Do Market Timing Hedge Funds Time the Market? - SSRN papers

Do Market Timing Hedge Funds Time the Market?

Yong Chen, Bing Liang∗

Journal of Financial and Quantitative Analysis Vol. 42, No. 4, Dec. 2007, pp. 827-856

Abstract This paper examines whether self-described market timing hedge funds have the ability to time the U.S. equity market. We propose a new measure for timing return and volatility jointly that relates fund returns to the squared Sharpe ratio of the market portfolio. Using a sample of 221 market timing funds during 1994–2005, we find evidence of timing ability at both the aggregate and fund levels. Timing ability appears relatively strong in bear and volatile market conditions. Our findings are robust to other explanations, including public information–based strategies, options trading, and illiquid holdings. Bootstrap analysis shows that the evidence is unlikely to be attributed to luck.

JEL Classification: G11; G23 Keywords: hedge funds; return timing; volatility timing; bootstrap

∗

Chen, [email protected], Pamplin College of Business, Virginia Tech, Blacksburg, VA 24061; Liang, [email protected], Isenberg School of Management, University of Massachusetts, Amherst, MA 01003. We thank Stephen Brown (the editor), Jeffrey Busse (the referee), Don Chance, Wayne Ferson, Mila Getmansky, Will Goetzmann, David Hsieh, Ravi Jagannathan, Hossein Kazemi, Jeff Pontiff, Tom Schneeweis, and seminar participants at the University at Albany, SUNY, University of Vienna, the 2005 Center for International Securities and Derivatives Markets (CISDM) annual conference at the University of Massachusetts at Amherst, 2005 European Finance Association meetings, and the Second Empirical Asset Pricing Retreat at the University of Amsterdam for helpful comments. We also thank Vikas Agarwal and Narayan Naik for providing option return data, and CISDM, HFR, and TASS for providing hedge fund data. We are responsible for all remaining errors.

Electronic copy available at: http://ssrn.com/abstract=676110

I. Introduction The question of whether professional money managers have the ability to time the market has attracted tremendous interest from both academics and practitioners. Market timing is a performance-enhancing strategy that adjusts fund beta based on the manager’s market return forecast. Following the pioneering work of Treynor and Mazuy (1966, hereafter TM), many academic efforts have focused on the timing ability of professional portfolio managers.1 With a few exceptions,2 most empirical tests find little evidence of timing ability in mutual funds or pension funds. However, the rapidly growing hedge fund industry provides a new platform for examining market timing ability. According to the estimates of Lipper TASS Inc., total assets under management by hedge funds increased from $39 billion in 1990 to over $1 trillion in 2005, during which time the number of hedge funds increased from 200 to about 8,000. As noted by Fung and Hsieh (1997) and others, hedge funds differ from traditional mutual funds by their more extensive use of dynamic trading strategies. Due to less regulatory oversight, hedge funds have flexibility to engage in short selling, leverage, and various types of arbitrage activities. Thus, if it is possible for portfolio managers to time the market, we would expect the hedge fund industry to be a more natural place to locate such ability. In this paper, we examine the timing ability of the self-reported “market timing” hedge funds. Thus far, there have been only a few studies relevant to market timing of hedge funds. Fung and Hsieh (1997) show that dynamic strategies employed by hedge funds can result in option-like returns, suggesting the possible existence of timing ability. Fung and Hsieh (2001) construct a look-back straddle factor to model the nonlinear returns of trend-following hedge funds. Chen (2005) examines the ability of hedge funds in various investment categories to time their focus markets. He finds that a few fund categories (e.g., global macro and managed futures) can time the bond and currency markets, but timing ability is sparse in the equity market.

1

A partial list includes Jensen (1972), Fama (1972), Merton (1981), Henriksson and Merton (1981, hereafter HM), Henriksson (1984), Chang and Lewellen (1984), Admati et al. (1986), Jagannathan and Korajczyk (1986), Ferson and Schadt (1996), Becker et al. (1999), Busse (1999), Goetzmann et al. (2000), Bollen and Busse (2001), Laplante (2003), Jiang (2003), and Jiang et al. (2005). 2 Busse (1999) and Bollen and Busse (2001), who employ daily return data, and Laplante (2003) and Jiang et al. (2005), who use information on portfolio holdings, find supportive evidence of market timing in mutual funds.

1 Electronic copy available at: http://ssrn.com/abstract=676110

This paper contributes to the market timing literature in several respects. First, instead of studying all hedge funds, we concentrate on the self-described “market timers,” which would presumably be the funds most likely to successfully time the market. These funds are drawn from three major hedge fund databases, namely the Center for International Securities and Derivatives Markets (CISDM), Hedge Fund Research, Inc. (HFR), and Lipper TASS (TASS). Second, we examine the ability to time market volatility as well as to time market return. Many hedge funds trade volatility and thus are sensitive to market volatility changes. Hence, it makes sense to extend market timing tests to the volatility dimension. To our knowledge, this is the first paper to evaluate volatility timing in the hedge fund industry. Third, we propose a new market timing measure, consistent with the models of Jensen (1972) and Admati et al. (1986). By relating fund returns to the squared Sharpe ratio of the market portfolio, this new measure tests for return timing and volatility timing jointly. Fourth, we apply a bootstrap analysis to distinguish timing skills from luck. Given that hedge funds often have short histories and non–normally distributed returns, the bootstrap technique enhances the reliability of our inferences. Finally, we analyze the cross-sectional relationship between timing ability and various fund characteristics. Using a sample from January 1994 to June 2005 of 221 market timing funds, we find economically and statistically significant evidence of timing ability, including return timing, volatility timing, and joint timing, both at the aggregate level and at the individual-fund level. In addition, timing ability appears especially strong in bear and volatile markets, suggesting that market timing funds provide investors with protection against extreme market states. Moreover, we find that small funds and onshore funds tend to time better, other things being equal. There is also some evidence that the timing funds exhibit performance persistence. Our findings are robust to alternative explanations. In particular, we recognize the challenge of examining the timing ability of hedge funds because they may employ dynamic trading strategies that can be confused as market timing skills. Jagannathan and Korajczyk (1986) show that spurious timing ability may arise if the fund trades options and leveraged securities. Ferson and Schadt (1996) find that the timing measure can be biased if the fund systematically reacts to public information that can predict market movement. Therefore, to distinguish timing ability from artificial evidence, we conduct robustness tests controlling for funds’ options trading, leverage use, illiquid holdings, and reactions to public information. The evidence of timing ability

2 Electronic copy available at: http://ssrn.com/abstract=676110

is robust to these explanations. In addition, a bootstrap analysis shows that the evidence of timing ability is unlikely to be attributed to luck. The rest of this paper proceeds as follows. Section II describes the data on market timing hedge funds and economic factors. In Section III, we discuss various market timing models. Motivated by the work of Jensen (1972) and Admati et al. (1986), we propose a joint measure of return timing and volatility timing. Sections IV, V, and VI present the empirical evidence at the aggregate level, extensions and robustness tests, and the evidence at the fund level, respectively. Finally, Section VII offers some concluding remarks.

II. The Data A. Market Timing Funds The data of market timing funds in this paper are drawn from three major hedge fund databases— CISDM, HFR, and TASS. CISDM and HFR include a specific fund style of “market timing.” Furthermore, we find that TASS also contains funds that focus on market timing strategies, although the database does not explicitly group them into a market timing category. Specifically, we manually check the “Notes” document, obtained from TASS, which contains information about fund investment styles from the fund prospectuses. Based on the descriptions, we identify funds that claim to employ market timing strategies.3 Thus, from the three databases, we are able to identify 257 market timing funds during the period of January 1990 to June 2005, which consist of 14,404 fund–month return records. They comprise 72 live and 51 defunct funds from TASS, 40 live and 71 defunct funds from HFR, and 15 live and eight defunct funds from CISDM. After deleting 25 duplicate funds and 11 funds with incomplete or non-monthly return series, we have 221 funds remaining in the sample, including 106 active funds and 115 defunct funds. Survivorship bias arises if return information only from live funds is employed to measure performance (e.g., see Brown et al., 1992; Elton et al., 1996). Similarly, making inferences conditional on fund survival can bias the estimates of timing ability if poorly timing funds, on average, are more likely to disappear than well-timing funds. Table 1 presents the

3

These market timing funds are from the TASS categories of “long–short equity hedge,” “multi-strategy,” “fund of funds,” “managed futures,” and “global macro.”

3

annual attrition rates for these market timing funds from 1994–2005. The attrition rates are calculated as the ratio of funds disappearing in a given year to the number of funds existing at the start of the year. We do not observe funds disappearing prior to 1994 because the hedge fund databases began including defunct funds only from that year. In our sample, 19 market timing funds existed in 1993 and the number of funds had grown to 106 as of June 2005. During the period 1994–2005, 202 timers entered the databases while 115 funds were dropped. The average annual attrition rate was 12.3% over the period of 1994–2005, which is higher than the rate for TASS funds as a whole during the same period (8.6%).4 In later analyses, we employ only the fund return data from January 1994 to mitigate possible survivorship bias. Accordingly, 11,623 fund–month observations remain in the sample. [Insert Table 1 here]

To further address the survival-conditioning problem, we employ the statistical technique of Baquero et al. (2005) to adjust monthly returns on the funds. In tests for the persistence of hedge fund performance, Baquero et al. apply a weighting procedure to address look-ahead bias—one type of selection bias from ex post survival conditioning. The rationale of the technique is as follows. In each period, the observed (average) return on a fund is conditional on its survival. Thus, to obtain an unconditional expected return, one can multiply the observed return by a weighting factor that is the ratio of the unconditional probability of fund survival to the conditional probability in the period. In this paper, the unconditional survival probability is the proportion of funds that survived until the end of the period divided by the number of funds present at the beginning of the period. We measure the conditional survival probability with a pooled probit regression of fund survival in a month on prior fund performance and various fund characteristics. Appendix A provides details about the adjusting procedure. In the rest of the paper, we shall use only the adjusted return series to test market timing ability.

4

The attrition rates vary across different fund categories. For example, in the TASS database, the average attrition rate ranges from 5.5% per year with event-driven funds to 13.2% per year with managed futures funds during 1994–2005. Details about attrition rates of the TASS database are available from the authors upon request. Brown et al. (1999) report an average attrition rate of 19% for offshore hedge funds over the period 1989–1995. Liang (2000) documents an average attrition rate of 8.3% per year for the TASS funds from 1994–1998. Getmansky et al. (2004), also using the TASS fund sample, estimate an average attrition rate of 9.11% during 1994–1999.

4

Panel A of Table 2 displays summary statistics for these market timing funds. After adjusting the returns for survival conditioning, we find that the timing funds provide an average net-of-fee return of 1.075% per month and fund volatility of 1.93% per month during the period 1994–2005.5 During the sample period, the minimum return for the equally weighted portfolio of the timing funds is -2.91% in February 2001, while the maximum is 8.35% in December 1999. For the market timing tests at the aggregate level, we mainly employ the adjusted equal-weighted portfolio of the market timing funds (AMTF). The average monthly return for AMTF is slightly less than the unadjusted return (1.086%). The first-order autocorrelation in monthly fund returns is 0.11, slightly below the average level (0.12) for all hedge fund categories documented by Getmansky et al. (2004). [Insert Table 2 here]

The sample of 221 market timing funds should be fairly representative of this investment style, although it may not cover the universe of such funds. After all, market timing funds are in the minority in the hedge fund industry, as compared to investment styles such as event driven, long–short equity hedge, and market neutral. Moreover, the market timing literature suggests that the group of professional market timers and timing-oriented funds is relatively small. Becker et al. (1999), for instance, examine the ability of 114 asset-allocation mutual funds to time the market. Chance and Hemler (2001) evaluate the timing ability of 30 professional timers from 1986–1994. Laplante (2003) measures timing ability among 357 balanced and asset-allocation mutual funds during the period 1992–2002. Most other studies on market timing have employed even more limited samples. Therefore, the sample of market timers in this paper is relatively large. In addition, since the sample is drawn from three major hedge fund databases, it should cover a substantial portion of timing-oriented funds in the hedge fund industry.

