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Can mutual funds time risk factors?
The Quarterly Review of Economics and Finance 50 (2010) 509–514
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Can mutual funds time risk factors?夽 Evangelos Benos, Marek Jochec ∗,1 , Victor Nyekel 1206 S Sixth St., 340 Wohlers Hall, Champaign, United States
a r t i c l e
i n f o
Article history: Received 9 April 2009 Received in revised form 18 May 2010 Accepted 24 May 2010 Available online 18 June 2010 Keywords: Risk factors Mutual funds Market timing Factor timing
a b s t r a c t Using daily observations from 448 actively managed funds, we employ the methodology in Bollen and Busse (2001) in order to assess the ability of fund managers to time systematic risk factors. We first construct synthetic portfolios in order to obtain the empirical distribution of timing coefficients under the null hypothesis of no timing ability and then compare this distribution to that of the timing coefficients of the actual funds. Fund managers do not seem to be timing any of the risk factors. We interpret this result as evidence that factor timing ability does not persist over long time periods. © 2010 The Board of Trustees of the University of Illinois. Published by Elsevier B.V. All rights reserved.
1. Introduction A mutual fund manager has two ways to generate returns in excess to what is implied by a portfolio’s exposure to various risk factors: the manager can either select individual stocks that, for various reasons, yield such higher risk adjusted returns (stock picking) or buy and sell stocks at specific times so as to capture the market upturns and avoid its downturns (market timing). In the latter case, a manager would buy stocks with a high sensitivity to the market prior to an upward market movement and would either buy low sensitivity stocks or hold cash prior to a downward market movement. The concept of “market timing” can potentially be generalized to include the systematic risk factors of the Carhart (1997) and Fama and French (1993) models as well. That is, if a manager could predict how the size (SMB), book-to-market (HML) and momentum (MOM) factors would move, he could purchase stocks with high or low sensitivities to these factors the exact same way he would for the market. There is evidence suggesting that some risk factors may be predictable. For example, Cooper, Gulen, and Vassalou (2001) argue that whether small stocks outperform large ones or vice versa
夽 This paper was completed while Evangelos Benos and Victor Nyekel were at the University of Illinois at Urbana-Champaign. We would like to thank Jay Wang, Heitor Almeida, Bo Becker and George Pennacchi for helpful comments. All errors are ours. ∗ Corresponding author. E-mail address: [email protected] (M. Jochec). 1 ISCTE.
is related to fundamental, non-diversifiable risk. They regress monthly values of the SMB factor on lagged values of all risk factors and of other economic variables and then use the estimated sensitivities to perform next-month, out-of-sample forecasts of SMB. Based on these forecasts, they execute a trading strategy that buys the SMB portfolio whenever it is forecasted to yield a positive return; otherwise it buys the Treasury bill. This strategy significantly outperforms the passive SMB strategy suggesting that the SMB factor is to some extent predictable. The authors find no evidence of predictability for HML and MOM whereas the market premium turns out to be predictable (using the same methodology) only in times of recession. That the particular strategy fails to predict the other risk factors does not mean that they are not predictable. For one thing, Cooper et al. (2001) argue that the factors are proxies of systematic risk and only use real economic variables as regressors. However, whether the risk factors capture fundamental risk is a hotly debated issue.2 This means that perhaps these factors may be predictable if alternative regressors are used to explain them. Overall, if a strategy predicts one factor but not another, this only suggests that different underlying economic processes give rise to these factors. Regardless however of whether the factors capture systematic risk or not, exploring the timing ability of mutual fund managers is still worthwhile. Since a successful risk-factor timer buys when the
2 See for instance Lakonishok et al. (1994) for a behavioral explanation of the B/M premium. These authors argue that the effect is due to the fact that investors extrapolate past performance (too far) into the future. If the size, B/M and momentum premia are not compensations for risk, then a fund manager can generate abnormal returns by simply purchasing stocks with the relevant characteristics.
1062-9769/$ – see front matter © 2010 The Board of Trustees of the University of Illinois. Published by Elsevier B.V. All rights reserved. doi:10.1016/j.qref.2010.05.001
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risk factor is “low” and sells when it is “high”, his realized returns will be a convex function of the risk factor returns. Earlier market timing studies have thus attempted to measure market timing ability by including a convex function of the market in the standard linear capital asset pricing model. Timing ability is then established by the statistical and economic significance of the coefficient of the convex term. Treynor and Mazuy (1966) use a quadratic function of the market whereas Henriksson (1984) and Chang and Lewellen (1984) use a piecewise-linear one. All of these studies conclude that managers possess no market timing ability. Bollen and Busse (2001) [henceforth BB (2001)] take an issue with this methodology on two fronts. First, they argue that one cannot conclude whether a manager times the market successfully by just looking at the estimated coefficient of the convex term. If spurious sources of significance are present, then fund managers will likely exhibit positive and significant timing coefficients. Thus, one needs to compare the cross-sectional distribution of these coefficients with their cross-sectional distribution under the assumption of no timing ability. To achieve this, they match each of the funds in their sample with a synthetic one that mimics the original fund’s investment style but which by construction has no timing ability. Then, they compare the two resulting cross-sectional distributions. The second point that BB (2001) make is that the tests in the previous studies have low power because they use monthly or annual data. By means of simulations they show that using daily observations, significantly increases statistical power. Intuitively, this is because timing strategies are likely to last less than a year or even a month. In that case, annual and monthly observations will simply be too noisy and will make it easy to accept the null of no timing ability when in fact the null is false. After accounting for these issues, BB find, in a sample of 230 funds, evidence (albeit weak) of timing ability. Our paper also employs the methodology in BB (2001) to test for the existence of timing ability. Our study contains two new elements. First, we control and test for timing ability in the other systematic risk factors of the Carhart (1997) model: SMB, HML and momentum. If managers are able to time these other factors, then not only is this interesting in itself but it could bias the market timing coefficient if not properly accounted for. If the risk factors are not orthogonal to each other, then a coefficient on market timing could be positive and significant simply because the manager times, for example, the SMB factor and the two factors happen to be correlated. Second, we use a more recent and substantially larger sample of 448 (versus 230) funds. Incidentally, our data covers the 1999–2007 time period which includes one of the largest equity booms and busts in the US equity market; this means that fund managers had plenty of opportunity to use their timing ability and that the benefits of successful timing would have been large. Our results conflict with those of BB (2001) in that we find no evidence of market or other factor timing ability. The fractions and average values of the statistically significant actual and synthetic fund timing coefficients are either very similar or seem to suggest that the synthetic funds have better timing abilities than the actual funds. These results agree with the earlier literature and are also consistent with the absence of long-term persistence in fund managers’ abilities.
