Performance and Persistence of CTAs-Parametric Evidence
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Transcript of Performance and Persistence of CTAs-Parametric Evidence
Performance and persistence of Commodity Trading
Advisors: Parametric Evidence
Greg Gregoriou, Georges Hübner, Maher Kooli
September 06 / N° 200609/01
CAHIER DE RECHERCHE / WORKING PAPER
Performance and persistence of Commodity Trading Advisors: Parametric Evidence
Greg N. Gregoriou
Georges Hübner
Maher Kooli
September 2006 version
JEL Classification: G2, G11, G15 Keywords: CTA; Performance persistence; Multifactor models; managed futures
Greg N. Gregoriou is Associate Professor of Finance at State University of New York (Plattsburgh), 101 Broad Street, Plattsburgh, New York 12901, E-mail: [email protected], Tel: (518)564-4202; Fax: (518) 564-4215. Georges Hübner is the Deloitte Professor of Financial Management at HEC Management School – University of Liège, Liège, Bld du Rectorat 7, B31, 4000 Liège, Belgium, E-mail: [email protected]. Tel : (32) 43662765.Fax: (32) 43662767; Associate Professor of Finance at the University of Maastricht; Senior Researcher at the Luxembourg School of Finance, University of Luxembourg, and Affiliate Professor of Finance at EDHEC.. Maher Kooli is Assistant Professor of Finance at University of Quebec at Montreal, School of Business and Management, Montreal, Quebec, P.O Box 8888, Station (Centre-Ville), H3C 3P8, E-mail, kooli,[email protected]. Tel: (514) 987-3000 ext. 2082. Fax: (514) 987-0422
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Performance and persistence of Commodity Trading Advisors: Parametric Evidence
Abstract We re-examine the performance of Commodity Trading Advisors (CTAs) using a parametric calendar time approach during the 1996-2005 period. We compare abnormal performance based on a number of alternative existing models, as well as a category-specific model introducing asset-, option- and moments-based factors. Taking more factors into account significantly raises the explanatory power, but only four out of 7 CTA categories significantly outperform the market. We find that numerous CTAs show persistence over a horizon of at least three months and they also more likely to be persistent over a longer period. Yet, most of the persistence fades away upon the “acid test” of considering only the top and bottom quartiles of the managers.
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Performance and persistence of Commodity Trading Advisors: Parametric Evidence
1. Introduction
For individual or institutional investors that are both simultaneously performance-oriented
and risk-conscious, the main question is how best to achieve a higher overall rate of return with
acceptable level of risk. The answer could be a diversified investment portfolio with a certain
portion of the total assets allocated to alternative investments, more specifically managed futures.
A Commodity Trading Advisors (CTAs) is any money manager that accepts compensation for
advising clients on either buying or selling commodity futures, forwards, options deemed as
managed futures contracts. Managed futures provide access to investment not easily available
through traditional stock and bonds and they have witnessed a dramatic increase in assets during the
last decade. For instance, Managed Accounts Reports (MAR) cites an increase in managed futures1
from less than $1 billion in 1980 to almost $131 billion in 2004 (Schneeweis, 2005). However,
there is still some confusion about the performance of managed futures as the number of CTAs has
grown during this period.
When using the composite performance of 15 trading advisors, Lintner (1983) shows that
the risk-return ratio is greater than a well-diversified stock and bond portfolio. Furthermore, the
author finds a low correlation between the returns of trading advisors and those of stocks, bonds, or
a combined stock/bond investment portfolio. It is well-known that CTA returns produce negative
correlation to stock and bond market indices. In addition, Schneeweis and Spurgin (1997) show
that various CTA and hedge-fund-energy-based investment provide risk and return opportunities
not available from a wide range of traditional commodity investments or real estate investments. 1 The term managed futures describes an industry made up of professional money managers known as commodity trading advisors (CTA). These trading advisors managed client assets on a discretionary basis using global futures markets as an investment medium.
4
During the one of the strongest stock market periods in U.S. history (1980-2005) managed
futures (as measured by the Barclay CTA Index) had a compound annual return of about 12.76%
comparing favorably with the 13.24% return the S&P 500 index produced during the same period.
The Barclay CTA index exceeded the Smith-Barney U.S. Government Bond Index and returned
8.48% during the same period. Moreover, during the 1980-2005 time frame, analysis shows that a
portfolio comprised of a partial allocation to managed futures had similar profitability with far less
risk. Therefore, CTA can be considered as good hedging instruments in down markets for hedge
funds, fund of funds, and the equity markets (Liang, 2003).
Numerous academic studies during the last 20 years have examined the performance of
managed futures with mixed results and with the lack of consensus. Using regression analysis, this
study investigates the performance persistence issue as a well during both bull and bear market
periods. We aim at providing a comprehensive set of evidence as to whether CTAs can truly add
value and sustain their performance. Since the attrition rate of CTAs is typically higher than mutual
funds it is an important subject to analyze during both the short and long-term periods.
A multi-period time frame analysis differentiates between performance persistence due to
luck and due to managerial skill. We assess and differentiate the results from a multi-period
framework with the results from the conventional two-period analysis. Moreover, we provide a set
of new “acid tests” on persistence by considering the ability of CTA managers to sustain
performance over different horizons and with different ranking schemes. The procedure enables us
to considerably deepen our insights over the durability of CTA performance per categories.
With this approach, never previously used for CTAs, we shed new light on previous studies
on CTA performance (see for example, Elton, Gruber and Rentzler, 1987; Liang, 2003) who
conclude that investors cannot select top performing funds using historical performance.
5
The rest of the paper is organized as follows. Section 2 is the literature review. Section 3
sets out the data and the performance models considered. Section 4 brings some insights on CTA
performance and reports the main results. Section 5 concludes the paper.
2. Literature review
While examining the benefits of managed funds, Schneeweis and Georgiev (2002)
demonstrate that CTAs reduce portfolio volatility risk and enhance portfolio returns in most
economic environments where stock and bond offer limited opportunities. However, these authors
sustain that for managed futures to grow as an investment alternative class, investors need to
increase their knowledge and comfort level as to the use of managed futures in their investment
portfolios.
Irwin, Zulauf and Ward (1992a) study 363 CTAs during the 1979-1989 period and find that
there is a lack of performance persistence when the authors looked at past CTA returns to predict
future returns. Irwin, Krukemeyer, and Zulauf (1992b) examine commodity pools during the 1979-
1990 period and use quintiles to separate CTAs but the results are not robust. Irwin et al. (1994)
focus on individual CTAs, and their results concur with the previous findings of little evidence of
predictability in average CTA returns.
In an early study McCarthy, Schneeweis and Spurgin (1996) find some performance
persistence. However; their sample size of CTAs used is relatively small with 56 CTAs using the
1985-1991 time frame. The same authors observe that multi-advisor managed futures funds have
more persistence than single advisor CTAs (McCarthy, Schneeweis and Spurgin, 1997). Brorsen
(1998) investigates data from private and public funds, and CTAs using various statistical methods
such as regression analysis, Monte Carlo methods, and out-of-sample tests and finds that there
exists limited evidence of performance persistence. The main drawback of the above studies is the
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short examination period during a bull market, not encompassing any sustained bear market
environment.