5

The return profile of the market timing funds is similar to reported in the existing hedge fund literature. For example, Fung and Hsieh (1999) find that hedge funds realize an annual mean return of 15.1% with a standard deviation of 5.7% from 1990–1997. Brown et al. (1999), using offshore hedge fund data from 1989–1995, document an average annual return of 22.05% for market timing hedge funds. Moreover, Getmansky et al. (2004) report an annual mean return of 13.72% with a standard deviation of 9.46% for the TASS hedge funds during the period 1977–2001.

5

B. Factors and Instruments Panel B of Table 2 summarizes the economic factors used in the market timing models. They are monthly observations of the following variables: the Center for Research in Security Prices (CRSP) value-weighted market index, the Fama-French size and book-to-market factors, and a momentum portfolio similar to Carhart (1997). We employ the Chicago Board Options Exchange implied volatility index (VIX) to proxy market volatility. Since the original data from VIX measure annual volatility at daily frequency, we divide the end-of-month VIX values by 12 to obtain monthly market volatility. For robustness, we also use the realized market volatility, i.e., the standard deviation of monthly market returns. The average market return is 0.9% per month over 1994–2005, with a standard deviation of 4.5%. The lowest monthly market return is -15.8%, in August 1998, and the highest is 8.4%, in April 2001. The conditional performance evaluation takes into account the reaction of fund beta to public information that has predictability to the market return (see Ferson and Schadt, 1996). In this paper, we use four lagged instruments to represent public information, namely, the threemonth T-bill rate, the term spread between 10-year and three-month Treasury bonds, the quality spread between Moody's BAA- and AAA-rated corporate bonds, and the dividend yield of the S&P 500 index. The instruments’ data are obtained from the Federal Reserve Bank of St. Louis and Datastream databases. Panel C presents summary statistics for these instruments. Panel D reports the correlations among the portfolio of the market timing funds (AMTF), the return for a market timing strategy (MTS), and other factors. MTS describes the payoffs of a hypothetical market timer who can accurately forecast whether the market return (MKT) will be greater than a risk-free rate (RF) in the next month. Thus, the “perfect” timer would either fully invest in the stock market when MKT>RF or otherwise fully invest in the risk-free asset. Consequently, the timer realizes a return MTS = max(MTK, RF) for each month. The correlation between AMTF and MTS is 0.68, indicating that the payoffs of the timing funds, to some extent, resemble those of a perfect market timer.

III. The Methodology In this section, we describe the market timing models that we employ in the empirical analyses. In subsections A through C, we review the market timing models of TM (1966), HM

6

(1981), and Busse (1999). Motivated by the models of Jensen (1972) and Admati et al. (1986), we propose in subsection D a joint timing measure that relates fund returns to the squared Sharpe ratio of the market portfolio.

A. Market Timing Market timing models describe how a fund manager possessing superior information about the market should adjust his portfolio’s market exposure when he observes a signal about future market return. Assume that fund returns are generated by the following factor model: (1)

rp ,t +1 = α + β t rm ,t +1 + ε t +1 ,

t = 0,...,T-1,

where rp,t+1 is the excess return on fund p over the one-month T-bill rate at month t+1, and rm,t+1 is the market excess return. β t is the fund beta that varies with the manager’s timing signal at time t. εt+1 is the idiosyncratic risk. We assume that E(εt+1) = 0 and Cov(rm,t+1, εt+1) = 0. If fund beta β t is constant over time, the intercept becomes Jensen’s alpha, which measures selection ability or micro-forecasting ability (see Jensen, 1968; Fama, 1972). However, if the manager engages in market timing, Jensen (1972) shows that the intercept from a constant-beta model measures neither selection ability nor total ability of selection and market timing. Allowing for time-varying market exposure, Admati et al. (1986) show that a utility-maximizing manager should display the following beta: (2)

βt =

E (rm ,t +1 | st )

θ * Var (rm ,t +1 | st )

,

where θ is the Rubinstein (1973) measure of risk aversion, which is assumed to be constant. st denotes the manager’s timing signal. Equation (2) describes how a market timer incorporates information into fund management: fund beta should increase with expected market return, i.e., E(rm,t+1|st), and decrease with the expected market variance, i.e., Var(rm,t+1|st). Hence, such an expression of beta justifies the examination of timing ability from two dimensions: market return and market volatility.

7

B. Market Return Timing The timing models of TM (1966) and HM (1981) can be expressed in the following generic form: K

(3)

rp ,t +1 = α + ∑ β j r j ,t +1 + γrm ,t +1 S t +1 + ε t +1 , j =1

where βj is the loading to factor j. The timing term is S t+1 = rm,t+1 in the TM model and S t+1 = I(rm,t+1>0) in the HM model. The coefficient γ measures return timing. K equals 1 for the singlemarket factor model, 3 for the Fama-French three-factor model, or 4 for the Carhart four-factor model. Goetzmann et al. (2000), based on simulation results, find that incorporating the FamaFrench factors improves the market timing model specifications by reducing measurement bias. Regression (3) can be derived from the more general expression of Equation (2) under the assumption that fund return, the timing signal, and the error term have a joint normal distribution. In this case, the conditional market variance Var(rm,t+1|st) is a constant term, and thus fund beta responds linearly to the timing signal st = rm,t+1+ut in the TM model (where ut is a zero-mean independent noise term), or to st = I(rm,t+1>0)+ut in the HM model.6 In fact, we can derive the TM and HM market timing models by substituting market beta in Equation (2) into (1). In both models, coefficient γ captures the convexity of fund returns to the market return, indicating successful timing ability. In addition, Jiang (2003) proposes a nonparametric market timing test for convexity by examining the probability that beta is higher in up markets than in down markets. The conditional performance evaluation argues that a fund manager who simply employs publicly available information should not be accredited with managerial skills. Given that hedge funds often employ dynamic trading strategies, they may adjust market exposure to public information. Therefore, following Ferson and Schadt (1996), we use the products of the lagged instruments with the market return to control for funds’ use of public information: (4)

6

K

L

j =1

l =1

rp ,t +1 = α + ∑ β j rj ,t +1 + ∑ δ l zl ,t rm,t +1 + γrm, t +1St +1 + ε t +1 .

Under the normality assumption, E(rm,t+1|st) = μ r +[Cov(rm,t+1, st)/Var(st)](st – μs), and Var(rm,t+1|st) = m

Var(rm,t+1) – [Cov(rm,t+1, st)]2/Var(st), where μ is the unconditional mean (see, e.g., Zellner, 1971). Thus, the conditional expectation of the market return is a linear function of timing signal st, while the conditional variance is constant here.

8

z’s are demeaned series of four (i.e., L = 4) lagged instruments, including the threemonth T-bill yield, the term premium, the quality spread, and the dividend yield of the S&P 500 index. Ferson and Schadt (1996) and Becker et al. (1999) show that the conditional measure helps eliminate spurious timing ability that could otherwise arise from an unconditional performance measure.

C. Market Volatility Timing A fund manager can also time market volatility according to information on volatility changes. Fung and Hsieh (2001), for example, show that the payoffs of trend-following hedge funds mimic those of a straddle contract, which may reflect bets on market volatility. Furthermore, because they enter into derivative contracts, many hedge funds are sensitive to changes in market volatility. In fact, Equation (2) indicates that, other things being equal, a market timer should reduce market exposure when foreseeing an increase in market volatility. Busse (1999) provides the first examination of volatility timing for mutual funds. He finds supportive evidence using daily fund return data. Laplante (2003) justifies the evaluation of volatility timing by generalizing the normality assumption in Admati et al. (1986) to a Student t-distribution. With the Student tdistribution, the conditional market volatility is stochastic (i.e., Var(rm,t+1|st) in Equation (2) varies with the timing signal); thus, it makes sense to study volatility timing. Busse (1999) shows, if fund beta is expressed as a linear function of the demeaned market volatility from Taylor’s approximation, the following regression measures volatility timing: K

(5)

rp ,t +1 = α + ∑ β j r j ,t +1 + λrm,t +1 (σ m ,t +1 − σ m ) + ε t +1 , j =1

where σm,t+1 represents market volatility. In this paper, we use two proxies for market volatility, the implied volatility (VIX) and the realized market volatility. Busse (1999) also considers estimating market volatility from conditional volatility models (e.g., EGARCH), and obtains the same inferences as those based on the implied volatility. In regression (5), a negative value for coefficient λ indicates successful volatility timing because it indicates decreasing fund beta when the market becomes more volatile. Again, K equals 1 for the single-market factor model, 3 for the

9

Fama-French three-factor model, or 4 for the Carhart four-factor model. We can extend the volatility timing model to a conditional version in a similar way to Equation (4).

D. Measuring Return and Volatility Timing Jointly A hedge fund can change its market exposure based on perceptions of both market return and market volatility. Even if the fund manager foresees a high level of market return, he may not take heavy positions in the market without considering market volatility, and vice versa. An expected high volatility makes the manager behave conservatively in adjusting portfolio holdings. Therefore, the expression of fund beta in Equation (2) is consistent with real-world practice. Although only return timing matters under the normality assumption (see footnote 6), some studies have suggested relaxing the normality assumption for equity returns. Kan and Zhou (2003) advocate the multivariate Student t-distribution as a better characterization of asset returns. Laplante (2003), assuming a joint t-distribution of asset returns and timing signal, presents a market timing model that explicitly incorporates the signals about both the level and variance of the market portfolio. Considering a flexible distribution (e.g., Student t-distribution) instead of the normal, we propose the following market timing measure consistent with Equation (2): (6)

rp ,t +1

⎛ rm ,t +1 = α + ∑ β j r j ,t +1 + γ ⎜ ⎜ σ m ,t +1|s j =1 t ⎝ K

2

⎞ ⎟ + ε t +1 , ⎟ ⎠

where γ measures the timing ability of a manager who can forecast both the level and volatility of the market portfolio. The model can be derived by substituting the expression of beta in Equation (2) for that in Equation (1). Timing signal of the market level is st = rm,t+1+ut, and the signal of market variance, Var(rm,t+1|st), is linearly related to (st – μs)2 under Student tdistribution. 7 The conditional volatility is approximated by the implied market volatility. The

7

Under Student t-distribution with degree of freedom ν, Var(rm,t+1|st) = [(ν-2)/(ν-1)]{1+(st – μs)2/[(ν2)Var(st)]}{Var(rm,t+1) – [Cov(rm,t+1, st)]2/Var(st)}, where μ is the unconditional mean (e.g., Zellner, 1971, p. 388). The value of (st – μs)2 equals (σm,t+12 + σu,t2), which contains the variance of forecasting errors in timing signal, as well as the market variance. Estimating σu2 is difficult even under the normality assumption (see Admati el al., 1986; Lee and Rahman, 1990) and becomes further complicated by the assumption of t-distribution and by studying return and volatility timing jointly. Therefore, we use the implied volatility to proxy the conditional volatility and do not attempt to retrieve the precision (i.e., σu,t2) of timing signal.