data is obtained from the CRSP mutual fund daily database. To construct our data set, we start from the CRSP universe and isolate the actively managed domestic (i.e. US) equity funds by including the following Lipper fund classes: EIEI (Equity Income Funds), G (Growth Funds), LCCE (Large-Cap Core Funds), LCGE (Large-Cap Growth Funds), LCVE (Large-Cap Value Funds), MCCE (Mid-Cap Core Funds), MCGE (Mid-Cap Growth Funds), MCVE (Mid-Cap Value Funds), MLCE (Multi-Cap Core Funds), MLGE (Multi-Cap Growth Funds), MLVE (Multi-Cap Value Funds), SCCE (Small-Cap Core Funds), SCGE (Small-Cap Growth Funds) and SCVE (Small-Cap Value Funds). However, these Lipper objective codes still include funds that are not actively managed and/or are not invested in domestic equity and/or are restricted in specific industries.3 To eliminate these funds, we search for keywords in the fund names that would indicate an undesired category (such as “government”, “real estate”, “international”, etc.) and drop from the sample all funds whose name contains such a keyword. In addition, we require that the funds have more than a year (252 trading days) of daily returns, more than $20 million of average annual total net assets (TNA) during the fund’s life and a turnover ratio above 10%. We also require that they have returns for at least 95% of trading days for the period when the fund is listed in the daily database. Finally, we eliminate all younger share classes of those funds that have multiple share classes.4 Table 1 shows cross-fund averages of key fund characteristics for each of the years spanned by our sample. For the construction of the synthetic portfolios we use the CRSP daily stock return database and apply the following filters: we delete observations with missing returns, permnos, dates, and returns that equal any of the CRSP codes for missing values: −66, −77, −88, −99. However, we keep the respective stocks which means that some of our stocks have several missing daily return values. Finally, we use daily risk factor and style portfolio returns from Kenneth French’s website.5 3. Methodology 3.1. Measuring factor timing ability A successful factor timer will realize returns that are a convex function of the risk factor(s). Thus, as is common in the literature, we measure a manager’s ability to time some risk factor by a term that captures this convexity of the realized returns. For each mutual fund p and for a multi-factor model of stock returns, the following specification is estimated over N trading days: Rpt − Rft = ˛p +
4 i=1
ˇip fit +
4
ip g(fit ) + εpt ,
t = 1, 2, . . . , N (1)
i=1
where Rpt is the fund’s realized return on day t, fit is the value of risk factor i on day t and i = 1–4 denotes the four risk factors of the Carhart (1997) model in the following order: Rmt − Rft , SMBt, HMLt and MOMt . Rft is the risk-free rate and Rmt is the market return. SMBt and HMLt are the values of Fama and French (1993) size and book-to-market factors and MOMt is the day t value of the Carhart (1997) momentum factor. The function g(.) is in our case either g(fit ) = fit2 or g(fit ) = fit I[fit ≥0] . The ability to time a given risk factor is captured by the coefficient ip of this convex term. We estimate
2. Data Our main data set consists of daily returns for 448 actively managed US equity mutual funds and our time range is a 9-year period starting on January 1, 1999 and ending on December 31, 2007. Each fund remains in our sample for an average of 6 years. The
3 Examples include real estate funds, money market funds, government securities funds, etc. 4 Starting from May 2008, fund classes are appended to a fund name with a semicolon as a separator. We strip everything after the semicolon, sort by the remaining portion of fund name and inception date, and keep the earliest record. 5 http://mba:tuck:dartmouth.edu/pages/faculty/ken.french/data library.html.
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Table 1 Cross-fund averages of various fund characteristics for each of the years of our sample. The turnover ratios, the expense ratios, the management fees and the loads are expressed as % of total net assets. Total net assets (TNA) are in millions of dollars. Year
No. of funds
1999 2000 2001 2002 2003 2004 2005 2006 2007
328 308 322 337 348 349 335 313 292
Average
326
Turnover ratio
Expense ratio
Management fee
Front load
Rear load
TNA ($million)
92 101 100 92 85 84 81 85 86
1.2 1.2 1.2 1.3 1.3 1.2 1.2 1.2 1.3
0.68 0.64 0.74 0.75 0.76 0.77 0.75 0.76 0.79
3.8 4.2 4.7 4.7 4.7 4.8 4.4 4.2 4.2
2.3 2.3 2.3 2.0 1.9 1.9 1.8 1.5 1.5
898 849 680 488 631 698 733 800 901
90
1.2
0.74
4.4
1.9
742
these coefficients using all the available daily returns from a fund’s life. We note that one needs to control for timing ability in all risk factors when measuring the ability to time any single factor. Otherwise it is impossible to tell a priori whether the estimated coefficient captures the timing ability of the particular factor; unless g(fit ) ⊥ g(fjt ) ∀j = / i, a model that includes a single timing factor will yield inconsistent estimates, since the estimated coefficient will also capture any timing effects from the other factors. More importantly, however, timing ability should be calculated controlling for the effect of the intercept alpha. In companion work (Benos & Jochec, 2009) we show that unless one controls for alpha, it drives the results and masks almost completely the timing coefficients. The choice of daily instead of monthly data is based on the findings of BB (2001) that the use of daily data tends to increase the power of the statistical tests. Intuitively, a monthly frequency will not capture a manager’s timing activity if this activity is more frequent than monthly. Thus, with daily data we are more likely to reject the null of no timing activity when the null is false. 3.2. Bootstrap standard errors In assessing the statistical significance of the estimated timing coefficients we cannot rely on standard t-tests because of the possibility of misspecification. Suppose for example that a fund manager executes a timing strategy that is best captured by the quadratic model (g(fit ) = fit2 ) but we instead estimate a piecewiselinear one (g(fit ) = fit I[fit ≥0] ). Then, for consecutive large values of fund returns (i.e. the dependent variable) the fitted line of the piecewise-linear model will fall below these values; this discrepancy will in turn be picked up by the error terms, thus inducing serial correlation. Furthermore, fund managers may not always engage in a timing strategy continuously. At times they may either not have a clear prediction of what future market movements will be or they may adjust their strategies in accordance to their compensation schemes to maximize their payoff.6 In either case, we are likely to have time-varying deviations from the standard regression assumptions which also means that the standard heteroscedasticity and autocorrelation corrections may not suffice to yield consistent estimates of the coefficient standard errors. To address these problems, we follow BB (2001) in letting the data speak for itself and calculating bootstrap standard errors. This is done in the following way: we first estimate for each fund the timing coefficients using all the available observations and compute the residuals. We then randomly reshuffle (with replacement) the estimated residuals and using the already estimated coefficients we “predict” the dependent variable (fund returns), thus
6
See Brown, Harlow, and Starks (1996).