One of the pioneering studies on managed futures by Elton, Gruber and Rentzler (1990) use
152 commodity pools during the 1990-1998 period to examine the performance issue. The authors
find no evidence of performance and suggest that management fees and transaction costs must be
reduced for commodity investments to be more appealing. Brown, Goetzmann and Park (1999) find
no persistence in CTA returns using a non-parametric approach during the 1989-1998 period
confirming the results of Edwards and Caglayan (2001). These authors, using Managed Account
Reports data on 2,345 commodity funds during the January 1990 to August 1998 period, find no
support regarding performance persistence either. However, using regression analysis may offer
some more robust results than non-parametric analysis.
Diz (1996) used 925 managed futures programs from the Barclay CTA database during the
1975-1995 and concludes that survival of CTAs is connected to performance but performance is not
essentially linked with survival. Fung and Hsieh (1997) use 901 private CTA funds during the
1989-1996 period and find that the survivorship bias is 3.4% per year implying that CTA returns of
live funds are on average 3.4% higher than the returns of both live and dead funds.
Brorsen and Townsend (2003) use the 1990-1999 period and find a small amount of
performance persistence using regression analysis. More recently, Capocci (2004) investigates the
long-term performance persistence of live and dissolved CTAs by combining three databases, (1) the
Barclay Trading Group (2) TASS and (3) Managed Account Reports during the 1985-2002 period
(throughout both bull and bear markets) while encompassing numerous extreme market events. To
examine the performance issue, the author ranks CTA strategies in deciles and finds that out of 11
strategies only 7 significantly outperform the CTA Global Index. In terms of performance
persistence a large majority of deciles underperforms the CTA Global Index during the entire period.
7
However, sub-period analysis reveals that only one decile appears to outperform the CTA Global
Index. Furthermore, the low significance level of his regressions does not lend strong economic
support to his results;
Financial research has further suggested that managed futures provide positive skewness and
lower kurtosis when included with hedge funds in a traditional investment portfolio (Kat, 2005).
Although managed futures are considered high risk investments, indices such as the S&P 500 have
produced higher volatility than the Center for International Securities and Derivatives Markets
(CISDM) CTA index during the 1990-2004 period. Yet, when managed futures are coupled with
hedge funds, stocks and bonds, they are usually claimed to enhance the overall portfolio
performance, provide instant diversification and reduce risk.
Liang (2003) uses the Zurich database and examines 294 live CTAs and 1,216 defunct
CTAs and concludes that they underperform hedge funds and funds of hedge funds due to their
management fees, higher attrition rates and survivorship bias.
To our knowledge, no comprehensive analysis of CTA performance and persistence using a
similar approach to ours has been carried out so far. This is probably due to the fact that regression
methods that have been tested so far have hardly produced any satisfactory significance levels. This
has probably precluded the safe run of performance persistence analysis using in a multi-period
framework.
3. Data and method
3.1 Data
The data set consists of 527 live and 1290 dead CTAs that reported monthly performance
figures net of all fees to the Barclay Group database during the period January 1996 to December
2005, a total of 123 months. We select this time frame because previous studies examining the
8
performance of CTAs are during the bull market period (pre-1999). Because of their negative
correlations, CTAs perform poorly in bull markets. To ratify this we use both the bull and bear
market periods to properly determine how CTAs perform in these types of markets. Our study is the
first to include the bear market starting with the bursting of the tech bubble in the Spring of 2000.
When database vendor’s backfill CTA returns, data is upwardly biased and that this type of
bias can add a yearly return of 1.4% (Fung and Hsieh, 2000). We remove CTAs born prior to
January 1996 to eliminate backfill bias, and omit CTAs with missing classifications and no
covariate data. In this paper, CTAs enter the Barclay database and remain alive until they stop
reporting results for three consecutive months, at which time they are considered defunct and
removed. They can, however, re-enter the database and backfill their unreported data.
To qualify for inclusion in the database, a CTA must have at least four years of preceding
historical performance. New programs introduced by CTAs are only added after the second year to
the Barclay database. These limitations are enforced to compensate for the high turnover rates of
CTAs because of their high short-term performance to guarantee precise and consistency of the
Barclay database.
Each of the seven CTA classifications is examined to obtain more informative and precise
results, which would be beneficial to money managers and investors in terms of performance. The
definitions of the classifications are presented in Table 1. Discretionary and systematic are trading
styles, whereas the other classifications are usually considered as portfolios of options and futures.
*** Insert Table 1 about here***
3.2. Methods
Following Fama and French (1993), we choose the value-weighted portfolio of all NYSE, Amex
and NASDAQ stocks as a market index. We also consider using the Russell 3000 index as well.
9
The comparison of descriptive statistics of the two indices suggests that both market proxies are
very similar. Thus, the results of the study should not be influenced by the market proxy chosen.
We use the 1-month U.S. T-bill rate from Ibbotson Associates as the risk-free rate.
3.2.1 Traditional Models
In the alternative investments literature, typically multifactor models have been preferred over the
well-known CAPM for performance evaluation, but there is no universally accepted model. In this
paper, we use several specifications in order to compare our results. We start with the market model
derived from the CAPM. It provides a simple benchmark to assess the gains in significance levels
obtained with more sophisticated specifications.
Market model: Assume that CTA returns follow the one-factor return generating process,
Rjt =αj+βjRMt+εjt (1)
where Rjt is the rate of return of the CTA j on month t; RMt is the rate of return of a market index on
month t; εjt is the error term.
The Fama and French (1993) three-factor model2: It takes the size and the book-to-market ratio of
the firms into account and is estimated from the following extension of the CAPM regression
Rjt−RFt=αj + βj1(RMt−RFt) + βj2SMBt + βj3HML t + jtε (2)
where SMBt=the factor-mimicking portfolio for size (small minus big) and HMLt=the factor-
mimicking portfolio for book-to-market equity (high minus low).
2 See Fama and French (1993) for a complete description of the factor returns.
10
The Fama and French (1993) model with Ibbotson’s (1975) “Returns Across Time and Securities”
(RATS) procedure: The RATS technique allows the estimate of beta to vary during returns window.
In other words, it presumes that the betas of the portfolio should vary over time as new information
becomes readily available.
The Fama and French (1993) model with RATS procedure provides:
Rjt−RFt=αj + βj1t(RMt−RFt) + βj2SMBt + βj3HMLt + jt (3)
3.2.2 Adapted Models
Unlike previous studies, rather than considering a general multifactor model for all CTA categories,
we use a more rigorous approach that takes into account the many dimensions of financial risk
inherent to CTA. More specifically, using a large set of potential variables, including moment
factors and options factors, we choose first a subset of significant variables for each CTA category
through a stepwise regression procedure. We calculate then the performance for each CTA category
using a calendar time approach discussed later. To the best of our knowledge this the first global
study that considers a specific model for each CTA category.