10

timing term is like the squared Sharpe ratio of the market portfolio—the ratio of expected excess return to the (conditional) standard deviation. Existing market timing measures (e.g., TM and HM) have concentrated on the convexity of fund returns to the market return and ignored the fund reaction to changes in market volatility. The volatility timing model of Busse (1999) is a linear approximation of the relationship between fund beta and market volatility. However, our joint timing measure corresponds closely to the classical models of Jensen (1972) and Admati et al. (1986). It also has an intuitive appeal by relating fund return to the Sharpe ratio of the market portfolio. In Equation (6), for a fund employing buy-and-hold strategies, βm alone captures the fund’s market exposure and coefficient

γ should be zero. However, a market timing fund can enhance portfolio performance as long as the market’s Sharpe ratio is non-zero. The timer should increase his market exposure with the expected Sharpe ratio of the market portfolio. Finally, an alternative way to jointly measure return and volatility timing, as suggested by Busse (1999), is running the following regression: K

(7)

rp ,t +1 = α + ∑ β j r j ,t +1 + γrm ,t +1 + λrm ,t +1 (σ m ,t +1 − σ m ) + ε t +1 . 2

j =1

In the regression, a fund’s time-varying beta is approximated to be a linear function of both the market return and volatility, according to the first-order Taylor series expansion.

IV. Empirical Results at the Aggregate Level This section reports the empirical results about abnormal performance and timing ability at the aggregate level. The return series is from the equal-weighted portfolio of the 221 market timing funds from 1994–2005.8

8

We also employ a value-weighted portfolio of the timing funds and obtain qualitatively similar results. The value-weighted portfolio does not use all the return data in our sample because information on assets under management is unavailable for some funds in some months. Thus, we report the evidence based on the equal-weighted portfolio of the timing funds, but results from the value-weighted portfolio are available from the authors upon request.

11

A. Abnormal Performance Table 3 shows the abnormal performance of the market timing fund portfolio estimated by the single-factor, Fama-French three-factor, Carhart four-factor, and conditional four-factor models. Alphas from the four models are all positive and statistically significant, suggesting that, on average, the timing funds outperform a buy-and-hold strategy with a similar level of factor exposures. The alphas, all statistically significant at the 1% level, range from 0.53% per month (about 6.4% annually) to 0.62% per month (about 7.4% annually). Moreover, the funds show positive exposure to the market, but with a magnitude (about 0.3) lower than that of most equity mutual funds. The funds exhibit positive coefficients on the size portfolio and momentum portfolio and a negative loading to the value portfolio, suggesting that they tend to buy small-cap stocks, growth stocks, and stocks with good past performance. At the aggregate level, the funds do not seem to use public information, since the coefficients on the lagged instruments are not statistically significant. The results indicate that the market timing hedge funds deliver abnormal performance. Brown et al. (1999), using a sample of offshore hedge funds during 1989–1995, also find that the market timing–style funds exhibit a Jensen’s alpha of 12.1% per year, although they do not examine the timing ability of those funds. [Insert Table 3 here]

B. Return Timing Figure 1 clearly displays the convexity of fund returns to equity market return. It plots the returns on the market timing fund portfolio against the market excess return from January 1994 to June 2005. The graph shows that the market timing funds, on average, exhibit a higher slope (market beta) in an up market than in a down market. This reflects the essence of return timing: realizing high returns in good market states and lessening losses in poor market conditions. [Insert Figure 1 here]

We present the results from formal tests of market return timing based on the TM and HM models in Table 4. Overall, the timing funds do exhibit the ability to time the equity market regardless of model specification. The timing coefficients across the eight regressions are all positive and statistically significant at the 1% level. For example, timing coefficient γ from the

12

single-factor TM model is 1.29 with a t-statistic of 3.95. After controlling for return timing, we find that the alpha, compared to the values in Table 3, becomes less important with a smaller magnitude, and is not statistically significant in some cases. For instance, the alpha from the single-factor timing model is reduced by about 50%—from 0.56% per month in Table 3 to 0.28% per month. This implies that the value added from market timing strategies can explain a substantial portion of the aggregate abnormal return. Thus, these timing funds seem to focus on market timing strategies, which is consistent with their self-described investment objectives. [Insert Table 4 here]

Return timing of the funds is of economic significance as well. Consider the evidence from the single-factor TM model. The timing funds have an average beta of 0.367 and average timing coefficient is 1.29. This means that, if the timing signal forecasts a market excess return of 5% in the next month, the fund will increase market beta by about 0.064 (1.29 × 0.05), more than one-sixth of the average beta level. Conversely, an expectation of negative market excess return would decrease the fund’s market exposure, other things being equal. Results from the other model specifications provide a similar impression about the economic significance of return timing. Clearly, the timing funds adjust market exposure to their timing signals in a non-trivial way. We can also observe the economic value of timing ability from the evidence of the HM regression. Note that the timing term in the HM model, rm*S = max (Rm-RF, 0), is equivalent to the payoff from an option. Merton (1981) shows that the value of timing ability can be calculated using the Black–Scholes formula if relevant assumptions are satisfied. Specifically, we follow Merton’s assumptions on the values of the underlying stock price and strike price and find the market timing funds deliver 2.2 cents per annum from timing ability for each dollar invested.9

9

According to the Black–Scholes formula, the option value V = S Φ(x1) – X e-rT Φ(x2), where x1 = [ln(S/X) + (r+0.5 σ2)T]/ σ T , x2 = x1 – σ T , Φ(x1) is the cumulative normal distribution function, S is the underlying stock price, X is the strike price, r is the instantaneous rate of interest, T is the expiration period, and σ is the return volatility per period (month, here). We follow Merton’s (1981) assumptions: S = 1, X = RF, and e-rT = 1/RF. Under these assumptions, it is straightforward to show that V = 2 Φ[0.5 σ T ] – 1. From our data, we use the average monthly VIX as σ, set T = 12 for a year, and obtain V = 0.082. Therefore, for a timing coefficient 0.266 from the single-factor HM regression, the added value from timing skills is 0.022 (= 0.266*0.082). Of course, this value is at best an approximation, depending on the Black–Scholes conditions.

13

The conditional approach shows little impact on the inference about timing ability in this setting. This result contrasts with mutual funds (e.g., see Ferson and Schadt, 1996), where public information can help explain the “negative” timing ability found in an unconditional model. Ferson and Warther (1996) find that a mutual fund typically experiences money inflows during a period of high expected market return based on public information. Such fund inflows reduce the fund’s market exposure because the fund has to hold more cash before eventually allocating the new money to the market. Consequently, there arises a negative relationship between the expected market return and the fund’s market exposure, which is consistent with negative timing ability estimated for mutual funds by an unconditional model. Hedge funds, however, may have different money-flow patterns from mutual funds because they can effectively manage money flow with greater discretion. For instance, hedge funds can discourage undesired fund inflows by choosing to be closed to new capital. They can restrict money outflows by imposing redemption restrictions (e.g., lock-up provisions). Therefore, these features of hedge fund flows could possibly explain the low explanatory power of public information. We leave this topic for future research.10

C. Volatility Timing Table 5 reports the results on volatility timing from various specifications of model (5). We measure market volatility by two indexes, namely, the implied volatility and the realized volatility. Among various regressions, the volatility timing coefficient λ shows a value of about -3.5 (1% significance level). For example, in the single-factor model using VIX, the estimated λ is -3.49, with a t-statistic of -3.89. This means that the timing funds, on average, reduce their market exposure when the market is expected to be more volatile (and vice versa), which corresponds to the intuition of volatility timing described in Equation (2). We draw very similar inferences based on the regressions using the implied volatility (Panel A) and the realized volatility (Panel B). Furthermore, the alpha is a positive 0.43% per month and significant at the 1% level. This implies that volatility timing alone cannot fully explain the funds’ abnormal performance and that return timing as well as securities selection may play a role. 10

However, in Section VI, where timing ability is measured at the fund level, we find that the results from the conditional models are, to some extent, different from those from the unconditional models, which suggests a certain level of heterogeneity in the money flow patterns among the timing funds.

14

In addition, the ability to time market volatility is economically important. Again, take the results from the one-factor model as an example. Here, the timing coefficient λ is -3.49 and the average beta is about 0.4. If the fund manager foresees market volatility to be 5% higher than the average level, he will reduce market exposure by 0.18 (-3.49 × 0.05), approximately 44% of the average beta. Hence, similar to Busse (1999), we find that the funds provide investors with a type of volatility hedge. Fleming et al. (2001), using a conditional mean–variance analysis, also show that volatility–timing strategies are of significant economic value, since payoffs of such strategies outperform those of an unconditionally efficient portfolio. [Insert Table 5 here]

D. Joint Timing We employ the proposed model (6) to measure return and volatility timing jointly. Panel A of Table 6 shows the results from the single-, three-, and four-factor and conditional regressions. The joint timing coefficient γ is between 0.005 and 0.006, statistically significant at the 1% level, across the four specifications. It shows a positive relationship between fund returns and the squared Sharpe ratio of the market portfolio.11 Although interpreting the joint timing coefficient is not as straightforward, we can still illustrate its impact on the adjustment of market exposure based on a numerical example using the coefficients from the single-factor model. Suppose the market in the current month can be characterized by an excess return of 0.1 and volatility 0.05 (variance 0.0025). The fund’s beta would then equal 0.56—the average beta of 0.36 + 0.2 (0.005 × 0.1/0.0025). Now, consider the fund manager receives a signal—market volatility will be 0.07 (variance 0.0049) in the next month, but the market level is unchanged. Accordingly, the manager will lower the fund beta by 18% to 0.46—0.36 + 0.10 (0.005×0.1/0.0049). This example demonstrates the role of joint timing in fund management. In addition, prior studies have discussed the economic value of market timing to the market level and volatility. For instance, Breen et al. (1989) find that the one-month interest rate is useful for forecasting the sign and variance of the market return from 1954–1986 and an active investor

11

Strictly speaking, the Sharpe ratio is different from the conventional term, because the market volatility here is a conditional volatility on past information.

15

using such forecast would realize a higher return with lower volatility compared to a passive index fund. [Insert Table 6 here]

Panel B of Table 6 reports the results from the combined return and volatility timing model of Busse (1999). These tests also show statistically significant evidence of both return timing and volatility timing, consistent with the evidence presented earlier in this section. While the Busse regression generates similar inferences as the joint timing model, the latter corresponds more closely to the classical work of Jensen (1972) and Admati et al. (1986).

V. Extensions and Robustness A. Timing Ability in Different Market Conditions We now examine whether the funds show different timing abilities in various market states. Such a test is interesting because a fund manager may receive different timing signals ahead of different market conditions. For example, we expect that the fund would time the market level better in a bear market than in a bull market. It is difficult to outperform a soaring market, while a bear market may leave some room for the manager to improve. Furthermore, it is arguably more important for a volatility timer to shun the market during volatile periods. Therefore, we estimate return timing separately for bull and bear markets, estimate volatility timing for stable and volatile markets, and measure joint timing for the high and low Sharpe ratio market conditions. Such market separation is motivated by the fact that different timing abilities focus on different market moments, as discussed in Section III. Table 7 shows the timing ability of the equal-weighted portfolio in different market states. Return timing is more apparent during bear markets (i.e., periods when the market return is less than the T-bill rate) than during bull markets. In bear markets, the timing coefficient γ is 1.75, with a t-statistic of 2.19. This pattern can also be observed from Figure 1, in which the convexity mostly manifests in the downside market portion. Moreover, volatility timing is significant in volatile market states (λ = -4.96, t-statistic = -4.43) over the sample period 1994–2005. Finally, there is no obvious difference in joint timing between the high Sharpe ratio and the low Sharpe ratio states.