constructing a bootstrap sample. This process is repeated 1000 times. The final step is to estimate anew the timing coefficients in each of the bootstrap samples, to derive their empirical distribution. The t-statistic of the originally estimated timing coefficient is then the estimated coefficient itself divided by the standard error of the coefficient empirical distribution: t=
ˆ pi bootstrap
(pi
)
3.3. Distribution of timing coefficients under the null and synthetic portfolio construction In order to use the distribution of the estimated fund timing coefficients to decide whether timing ability exists, we need to know the distribution of these coefficients under the null hypothesis of no timing ability. Even if fund managers have no timing ability, some funds will have positive and significant timing coefficients due to random chance. To derive the timing coefficient empirical distribution under the null of no timing ability, we construct for each available fund a synthetic counterpart that mimics the original fund’s style and risk exposure. We then estimate timing coefficients for the synthetic funds and obtain their empirical distribution. This distribution serves as a benchmark for comparing the distribution of the timing coefficients of the actual funds. We next describe in detail the construction of synthetic funds. We construct synthetic portfolios following the procedure in BB (2001). We pair each mutual fund with a synthetic one that is intended to mimic its style but exhibits, by construction, no timing ability. The first step in this process is to determine the sensitivity of a fund to a set of style portfolios whose returns are obtained from Kenneth French’s website. The style portfolios are six B/Msize portfolios formed by the intersection of two size and three B/M portfolios constructed by independent sorts as well as two momentum portfolios consisting of the top and bottom 30% of all stocks sorted by last year’s raw returns. The idea is to try to replicate as closely as possible the actual fund’s style; i.e. express its returns as a linear combination of the returns of benchmark style portfolios. For that, we estimate for each fund, the model: Rp,t =
8
bp,i ri,t + εp,t
(2)
i=1
where Rp,t is the day t realized return of fund p and ri,t is the day t return of benchmark style portfolio i. We estimate the bp,i s by minimizing the variance of εp,t subject to a non-negativity constraint for the estimated coefficients. For this estimation we use all the daily returns available over the fund’s life. Once the sensitivities of a fund to the risk factors have been estimated, we construct the mimicking synthetic fund by randomly
512
E. Benos et al. / The Quarterly Review of Economics and Finance 50 (2010) 509–514 Table 2 Panel A: Absolute differences between the betas of actual funds and synthetic portfolios. For each of the actual funds and the synthetic portfolios we first estimate the standard four-factor model: Rpt − Rft = ˛p + ˇ1p (Rmt − Rft ) + ˇ2p SMBit + ˇ3p HMLt + ˇ4p MOMt + εpt . We then sort all funds into deciles by the estimated factor betas and compare the average fund decile beta with the corresponding synthetic portfolio decile beta. Similar results are obtained by estimating model (1) instead. Panel B: Annualized return differences (in %) as a result of factor differences. We multiply the factor differences (in Panel A) with the geometric mean of the respective risk factor. The geometric mean is calculated over a 10-year period (1997–2007). Panel A Deciles
ˆ 2,act. − ˇ ˆ 2,synth. | |ˇ
ˆ 3,act. − ˇ ˆ 3,synth. | |ˇ
ˆ 4,act. − ˇ ˆ 4,synth. | |ˇ
1 (High) 2 3 4 5 6 7 8 9 10 (Low)
0.33 0.15 0.07 0.06 0.16 0.30 0.37 0.41 0.47 0.56
0.16 0.03 0.01 0.00 0.03 0.10 0.11 0.18 0.20 0.43
0.41 0.25 0.19 0.16 0.13 0.13 0.08 0.08 0.00 0.12
Panel B Deciles
ˆ 2,act. − ˇ ˆ 2,synth. |SMB |ˇ
ˆ 3,act. − ˇ ˆ 3,synth. |HML |ˇ
ˆ 4,act. − ˇ ˆ 4,synth. |MOM |ˇ
1 (High) 2 3 4 5 6 7 8 9 10 (Low)
0.77 0.35 0.16 0.14 0.37 0.70 0.86 0.95 1.09 1.30
0.60 0.11 0.04 0.00 0.11 0.38 0.42 0.68 0.76 1.63
0.26 0.16 0.12 0.10 0.08 0.08 0.05 0.05 0.00 0.07
Average
0.67
0.47
0.10
selecting 100 stocks that belong to the eight benchmark portfolios in proportions determined by the estimated sensitivities. Thus, the 8 proportion of stocks selected from factor portfolio i is bˆ p,i / i=1 bˆ p,i . The stocks initially receive equal weights and then evolve according to a buy-and-hold strategy. The stocks are randomly replaced with other stocks selected from the same style portfolios, with an average holding period of 1 year. Every time a stock is replaced, the weights are reset to equal. The set of stocks that are assigned to each of the eight benchmark portfolios is obtained from the CRSP universe after applying standard filters: we exclude stocks with too many missing values, prices smaller or equal to $1, and share codes other than 10 or 11 (to exclude foreign stocks, ADRs, shares of beneficial interest, depository partnership units and receipts, trusts, closed-end funds, and REITs). Table 2, Panel A, shows the absolute differences between the coefficients (on SMB, HML and MOM) of the actual funds and the synthetic portfolios. For five deciles the differences exceed 0.4 with the maximum difference being 0.56.7 In Panel B, we multiply these differences with the geometric mean8 of the relevant risk factor to obtain an idea of the differences in returns caused by the differences in the factors. For most deciles, the return differences are economically insignificant as they are lower than 1% per annum. Overall, these differences suggest that the synthetic portfolios do a good job at mimicking the sensitivities of the actual funds to various risk factors.
7 The absolute differences tend to be smaller for the middle deciles because the synthetic fund betas tend by construction to regress toward their mean. 8 Calculated over the 1997–2007 period.