The exposure of CTA returns to non-linear risk factors has been largely documented in the
recent literature (see Martellini and Vaissié, 2004). Liang (2004) applies the equity-based option
factors developed by Agarwal and Naik (2004) to a sample of CTAs and finds superior significance
levels for this class of securities than for hedge funds or funds of funds, with an increase in adjusted
R-square of 20.29% for the CTA index. On the other hand, the pervasive positive skewness and
excess kurtosis of CTA strategies that makes them useful diversification tools (Kat, 2004) also
explains their significant loading to the square and cube of market returns as shown by Hübner and
Papageorgiou (2004).
11
We select eight financial indexes on which option-based factors are constructed: three
exchange rates (USD/Yen, USD/Euro3, and USD/UK Pound Sterling), two interest rate indexes
(Lehman High Yield Bond index and the Lehman US Treasury LT Bond Index), and three
commodity indexes (GSCI Wheat, Gold and Crude Oil Indexes). We do not include an equity-based
option as it overlaps with the higher moments variables constructed below. For each index, we
compute the Black-Scholes (B-S) price of four six-week options (ATM Call and Put, and 5% OTM
Call and Put) on a monthly basis. We use a rolling estimate of the 12-month volatility as input. At
the end of the month, we compute the realized return with the new B-S price of the option.
To account for the likelihood that most CTAs follow non-directional strategies, we
complement this set of options with the corresponding long ATM straddles and OTM strangles
constructed with the samples of calls and put. Even though these portfolios are less complex than
the ones proposed by Fung and Hsieh (2001) in the context of hedge funds, they have the advantage
of reasonably replicating simple trading strategies.
Amongst the modeling approaches that aim at integrating moments of order three
(skewness) and four (kurtosis) into the asset pricing model, we have to select a method that
produces a tradable index. We adopt an approach advocated by Harvey and Siddique (2001), who
suggest building these variables in the same way as the SMB and HML variables of Fama and
French (1993), with stocks ranked on the basis of their coskewness with the stock index. We
simplify this procedure by collecting the S&P sub-industry indices from July 1994 to 2005 as raw
data (123 indices), and computing the lagged 12-month variance, and 6-month skewness and
kurtosis.4 Then, for each month, we rank the indexes in turn by their variance, skewness and
3 Prior to the freezing of parities, we take the USD/German Mark. 4 Our data show that variance shocks exhibit a longer memory than skewness or kurtosis shocks, and so the variance has to be computed on a longer time interval.
12
kurtosis and compute the corresponding risk premia by taking the difference between the top and
bottom third selected (67th percentile minus 33rd percentile).
We also include Carhart’s (1997) momentum risk premium.5 Consistently with its original
interpretation, this factor is able to capture some persistence in the stock returns and does not
overlap with the moment and option factors.6
3.2.3 Performance estimation
We employ the calendar-time method developed by Jaffe (1974) and Mandelker (1974)
which controls for cross-correlation. Lyon et al. (1999) show that the calendar time approach yields
well specified test statistics, because it entails calculating average returns of rolling, calendar-time
portfolios of event funds. Specifically, for each calendar month, we form an equally weighted τ-
month portfolios set up to include any CTA strategy which has a return during the previous τ-
months, for τ = 12, 24, and 36. The calendar time approach has the additional advantage that it
provides a direct measure of the opportunities available to investors attempting to exploit any
abnormal performance.
For each model specification, we define the out-or under-performance relative to the market
proxy used (i.e., the abnormal return) for the fund on month t as:
Ajt = Rjt −∑=
K
kktkt F
1
β̂ t =1,2,…,T (4)
where Fkt represents the k-th factor in the regression.
The average abnormal return AARt is the sample mean:
5 See Carhart (1997) for a description of the construction of PR1YR. 6 We have considered other indices: the MSCI World Index excluding US, the return of the Salomon World Government Bond Index, the return of the Goldman Sachs Commodity Index (GSCI), but the stepwise regression procedure rejects all of them for each strategy. We have also tested Fama and French (1998) international value, JP Morgan Emerging Market Bond Index, the term spread, implicit volatility, and currency factor)s. However, due to their high collinearity with other factors, we decide to not test these indices further
13
AARt = N
AN
jjt∑
=1 (5)
Over an interval of two or more trading months beginning with month T1, and ending with T2, the
cumulative average abnormal return (CAAR) is:
CAAR(T1,T2) = ∑∑=
N
j
T
TjtA
N 1
2
1
1 (6)
To test the null hypothesis that the mean abnormal return is equal to zero for a sample of n
CTAs, we first employ a cross-sectional t-statistic. The standard error for this test for each month is
computed across funds, not across time. To eliminate the skewness bias when long-run abnormal
returns are calculated, we also use the bootstrapped skewness-adjusted t-statistic.
4. Results
4.1 Basic performance
Table 2 reports means, standard deviations, medians Sharpe ratios, kurtosis and skewness, for the
seven CTA categories and the four factors based on monthly data for the 1996-2005 period. The
first part of Table 2 shows that the highest mean return was achieved by the Stock Index CTA
(1.46%) followed by the Energy CTA (1.00%). The Arbitrage CTA offers the lowest mean return
(0.34%). When standard deviation is taken into account through the Sharpe measure (the ratio of
excess return and standard deviation), results confirm our previous observations. CTA offering the
best trade-off between risk and return is the Index Stock CTA (0.49) and the worst Sharpe ratio is
obtained by the Arbitrage CTA (0.01), which is also the worst performing index when risk is not
taken into account. Table 2 also confirms the heterogeneity of CTA universe: some CTA categories
have relatively high volatility while other CTAs have lower volatility.
14
When CTA data are contrasted against the descriptive statistics of the market proxy, the
Fama and French (1993) SML and HML, and Carhart (1997) momentum’s factor, the statistics are
in favor of the managed futures strategies. The mean return of the Market Proxy is 0.26% per month
(about 4.78% per year). The average SMB and HML returns are 0.29% and 0.46%, respectively.
The highest mean return was obtained by the Momentum factor (0.87% per month). On average, the
Sharpe ratio obtained by the seven CTA categories (0.23) is higher than the one for the Market
Proxy (-0.01).
*** Insert Table 2 about here***
Table 3 reports correlation coefficients among CTA categories. There is a high variability
between different categories, ranging from 0.83 (between Financial/ Metal CTA and Diversified
CTA) to -0.28 (between Diversified CTA and Arbitrage CTA). Only one correlation coefficient is
greater than 0.70 and six of them are negative.
*** Insert Table 3 about here***
Table 4 reports correlation coefficients between CTA categories and equity, bond and
commodity indices. Correlation coefficients between CTA categories and the Market Proxy are, in
seven cases, smaller than or equal to 0.39. Hence, the addition of CTAs to a traditional portfolio
should improve its mean-variance trade-off. Liang (2003) also finds that returns from CTAs are
negatively correlated with other instruments, making CTAs suitable for hedging against downside
risk.