16

It appears that the funds provide investors with protection in bear and volatile markets.12 This payoff feature potentially mitigates losses in undesirable market states, and thus is valuable for risk-averse investors. Of course, different timing behavior in various market states does not affect the inference of overall timing ability. After all, fund beta is higher in bull markets than in bear markets, higher in stable markets than in volatile markets, and higher in high Sharpe ratio states than in low Sharpe ratio states.13 [Insert Table 7 here]

B. Time Variation in Timing Ability Timing ability is likely to vary over time due to changing market conditions. Thus, we investigate the time series pattern of timing coefficients. We run rolling regressions using a 36month window based on the TM return timing model and the Busse (1999) volatility timing model from January 1994 to June 2005. For each month, the timing coefficient t is estimated based on the return data from t to t+35. Figures 2 and 3 plot the coefficients for return timing and volatility timing over time, respectively. [Insert Figures 2 and 3 here]

Timing abilities (return and volatility timing) of the timing funds are stronger during September 1995–September 1998 than in other periods. In fact, the market return dropped by about 15% in August 1998, and the rolling regressions from September 1995 to September 1998 contain that observation. Again, this indicates that timing ability is especially apparent in extremely down market states, which is consistent with the results in Table 7. Nevertheless, if the evidence of timing ability were merely driven by an observation in one atypical period, much of the appeal of the findings would be reduced. We repeat all the market timing tests, excluding six monthly observations around August 1998 to remove the influence of this particular period. After excluding these months, we still find significant evidence 12

We admit that the way we define different market states is ex post; our purpose here is to provide a simple illustration. Ferson et al. (2006) employ ex ante variables to proxy the economic states to evaluate the conditional performance of the US government bond funds. 13 Although Table 7 shows a slightly higher average beta in volatile markets (βm = 0.45) than that in stable markets (βm = 0.42), the overall beta in volatile markets is less than that in stable markets. This is because of the negative volatility timing (λ = -4.96) that substantially reduces beta when the market is volatile.

17

of timing ability with the timing funds. For example, the return-timing coefficient is 1.13 with a tstatistic of 2.67 from the single-factor TM model, and the volatility–timing coefficient is -3.09 with a t-statistic of -2.38 from the volatility timing model (using the implied volatility).

C. Controlling for Options Trading Measuring timing ability (especially return timing) is to test for a convex relation between fund returns and a benchmark (e.g., the stock market index). It is well known, however, that such nonlinearity can arise from option-like trading. Jagannathan and Korajczyk (1986) point out that a fund manager simply holding options might be misinterpreted as a market timer because of the options’ nonlinear payoff. Interim trading, discussed by Goetzmann et al. (2000) and Ferson and Khang (2002), may also generate spurious evidence of timing ability. Recently, Brown et al. (2005) show if a fund manager engages in “informationless investing” (e.g., doubling trades), the portfolio payoffs can exhibit concavity to the benchmark. Therefore, we need to address the potential nonlinearity from option-like trading. First, to distinguish timing ability from payoffs of options trading, we divide the timing funds into two groups: the funds that use options and those that do not. In our sample, 100 funds show a status of whether they use options: 36 are options users and 64 are nonusers. We estimate abnormal return and timing ability for the two groups separately. Panel A of Table 8 tests for the difference in performance between the two groups, including t-test and Wilcoxon z-statistics. We find that the timing skills of options nonusers are similar and, in some cases, even superior to those of option users. Thus, our evidence of timing ability does not seem to be due to options trading.14 [Insert Table 8 here]

Second, Jagannathan and Korajczyk (1986) suggest including several nonlinear functions of the benchmark as “exclusion restrictions” in market timing regressions to examine model misspecification. Significant coefficients on such nonlinear terms would indicate misspecification of the market timing model. We employ two nonlinear functions of the market index, ln(|rm|) and 14

Some funds also show the status of whether or not to use leverage. Similarly, we separate them into two groups of leverage users and nonusers, and find that leverage use does not affect the market timing inference in our sample.

18

1/rm, as additional regressors in the regressions (3)–(7) and find the coefficients on the two variables are not statistically significant.15 The findings of timing ability are therefore unlikely due to model misspecification. Third, Glosten and Jagannathan (1994) approximate nonlinear fund returns using a series of options on the market index. Agarwal and Naik (2004) construct four option “factors” to measure the nonlinearity of hedge fund returns. The option factors include highly liquid at-themoney and out-of-the money European call and put options on the S&P 500 index, which exhibit certain explanatory power for hedge fund returns. We include these option factors as additional regressors to the market timing regressions.16 Table 8 Panel B shows that the evidence of timing ability is robust to these option factors. Finally, instead of using ad hoc regressors, Ferson et al. (2006) address the concerns of interim trading, options holdings, and informationless trading based on the continuous-time asset pricing model, since, theoretically, a continuous-time mode should price these portfolio strategies that do not use private information. Specifically, Ferson et al. (2006) include time-average state variables suggested by the pricing model as additional controls. 17 We include the monthly average of the logarithm of market price level in the market timing regression and find the general inference is unchanged. Hence, our results hold even after controlling for interim trading, options holding, and informationless investing.

15

Details about these robustness tests are available from the authors upon request. We thank Vikas Agarwal and Narayan Naik for generously providing their option return data. Since the option factor data end at February 2003, we use only the return data of the portfolio of the timing funds from January 1994 to February 2003 in the corresponding regressions. 17 Ferson et al. (2006) show that time aggregation of the state variable(s) in an asset pricing model, for discrete returns measured over the period from month t to month t+1, leads to the following stochastic discount factor (SDF): x tmt+1 = exp(a + b'A t+1 + c'[xt+1 – xt]), where x is the vector of state variables in the model and Axt+1 = Σi = 1,...1/Δ x(t+(i-1)Δ)Δ denotes the timeaveraged levels of the state variables over the return measurement period. The measurement period is divided into periods of length Δ = one trading day. Thus, the empirical factors suggested by the SDF are the discrete monthly changes in the state variables and their time averages within the month, i.e., (xt+1-xt) and Axt+1 respectively. In this setting, if the state variable is proxied by the logarithm of market price level, i.e., xt = ln(Pt), then interim trading problem can be controlled by the within-month average of the state variable. 16

19

D. Controlling for Illiquid Holdings Chen et al. (2005) show that systematic thin trading can also create spurious evidence of timing ability. Thin or nonsynchronous trading can bias the estimates of the portfolio beta (e.g., see Scholes and Williams, 1977; Dimson, 1979). For hedge funds, Asness et al. (2001) and Getmansky et al. (2004) point out that many funds are likely to hold illiquid assets that are traded infrequently and have stale prices. Chen et al. (2005) show that estimation of timing ability can be biased when the thinness of trading is systematically related to market conditions. They further show that such potential bias can be mitigated when the market timing regression incorporates lagged terms of the benchmark as regressors. Therefore, we employ two lagged market returns and their square terms to alleviate the thin-trading effect. 18 Table 9 reports the results. The estimates of contemporaneous timing ability are still significantly different from zero, although the second lagged market return and its square term pick up some explanatory power. This seems to suggest a certain level of thin trading with the timing funds, but the extent of thinness does not severely affect the inference about their timing skills. [Insert Table 9 here]

VI. Empirical Results at the Fund Level This section reports the fund-level tests for timing ability, the relation between timing skills and fund characteristics, and performance persistence. To obtain meaningful regressions, we require each individual fund to have at least 18 consecutive monthly return records during the sample period, which reduces the number of funds from 221 to 179.19

A. Timing Ability of Individual Funds Table 10 shows the evidence for various performance measures at the fund level. First, most of the funds (140 out of 179) have a positive abnormal return. At least 70 funds show significant alpha at the 5% level, while only about five funds exhibit significantly negative alpha. Second, 33 funds (more than 18%) display significant return timing at the 5% level according to the three-factor model, among which, 30 have positive timing and only three exhibit negative

18 19

We add more lagged terms to check robustness, and the inference is unchanged. We also require at least 24 or 36 consecutive monthly returns, and the inference is unaffected.

20

timing.20 Third, we also find strong evidence of volatility timing. For instance, based on the threefactor model, 59 funds have successful volatility timing ability (the volatility timing coefficient is multiplied by -1 in the table) at the 5% significance level, while 10 funds show perverse volatility timing. Finally, the joint timing tests convey a similar impression—roughly one-sixth of the funds show significantly positive joint timing. [Insert Table 10 here]

B. Bootstrap Analysis of Timing Ability Thus far, we have shown that among the market timing funds, there are many more funds exhibiting successful timing ability than exhibiting negative timing ability. However, there is still an important question to ask: could the evidence of timing ability come from pure luck? To answer this question, we conduct a bootstrap analysis of the timing ability. Following Kosowski et al. (2004), we randomly resample the regression residuals, estimate parameters based on the random residuals, and then calculate empirical standard errors. We bootstrap the t-statistics instead of the timing coefficients because the t-statistic is a pivotal statistic, whereas the coefficient estimator is not (e.g., see Horowitz, 2000). For each fund in our sample, we resample its regression residuals and construct 10,000 hypothetical funds whose returns have the same structure of factor loadings and idiosyncratic risk as the actual fund does, except that the timing ability is set to zero for these hypothetical funds. Next, we run market timing regressions for these hypothetical funds. Since the hypothetical funds are known to possess no timing ability, any evidence of timing ability should come from luck. Finally, we compare the timing ability of the actual fund with that of the hypothetical funds to distinguish true timing ability from artificial timing due to luck. For robustness, we also repeat the procedure by resampling both regression residuals and risk factors at the same time. Appendix B provides the details about the bootstrap procedure. Table 11 shows the top- and bottom-ranked fifteen funds in the actual sample according to t-statistics. The bootstrap p-values are based on 10,000 random replications. Specifically, by

20

Suppose γ’s are from independent Bernoulli distribution. Given that 18% of the γ’s are significant at the 5% level, these γ’s follow a binomial distribution with t-statistic = (0.18 – 0.05)/ 0.05 × (1 − 0.05) / 179 = 8.25, strongly rejecting the null hypothesis that all γ’s are zero.

21

comparing the ith ranked actual tγ with all the ith ranked hypothetical tbγ’s (with a total number of 10,000), we obtain the empirical p-values suggesting how likely the ith ranked actual tγ is due to randomness. We apply the bootstrap analysis to four performance measures: Jensen’s alpha, return timing, volatility timing, and joint timing. For each measure, we conduct two types of bootstrap: (1) resampling only the regression residuals (reported in the first row of bootstrap pvalues) and (2) resampling regression residuals and risk factors jointly (reported in the second row of bootstrap p-values). [Insert Table 11 here]

First, the bootstrap evidence on Jensen’s alpha shows that the top-ranked t-statistics are not likely attributed to luck, since the empirical p-values are nearly all zero. Second, we obtain a similar impression about return timing. Among the top fifteen t-statistics, p-values are below 0.05 for most of them (from the second to the 15th fund). For instance, the p-value associated with the second-ranked fund is 0.03, which means that from pure randomness we would have only 3% probability of obtaining a t-statistic as large as 3.75. By contrast, the negative timing of the funds may well be due to randomness, as the p-values associated with the 15 worst timing funds are all above 0.5. Results on volatility timing are generally similar, except that a negative sign indicates volatility timing (i.e., reducing beta when the predicted market volatility is high). Finally, results on joint timing are supportive of the existence of timing ability. Overall, the bootstrap analysis suggests that the evidence of timing ability is not likely due to luck.