4. Biases in the estimated timing coefficients To assess whether fund managers exhibit timing ability, we need to consider two sources of spurious timing ability that the literature has identified. The first is the cash flow bias described in Warther (1995). The idea is that when the market does well, funds attract more capital and – to the extent that they have limited investment opportunities – their cash holdings increase. The increased cash holdings lower their sensitivity to the market, in these good times, and thus their realized returns. As a result, the estimated timing coefficients will be biased downward and will understate the manager’s true timing ability. Observe that this bias will affect the coefficients of both the piecewise-linear and quadratic specifications the same way when the market premium (or some other risk factor) is positive but in a different way when it is negative. In that case, the effect is absent for the piecewise-linear specification because the timing coefficients are only estimated for positive factor values. The quadratic specification still contains a downward bias: when the market is bearish, investors withdraw money thus decreasing a fund’s cash balance and increasing its sensitivity to the market. This implies that the realized returns will be more negative which in turn will drive down (i.e. make more negative) the coefficients of the quadratic terms. Unfortunately, as Bollen and Busse (2001) admit, this bias is difficult to control for. However, this bias will likely be less of a problem in our study as fund managers have more recently begun using tools that enable them to efficiently invest excess cash. For instance, they can temporarily hold positions in stock index futures contracts or use services such as ReFlow Management. The synthetic portfolios do not suffer from this bias because they do not involve any cash flows. A second source of spurious timing ability is the possibility that funds hold portfolios that are more option-like than the market
E. Benos et al. / The Quarterly Review of Economics and Finance 50 (2010) 509–514 Table 3 Daily average raw returns (in %) of actual funds and synthetic portfolios. We sort the actual funds into deciles by their raw returns over their entire life and calculate the decile average daily raw return. We also calculate the average decile raw returns of the corresponding synthetic portfolios. The difference between the two returns is in the third column. Actual fund returns are net of operating expenses whereas synthetic portfolio returns are not. Deciles
Actual funds
Synth. portf.
Difference
(High) 1 2 3 4 5 6 7 8 9 (Low) 10
0.10 0.06 0.05 0.04 0.04 0.03 0.02 0.01 0.00 −0.03
0.12 0.07 0.07 0.07 0.06 0.06 0.06 0.06 0.06 0.04
−0.02 −0.01 −0.02 −0.02 −0.03 −0.03 −0.04 −0.04 −0.05 −0.07
513
proxy portfolio. This point is made in Jagannathan and Korajczyk (1986). To illustrate, consider a fund manager who has no timing ability. If this manager does have the ability to pick stocks with a call-option-like sensitivity to the risk factors, then estimation of model (1) will still yield positive and significant coefficients for the convex terms. This is an upward bias and thus has more serious implications than the cash flow bias. Since the constructed synthetic portfolios mimic the actual funds in terms of their portfolio composition, they exhibit by construction similar “stock selection” behavior (but no “timing ability”) to the actual funds. Thus, they account for the above bias which is induced by the selection of stocks with option-like payoffs.
5. Results We start by reporting in Table 3 the average daily raw returns (in %) of actual fund decile portfolios and of the corresponding synthetic portfolios. When comparing these returns one needs to consider that actual fund returns are net of operating expenses such as management and distribution fees. This reality may explain the
Table 4 Fractions and average timing coefficients of funds with positive (+) and negative (−) timing coefficients as well as significantly positive (++) and negative (− −) timing coefficients. The factor timing coefficients ip are estimated from model (1). We present the results for both the quadratic and the piecewise-linear specifications. Panel A shows fractions and average timing coefficients of the actual funds in our data set. Panel B shows fractions and average timing coefficients for the synthetic portfolios. Panel C shows the fraction of funds for which the difference between the actual and synthetic fund timing coefficients is positive/negative and significantly positive/negative. Significance is at five percent level and is established by the bootstrap. Panel A: Actual funds g(fit ) = fit2 Fraction 1p 2p 3p 4p
4
i=1
ip
Timing coefficient 1p 2p 3p 4p
4
i=1
g(fit ) = fit I[fit ≥0] − 0.30 0.36 0.52 0.50
+ 0.70 0.64 0.48 0.50
ip
++ 0.23 0.25 0.10 0.14
−− 0.06 0.07 0.09 0.15
+ 0.69 0.57 0.55 0.55
− 0.31 0.43 0.45 0.45
++ 0.17 0.08 0.04 0.16
−− 0.06 0.06 0.06 0.10
0.69
0.31
0.24
0.05
0.70
0.20
0.21
0.05
+ 0.99 2.39 3.34 1.63
− −0.88 −2.75 −2.37 −1.40
++ 1.55 3.33 7.25 2.78
−− −1.87 −5.39 −4.00 −2.73
+ 0.06 0.06 0.07 0.07
− −0.05 −0.08 −0.07 −0.06
++ 0.11 0.12 0.22 0.13
−− −0.11 −0.19 −0.13 −0.13
3.45
−3.12
5.41
−5.44
0.11
−0.10
0.18
−0.21
− 0.34 0.33 0.59 0.17
++ 0.20 0.07 0.05 0.42
−− 0.06 0.02 0.08 0.00
Panel B: Synthetic portfolios g(fit ) = fit2 Fraction 1p 2p 3p 4p
4
i=1
i=1
− 0.37 0.20 0.56 0.17
+ 0.63 0.80 0.44 0.83
ip
Timing coefficient 1p 2p 3p 4p
4
g(fit ) = fit I[fit ≥0]
ip
++ 0.25 0.32 0.05 0.34
−− 0.09 0.01 0.10 0.00
+ 0.66 0.67 0.41 0.83
0.82
0.18
0.46
0.01
0.80
0.20
0.41
0.02
+ 1.06 2.53 2.76 1.44
− −0.92 −3.22 −2.52 −1.33
++ 1.51 3.42 6.69 1.93
−− −1.85 −10.44 −3.74 −6.35
+ 0.06 0.05 0.07 0.08
− −0.04 −0.08 −0.08 −0.06
++ 0.10 0.12 0.17 0.11
−− −0.09 −0.27 −0.17 0.00
4.08
−5.04
5.05
−25.39
0.13
−0.13
0.18
−0.46
Panel C: Difference in timing coefficients g(fit ) = fit2
g(fit ) = fit I[fit ≥0]
Fraction 1p 2p 3p 4p
+ 0.52 0.36 0.54 0.27
− 0.48 0.64 0.46 0.73
++ 0.13 0.02 0.07 0.03
−− 0.13 0.13 0.05 0.27
+ 0.51 0.41 0.57 0.26
− 0.49 0.59 0.43 0.74
++ 0.08 0.02 0.04 0.02
−− 0.10 0.06 0.02 0.27
ip
0.35
0.65
0.04
0.21
0.35
0.65
0.04
0.20
4
i=1
514
E. Benos et al. / The Quarterly Review of Economics and Finance 50 (2010) 509–514