*** Insert Table 4 about here***
4.2 Calendar time abnormal performance
15
The discussion of performance models is performed for the whole 1996-2005 period. The
first performance model used is the CAPM-based single index model, taken as the benchmark to
assess the value-added of further improvements. Table 6 reports the results for the whole sample.
We estimate each CTA category (portfolio) individually using calendar time approach. In other
words, CTAs are grouped into portfolios by event date and by categories. A portfolio standard
deviation is estimated from the time series of portfolio abnormal returns in the estimation period,
and used to standardize the portfolio return.
Starting from 1996, we note that all CTA categories seem to significantly outperform the
market. In all cases, the alphas from CAPM (See Table 5) are significant at the 1% confidence
level. For example, after 3 years, the cumulative abnormal return for Energy CTA is 2.81% per
month (bootstrapped Skewness corrected t-statistic = 7.55).
*** Insert Table 5 about here***
In Table 6, we report the results for Fama and French (1993) three-factor model applied to
all CTA categories. Table 6 tends to confirm the seemingly superior performance of CTAs. The
positive and significant calendar time alphas range from a monthly percentage of 1.28% for Stock
Index CTA to 2.10% for Discretionary CTAs. The table also reveals that the premia on the SMB
and the HML factors are negative (except for HML factor for Energy CTAs). There are however
significant only for Systematic CTAs. Systematic CTA managers seem to prefer larger stocks and
those with low book-to-market ratios. The adjusted R2s range from 0.003 for Energy CTAs to 0.153
for Stock Index CTAs. As expected, the highest adjusted R2s are obtained when the alphas are the
lowest. However, these low adjusted R-squared coefficients confirm all outstanding evidence about
the powerlessness of most traditional asset pricing models.
*** Insert Table 6 about here***
16
Table 7 reports the result of Fama and French (1993) three-factor model applied to all CTA
categories using RATS procedure for different calendar time periods. Again, we confirm that the all
CTA categories outperform the market for the 1996-2005 period.
*** Insert Table 7 about here***
Table 8 reports the results of the multi-factor model. In a strong contrast to previous results,
we find that taking more factors into account induces that only four out of seven CTA categories
significantly outperform the market and one out of seven has positive but insignificant excess
returns. The alphas of Arbitrage and Energy CTAs are negative but only significant for arbitrage
CTAs. Based on alpha, the best strategy is Diversified (alpha = 4.03% per month).
Interestingly, in only two out of seven CTA categories we retain the premium on the SMB
factor but it is statistically insignificant. Also in one category, the premium on the Momentum
factor is insignificantly negative, reflecting that CTAs are generally not arbitragers in the equity
markets. Overall, the most significant factors for CTAs are option factors. Although managers may
not trade in the option markets directly, their returns may show non-linear or option-like patterns
due to some long-short combinations. Our observation is consistent with Fung and Hsieh (1997b)
and Liang (2003) that CTAs exhibit option-like return patterns with respect to equity markets.
Our multifactor models results provide some insight into the preferences of CTA managers:
(1) we find that Energy, Financial/Metals, Diversified, and Stock Index CTAs managers invest in
gold (as a proxy for metals); (2) Energy, Discretionary, and Stock Index CTAs managers invest in
oil (as a proxy for fossil energy materials); (3) Diversified and Financial/ Metal CTAs managers
invest in wheat (as a proxy for comestibles); (4) Diversified, Arbitrage, and Systematic CTAs
managers invest in credit-risky bonds; (5) the best performing category (Diversified CTA) invest in
government and corporate bonds, currency, wheat, and gold.
17
Overall, it seems that the multifactor models do a good job in explaining CTA behavior of
various categories. The average adjusted R2 increases from 0.06 for the Fama & French three-factor
model to 0.31 for the multifactor models (the adjusted R2s of the seven multifactor models range
from 0.07 to 0.49). But at the same time this means that although we can explain a substantial part
of the variation of CTA returns by the multifactor models, another, non-trivial part is still missing.
The set of explanatory variables considered seems particularly adapted to Diversified (0.49) and
Arbitrage (0.43) CTAs but does a poorer job with Discretionary CTA. However, we should mention
that our adjusted R2 are higher that those obtained by Liang (2003). He reports adjusted R2s from -
7.2% to 14.3%. Liang also concludes that CTAs are different from hedge funds or fund-of-funds in
trading strategies and those multifactor models have very low explanatory powers for CTAs.
*** Insert Table 8 about here***
Table 9 reports the same analysis of performance over different subperiods. First, we
subdivide the 1996-2005 period in two sub-periods of equal lengths (January 1, 1996-December 31,
2000 and January 1, 2001-December 31, 2005). Second, we consider the Asian crisis period. When
the time period is divided in two, we notice that the significant underperformance of Arbitrage CTA
for the 1996-2005 period is mainly due to the first sub-period. We also notice that Stock Index,
Diversified and Financial/Metal CTAs significantly outperform in both subperiods. Moreover,
during the Asian crisis, Energy and Stock Index CTAs took advantage of this period and earn
positive and significant excess return. Four CTAs categories outperform the market, though
insignificantly.
*** Insert Table 9 about here***
4.3 Relative performance persistence of CTAs.
18
The second objective of this study is to examine the performance persistence of CTAs over
different time periods. We follow Brown, Goetzmann and Ibbotson (1999) and Agarwal and Naik
(2002) and compare the performance measures in the current period on the performance measures
in the previous period. We rely on alpha as a performance measure, defined as the return of a CTA
following a particular strategy minus the average return for all CTAs following the same strategy.
Moreover, to investigate the issue of persistence in two consecutive periods, we rely on a non-
parametric method. More specifically, we construct a contingency table of winners and losers. A
CTA fund is a winner if the alpha of that fund is greater than the median alpha of all the CTA funds
following the same strategy in that period otherwise it is a loser. In this context, persistence refers to
the existence of CTA funds that are winners in two consecutive periods (one month, three months,
six months, and twelve months periods), denoted by WW, or losers in two consecutive periods,
denoted by LL. Similarly, winners in the first period and losers in the second period are denoted
WL and LW denote the reverse.
In this paper, we use both cross-product ratio (CPR) and Chi-square statistic to detect
persistence. The CPR test statistic is the ratio of the product of repeat winners (WW) and repeat
losers (LL) divided by the product of winner-losers (WL) and loser-winners (LW), i.e.
(WW×LL)/(LW×WL). A CPR of one would support the hypothesis that the performance in one
period is unrelated to that in another. A CPR greater than one indicates persistence, while a value
below one indicates that reversals in performance dominate the sample. We determine the statistical
significance of the CPR by using the standard error of the natural logarithm of the CPR is given by
(see Christensen, 1990)
σln(CPR) = LLLWWLWW
1111 +++ (7)
19
We also conduct a chi-square test comparing the observed frequency distribution of WW,
WL, LW, and LL with the expected frequency distribution. Carpenter and Lynch (1999) study the
specification and power of various persistence tests and find that the chi-square test based on the
number of winners and losers is well-specified, powerful, and more robust to the presence of
survivorship bias compared to other test methodologies.