C. Timing Ability and Fund Characteristics We now examine the relationship between timing ability and various fund characteristics to explore what kinds of funds are more likely to exhibit timing skills. Specifically, we regress timing coefficients estimated from the market timing regressions (the four-factor TM, volatility timing, and joint timing models) on fund characteristics. We look at nine fund attributes, including fund age, fund size, minimum investment requirement, management fee, incentive fee, the dummy of using high-water marks, lock-up period, advance notice period for fund redemption, and the offshore dummy. Table 12 reports the results. There is some evidence that smaller funds and onshore funds perform better than other funds in terms of return timing and joint timing. This

22

is perhaps because market timing requires a fund to move in and out of the market frequently and small funds are more nimble in performing timing strategies. Moreover, offshore funds, organized as corporations, typically have no restrictions on the number of investors, while onshore funds, organized as partnerships, limit the number of partners. This leads to the relatively large fund size of offshore funds 21 and large size may impede timing ability. On the whole, however, the relationship between timing ability and fund attributes is rather weak.

D. Persistence of Performance We conduct a simple test for the persistence of funds’ overall value-added ability. For each fund with at least 36 consecutive monthly returns, we measure total performance (i.e., selectivity and timing ability) for two equal subperiods of its return series.22 Then, we run a crosssectional regression of performance in the second subperiod on that in the first subperiod. A positive slope coefficient indicates performance persistence. For joint timing ability estimated from the four-factor model, the slope coefficient is 0.389 (t-statistic 5.58). Other model specifications deliver a similar result. This finding, together with the bootstrap evidence, confirms that randomness is unlikely to explain the evidence of timing ability with the market timing funds.

VII. Conclusions This paper examines whether market timing hedge funds have the ability to time the US equity market. Using a sample of 221 market timing funds drawn from three major hedge fund databases—CISDM, HFR, and TASS—we test for timing ability in both the market level and market volatility during the period 1994–2005. Motivated by the classical models of Jensen (1972) and Admati et al. (1986), we propose a new measure of timing return and volatility jointly, which relates fund returns to the squared Sharpe ratio of the market portfolio. We find significant evidence of timing ability both at the aggregate level and at the fund level. The timing ability generates significant economic value to investors. Moreover, timing ability appears especially strong during bear markets or when the market is more volatile, 21

In the sample, the average fund size for offshore timing funds is $36.9 million, while the average size for onshore funds is $24.0 million. 22 Note that the requirement of at least 36 monthly returns will not raise severe look-ahead bias, since, in Section II A, we have adjusted fund returns into return series unconditional on fund survival.

23

suggesting that the timing funds provide investors with protection against unfavorable market states. The findings are robust to alternative explanations, including public-information-based strategies, options trading, and illiquid holdings. A bootstrap analysis confirms that the evidence is unlikely to be explained by pure randomness. The evidence of timing ability with the market timing hedge funds appears much stronger than the previously documented for mutual funds. Therefore, despite little evidence of timing ability with traditionally managed portfolios (e.g., mutual funds), the hedge fund industry, with flexible investment strategies, seem to provide a fertile field for professional timers to time the market.

24

Appendix A: Adjusting Fund Returns for Survival Conditioning The observed fund returns are conditional on fund survival. This ex post conditioning may potentially bias the estimates of fund performance, especially the inference about performance persistence (see, e.g., Brown et al., 1992; Elton et al. 1996; Carhart, 1997). Ter Horst et al. (2001) propose a weighting procedure based on a probit regression to correct for the look-ahead bias and Baquero et al. (2005) apply this technique to study hedge fund performance persistence. In this paper, we employ their procedure to adjust the monthly returns on the market timing funds in our sample. Specifically, for each month t, we observe the return rp,t on a fund (say, fund p) given that the fund is alive. Thus, rp,t is a conditional return on fund survival. Based on the standard conditioning arguments, Ter Horst et al. (2001) derive the expression of an adjusted fund returns. (A1)

r pa,t = r p ,t *

P( Survivalt ) P( Survival | X p ,t −1 )

where rpa,t is the adjusted fund return. Xp,t-1 denotes available information about the fund at time t, including historical fund returns and various fund characteristics. P(Survivalt) is the unconditional probability of fund survival (i.e., one minus the attrition rate) in the period t. P(Survivalt|Xp,t-1) is the conditional likelihood of survival, estimated from a pooled probit regression of the survival dummy on past performance and fund characteristics. Table A1 reports the results of the pooled probit regression using the data of 221 market timing funds during the period 1994–2005. We adjust the return series for all the funds in the sample using this correction procedure. High survival probability of a fund is generally associated with high historical returns, especially returns in the past three quarters. This suggests that the effect of past returns on fund survival decreases with the lagged period, consistent with the finding in Baquero et al. (2005). Moreover, larger funds are less likely to liquidate, while the incentive fee has a negative impact on fund survival. The effect of fund age on survival is nonlinear: younger funds are more likely to survive, but the liquidation likelihood decreases with fund seasoning. In general, our results from Table A1 are very similar to Baquero et al. (2005). [Insert Table A1 here]

25

Table A1 Probit Regression of Fund Survival Variable

Coeff.

Std error

ret_1 ret_2 ret_3 ret_4 ret_5 ret_6 ret_7 ret_8 ret_9 ret_10 ret_11 ret_12

0.022 0.015 0.019 0.022 0.010 0.016 0.021 0.029 0.031 -0.003 0.007 -0.006

0.010 0.008 0.008 0.010 0.009 0.011 0.009 0.010 0.011 0.008 0.007 0.009

Variable

Coeff.

Std error

Std deviation Ln(Fund size) Ln(Fund age) Ln(Fund age)2 Management fee Incentive fee Offshore dummy

0.015 0.093 -0.704 0.078 -0.161 -0.021 0.138

0.017 0.026 0.221 0.035 0.051 0.005 0.087

Observations Pseudo R2

11,285 0.137

Note: Ret_n denotes fund return realized in the past n-th month. Standard deviation is measured over the past 12 months. Year dummies are included, but not reported. The standard errors are clustered by fund to adjust for correlation across observations belonging to the same fund.

26

Appendix B: Bootstrap Analysis of Timing Ability Our bootstrap analysis follows Kosowski et al. (2004), built on the work of Efron (1979). Based on the TM (1966) model, we illustrate the bootstrap procedure used to examine timing abilities for the individual funds. Application of the bootstrap procedure to other market timing models will be straightforward. (B1)

rp,t = α + β rm,t + γ rm,t2 + εp,t, t = 1, …, Tp.

where rp,t is the excess return on fund p in month t, and rm,t is the market excess. First, for each fund (p) in the sample, we run a time series regression and save the following information: the estimated coefficient βˆ ; the t-statistic of the timing coefficient γ, i.e., tγ, and the residuals εp,t, for t = 1, … Tp. Second, we resample the fund’s residuals that are saved from the first step by drawing a random sample with replacement from the fund’s residuals. By doing so, we generate a time series of resampled residuals, { εbp,t, t = sb1, sb2, …, sbTp}. We repeat this resampling procedure B times, and thus b = 1, 2, …, B. In the bootstrap analysis of this paper, we set B to 10,000. Third, for each bootstrap iteration b, we construct a time series of bootstrap returns rbp,t for fund p, imposing the null hypothesis that the fund has neither selection nor timing ability, i.e.,

α = γ = 0 (equivalently, tα = tγ = 0). (B2)

rbp,t = βˆ rm,t + εbp,t, t = sb1, sb2, …, sbTp.

The sequence sb1, sb2, …, sbTp corresponds to the bootstrap iteration b. Therefore, rbp,t is the return series of a hypothetical fund that has the same market beta as fund p does. However, the hypothetical fund has no superior ability, since both α and γ are set to zero and the residuals are randomly drawn from a zero-mean noise. Fourth, we run the market timing regression (B1) for the hypothetical fund returns rbp,t, and keep the record of tbγ,p. If tbγ,p is statistically significant different from zero, the evidence can come only from randomness. Fifth, we repeat the last two steps B times for fund p, and keep the record of all tbγ,p’s, with b = 1, …, B. Finally, we repeat the above procedure for all the individual funds in the sample. By comparing the ith-ranked actual tγ among all individual funds with all the ith-ranked hypothetical

27

tbγ’s (b = 1, …, B), we obtain the p-value indicating the likelihood that the ith-ranked actual tγ could be due to random chance. The smaller the p-value is, the less likely it is that the actual timing ability comes from luck.23

23

To check the robustness, we also extend the above bootstrap approach to resampling both regression residuals and risk factors together, following Kosowski et al. (2004). The only difference appears in the third step. Now, for each bootstrap iteration b, the hypothetical fund return rbp,t is constructed as follows: b b b b b b rpb,t = βˆrm ,t + ε bp ,t , tε = s 1, s 2, …, s Tp, and tF = t 1, t 2, …, t Tp, F

ε

where, tε and tF are two independent resamplings for regression residuals and risk factor, respectively. The findings are qualitatively the same.

28

References Ackermann, C.; R. McEnally; and D. Ravenscraft. “The Performance of Hedge Funds: Risk, Return, and Incentives.” Journal of Finance 54 (1999), 833–874. Admati, A., S. Bhattacharya, P. Pfleiderer, and S. Ross. “On Timing and Selectivity.” Journal of Finance 41 (1986), 715–730. Agarwal, V., and N. Naik. “Risks and Portfolio Decisions Involving Hedge Funds.” Review of Financial Studies 17 (2004), 63–98. Asness, C.; R. Krail; and J. Liew. “Do Hedge Funds Hedge?” Journal of Portfolio Management 28 (2001), 6–19. Baquero, G.; J. ter Horst; and M. Verbeek. “Survival, Look-Ahead Bias, and Persistence in Hedge Fund Performance.” Journal of Financial and Quantitative Analysis 40 (2005), 493–517. Becker, C.; W. Ferson; D. Myers; and M. Schill. “Conditional Market Timing with Benchmark Investors.” Journal of Financial Economics 52 (1999), 119–148. Bollen, N., and J. Busse. “On the Timing Ability of Mutual Fund Managers.” Journal of Finance 56 (2001), 1075–1094. Breen, W.; L. Glosten; and R. Jagannathan. “Economic Significance of Predictable Variations in Stock Index Returns.” Journal of Finance 44 (1989), 1177–1189. Brown, S.; D. Gallagher; O. Steenbeek; and P. Swan. “Doubling or Nothing: Patterns of Equity Fund Holdings and Transaction.” Working Paper, New York Univ. (2005) Brown, S.; W. Goetzmann; and R. Ibbotson. “Offshore Hedge Funds: Survival and Performance 1989–95.” Journal of Business 72 (1999), 91–117. Brown, S.; W. Goetzmann; R. Ibbotson; and S. Ross. “Survivorship Bias in Performance Studies.” Review of Financial Studies 5 (1992), 553–580. Busse, J. “Volatility Timing in Mutual Funds: Evidence from Daily Returns.” Review of Financial Studies 12 (1999), 1009–1041. Carhart, M. “On Persistence in Mutual fund Performance.” Journal of Finance 52 (1997), 57–82. Chance, D., and M. Hemler. “The Performance of Professional Market Timers: Daily Evidence from Executed Strategies.” Journal of Financial Economics 62 (2001), 377–411. Chang, E., and W. Lewellen. “Market Timing and Mutual Fund Investment Performance.” Journal of Business 57 (1984), 57–72. Chen, Y. “Timing Ability in the Focus Market of Hedge Funds.” Working Paper, Boston College. (2005) Chen, Y.; W. Ferson; and H. Peters. “Measuring the Timing Ability of Fixed Income Mutual Funds.” Working Paper, Boston College. (2005)