systematic negative difference in returns across deciles9 but it also suggests that overall and over long horizons fund managers possess no timing ability. Otherwise, some of the differences would be zero or positive; remember, the synthetic portfolios match the actual funds by risk exposure and any differences to their raw returns cannot be attributed to risk. Table 4 shows the estimates of the timing coefficients of model (1). In Panel A, we show (ala BB (2001)) the fraction of positive/negative and significantly positive/negative timing coefficients of the actual funds as well as their simple averages. We estimate these coefficients for both the quadratic and piecewiselinear specifications. In Panel B we show the same results for the synthetic funds which by construction exhibit no timing ability. Thus, the fraction of significantly positive and negative timing coefficients in Panel B is the benchmark percentage of significant coefficients under the null hypothesis of no timing ability. Interestingly, under the null, 20–25% of funds are expected to have positive and significant market timing coefficients depending on the specification. A simple inspection of Panels A and B shows that the actual funds have neither a higher fraction of significantly positive timing coefficients nor higher coefficients on average. In fact, for the timing coefficients of the market, size and B/M premia, the fractions are almost the same. Regarding momentum, synthetic funds have higher fractions of significantly positive timing coefficients; this is the opposite of what one would expect had managers been able to time the momentum factor. We should bear in mind that the estimated coefficients of the actual funds are subject to the cash flow bias discussed earlier. We are in no position to assess the magnitude of the bias and thus to conclude if, absent the bias, the actual fund coefficients would have differed appreciably. One potential way around this problem is to more frequently adjust the synthetic fund coefficients. By doing so, one could perhaps model a fund’s changing holdings and style as money flows in and out of the fund. We leave this for future research. In Panel C we show the percentage of funds whose coefficients are lower/higher and significantly lower/higher than those of their synthetic counterparts. The significance of the difference of the two coefficients is established by the standard error of the difference: (difference) =
2 (ˆ actual ) + 2 (ˆ synthetic )
where (ˆ actual ) and (ˆ synthetic ) are the bootstrap standard deviations of the actual and synthetic fund coefficients. If fund managers did exhibit timing ability one would expect the fraction of funds with significantly higher timing coefficients than their synthetic counterparts to be greater than the fraction of funds with significantly lower timing coefficients. As one can see in Panel C however, these fractions are either very similar or lower for the actual funds. For example, for the quadratic specification and the market factor, 13% of funds have significantly higher coefficients than their synthetic counterparts but the exact same fraction of funds has significantly lower coefficients. For the other risk factors too, these fractions are either similar or more synthetic funds have greater timing coefficients than do actual funds. These results suggest that no market or other risk factor timing ability is persistent and lasts long enough so as to be captured by the timing model in Eq. (1). This does not necessarily mean that timing ability does not exist at all. If managers only occasionally time the market, then a model that uses data from the entire lifetime of a
9 The differences are also larger for the bottom deciles. This is consistent with the well-established fact that poorer performers charge higher fees.
fund will likely fail to detect this occasional market/factor timing. The results do imply however that even if timing ability exists it is either sporadic (i.e. very few managers possess it) and/or fund managers do not exhibit timing ability for prolonged periods. In light of findings suggesting that some managers do exhibit timing abilities over a short term (e.g. Benos & Jochec, 2009; Bollen & Busse, 2004), we interpret these results as evidence that timing ability generally does not persist over longer horizons. Overall, using a similar procedure as BB (2001) on a larger and more recent sample, our findings conflict with theirs. Our data includes the late 1990s equity boom and bust which means that fund managers had ample opportunity to use the timing skills that they might possess and thereby generate substantial abnormal returns. Thus, if at least market timing ability existed and were persistent for some funds in our sample, it should have been detected. Our results are consistent with much of the rest of the mutual fund literature that fails to detect timing ability in longer horizons and in a persistent manner. 6. Summary and Conclusion We use data for a large recent set of mutual funds in order to explore whether they exhibit market and other risk factor timing abilities. As demonstrated by BB (2001), the existence of spuriousness, does not allow one to simply rely on the statistical significance of estimated coefficients in timing models. Instead, one needs to know the cross-sectional distribution of timing coefficients under the null hypothesis of no timing ability. We obtain this distribution by constructing synthetic funds that match the actual ones in terms of their investment style but which by construction have no timing ability. The percentages and average values of the positive and statistically significant timing coefficients of the two types of funds suggest that managers generally do not possess factor timing abilities. Given however evidence that there are some fund managers who do possess short-term timing abilities (e.g. Benos & Jochec, 2009; Bollen & Busse, 2004), we interpret these results as evidence that timing ability does not persist over long time horizons. References Benos, E. & Jochec, M. (2009). Short term persistence in mutual fund market timing and stock selection abilities. Working Paper, University of Illinois. Bollen, N., & Busse, J. (2001). On the timing ability of mutual fund managers. Journal of Finance, 56, 1075–1094. Bollen, N., & Busse, J. (2004). Short-term persistence in mutual fund performance. The Review of Financial Studies, 18, 569–597. Brown, K., Harlow, W. V., & Starks, L. (1996). Of tournaments and temptations: An analysis of managerial incentives in the mutual fund industry. Journal of Finance, 51, 85–110. Carhart, M. (1997). On persistence in mutual fund performance. Journal of Finance, 52, 57–82. Chang, E., & Lewellen, W. (1984). Market timing and mutual fund investment performance. Journal of Business, 57(1, pt. 1), 57–72. Cooper, M., Gulen, H., & Vassalou, M. (2001). Investing in size and book-to-market portfolios using information about the macroeconomy: Some new trading rules. Working Paper. Fama, E., & French, K. (1993). Common risk factors in the returns on stocks and bonds. Journal of Financial Economics, 33, 3–56. Henriksson, R. (1984). Market timing and mutual fund performance: An empirical investigation. Journal of Business, 57(1, pt. 1), 73–97. Jagannathan, R., & Korajczyk, R. (1986). Assessing the market timing performance of managed portfolios. Journal of Business, 59, 217–235. Lakonishok, J., Shleifer, A., & Robert, V. (1994). Contrarian investment extrapolation and risk. The Journal of Finance, 5, 1541–1578. Treynor, J., & Mazuy, K. (1966). Can mutual funds outguess the market? Harvard Business Review, 44, 131–136. Warther, V. (1995). Aggregate mutual fund flows and security returns. Journal of Financial Economics, 39, 209–235.