The chi-square statistic is defined as:
4
24
3
23
2
22
1
212 )()()()(
ˆD
DLL
D
DLW
D
DWL
D
DWW −+
−+
−+
−=χ (8)
where
LLLWWLWWNN
LLWLLLLWD
N
LWWWLLLWD
N
LLWLWLWWD
N
LWWWWLWWD
+++=
++=
++=
++=
++=
))((
))((
))((
))((
4
3
2
1
We test this statistic at the 5% significance level, which corresponds to a critical value of
Chi-square statistic of 3.84 (one degree of freedom).
Table 10 shows our empirical results. For each formation/holding period, the sample is split
into overlapping (to maximize power) periods of the required frequency. Each panel of Table 10 (A
to D) displays the percentage of occurrences of WW, WL, LW, and LL over the sample period, the
cross-product ratio (CPR) with its Z-statistic, and the chi-square test result. For the latter statistic,
we report the percentage of cases where statistically significant persistence was observed in each
CTA category.
20
We first observe that, in general, both the CPR and chi-square tests indicate a greater extent
of persistence, i.e. persistence is observable for longer holding periods. In particular for holding
periods of three, six and twelve months, Diversified, Financial/Metal and Systematic CTAs are
more persistent than the others categories in terms of the percentage of cases where persistence is
statistically significant. For instance, for a holding period of twelve months, the percentage of cases
where persistence is statistically significant is 90%, 90% and 92%, for Diversified, Systematic, and
Financial/Metal CTAs, respectively. On the other hand, we find that Arbitrage CTA managers are
less persistent than other CTA managers. Surprisingly, we find a weak presence of persistence
when the holding period is one month. For all CTA categories, their corresponding CPRs are not
statistically different from one. Finally, contrary to hedge funds evidence (Agarwal and Naik, 2002)
the extent of CTA persistence does not seem to be related to return measurement intervals. Overall,
we find that managers who show persistence over a short time horizon is more likely to be
persistent over a longer one.
In Table 11, we extend our investigation to examine what happens after periods during
which some CTAs exhibited some persistence. In other words, we show among the periods for
which we find 1 month persistence for instance, how much are still persistent after 3, 6 and 12
months and vice versa. This indicates whether the same periods yielded persistence at various
horizons. For example, for Diversified CTAs, among the 45.11% results with a significant chi-
square, 4.48%, 0.38% and 0.04% (percents based on the whole number of funds) were also
significant with a 3, 6 and 9 months holding periods, respectively.
The results show a striking difference between one-month persistence and persistence over
longer periods. Conditionally on observing short-term persistence over a given month, the same sets
of portfolios (based on a one-month formation period) show very weak persistence over longer
periods. The loss in persistence when the holding period increases from one to several months is
21
especially strong for those strategies that exhibit the largest short term persistence, namely
Diversified and Financial/Metal. The converse holds for the Arbitrage and Energy strategies, for
which 10.02% and 9.09% of the periods sustain one-month and three-month persistence altogether.
These strategies, that exhibit the weakest short-term persistence, seem able to sustain this
persistence over longer periods. They also display low levels of medium- and long-term persistence.
This indicates that, while there is scarcer evidence of short- and long-term persistence for these
CTAs, persistence is more robust to the passage of time. For the other strategies, persistence over
the very short term does not signal persistence over longer periods.
*** Insert Table 11 about here***
Table 12, shows persistence for different sub-periods. For all but the Stock Index and
Energy sectors, persistence over very short (one month) and short periods is better during the first
(bullish) sub-period. For these holding periods, managers the Energy sector particularly suffered
from the Asian crisis, where very little persistence could be observed. For 12 month persistence
however, all CTA strategies exhibit lower persistence in the second sub-period. The impact is
particularly strong for Energy CTAs as well. This suggests that, for this particular strategy,
persistence has significantly shifted from longer to shorter holding periods from one sub-period to
another.
Evidence reported in this Table suggests that persistence has consistently deteriorated over time,
especially for longer holding periods. During the second sub-period there is a clear absence of long-
term trends. The market has been moving sideways, with lots of minor bumps during the 2001-2005
period. Trend-follower models cannot cope with that, since they represent more than 70% of
CTAs. A few trends (oil) still exist, but most markets are trend-less. Short-term persistence results
of CTAs do not lead to significant evidence but when they are examined every two consecutive
22
yearly periods i.e, 1994-1995 , 1995-1996 up to 2002, performance persistence is strong and
statistically significant. However, Vuille and Crisan (2004) observe that long-term
persistence does not led to significant persistence during June 1, 1994-May 31, 1998 and June 1,
1998 and May 3, 2002 periods.
This result is very consistent across strategies, unlike evidence presented in Table 9 showing that
performance was not monotonically evolving over time for all strategies.
*** Insert Table 12 about here***
We perform additional tests to analyze the persistence in the extremities of the rankings.
More specifically, our performance analysis award a “win” to those funds with a ranking in the top
quartile (normalized ranking greater than or equal to 0.75), and a “lose” to those funds with a
ranking in the bottom quartile (normalized ranking less than 0.25). If a CTA fund earns a ranking
placing them in either of the middle quartiles (greater than 0.25 or less than 0.75) it is assigned a
rating of NS. Only CTA funds in the top or bottom quartile are paired with a subsequent fund. As
we are principally interested in the extreme performers, we only present results for WTWT (top “T”
funds that are winners in two consecutive periods) and LBLB (bottom “B” funds that are losers in
two consecutive periods); The results are shown in Table 13, which should be analyzed in
conjunction with Table 10.
In Panel A, we find percentages that are considerably below the expected frequencies under
the null (25%) for all but the Arbitrage categories. Thus, in the short run, most extreme performers
among the CTA managers tend to “join the pack”. The very high rejection rate using the khi-square
statistics suggest that this behavior is hardly random, and sharply contrasts with evidence presented
in Table 10 for the same period.
23
This gregarious behavior fades away with the three-month period, except for Discretionary
CTAs. Next, in Panels C and D, we observe a reversal. There is again some evidence of persistence,
but mostly located in the bottom quartile. Good managers manage to sustain their rank for
Financial/Metals and, to a lesser extent (as indicated by the khi-square test) by Stock Index
managers. Discretionary CTAs consistently exhibit a return-to-the-mean behavior across all test
periods.
*** Insert Table 13 about here***
5. Conclusion
In this paper we have re-examined the performance of CTAs over the period 1996 to 2005.
We assess abnormal performance using a number of alternative benchmarks and an approach,
originally used in event studies. More specifically, the benchmarks employed allow for the standard
CAPM, the Fama-French three-factor model, the RATS technique, and a customized multifactor
model. In addition, we use the calendar-time approach as developed by Jaffe (1974) and Mandelker
(1974). This approach has the added advantage that it provides a direct measure of the opportunities
available to investors attempting to exploit any abnormal performance.
We find that, using the market model or the Fama and French (1993) three factor model as
benchmarks, CTA categories do outperform the market. However, taking more factors into account
induces that only four CTA categories significantly outperform the market and only one has
positive but insignificant excess returns. Based on alpha, the best strategy is Diversified Further,
we find that the most significant risk drivers for CTAs are option-based factors, which confirms the
empirical finding of. Fung and Hsieh (1997b) and Liang (2003).