29

Dimson, E. “Risk Management When Shares are Subject to Infrequent Trading.” Journal of Financial Economics 7 (1979), 197–226. Efron, B. “Bootstrap Methods: Another Look at the Jackknife.” Annals of Statistics 7(1979), 1–26. Elton, E.; M. Gruber; and C. Blake. “Survivorship Bias and Mutual Fund Performance.” Review of Financial Studies 9 (1996), 1097–1120. Fama, E. “Components of Investment Performance.” Journal of Finance 27 (1972), 551–567. Fama, E., and K. French. “Common Risk Factors in the Returns on Bonds and Stocks.” Journal of Financial Economics 23 (1993), 3–56. Ferson, W.; T. Henry; and D. Kisgen. “Evaluating Government Bond Funds with Stochastic Discount Factors.” Review of Financial Studies 19 (2006), 423–455. Ferson, W., and K. Khang. “Conditional Performance Measurement Using Portfolio Weights: Evidence from Pension Funds.” Journal of Financial Economics 65 (2002), 249–282. Ferson, W., and R. Schadt. “Measuring Fund Strategy and Performance in Changing Economic Conditions.” Journal of Finance 51 (1996), 425–462. Ferson, W., and V. Warther. “Evaluating Fund Performance in a Dynamic Market.” Financial Analysts Journal 52 (1996), 20–28. Fleming, J.; C. Kirby; and B. Ostdiek. “The Economic Value of Volatility Timing.” Journal of Finance 56 (2001), 329–353. Fung, W., and D. Hsieh. “Empirical Characteristics of Dynamic Trading Strategies: The Case of Hedge Funds.” Review of Financial Studies 10 (1997), 275–302. Fung, W.; and D. Hsieh. “A Primer on Hedge Funds.” Journal of Empirical Finance 6 (1999), 309-331. Fung, W., and D. Hsieh. “The Risk in Hedge Fund Strategies: Theory and Evidence from Trend Followers.” Review of Financial Studies 14 (2001), 313–341. Getmansky, M.; A. Lo; and I. Makarov. “An Econometric Model of Serial Correlation and Illiquidity in Hedge Funds Returns.” Journal of Financial Economics 74 (2004), 529–609. Glosten, L., and R. Jagannathan. “A Contingent Claim Approach to Performance Evaluation.” Journal of Empirical Finance 1 (1994), 133–160. Goetzmann, W.; J. Ingersoll; and Z. Ivkovich. “Monthly Measurement of Daily Timers.” Journal of Financial and Quantitative Analysis 35 (2000), 257–290. Henriksson, R. “Market Timing and Mutual Fund Performance: An Empirical Investigation.” Journal of Business 57 (1984), 73–96. Henriksson, R., and R. Merton. “On Market Timing and Investment Performance II. Statistical Procedures for Evaluating Forecasting Skills.” Journal of Business 54 (1981), 513–533.

30

Horowitz, J. “The Bootstrap.” Working Paper, Northwestern Univ. (2000) Jagannathan, R., and R. Korajczyk. “Assessing the Market Timing Performance of Managed Portfolios.” Journal of Business 59 (1986), 217–235. Jensen, M. “The Performance of Mutual Funds in the Period 1945–1964.” Journal of Finance 23 (1968), 389–346. Jensen, M. “Optimal Utilization of Market Forecasts and the Evaluation of Investment Performance.” Mathematical Methods in Finance, North-Holland. (1972) Jiang, G.; T. Yao; and T. Yu. “Do Mutual Funds Time the Market? Evidence from Portfolio Holdings.” Working Paper, Univ. of Arizona. (2005) Jiang, W. “A Nonparametric Test of Market Timing.” Journal of Empirical Finance 10 (2003), 399–425. Kan, R., and G. Zhou. “Modeling Non-Normality Using Multivariate t: Implications for Asset Pricing.” Working paper, Washington Univ. at St Louis. (2003) Kosowski, R.; A. Timmermann; H. White; and R. Wermers. “Can Mutual Fund ‘Stars’ Really Pick Stocks? New Evidence from a Bootstrap Analysis.” Journal of Finance, (forthcoming 2004) Laplante, M. “Conditional Market Timing with Heteroskedasticity.” Unpubl. Ph.D. dissertation, Univ. of Washington. (2003) Lee, C., and S. Rahman. “Market Timing, Selectivity, and Mutual Fund Performance: An Empirical Investigation.” Journal of Business 63 (1990), 261–278. Liang, B. “Hedge Funds: the Living and the Dead.” Journal of Financial and Quantitative Analysis 35 (2000), 309–326. Merton, R. “On Market Timing and Investment Performance I: An Equilibrium Theory of Value for Market Forecasts.” Journal of Business 54 (1981), 363–407. Rubinstein, M. “A Comparative Static Analysis of Risk Premium.” Journal of Business 46 (1973), 605–615. Scholes, M., and J. Williams. “Estimating Betas from Nonsynchronous Data.” Journal of Financial Economics 5 (1977), 309–328. ter Horst, J.; T. Nijman; and M. Verbeek. “Eliminating Look-Ahead Bias in Evaluating Persistence in Mutual Fund Performance.” Journal of Empirical Finance 8 (2001), 345–373. Treynor, J., and K. Mazuy. “Can Mutual Funds Outguess the Market?” Harvard Business Review 44 (1966), 131–136. Zellner, A. “An Introduction to Bayesian Inferences in Econometrics.” John Wiley & Sons, New York. (1971)

31

Figure 1

Timing-Fund Portfolio Return vs. Market Return 0.12

0.09

Rp-Rf

0.06

0.03

0 -0.18

-0.15

-0.12

-0.09

-0.06

-0.03

0

0.03

0.06

0.09

0.12

-0.03

-0.06

Rm-Rf

Rp denotes return on the equal-weighted portfolio of 221 market timing hedge funds from CISDM, HFR, and TASS. Rm is the market return and Rf is the one-month T-bill rate. The sample period is from January 1994 to June 2005.

32

Figure 2

Time Variation of Return Timing 12 10 8 6 4 2

19 94 0 19 1 94 04 19 94 0 19 7 94 10 19 95 0 19 1 95 0 19 4 95 07 19 95 1 19 0 96 01 19 96 0 19 4 96 07 19 96 1 19 0 97 0 19 1 97 04 19 97 0 19 7 97 10 19 98 0 19 1 98 04 19 98 0 19 7 98 1 19 0 99 0 19 1 99 04 19 99 0 19 7 99 10 20 00 0 20 1 00 04 20 00 0 20 7 00 1 20 0 01 01 20 01 0 20 4 01 0 20 7 01 1 20 0 02 0 20 1 02 04 20 02 07

0 -2 -4 -6 -8 -10 -12 -14 -16 gamma

t-gamma

Rm-Rf

The fund return series are from the equal-weighted portfolio of 221 market timing funds. The return timing ability is measure by the Treynor-Mazuy (1966) model. The rolling regression window is 36 months. The sample period is from January 1994 to June 2005. The solid line represents t-statistics of the timing coefficient, the dash line is estimates of the timing coefficient, and the dotted line is the market excess return.

33

Figure 3

Time Variation of Volatility Timing 12 10 8 6 4 2

19 94 0 19 1 94 04 19 94 0 19 7 94 10 19 95 0 19 1 95 0 19 4 95 07 19 95 1 19 0 96 01 19 96 0 19 4 96 07 19 96 1 19 0 97 0 19 1 97 04 19 97 0 19 7 97 10 19 98 0 19 1 98 04 19 98 0 19 7 98 1 19 0 99 0 19 1 99 04 19 99 0 19 7 99 10 20 00 0 20 1 00 04 20 00 0 20 7 00 1 20 0 01 01 20 01 0 20 4 01 07 20 01 1 20 0 02 0 20 1 02 04 20 02 07

0 -2 -4 -6 -8 -10 -12 -14 -16 lamda

tlamda

Rm-Rf

The fund return series are from the equal-weighted portfolio of 221 market timing funds. The volatility timing ability is measured by the Busse (1999) volatility timing model. The rolling regression window is 36 months. The sample period is from January 1994 to June 2005. The solid line represents t-statistics of the timing coefficient, the dashed line is estimates of the timing coefficient, and the dotted line is the market excess return.

34

Table 1 Attrition Rates of Market Timing Funds The market timing funds are from the CISDM, HFR, and TASS databases. The sample contains 221 funds—106 live funds and 115 defunct funds—during the period of January 1994 to June 2005.

Year 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 a

Year start 13 19 24 28 39 47 67 87 108 130 126 107 109

Entries 6 5 7 13 18 25 25 27 30 16 16 15 5

Dissolved 0 0 3 2 10 5 5 6 8 20 35 13 8

Average annual attrition rate (1994–2005) a

Attrition rate is as of June 2005.

35

Year end 19 24 28 39 47 67 87 108 130 126 107 109 106

Attrition rate (%) 0 0 12.50 7.14 25.64 10.64 7.46 6.90 7.41 15.38 27.78 12.15 7.34 12.31

Table 2 Summary Statistics Returns are in monthly percent from January 1994 to June 2005. Mean is the sample mean. STD is the sample standard deviation. ρ1 is the first-order autocorrelation. MTF is the equal-weighted portfolio of 221 market timing funds. AMTF is the equal-weighted portfolio of the market timing funds, with fund returns adjusted by the Baquero et al. (2005) technique. MKT is the return on the CRSP value-weighted market index. MTS is the return on a hypothetical market timing strategy. SMB and HML are the Fama-French size and book-to-market factors, and UMD is a momentum factor. VIX is the implied market volatility. SIGMA is the realized market volatility. Public information includes lagged value of the three-month T-bill yield, the term premium, the quality spread, and the dividend yield of the S&P 500 index. Mean

STD

Min

Max

ρ1

Panel A: Market timing funds MTF AMTF

1.086 1.075

1.955 1.932

-2.899 -2.913

8.753 8.348

0.119 0.110

Panel B: Factors MKT MTS SMB HML UMD VIX SIGMA

0.914 2.453 0.199 0.407 0.843 5.936 4.309

4.460 2.397 4.112 3.757 5.387 1.895 2.098

-15.77 0.080 -16.62 -12.65 -24.96 3.069 1.245

8.420 8.420 21.83 13.65 18.38 12.78 11.48

0.047 0.052 -0.075 0.050 -0.071 0.812 0.670

Panel C: Instruments T-bill yield Term premium Yield spread Dividend yield

3.806 1.721 0.801 1.792

1.711 1.087 0.221 0.515

0.880 -0.530 0.550 1.080

6.170 3.700 1.410 2.910

0.992 0.970 0.955 0.980

Panel D: Correlation Matrix AMTF MKT AMTF 1.00 MKT 0.72 1.00 MTS 0.68 0.85 SMB 0.36 0.19 HML -0.58 -0.54 UMD 0.11 -0.21 VIX 0.12 0.08 SIGMA -0.17 -0.29

