 4.61 1.07
 (4.02)
IV-V spread 1.35 3.07 0.44
 (1.65)
I-II spread 2.98 3.05 0.98
 (3.66)
I-IIIspread 2.49 3.75 0.66
 (2.48)

Notes: Each December, all funds that have at least 24 months
of data and at least US$1 million in assets under management
are ranked using the t-statistics of alpha with respect to
the Barclay CTA index. Equally weighted unleveraged portfolios
are formed for each quintile and rebalanced annually. The
t-statistics are in parentheses.

From the results, we can observe very obvious patterns. Not properly adjusting for the incubation and backfill biases could significantly overstate relative performance of the funds from the top quintile and understate relative underperformance of the worst performers. The spreads between the top performers and the bottom performers, however, as well as the spreads between the fourth and fifth quintiles, are consistently significant in all three cases. Our results are consistent with those reported previously, suggesting strong persistence of the worst-performing funds and weak persistence of the top performers.

We further examine transition probabilities. Exhibit 9 displays estimated transition probabilities.

EXHIBIT 9

Estimated Transition Probabilities

 I II III IV V

I 24.27% 17.56% 19.55% 17.00% 14.35%

II 18.19% 17.81% 19.04% 17.91% 18.38%

III 17.09% 18.51% 18.13% 18.04% 17.00%

IV 13.68% 19.25% 18.40% 19.15% 17.26%

V 14.53% 14.43% 12.26% 15.47% 20.75%

 Closed Liquidated Unknown

I 1.51% 4.63% 1.13%

II 0.94% 5.47% 2.26%

III 0.38% 7.74% 3.12%

IV 0.75% 9.53% 1.98%

V 0.66% 19.72% 2.17%

Notes: Each row represents five original states (quintiles I-V)
calculated during portfolio formation. Each column represents eight
future states; quintiles l through V, "liquidated" funds that stopped
reporting because of bad performance, "closed" funds that
stopped reporting because of lack of interest in attracting new
investors, and "unknown" funds that stopped reporting for an
unknown reason.

There is a very definite pattern of increasing attrition rates with a decline in relative performance. For example, the worst-ranked funds have a probability of 19.72% to liquidate during the next 12 months, whereas funds from the top quintile have an attrition rate of only 4.63%. We test the hypothesis that the funds from. the bottom quintile V have the same attrition rate as the funds from the next-worst quintile IV by focusing on two future states: staying in business (by combining states of future rank I-V) or liquidating during the 12 months following the portfolio formation. The [x.sup.2] one-tailed test produces a t-statistic value of 6.64, which yields a P-value of 0. The Fisher's exact test .also gives a P-value of 0. Thus, both tests reject the hypothesis that funds from quintiles IV and V have the same attrition rates, which means that funds from the lowest quintile are statistically more likely to liquidate than funds from the other four quintiles.

We perform an additional test of persistence focusing on two states: quintile I and quintile V. We test the hypothesis of whether a fund from quintile I has the same conditional probability of staying in quintile I over the next 12 months as a fund from quintile 5 has of remaining in quintile 5. The [x.sup.2] one-tailed test produces a f-statistics value of 6.06, which yields a P-value of 0. The Fisher's exact test also yields a P-value of 0. Thus, both tests reject the hypothesis that funds in quintiles I and V have the same conditional probabilities of transitioning to quintile I versus transitioning to quintile V during the next 12 months.

To investigate the potential impact of the incubation and backfill biases on the above results, we repeat our analysis by excluding the first 24 months of the data and then once again without excluding any data. In both cases, we obtain similar results, confirming that funds from the bottom quintile have a higher probability of liquidation than funds from the other four quintiles. We also find that funds from quintile I have higher conditional probability of remaining in quintile I versus transitioning to quintile V during the next 12 months, compared with the conditional probability that funds from quintile V transition to quintile I versus remaining in quintile V.

CONCLUSIONS

This article reports the test results of the performance persistence hypothesis for commodity trading advisors. Using FM regression and quintile analysis, we find that ranking CTAs using the t-statistics of alpha with respect to a CTA benchmark is predictive of future unleveraged returns. Sorting on the t-statistics of alpha yields an approximate 4.6% annual spread of unleveraged returns between equally weighted portfolios of the top and bottom quintiles. This finding is robust to the choice of CTA benchmark and model parameters.

We examine the impact of incubation .and backfill biases on the aforementioned results by repeating the analysis after excluding the first 12 and 24 months of data for each fund. We find that although on average there is no impact on the relationship between previous rankings and future unleveraged returns, nor on the persistence of the worst performing funds, the identified strong persistence of the best-performing funds is potentially solely driven by the incubation and backfill biases.