The second objective of this study is to examine the performance persistence of CTAs over
different time periods. We first find that for Diversified, Systematic, and Financial/Metal CTAs are
consistently beating the others categories in terms of the percentage of managers that are
24
performing above their median. Second, we find that the performance of Arbitrage CTA managers
is always less persistent than the one of other CTA managers. Overall, a manager who shows
persistence over a horizon of at least three months is more likely to be persistent over a longer one.
However, most of these results do not stand the “acid test” of considering the ability of a manager
to stay in a top quartile rather than the top half of a category.
As noted by several academics, research in alternative investments, in general, is still at its
infancy. Our studies primarily shows that CTAs, in particular, address new challenges to financial
theory and a lot remains to be done to identify CTA performance drivers. Their return generating
process shows more than half of total variance unexplained. This probably indicates a high
instability in the CTA risk exposures. Furthermore, our study clearly shows that short- and long-
term measurement of persistence, as well as the ranking scheme of the managers, induce
interpretations that can greatly vary from one category to another.
25
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30
Table 1: Definition of CTA Classifications Classification Definition Arbitrage Traders who trade either intra-commodity or inter-commodity spread trading as their
predominant trading method. Energy Traders who trade exclusively energy contracts such as crude oil, gasoline, natural gas,
etc. Discretionary Traders who, in response to a questionnaire, indicated that at least 65% of their trading
decision process was judgmental or discretionary Diversified Traders who trade a diversified portfolio, including most of the major sectors Financial/Metals Traders who trade at least two of the following: currencies, interest rates, stock indices,
precious metals Stock Index Traders who trade stock indices Systematic Traders who, in response to a questionnaire, indicated that at least 95% of their trading
decision process was systematic Source. The Barclay Group.
31
Table 2: Descriptive statistics for all CTA categories. This table shows mean returns, t-statistics, medians, standard deviations, Sharpe ratios, skewness, and kurtosis for all CTA categories and indexes for the 1996-2005 sample period. RMt = return of the Market Proxy on month t; SMBt = the factor-mimicking portfolio for size (small minus big); HMLt = the factor-mimicking portfolio for book-to-market equity (high minus low); PR1YRt = the factor-mimicking portfolio for the momentum effect. We calculate the Sharpe ratio considering Ibbotson Associates 1-month T-bills. All numbers in table are monthly percentages.
Arithmetic Mean (%)
t-statistic Median (%)
Standard Deviation
(%)
Sharpe Ratio Skewness Kurtosis
CTAs Diversified 0.94 3.01 0.57 3.43 0.19 0.35 0.05 Arbitrage 0.34 0.96 0.37 3.87 0.01 -0.47 3.36
Systematic 0.78 5.00 0.71 1.72 0.28 0.11 0.11 Stock Index 1.46 6.70 1.54 2.38 0.49 -0.92 2.36
Energy 1.00 2.11 0.53 5.17 0.13 1.43 7.44 Financial/ Metal 0.87 4.78 0.56 1.99 0.29 0.51 0.19
Discretionary 0.85 4.35 0.75 2.13 0.26 0.56 1.57
Indexes RMt 0.26 0.60 0.94 4.67 -0.01 -0.73 0.62
SMBt 0.29 0.74 0.19 4.35 0.00 0.75 5.90 HMLt 0.46 1.27 0.53 3.95 0.04 0.02 1.94
PR1YRt 0.87 1.66 1.09 5.75 0.10 -0.64 3.93
32
Table 3: Correlation among CTA categories This table shows the linear (Pearson) correlation coefficient among CTA categories for the 1996-2005 sample period.
Energy Systematic Stock Index Arbitrage
Financial/ Metal Diversified Discretionary
Energy 1 Systematic 0.06 1 Stock Index -0.06 0.21 1 Arbitrage -0.06 -0.19 0.12 1
Financial/Metal 0.08 0.65 0.14 -0.26 1 Diversified 0.07 0.55 0.09 -0.28 0.83 1
Discretionary 0.03 0.11 -0.07 0.02 0.07 0.22 1
33
Table 4: Correlation matrix among passive indexes and between all CTA categories and passive indexes. This table shows the linear (Pearson) correlation coefficient among passive indexes and between all CTA categories and passive indexes for the 1996-2005 sample period. RMt = return of the Market Proxy on month t; SMBt = the factor-mimicking portfolio for size (small minus big); HMLt = the factor-mimicking portfolio for book-to-market equity (high minus low); PR1YRt = the factor-mimicking portfolio for the momentum effect; MSWXUSt = return of the MSCI World Index excluding US; SWGBIt = return of the Salomon World Government Bond Index; GSCIt = return of the Goldman Sachs Commodity Index.
RMt SMBt HMLt PR1YRt Energy Systematic Stock Index Arbitrage Financial/ Metal
Diversified Discretionary
RMt 1
SMBt 0.21 1
HMLt -0.55 -0.50 1
PR1YRt -0.23 0.17 -0.06 1
Energy 0.07 0.06 0.00 -0.05 1
Systematic 0.24 -0.04 -0.19 0.03 0.06 1
Stock Index 0.39 0.17 -0.30 0.03 -0.05 0.19 1
Arbitrage 0.13 0.14 -0.17 -0.07 -0.05 -0.18 0.12 1
Financial/Metal -0.02 -0.03 0.06 0.06 0.07 0.63 0.11 -0.23 1
Diversified -0.14 0.00 0.11 0.16 0.07 0.54 0.07 -0.26 0.83 1
Discretionary -0.02 -0.17 -0.02 0.04 0.03 0.08 -0.08 0.02 0.05 0.20 1
34
Table 5: Abnormal performance using the market model Each panel displays the calendar time alpha in percentage using the one-factor market model for different portfolio formation periods during the 1996-2005 sample period. Bootstrapped Skewness Corrected t-statistics are in parentheses. *** Significant at the 1% level.
Calendar months 12 months 24 months 36 months Diversified 2.31%*** 1.85%*** 1.60%*** (17.12) (19.25) (20.53) Arbitrage 1.62%*** 1.03%** 1.37%*** (2.90) (2.55) (3.65) Systematic 1.71%*** 0.92%*** 0.63%*** (8.40) (6.85) (5.82) Stock Index 1.64%*** 1.29%*** 1.07%*** (5.00) (5.24) (5.02) Energy 3.71%*** 3.41%*** 2.81%*** (5.85) (7.08) (7.55) Financial/ Metal 2.20%*** 1.75%*** 1.42%*** (12.86) (14.28) (14.93) Discretionary 2.34%*** 1.59%*** 1.61%*** (6.78) (6.86) (7.67)
35
Table 6: Performance measurement using the Fama and French (1993) three-factor model Each panel displays the monthly calendar time alpha in percentage using the Fama and Fench (1993) three factor model for the 1996-2005 sample period. Heteroscedasticity consistent t-statistics are in parentheses. *Significant at the 10% level. ** Significant at the 5% level. *** Significant at the 1% level.