MTS 1.00 0.12 -0.46 -0.18 0.28 -0.04

SMB

1.00 -0.50 0.18 0.02 -0.16

36

HML

1.00 -0.06 -0.15 0.06

UMD

1.00 -0.09 -0.12

VIX

1.00 0.73

SIGMA

1.00

Table 3 Abnormal Performance This table shows the abnormal return of the market timing funds from January 1994 to June 2005. The results are from the following ordinary least squares (OLS) regressions. K

rp ,t +1 = α + ∑ β j r j ,t +1 + ε t +1 , j =1

where rp is the excess return on the equal-weighted portfolio of the funds. K = 1, 3, or 4 for the single-market factor, Fama-French three-factor, or Carhart four-factor models, respectively. ε is the idiosyncratic risk. We measure the conditional abnormal return from the following regression. K

L

j =1

l =1

rp ,t +1 = α + ∑ β j r j ,t +1 + ∑ δ l z l ,t rm ,t +1 + ε t +1 ,

where z’s are demeaned lagged series of four (i.e., L = 4) predetermined instruments, including the three-month T-bill yield, the term premium, the quality spread, and the dividend yield of S&P 500 index. α is in monthly percent. tstatistics are in parentheses. Model Single factor FF 3 factor Carhart 4 factor Conditional

α 0.557 (5.54) 0.616 (6.35) 0.547 (5.74) 0.533 (5.33)

βm 0.340 (15.14) 0.288 (11.54) 0.312 (12.46) 0.322 (12.21)

βSMB

βHML

βUMD

δTB

δTERM

δQUAL

δDY

R

2

0.625 0.053 (2.00) 0.040 (1.57) 0.049 (1.82)

-0.093 (-2.78) -0.080 (-2.44) -0.076 (-2.03)

37

0.674 0.060 (3.40) 0.047 (2.40)

0.697 2.951 (0.90)

2.339 (0.50)

-3.505 (-0.23)

4.239 (0.58)

0.696

Table 4 Return Timing This table shows the ability of the market timing funds to time the market level from January 1994 to June 2005. The results are from ordinary least squares (OLS) regressions of the Treynor-Mazuy and Henriksson-Merton models. K (3) r = α + β r + γr S + ε ,

∑

p ,t +1

j =1

j j ,t +1

m ,t +1

t +1

t +1

where rp is the excess return on the equal-weighted portfolio of the funds. K = 1, 3, or 4 for the single-market factor, Fama-French three-factor, or Carhart four-factor models, respectively. The timing term S t+1 = rm,t+1 in the TM model or St+1 = I(rm,t+1>0) in the HM model. εt+1 is the idiosyncratic risk. We measure conditional market return timing following the method of Ferson-Schadt (1996). K L (4) r =α + β r + δ z r + γr S + ε ,

∑

p ,t +1

j =1

j j ,t +1

∑ l =1

l

l ,t m ,t +1

m ,t +1

t +1

t +1

where z’s are demeaned lagged series of four (i.e., L = 4) predetermined instruments including the three-month T-bill yield, the term premium, the quality spread, and the dividend yield of S&P 500 index. α is in monthly percent. tstatistics are in parentheses.

γ

Model βm α Panel A: Treynor-Mazuy models Single factor 0.282 0.367 (2.38) (16.38) FF 3 factor 0.317 0.319 (2.84) (13.13) Carhart 4 factor 0.251 0.342 (2.32) (14.19) Conditional 0.207 0.351 (1.84) (14.10)

1.289 (3.95) 1.366 (4.54) 1.359 (4.71) 1.483 (5.01)

Panel B: Henriksson-Merton models Single factor 0.060 0.219 (0.35) (5.41) FF 3 factor 0.089 0.163 (0.55) (4.15) Carhart 4 factor 0.023 0.188 (0.15) (4.89) Conditional -0.010 0.189 (-0.06) (4.73)

0.266 (3.51) 0.279 (3.98) 0.278 (4.13) 0.290 (4.25)

βSMB

βHML

βUMD

δTB

δTERM

δQUAL

δDY

R

2

0.661 0.065 (2.61) 0.052 (2.18) 0.068 (2.73)

-0.085 (-2.71) -0.072 (-2.37) -0.049 (-1.41)

0.715 0.060 (3.63) 0.044 (2.40)

0.739 3.108 (1.03)

0.148 (0.03)

-2.933 (-0.21)

3.203 (0.47)

0.744

0.654 0.062 (2.46) 0.049 (2.02) 0.062 (2.46)

-0.087 (-2.72) -0.073 (-2.38) -0.056 (-1.60)

38

0.706 0.060 (3.58) 0.045 (2.41)

0.730 4.006 (1.29)

2.037 (0.46)

0.775 (0.05)

2.876 (0.42)

0.732

Table 5 Volatility Timing This table shows the ability of the market timing funds to time market volatility from January 1994 to June 2005. The results are from ordinary least squares (OLS) regressions of the Busse (1999) volatility timing models. (5)

K

rp ,t +1 = α + ∑ β j rj ,t +1 + λrm ,t +1 (σ m ,t +1 − σ m ) + ε t +1 , j =1

where rp is the excess return on the equal-weighted portfolio of the funds. K = 1, 3, or 4 for the single-market factor, Fama-French three-factor, or Carhart four-factor models, respectively. σm,t+1 is market volatility, proxied by the implied volatility (VIX) and by the realized volatility (SIGMA). εt+1 is the idiosyncratic risk. We measure conditional volatility timing with the following regression: K

L

j =1

l =1

rp ,t +1 = α + ∑ β j rj , t +1 + ∑ δ l zl , t rm, t +1 + λrm, t +1 (σ m, t +1 − σ m ) + ε t +1 ,

where z’s are demeaned lagged series of four (i.e., L = 4) predetermined instruments including the three-month T-bill yield, the term premium, the quality spread, and the dividend yield of S&P 500 index. α is in monthly percent. tstatistics are in parentheses. Model βm α λ Panel A: Using implied volatility (VIX) Single factor 0.427 0.398 -3.492 (4.21) (15.27) (-3.89) FF 3 factor 0.484 0.347 -3.508 (5.01) (12.7) (-4.23) Carhart 4 factor 0.435 0.363 -3.224 (4.59) (13.46) (-3.99) Conditional 0.41 0.368 -3.587 (4.10) (13.32) (-3.92) Panel B: Using realized volatility (SIGMA) Single factor 0.429 0.392 -3.664 (4.31) (16.05) (-4.25) FF 3 factor 0.481 0.342 -3.747 (5.09) (13.24) (-4.72) Carhart 4 factor 0.435 0.358 -3.435 (4.68) (13.96) (-4.42) Conditional 0.417 0.359 -3.742 (4.26) (13.66) (-4.25)

βSMB

βHML

βUMD

δTB

δTERM

δQUAL

δDY

R

2

0.660 0.054 (2.19) 0.043 (1.78) 0.053 (2.09)

-0.092 (-2.91) -0.08 (-2.59) -0.057 (-1.60)

0.710 0.052 (3.11) 0.044 (2.36)

0.728 0.487 (0.15)

-2.849 (-0.61)

-1.965 (-0.13)

0.988 (0.14)

0.727

0.667 0.059 (2.40) 0.048 (1.98) 0.059 (2.33)

-0.089 (-2.85) -0.078 (-2.55) -0.05 (-1.41)

39

0.718 0.05 (3.01) 0.045 (2.42)

0.734 1.829 (0.59)

-2.193 (-0.48)

9.921 (0.67)

0.917 (0.13)

0.732

Table 6 Joint Timing This table shows the ability of the market timing funds to time the market level and volatility jointly from January 1994 to June 2005. The results are from ordinary least squares (OLS) regressions of the joint timing model. K

(6)

rp ,t +1 = α +

∑ j =1

⎛ r β j r j ,t +1 + γ ⎜ m ,t +1 ⎜ σ m ,t +1|s t ⎝

2

⎞ ⎟ + ε t +1 , ⎟ ⎠

where rp is the excess return on the equal-weighted portfolio of the funds. K = 1, 3, or 4 for the single-market factor, Fama-French three-factor, or Carhart four-factor models, respectively. We proxy market volatility by the implied volatility (VIX). εt+1 is the idiosyncratic risk. Alternatively, we run the Busse (1999) regression to estimate both return timing and volatility timing. K

(7)

r p ,t +1 = α +

∑β r

+ γrm ,t +1 + λrm ,t +1 ( σ m ,t +1 − σ m ) + ε t +1 . 2

j j ,t +1

j =1

α is in monthly percent. t-statistics are in parentheses. Model α Panel A: Joint timing Single factor 0.276 (2.09) FF 3 factor 0.296 (2.40) Carhart 4 factor 0.246 (2.05) Conditional 0.220 (1.77)

βm

γ

0.363 (15.81) 0.312 (12.72) 0.334 (13.63) 0.339 (13.36)

0.005 (3.14) 0.006 (3.89) 0.005 (3.86) 0.006 (3.91)

Panel B: Return and volatility timing Single factor 0.271 0.397 (2.34) (16.18) FF 3 factor 0.316 0.346 (2.91) (13.68) Carhart 4 factor 0.260 0.360 (2.43) (14.43) Conditional 0.209 0.362 (1.88) (14.24)

1.355 (4.23) 1.422 (4.85) 1.403 (4.93) 1.559 (5.26)

λ

βSMB

βHML

βUMD

δTB

δTERM

δQUAL

δDY

R

2

0.648 0.060 (2.38) 0.048 (1.94) 0.059 (2.32) -2.999 (-2.70) -3.035 (-2.97) -2.325 (-2.28) -2.284 (-1.83)

-0.096 (-3.01) -0.083 (-2.68) -0.067 (-1.90)

0.705 0.057 (3.37) 0.043 (2.29)

0.726 2.462 (0.79)

0.497 (0.11)

-4.52 (-0.31)

2.258 (0.32)

0.727

0.676 0.057 (2.34) 0.048 (2.03) 0.062 (2.47)

40

-0.095 (-3.09) -0.081 (-2.70) -0.052 (-1.51)

0.731 0.051 (3.07) 0.043 (2.37)

0.747 1.061 (0.33)

-3.193 (-0.68)

1.025 (0.07)

2.041 (0.30)

0.749

Table 7 Timing Ability in Different Market Conditions This table shows timing abilities of the market timing funds in different market conditions from January 1994 to June 2005. We run the 4-factor TM return timing, volatility timing, and joint timing models. Bull (bear) market states are defined as the months when the market return is greater (less) than the one-month T-bill rate; volatile (stable) markets are the months when the implied volatility is higher (lower) than the average level during the sample period; high (low) Sharpe-ratio markets are when the Sharpe ratio of the market portfolio is higher (lower) than the average level during the sample period. t-statistics are in parentheses. Return timing (TM model)

Volatility timing (VIX)

Joint timing

Bull market βm γ 0.509 -0.915 (2.48) (-0.37) Stable market λ βm 0.419 0.485 (7.86) (0.13) High Sharpe-ratio market βm γ 0.404 0.003 (4.17) (0.67)

41

Bear market βm γ 0.367 1.746 (3.13) (2.19) Volatile market βm λ 0.447 -4.964 (10.03) (-4.43) Low Sharpe-ratio market βm γ 0.217 0.001 (2.09) (0.14)