Contents lists available at ScienceDirect
The Quarterly Review of Economics and Finance journal homepage: www.elsevier.com/locate/qref
Can mutual funds time risk factors?夽 Evangelos Benos, Marek Jochec ∗,1 , Victor Nyekel 1206 S Sixth St., 340 Wohlers Hall, Champaign, United States
a r t i c l e
i n f o
Article history: Received 9 April 2009 Received in revised form 18 May 2010 Accepted 24 May 2010 Available online 18 June 2010 Keywords: Risk factors Mutual funds Market timing Factor timing
a b s t r a c t Using daily observations from 448 actively managed funds, we employ the methodology in Bollen and Busse (2001) in order to assess the ability of fund managers to time systematic risk factors. We first construct synthetic portfolios in order to obtain the empirical distribution of timing coefficients under the null hypothesis of no timing ability and then compare this distribution to that of the timing coefficients of the actual funds. Fund managers do not seem to be timing any of the risk factors. We interpret this result as evidence that factor timing ability does not persist over long time periods. © 2010 The Board of Trustees of the University of Illinois. Published by Elsevier B.V. All rights reserved.
1. Introduction A mutual fund manager has two ways to generate returns in excess to what is implied by a portfolio’s exposure to various risk factors: the manager can either select individual stocks that, for various reasons, yield such higher risk adjusted returns (stock picking) or buy and sell stocks at specific times so as to capture the market upturns and avoid its downturns (market timing). In the latter case, a manager would buy stocks with a high sensitivity to the market prior to an upward market movement and would either buy low sensitivity stocks or hold cash prior to a downward market movement. The concept of “market timing” can potentially be generalized to include the systematic risk factors of the Carhart (1997) and Fama and French (1993) models as well. That is, if a manager could predict how the size (SMB), book-to-market (HML) and momentum (MOM) factors would move, he could purchase stocks with high or low sensitivities to these factors the exact same way he would for the market. There is evidence suggesting that some risk factors may be predictable. For example, Cooper, Gulen, and Vassalou (2001) argue that whether small stocks outperform large ones or vice versa
夽 This paper was completed while Evangelos Benos and Victor Nyekel were at the University of Illinois at Urbana-Champaign. We would like to thank Jay Wang, Heitor Almeida, Bo Becker and George Pennacchi for helpful comments. All errors are ours. ∗ Corresponding author. E-mail address: [email protected] (M. Jochec). 1 ISCTE.
is related to fundamental, non-diversifiable risk. They regress monthly values of the SMB factor on lagged values of all risk factors and of other economic variables and then use the estimated sensitivities to perform next-month, out-of-sample forecasts of SMB. Based on these forecasts, they execute a trading strategy that buys the SMB portfolio whenever it is forecasted to yield a positive return; otherwise it buys the Treasury bill. This strategy significantly outperforms the passive SMB strategy suggesting that the SMB factor is to some extent predictable. The authors find no evidence of predictability for HML and MOM whereas the market premium turns out to be predictable (using the same methodology) only in times of recession. That the particular strategy fails to predict the other risk factors does not mean that they are not predictable. For one thing, Cooper et al. (2001) argue that the factors are proxies of systematic risk and only use real economic variables as regressors. However, whether the risk factors capture fundamental risk is a hotly debated issue.2 This means that perhaps these factors may be predictable if alternative regressors are used to explain them. Overall, if a strategy predicts one factor but not another, this only suggests that different underlying economic processes give rise to these factors. Regardless however of whether the factors capture systematic risk or not, exploring the timing ability of mutual fund managers is still worthwhile. Since a successful risk-factor timer buys when the
2 See for instance Lakonishok et al. (1994) for a behavioral explanation of the B/M premium. These authors argue that the effect is due to the fact that investors extrapolate past performance (too far) into the future. If the size, B/M and momentum premia are not compensations for risk, then a fund manager can generate abnormal returns by simply purchasing stocks with the relevant characteristics.
1062-9769/$ – see front matter © 2010 The Board of Trustees of the University of Illinois. Published by Elsevier B.V. All rights reserved. doi:10.1016/j.qref.2010.05.001
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risk factor is “low” and sells when it is “high”, his realized returns will be a convex function of the risk factor returns. Earlier market timing studies have thus attempted to measure market timing ability by including a convex function of the market in the standard linear capital asset pricing model. Timing ability is then established by the statistical and economic significance of the coefficient of the convex term. Treynor and Mazuy (1966) use a quadratic function of the market whereas Henriksson (1984) and Chang and Lewellen (1984) use a piecewise-linear one. All of these studies conclude that managers possess no market timing ability. Bollen and Busse (2001) [henceforth BB (2001)] take an issue with this methodology on two fronts. First, they argue that one cannot conclude whether a manager times the market successfully by just looking at the estimated coefficient of the convex term. If spurious sources of significance are present, then fund managers will likely exhibit positive and significant timing coefficients. Thus, one needs to compare the cross-sectional distribution of these coefficients with their cross-sectional distribution under the assumption of no timing ability. To achieve this, they match each of the funds in their sample with a synthetic one that mimics the original fund’s investment style but which by construction has no timing ability. Then, they compare the two resulting cross-sectional distributions. The second point that BB (2001) make is that the tests in the previous studies have low power because they use monthly or annual data. By means of simulations they show that using daily observations, significantly increases statistical power. Intuitively, this is because timing strategies are likely to last less than a year or even a month. In that case, annual and monthly observations will simply be too noisy and will make it easy to accept the null of no timing ability when in fact the null is false. After accounting for these issues, BB find, in a sample of 230 funds, evidence (albeit weak) of timing ability. Our paper also employs the methodology in BB (2001) to test for the existence of timing ability. Our study contains two new elements. First, we control and test for timing ability in the other systematic risk factors of the Carhart (1997) model: SMB, HML and momentum. If managers are able to time these other factors, then not only is this interesting in itself but it could bias the market timing coefficient if not properly accounted for. If the risk factors are not orthogonal to each other, then a coefficient on market timing could be positive and significant simply because the manager times, for example, the SMB factor and the two factors happen to be correlated. Second, we use a more recent and substantially larger sample of 448 (versus 230) funds. Incidentally, our data covers the 1999–2007 time period which includes one of the largest equity booms and busts in the US equity market; this means that fund managers had plenty of opportunity to use their timing ability and that the benefits of successful timing would have been large. Our results conflict with those of BB (2001) in that we find no evidence of market or other factor timing ability. The fractions and average values of the statistically significant actual and synthetic fund timing coefficients are either very similar or seem to suggest that the synthetic funds have better timing abilities than the actual funds. These results agree with the earlier literature and are also consistent with the absence of long-term persistence in fund managers’ abilities.