Alpha (%) RMt - RFt SMBt HMLt R-squared Diversified 2.02%*** -0.06 -0.15 -0.06 0.048 (5.41) (-0.6) (-1.55) (-0.47) Arbitrage 1.36%*** 0.007 -0.06 -0.38 0.028 (3.04) (0.05) (-0.33) (-1.38) Systematic 0.87%*** 0.09* -0.19*** -0.15*** 0.129 (5.23) (1.81) (-3.52) (-2.54) Stock Index 1.28%*** 0.14 -0.13 -0.18 0.153 (4.20) (0.93) (-1.29) (-1.55) Energy 1.89%*** 0.10 -0.03 0.03 0.003 (4.55) (0.94) (-0.23) (0.24) Financial/ Metal 2.05%*** -0.12 -0.10 -0.12 0.028 (6.90) (-1.09) (-1.07) (-1.05) Discretionary 2.10%*** -0.07 -0.17 -0.22 0.018 (4.72) (-0.52) (-1.33) (-1.13)
36
Table 7: Performance measurement using the Fama and French (1993) three-factor model with Ibbotson (1975) RATS procedure Each panel displays the monthly calendar time alpha in percentage using the Fama and Fench (1993) three factor model with Ibbotson (1975) “Returns Across Time and Securities” (RATS) procedure, for different portfolio formation periods during the 1996-2005 sample period. With the RATS technique, we presume that the betas of each calendar time portfolio vary over time as new information becomes readily available. Heteroscedasticity consistent t-statistics are in parentheses. *Significant at the 10% level, ** significant at the 5% level, *** significant at the 1% level. .
Calendar time period 12 months 24 months 36 months Diversified 2.31%*** 3.69%*** 4.79%*** (17.12) (19.25) (20.53) Arbitrage 1.62%*** 2.05%*** 4.12%*** (2.90) (2.55) (3.65) Systematic 1.71%*** 1.85%*** 1.90%*** (8.40) (6.85) (5.82) Stock Index 1.64%*** 2.58%*** 3.20%*** (5.01) (5.24) (5.03) Energy 3.71%*** 6.82%*** 8.44%*** (5.85) (7.08) (7.55) Financial/ Metal 2.20%*** 3.51%*** 4.25%*** (12.86) (14.29) (14.93) Discretionary 2.34%*** 3.18%*** 4.84%*** (6.78) (6.86) (7.67)
37
Table 8: Performance measurement using a specific multifactor model for each CTA categories This table presents the results of the estimation of the multifactor models on monthly data for the 1996-2005 sample period. Mkt = excess return of the Market Proxy; SMB = the factor-mimicking portfolio for size (small minus big); HML = the factor-mimicking portfolio for book-to-market equity (high minus low); PR1YR = the factor-mimicking portfolio for the momentum effect; Var, Skew, Kurt = the factor-mimicking portfolios for variance, skewness and kurtosis (higher 33% minus lower 33%), respectively. For each underlying, the reported coefficient of option-based factors corresponds to the double-letter code to the left: “A” means ATM, “O” means OTM (+5% for calls, - 5% for puts), “C” means call, “P” means put, “S” means straddle or strangle. t-statistics (not reported) are heteroskedasticity consistent. *Significant at the 10% level, ** significant at the 5% level, *** significant at the 1% level.
Diversified Arbitrage Financial/metal Systematic Energy Discretionary Stock index αααα 4.03%*** -5.19%*** 2.19%*** 0.45% -0.17% 1.06%*** 1.68%***
Indexes Mkt 0.011 0.0259** 0.0077 SMB 0.0006 -0.5009 PR1YR -0.0535 Moments Var 0.0001 0.0027 -1.0452 -2.3815** 0.0022 0.0957* 0.0738 Skew -0.0432 -0.4762* -0.0496 -0.1174* -0.0868 0.1323 -0.0051 Kurt -0.0419 1.2938*** -0.0197 0.0296 0.1017 0.0079 -0.0248 Options FX-$/€ OC -0.0014*** OS -0.0341 AS -0.0005 OC 0.168 AP 0.0084*** FX-$/£ OP 0.0154*** AP -0.0533*** OS 0.0183* OS -0.0008*** AP 0.128 OS -0.0008* AC 0.0098 FX-$/¥ OS -0.2538** OS -0.1314* OC 0.0861 IR-Credit OP 0.009*** AP 0.0373*** OS 0.0031** AP 0.0025* AP 0.0142*** IR-Term OP -0.0184** AC -0.0233*** AC 0.0012 AC 0.0029* OP 0.0057 OS 0.0104** AS -0.0575 Com-Gold AC 0.1414*** AP 0.0504*** OC 0.0063*** AC 0.0098 Com-Oil OC -0.034** OC 0.0112 OP 0.2628** OP -0.0067*** AP -0.0288*** AC 0.299*** AP 0.0109** OS -0.07*** OS -0.2852*** AS -0.1161** Com-Wheat OS -0.0077*** AC 0.011*** AC 0.0686 AS -0.0609*
R2adj 0.4939 0.4311 0.3453 0.2914 0.3233 0.0710 0.2454
38
Table 9: Performance of CTAs using the multifactor model in different subperiods This table presents the performance of CTAs using the multifactor model for different subperiods. t-statistics (not reported) are heteroskedasticity consistent. *Significant at the 10% level, ** significant at the 5% level, *** significant at the 1% level.
Whole period 2 subperiods Asian crisis CTA Category 1996-2005 1/1996- 12/2000 1/2001- 12/2005 1/1997-6/1998
Diversified 4.03%*** 4.14%*** 3.38%*** 10.56% Arbitrage -5.19%*** -1.40%** -0.13% -5.32%
Systematic 0.45% 0.07%*** 0.01% 0.31% Stock Index 1.68%*** 1.82%*** 0.08%*** 2.14%**
Energy -0.17%*** 1.72% 1.17% 7.05%* Financial/Metal 2.19%*** 2.46%*** 3.20%*** 3.32% Discretionary 1.06%*** 0.18% 0.97% 0.25%
39
Table 10: Performance persistence of CTAs For each formation/holding period, the sample is split into overlapping (to maximize power) periods of the required frequency during the 1996-2005 sample period. WW denotes funds that are winners in two consecutive periods; LL denotes funds that are losers in two consecutive periods; WL denotes funds that are winners in the first period and losers in the second period; and LW denotes the reverse. Each panel displays the percentage of occurrences of WW, WL, LW, and LL over the sample period, the chi-square test result (the percentage of cases where statistically significant persistence was observed in each CTA category), and the cross-product ratio (CPR). The statistical significance of the CPR is tested with a Z-statistic, which measures the ratio of the natural log of CPR to its standard error. The CPR and chi-square statistic are calculated as per Section 4.3.