Table 8 Timing Ability and the Use of Options This table tests the robustness of timing ability to the use of options by the market timing funds. Panel A shows the performance differences between the funds that use options and those that do not. The performance measures include abnormal return (alpha), return timing, volatility timing, and joint timing, estimated from models (1), (3), (5), and (6), respectively. In the sample, 100 funds show information about the use options. t-test has the null hypothesis that the mean performance of options users is equal to that of nonusers. Wilcoxon is a nonparametric test for the difference in performance distributions. Alpha is in monthly percent. N is the number of funds. Panel B reports results from the market timing regressions incorporating the Agarwal and Naik (2004) option factors. The option factors are at-the-money and out-of-the-money European call options on the S&P 500 index (SPCa and SPCo, respectively), and at-the-money and out-of-the-money European put option on the S&P 500 index (SPPa and SPPo, respectively). α is in monthly percent. t-statistics are in parentheses. Panel A: Performance of options users vs. nonusers

Alpha

Total Mean N Perf 100 0.562

Users Mean N Perf 36 0.369

Nonusers Mean N Perf 64 0.671

TM timing

100

1.154

36

0.304

64

1.632

Vol. timing

100

-1.795

36

0.722

64

-3.211

Joint timing

100

0.005

36

0.001

64

0.008

Tests of Differences t-test Wilcoxon (p-value) (p-value) -1.711 -1.278 (0.09) (0.20) -1.584 -3.145 (0.12) (0.00) 1.004 3.059 (0.32) (0.00) -1.974 -2.944 (0.05) (0.00)

Panel B: Incorporating option factors Model TM timing

α

γ or λ

0.211 (1.16) 0.218 (1.35)

βm 0.372 (6.70) 0.263 (4.89)

1.793 (3.70) 1.687 (4.03)

0.477 (3.55) 0.539 (4.29)

0.503 (7.69) 0.355 (5.29)

-4.78 (-3.97) -3.254 (-2.93)

0.024 (0.09) 4-factor joint timing 0.121 (0.52)

0.375 (6.60) 0.260 (4.66)

0.009 (2.93) 0.008 (2.83)

4-factor TM timing Vol. timing 4-factor vol. timing Joint timing

βSMB

0.075 (2.61)

0.059 (1.99)

0.061 (2.06)

βHML

-0.068 (-1.94)

-0.076 (-2.10)

-0.087 (-2.42)

42

βUMD

β SPC

0.057 (1.05) 0.047 (1.01)

0.008 (0.06) -0.044 (-0.34)

-0.047 (-0.35) -0.012 (-0.11)

0.669

0.058 (3.22)

-0.087 (-1.35) -0.034 (-0.60)

0.029 (0.55) 0.023 (0.47)

0.048 (0.33) -0.009 (-0.07)

-0.023 (-0.17) 0.017 (0.14)

0.674

0.050 (2.67)

-0.067 (-1.08) -0.005 (-0.10)

0.055 (2.93)

-0.067 (-1.02) -0.010 (-0.17)

0.018 (0.32) 0.010 (0.20)

0.052 (0.34) -0.006 (-0.05)

-0.108 (-0.76) -0.057 (-0.46)

a

β SPC

o

β SPP

a

β SPP

o

R

2

0.758

0.740 0.653 0.739

Table 9 Timing Ability with Controls for Illiquid Holdings This table shows the results from various market timing regressions, controlling for illiquid holdings by adding lagged market returns (rm,t and rm,t-1) and their square terms (rm,t2 and rm,t-12). α is in monthly percent. t-statistics are in parentheses. Model TM timing 4-factor TM timing Vol. timing 4-factor vol. timing Joint timing

α

γ or λ

0.119 (0.84) 0.100 (0.79)

βm 0.357 (16.13) 0.334 (14.60)

0.115 (0.83) 0.125 (0.99)

0.386 -3.650 (15.43) (-4.14) 0.356 -3.275 (14.05) (-4.19)

0.035 (0.22) 4-factor joint timing 0.005 (0.04)

0.35 (15.79) 0.326 (14.17)

1.258 (3.90) 1.296 (4.60)

0.005 (3.30) 0.005 (4.01)

βSMB

0.041 (1.76)

0.030 (1.27)

0.036 (1.52)

βHML

-0.073 (-2.45)

-0.075 (-2.49)

-0.078 (-2.57)

43

βUMD

0.067 (4.09)

βm,lag1 0.017 (0.77) 0.031 (1.55)

γm,lag1

γm,lag2

-0.391 (-1.24) -0.393 (-1.43)

βm,lag2 0.059 (2.73) 0.037 (1.94)

1.051 (3.25) 1.025 (3.56)

0.065 (3.94)

0.014 (0.67) 0.029 (1.43)

0.049 (0.15) 0.023 (0.08)

0.056 (2.62) 0.034 (1.77)

1.324 (4.20) 1.307 (4.60)

0.068 (4.12)

0.010 (0.46) 0.025 (1.26)

-0.237 (-0.74) -0.223 (-0.80)

0.056 (2.55) 0.033 (1.73)

1.293 (4.02) 1.273 (4.45)

R

2

0.694 0.772 0.698 0.766 0.685 0.763

Table 10 Timing Ability at the Fund Level This table shows abnormal return and timing abilities at the fund level, using the single-factor, Fama-French three-factor, Carhart four-factor, and conditional four-factor models during the period of January 1994 to June 2005. We require each individual fund to have at least 18 consecutive monthly returns, and thus the number of funds reduces to 179. Alpha is estimated from a constant-beta regression. The return timing, volatility timing, and joint timing coefficients are estimated from regressions (3), (5), and (6), respectively. Coefficient γ denotes return timing, volatility timing (multiplied by -1), or joint timing, depending on the model used. #α >0

#|tα|>2.0

#tα>2.0

140 138 138 136

70 73 75 74

65 66 66 66

Return Timing (TM) Single factor FF 3 factor Carhart 4 factor Conditional 4 factor

130 119 118 120

54 61 61 56

48 51 49 46

127 129 131 125

30 33 38 35

27 30 35 32

179 179 179 179

Volatility Timing Single factor FF 3 factor Carhart 4 factor Conditional 4 factor

139 134 133 127

62 71 73 62

55 60 60 54

132 130 128 121

72 69 65 58

63 59 54 47

179 179 179 179

Joint Timing Single factor FF 3 factor Carhart 4 factor Conditional 4 factor

125 118 116 118

62 65 66 65

53 54 54 54

126 126 129 121

28 31 35 31

25 30 33 29

179 179 179 179

Model Alpha Single factor FF 3 factor Carhart 4 factor Conditional 4 factor

44

#γ >0

#|tγ| >2.0

#tγ >2.0

# funds 179 179 179 179

Table 11 Bootstrap Analysis of the Best and Worst Timing Funds This table shows results from the bootstrap analysis of abnormal return, return timing, volatility timing, and joint timing, based on 10,000 replications. The abnormal return is measured by single-factor Jensen’s alpha. The return timing, volatility timing, and joint timing are estimated by the single-factor regressions (3), (5), and (6), respectively. “n.min” (“n.max”) denotes the nth smallest (largest) t-statistic, using the actual fund data. The empirical p-value indicates how likely a t-statistic of the same magnitude as the sample estimate comes from randomness. In each panel, the second row (a) reports the bootstrap p-values from resampling residual only, and the third row (b) reports the bootstrap p-values from resampling both residuals and the factors. Bottom

2.min

3.min

4.min

5.min

10.min

15.min

15.max

10.max

5.max

4.max

3.max

2.max

Top

Alpha tα bootstrap p-value of tα (a) bootstrap p-value of tα (b)

-2.956 0.915 0.825

-2.461 0.945 0.897

-2.167 0.961 0.935

-2.147 0.914 0.857

-2.103 0.826 0.773

-1.635 0.862 0.802

-0.641 1.000 1.000

4.577 0.000 0.000

5.063 0.000 0.000

5.516 0.000 0.000

5.947 0.000 0.000

6.209 0.000 0.000

12.908 0.000 0.000

13.460 0.000 0.000

Return Timing (TM) tγ bootstrap p-value of tγ (a) bootstrap p-value of tγ (b)

-3.697 0.555 0.562

-3.146 0.539 0.548

-2.377 0.952 0.935

-1.980 0.992 0.994

-1.727 1.000 0.999

-1.099 1.000 1.000

-1.086 1.000 1.000

2.603 0.000 0.000

2.873 0.000 0.000

3.593 0.000 0.001

3.647 0.008 0.004

3.745 0.033 0.029

4.456 0.030 0.030

5.183 0.103 0.092

Volatility Timing (VIX) tλ bootstrap p-value of tλ (a) bootstrap p-value of tλ (b)

-6.940 0.038 0.027

-5.798 0.004 0.003

-5.713 0.000 0.000

-5.565 0.000 0.000

-5.501 0.000 0.000

-4.059 0.000 0.000

-3.708 0.000 0.000

1.193 0.999 0.999

1.884 0.926 0.906

2.705 0.508 0.583

2.935 0.450 0.515

3.255 0.381 0.428

3.368 0.594 0.587

3.522 0.807 0.798

Joint Timing tγ bootstrap p-value of tγ (a) bootstrap p-value of tγ (b)

-2.293 0.998 0.994

-2.009 0.999 0.999

-2.008 0.994 0.992

-1.996 0.988 0.978

-1.992 0.967 0.939

-1.323 0.999 0.998

-1.043 1.000 1.000

2.370 0.000 0.000

2.759 0.000 0.000

3.585 0.000 0.000

3.657 0.001 0.002

3.753 0.012 0.015

3.905 0.055 0.051

4.719 0.112 0.105

45

Table 12 Timing Ability and Fund Characteristics The dependent variable is the timing coefficient estimated from the four-factor TM, volatility timing, and joint timing models. The volatility timing coefficient is multiplied by -1, so that the regressions have the same interpretation. N is the number of funds. t-statistics are in parentheses. Constant Log(fund age) Log(fund size) Ln(minimum investment) Management fee (%) Incentive fee (%) High-water mark dummy Lockup period (months) Advance notice period Offshore dummy N R

2

Return Timing 5.802 4.293 (2.30) (1.82) -0.768 -0.675 (-1.46) (-1.42) -0.397 (-2.43) 0.454 0.165 (1.87) (0.80) -0.170 0.225 (-0.42) (0.63) 0.022 -0.007 (0.66) (-0.24) 0.623 (1.09) -0.017 (-0.29) -0.018 (-1.29) -1.660 (-3.40)

Vol. Timing -9.841 -11.785 (-0.72) (-0.78) -0.881 -0.579 (-0.31) (-0.19) 0.080 (0.09) -0.911 -1.541 (-0.69) (-1.17) 2.667 3.055 (1.22) (1.34) 0.297 0.399 (1.63) (2.12) -2.796 (-0.76) -0.339 (-0.89) 0.049 (0.53) -1.845 (-0.59)

Joint Timing 0.0188 0.0082 (1.86) (0.78) -0.0015 -0.0004 (-0.73) (-0.17) -0.0016 (-2.47) 0.0014 0.0010 (1.46) (1.06) -0.0009 0.0001 (-0.56) (0.02) -0.0001 -0.0001 (-0.05) (-0.37) 0.0033 (1.30) -0.0001 (-0.02) -0.0001 (-0.81) -0.0049 (-2.24)

156 0.049

156 0.001

156 0.023

156 0.055

46

156 0.003

156 0.006