data is obtained from the CRSP mutual fund daily database. To construct our data set, we start from the CRSP universe and isolate the actively managed domestic (i.e. US) equity funds by including the following Lipper fund classes: EIEI (Equity Income Funds), G (Growth Funds), LCCE (Large-Cap Core Funds), LCGE (Large-Cap Growth Funds), LCVE (Large-Cap Value Funds), MCCE (Mid-Cap Core Funds), MCGE (Mid-Cap Growth Funds), MCVE (Mid-Cap Value Funds), MLCE (Multi-Cap Core Funds), MLGE (Multi-Cap Growth Funds), MLVE (Multi-Cap Value Funds), SCCE (Small-Cap Core Funds), SCGE (Small-Cap Growth Funds) and SCVE (Small-Cap Value Funds). However, these Lipper objective codes still include funds that are not actively managed and/or are not invested in domestic equity and/or are restricted in specific industries.3 To eliminate these funds, we search for keywords in the fund names that would indicate an undesired category (such as “government”, “real estate”, “international”, etc.) and drop from the sample all funds whose name contains such a keyword. In addition, we require that the funds have more than a year (252 trading days) of daily returns, more than $20 million of average annual total net assets (TNA) during the fund’s life and a turnover ratio above 10%. We also require that they have returns for at least 95% of trading days for the period when the fund is listed in the daily database. Finally, we eliminate all younger share classes of those funds that have multiple share classes.4 Table 1 shows cross-fund averages of key fund characteristics for each of the years spanned by our sample. For the construction of the synthetic portfolios we use the CRSP daily stock return database and apply the following filters: we delete observations with missing returns, permnos, dates, and returns that equal any of the CRSP codes for missing values: −66, −77, −88, −99. However, we keep the respective stocks which means that some of our stocks have several missing daily return values. Finally, we use daily risk factor and style portfolio returns from Kenneth French’s website.5 3. Methodology 3.1. Measuring factor timing ability A successful factor timer will realize returns that are a convex function of the risk factor(s). Thus, as is common in the literature, we measure a manager’s ability to time some risk factor by a term that captures this convexity of the realized returns. For each mutual fund p and for a multi-factor model of stock returns, the following specification is estimated over N trading days: Rpt − Rft = ˛p +
4 i=1
ˇip fit +
4
ip g(fit ) + εpt ,
t = 1, 2, . . . , N (1)
i=1
where Rpt is the fund’s realized return on day t, fit is the value of risk factor i on day t and i = 1–4 denotes the four risk factors of the Carhart (1997) model in the following order: Rmt − Rft , SMBt, HMLt and MOMt . Rft is the risk-free rate and Rmt is the market return. SMBt and HMLt are the values of Fama and French (1993) size and book-to-market factors and MOMt is the day t value of the Carhart (1997) momentum factor. The function g(.) is in our case either g(fit ) = fit2 or g(fit ) = fit I[fit ≥0] . The ability to time a given risk factor is captured by the coefficient ip of this convex term. We estimate
2. Data Our main data set consists of daily returns for 448 actively managed US equity mutual funds and our time range is a 9-year period starting on January 1, 1999 and ending on December 31, 2007. Each fund remains in our sample for an average of 6 years. The
3 Examples include real estate funds, money market funds, government securities funds, etc. 4 Starting from May 2008, fund classes are appended to a fund name with a semicolon as a separator. We strip everything after the semicolon, sort by the remaining portion of fund name and inception date, and keep the earliest record. 5 http://mba:tuck:dartmouth.edu/pages/faculty/ken.french/data library.html.
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Table 1 Cross-fund averages of various fund characteristics for each of the years of our sample. The turnover ratios, the expense ratios, the management fees and the loads are expressed as % of total net assets. Total net assets (TNA) are in millions of dollars. Year
No. of funds
1999 2000 2001 2002 2003 2004 2005 2006 2007
328 308 322 337 348 349 335 313 292
Average
326
Turnover ratio
Expense ratio
Management fee
Front load
Rear load
TNA ($million)
92 101 100 92 85 84 81 85 86
1.2 1.2 1.2 1.3 1.3 1.2 1.2 1.2 1.3
0.68 0.64 0.74 0.75 0.76 0.77 0.75 0.76 0.79
3.8 4.2 4.7 4.7 4.7 4.8 4.4 4.2 4.2
2.3 2.3 2.3 2.0 1.9 1.9 1.8 1.5 1.5
898 849 680 488 631 698 733 800 901
90
1.2
0.74
4.4
1.9
742
these coefficients using all the available daily returns from a fund’s life. We note that one needs to control for timing ability in all risk factors when measuring the ability to time any single factor. Otherwise it is impossible to tell a priori whether the estimated coefficient captures the timing ability of the particular factor; unless g(fit ) ⊥ g(fjt ) ∀j = / i, a model that includes a single timing factor will yield inconsistent estimates, since the estimated coefficient will also capture any timing effects from the other factors. More importantly, however, timing ability should be calculated controlling for the effect of the intercept alpha. In companion work (Benos & Jochec, 2009) we show that unless one controls for alpha, it drives the results and masks almost completely the timing coefficients. The choice of daily instead of monthly data is based on the findings of BB (2001) that the use of daily data tends to increase the power of the statistical tests. Intuitively, a monthly frequency will not capture a manager’s timing activity if this activity is more frequent than monthly. Thus, with daily data we are more likely to reject the null of no timing activity when the null is false. 3.2. Bootstrap standard errors In assessing the statistical significance of the estimated timing coefficients we cannot rely on standard t-tests because of the possibility of misspecification. Suppose for example that a fund manager executes a timing strategy that is best captured by the quadratic model (g(fit ) = fit2 ) but we instead estimate a piecewiselinear one (g(fit ) = fit I[fit ≥0] ). Then, for consecutive large values of fund returns (i.e. the dependent variable) the fitted line of the piecewise-linear model will fall below these values; this discrepancy will in turn be picked up by the error terms, thus inducing serial correlation. Furthermore, fund managers may not always engage in a timing strategy continuously. At times they may either not have a clear prediction of what future market movements will be or they may adjust their strategies in accordance to their compensation schemes to maximize their payoff.6 In either case, we are likely to have time-varying deviations from the standard regression assumptions which also means that the standard heteroscedasticity and autocorrelation corrections may not suffice to yield consistent estimates of the coefficient standard errors. To address these problems, we follow BB (2001) in letting the data speak for itself and calculating bootstrap standard errors. This is done in the following way: we first estimate for each fund the timing coefficients using all the available observations and compute the residuals. We then randomly reshuffle (with replacement) the estimated residuals and using the already estimated coefficients we “predict” the dependent variable (fund returns), thus
6
See Brown, Harlow, and Starks (1996).