In addition to using our simple ranking to predict future returns, we find that it is also predictive of future liquidations. We use [x.sup.2] and Fisher tests to confirm that the worst-performing funds have a significantly higher probability of liquidation than those of the other quintiles. In addition, the top-performing funds have a higher conditional probability of staying top performers versus becoming worst performers than the conditional probability of the worst-performing funds becoming top performers versus remaining worst performers.

In the past, the CTA universe was dominated by long-term trend followers, but today the CTA universe is very diverse. Further research may include recognizing that heterogeneity, classifying the universe into relatively homogeneous CTA groups, and examining performance persistence of CTAs within each group. In addition, we will focus our research on the portfolio implications of our CTA performance persistence findings.

APPENDIX A

FUND STATUS

There are three categories of funds that stop reporting. The first category, "liquidated funds," consists of funds with returns that are insufficient to cover operational expenses because of either poor performance or an inability to raise assets. The second category, "closed funds," consists of successful funds that are not interested in attracting more investors, either because they have already reached capacity or because they have a good client network sufficient to reach that level. The third category, "unknown," consists of funds closed for reasons unrelated to performance (for example, the owners decide to retire, and so on).

The Barclay database provided reasons for discontinued reporting for only 403 funds, 36 of which were closed and 367 of which were liquidated. We attempt to make some reasonable assumptions to categorize the remaining 1,357 funds with uncertain status. First, we assign "closed" status to 98 funds that have Sharpe ratios greater than 1 with AUM exceeding US$10 million and length of drawdowns under six months, because we assume they stopped reporting because of a lack of interest in attracting more investors. Second, we assign "liquidated" status to 1,050 funds that stopped reporting while being in drawdown for more than 24 months, or whose depth of drawdown exceeded their annual volatility, or that had AUM below US$5 million, or that had a track record shorter than 12 months.

After performing these cleaning procedures, we had 835 active CTAs, 1,417 funds with "liquidated" status, 134 funds with "closed" status, and 209 with "unknown" status.

APPENDIX B

UNLEVERAGED RETURNS

The concept of leverage can be illustrated with a simple example. Consider CTA A, with expected annual return of 20% and expected annual standard deviation of 10%. If an investor's risk appetite, measured in terms of expected annual standard deviation (or volatility), is equal to 15%, then the investor can request that the CTA increase its position size by 50%. For the investor, leveraged A's expected annual return becomes 30%, and the expected annual standard deviation is 15%.

Now consider two funds, A and B. The annual return of A is 20%, and its annual standard deviation is 10%. The annual return of fund B is 25%, and its annual standard deviation is 30%. The investor can use leverage to scale both CTAs to 15% volatility. Leveraged A has annual return of 30% and annual standard deviation of 15%; leveraged B has annual return of 12.5% and annual standard deviation of 15%. This approach is commonly used by practitioners in the managed futures industry. It has a limitation, however. If a CTA's volatility is very low, the leverage coefficient may be too high to scale a CTA to a target volatility level, because of margin requirement constraints. If a CTA's volatility is below a certain level, that assigned minimum level, should be used for leverage calculation. Without loss of generality, we define the un-leverage factor as

[[lambda].sub.t.sup.i](k) = min([[lambda].sub.max], TVol.Vo[l.sub.t.sup.i](k))

where TVol is the target volatility, Vo[l.sub.t.sup.i](k)) is the annualized standard deviation of the CTA i calculated at point t using k most recent monthly returns, and [[lambda].sub.max] is the maximum un-leverage factor. In this study, TVol is considered 15% and [[lambda].sub.max] is equal to 3.

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ENDNOTES

The authors are grateful to Eugene Fama, participants of his PhD research class, and the Illinois Institute of Technology Stuart School of Business faculty for their valuable comments. We thank Sol Waksman for providing the Barclay graveyard database. We also appreciate excellent suggestions given by Ernest Jaffarian, Keli Han, Zhongjin Yang, and other members of the Efficient team. We are grateful for the emotional support we received from Julia Molyboga, Mihye Go, and other family members.

(1.) Eugene Fama suggested using the Fama-MacBeth regression methodology for evaluating persistence in performance. We appreciate his comment.

MARAT MOLYBOGA is the director of research at Efficient Capital Management, LLC in Warrenville, IL. molyboga@efficientrapital.com

SEUNGHO BAEK is a quantitative analyst at Efficient Capital Management, LLC in Warrenville, IL. sbaek@efficientcapital.com

JOHN F.O. BILSON is associate dean and a professor of finance at the Illinois Institute of Technology Stuart School of Business in Chicago, IL. bilson@stuart.iit.edu