Panel A: 1 month WW WL LW LL CPR Z-stat χχχχ2
Diversified 25% 25% 25% 25% 1.00 0.03 45% Arbitrage 25% 19% 18% 40% 2.92 0.54 14% Systematic 25% 23% 23% 27% 1.28 0.51 24% Stock Index 24% 20% 19% 36% 2.27 1.11 24% Energy 22% 23% 23% 32% 1.33 0.19 17% Financial/ Metal 25% 24% 23% 27% 1.22 0.58 41% Discretionary 25% 23% 22% 29% 1.43 0.51 12% Panel B: 3 months Diversified 35% 14% 15% 35% 5.83 6.35 90% Arbitrage 33% 11% 11% 45% 12.27 1.02 26% Systematic 34% 13% 14% 37% 6.91 2.90 79% Stock Index 31% 11% 11% 46% 11.79 2.73 71% Energy 34% 13% 13% 41% 8.25 1.12 45% Financial/ Metal 35% 13% 15% 37% 6.64 4.67 85% Discretionary 35% 13% 14% 37% 7.12 2.51 62% Panel C: 6 months Diversified 37% 10% 12% 40% 12.33 7.50 91% Arbitrage 37% 6% 5% 51% 62.90 1.16 32% Systematic 36% 12% 11% 39% 10.64 3.35 88% Stock Index 34% 7% 8% 49% 29.75 3.16 87% Energy 36% 10% 10% 44% 15.84 1.25 54% Financial/ Metal 38% 10% 12% 40% 12.67 5.61 90% Discretionary 37% 10% 11% 41% 13.79 2.51 80% Panel D: 12 months Diversified 39% 7% 10% 42% 23.40 7.59 90% Arbitrage 40% 5% 4% 49% 98.00 1.15 33% Systematic 38% 8% 9% 42% 22.17 3.54 89% Stock Index 35% 5% 7% 52% 52.00 3.19 92% Energy 38% 6% 6% 48% 50.67 1.32 50% Financial/ Metal 40% 8% 10% 41% 20.50 5.96 90% Discretionary 39% 7% 10% 43% 23.96 2.54 83%
40
Table 11: Performance persistence of CTAs For each period we report the (n+1) period persistence conditional on (n) period persistence for the 1996-2005 sample period. Each panel displays the chi-square test result (the percentage of cases where statistically significant persistence is observed in each CTA category), The chi-square statistic is calculated as per Section 4.3.
Period Diversified Arbitrage Systematic Stock Index Energy Financial/
Metal Discretionary
CTA with 1 month persistence 45.11% 13.53% 23.31% 24.06% 16.54% 40.60% 12.03%
3 month persistence conditional on 1 month persistence 4.48% 10.02% 4.80% 6.98% 9.09% 5.89% 4.50%
6 month persistence conditional on previous period persistence 0.38% 6.73% 0.56% 0.87% 4.19% 0.60% 0.91%
12 month persistence conditional on previous period persistence 0.04% 4.47% 0.06% 0.07% 2.06% 0.06% 0.16%
CTA with 3 month persistence 89% 25% 79% 70% 44% 85% 62%
6 month persistence conditional on 3 month persistence 87% 19% 69% 49% 28% 79% 43%
12 month persistence conditional on previous period persistence 84% 15% 60% 36% 13% 74% 31%
CTA with 6 month persistence 91% 32% 88% 87% 53% 89% 79%
12 month persistence conditional on 6 month persistence 88% 28% 82% 79% 31% 88% 69%
41
Table 12: Performance persistence of CTAs in different subperiods This table presents the performance persistence of CTAs for different subperiods for the 1996-2005 sample period. Persistence is based on the chi-square test result (the percentage of cases where statistically significant persistence was observed in each CTA category), The chi-square statistic is calculated as per Section 4.3.
Whole period 2 subperiods Asian crisis Panel A: 1 month 1996-2005 1/1996- 12/2000 1/2001- 12/2005 1/1997-6/1998
Diversified 45% 47% 44% 37% Arbitrage 14% 15% 12% 16% Systematic 24% 27% 20% 32% Stock Index 24% 23% 26% 26% Energy 17% 11% 23% 5% Financial/ Metal 41% 44% 38% 47% Discretionary 12% 15% 9% 15% Panel B: 3 months Diversified 90% 97% 83% 100% Arbitrage 26% 24% 27% 55% Systematic 79% 85% 73% 90% Stock Index 71% 62% 80% 68% Energy 45% 40% 50% 32% Financial/ Metal 85% 92% 78% 84% Discretionary 62% 70% 55% 68% Panel C: 6 months Diversified 91% 97% 85% 100% Arbitrage 32% 42% 21% 63% Systematic 88% 94% 82% 95% Stock Index 87% 86% 89% 85% Energy 54% 56% 51% 53% Financial/ Metal 90% 97% 82% 100% Discretionary 80% 87% 72% 95% Panel D: 12 months Diversified 90% 97% 82% 100% Arbitrage 33% 42% 22% 47% Systematic 89% 97% 80% 100% Stock Index 92% 94% 90% 95% Energy 50% 70% 27% 57% Financial/ Metal 90% 97% 82% 100% Discretionary 83% 91% 72% 95%
42
Table 13: Performance persistence of CTAs in the extremities of the rankings We use data for the 1996-2005 sample period. The performance analysis award a “win” to those funds with a ranking in the top quartile “T”(normalized ranking greater than or equal to 0.75), and a “lose” to those funds with a ranking in the bottom quartile “B” (normalized ranking less than 0.25). If a CTA fund earns a ranking placing them in either of the middle quartiles (greater than 0.25 or less than 0.75) it is assigned a rating of NS. Only CTA funds in the top or bottom quartile are paired with a subsequent fund. As we are principally interested in the extreme performers, we only present results for WTWT (top “T” funds that are winners in two consecutive periods) and LBLB (bottom “B” funds that are losers in two consecutive periods); Each panel displays the percentage of occurrences of WTWT and LBLB over the sample period and the chi-square test result (the percentage of cases where statistically significant persistence was observed in each CTA category). The chi-square statistics are calculated as per Section 4.3.
Panel A: 1 month WT WT LBLB χχχχ2
Diversified 13% 10% 92% Arbitrage 22% 20% 1% Systematic 16% 13% 76% Stock Index 17% 14% 50% Energy 18% 16% 5% Financial/ Metal 12% 11% 98% Discretionary 17% 14% 58% Panel B: 3 months Diversified 23% 22% 48% Arbitrage 25% 26% 0% Systematic 23% 24% 4% Stock Index 26% 25% 7% Energy 23% 20% 2% Financial/ Metal 24% 22% 46% Discretionary 18% 12% 49% Panel C: 6 months Diversified 28% 27% 47% Arbitrage 27% 29% 0% Systematic 30% 28% 12% Stock Index 30% 30% 15% Energy 23% 24% 1% Financial/ Metal 27% 27% 27% Discretionary 21% 12% 40% Panel D: 12 months Diversified 8% 48% 70% Arbitrage 29% 30% 0% Systematic 14% 35% 39% Stock Index 32% 33% 19% Energy 28% 28% 0% Financial/ Metal 31% 31% 54% Discretionary 12% 23% 54%
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