constructing a bootstrap sample. This process is repeated 1000 times. The final step is to estimate anew the timing coefficients in each of the bootstrap samples, to derive their empirical distribution. The t-statistic of the originally estimated timing coefficient is then the estimated coefficient itself divided by the standard error of the coefficient empirical distribution: t=
ˆ pi bootstrap
(pi
)
3.3. Distribution of timing coefficients under the null and synthetic portfolio construction In order to use the distribution of the estimated fund timing coefficients to decide whether timing ability exists, we need to know the distribution of these coefficients under the null hypothesis of no timing ability. Even if fund managers have no timing ability, some funds will have positive and significant timing coefficients due to random chance. To derive the timing coefficient empirical distribution under the null of no timing ability, we construct for each available fund a synthetic counterpart that mimics the original fund’s style and risk exposure. We then estimate timing coefficients for the synthetic funds and obtain their empirical distribution. This distribution serves as a benchmark for comparing the distribution of the timing coefficients of the actual funds. We next describe in detail the construction of synthetic funds. We construct synthetic portfolios following the procedure in BB (2001). We pair each mutual fund with a synthetic one that is intended to mimic its style but exhibits, by construction, no timing ability. The first step in this process is to determine the sensitivity of a fund to a set of style portfolios whose returns are obtained from Kenneth French’s website. The style portfolios are six B/Msize portfolios formed by the intersection of two size and three B/M portfolios constructed by independent sorts as well as two momentum portfolios consisting of the top and bottom 30% of all stocks sorted by last year’s raw returns. The idea is to try to replicate as closely as possible the actual fund’s style; i.e. express its returns as a linear combination of the returns of benchmark style portfolios. For that, we estimate for each fund, the model: Rp,t =
8
bp,i ri,t + εp,t
(2)
i=1
where Rp,t is the day t realized return of fund p and ri,t is the day t return of benchmark style portfolio i. We estimate the bp,i s by minimizing the variance of εp,t subject to a non-negativity constraint for the estimated coefficients. For this estimation we use all the daily returns available over the fund’s life. Once the sensitivities of a fund to the risk factors have been estimated, we construct the mimicking synthetic fund by randomly
512
E. Benos et al. / The Quarterly Review of Economics and Finance 50 (2010) 509–514 Table 2 Panel A: Absolute differences between the betas of actual funds and synthetic portfolios. For each of the actual funds and the synthetic portfolios we first estimate the standard four-factor model: Rpt − Rft = ˛p + ˇ1p (Rmt − Rft ) + ˇ2p SMBit + ˇ3p HMLt + ˇ4p MOMt + εpt . We then sort all funds into deciles by the estimated factor betas and compare the average fund decile beta with the corresponding synthetic portfolio decile beta. Similar results are obtained by estimating model (1) instead. Panel B: Annualized return differences (in %) as a result of factor differences. We multiply the factor differences (in Panel A) with the geometric mean of the respective risk factor. The geometric mean is calculated over a 10-year period (1997–2007). Panel A Deciles
ˆ 2,act. − ˇ ˆ 2,synth. | |ˇ
ˆ 3,act. − ˇ ˆ 3,synth. | |ˇ
ˆ 4,act. − ˇ ˆ 4,synth. | |ˇ
1 (High) 2 3 4 5 6 7 8 9 10 (Low)
0.33 0.15 0.07 0.06 0.16 0.30 0.37 0.41 0.47 0.56
0.16 0.03 0.01 0.00 0.03 0.10 0.11 0.18 0.20 0.43
0.41 0.25 0.19 0.16 0.13 0.13 0.08 0.08 0.00 0.12
Panel B Deciles
ˆ 2,act. − ˇ ˆ 2,synth. |SMB |ˇ
ˆ 3,act. − ˇ ˆ 3,synth. |HML |ˇ
ˆ 4,act. − ˇ ˆ 4,synth. |MOM |ˇ
1 (High) 2 3 4 5 6 7 8 9 10 (Low)
0.77 0.35 0.16 0.14 0.37 0.70 0.86 0.95 1.09 1.30
0.60 0.11 0.04 0.00 0.11 0.38 0.42 0.68 0.76 1.63
0.26 0.16 0.12 0.10 0.08 0.08 0.05 0.05 0.00 0.07
Average
0.67
0.47
0.10
selecting 100 stocks that belong to the eight benchmark portfolios in proportions determined by the estimated sensitivities. Thus, the 8 proportion of stocks selected from factor portfolio i is bˆ p,i / i=1 bˆ p,i . The stocks initially receive equal weights and then evolve according to a buy-and-hold strategy. The stocks are randomly replaced with other stocks selected from the same style portfolios, with an average holding period of 1 year. Every time a stock is replaced, the weights are reset to equal. The set of stocks that are assigned to each of the eight benchmark portfolios is obtained from the CRSP universe after applying standard filters: we exclude stocks with too many missing values, prices smaller or equal to $1, and share codes other than 10 or 11 (to exclude foreign stocks, ADRs, shares of beneficial interest, depository partnership units and receipts, trusts, closed-end funds, and REITs). Table 2, Panel A, shows the absolute differences between the coefficients (on SMB, HML and MOM) of the actual funds and the synthetic portfolios. For five deciles the differences exceed 0.4 with the maximum difference being 0.56.7 In Panel B, we multiply these differences with the geometric mean8 of the relevant risk factor to obtain an idea of the differences in returns caused by the differences in the factors. For most deciles, the return differences are economically insignificant as they are lower than 1% per annum. Overall, these differences suggest that the synthetic portfolios do a good job at mimicking the sensitivities of the actual funds to various risk factors.
7 The absolute differences tend to be smaller for the middle deciles because the synthetic fund betas tend by construction to regress toward their mean. 8 Calculated over the 1997–2007 period.
4. Biases in the estimated timing coefficients To assess whether fund managers exhibit timing ability, we need to consider two sources of spurious timing ability that the literature has identified. The first is the cash flow bias described in Warther (1995). The idea is that when the market does well, funds attract more capital and – to the extent that they have limited investment opportunities – their cash holdings increase. The increased cash holdings lower their sensitivity to the market, in these good times, and thus their realized returns. As a result, the estimated timing coefficients will be biased downward and will understate the manager’s true timing ability. Observe that this bias will affect the coefficients of both the piecewise-linear and quadratic specifications the same way when the market premium (or some other risk factor) is positive but in a different way when it is negative. In that case, the effect is absent for the piecewise-linear specification because the timing coefficients are only estimated for positive factor values. The quadratic specification still contains a downward bias: when the market is bearish, investors withdraw money thus decreasing a fund’s cash balance and increasing its sensitivity to the market. This implies that the realized returns will be more negative which in turn will drive down (i.e. make more negative) the coefficients of the quadratic terms. Unfortunately, as Bollen and Busse (2001) admit, this bias is difficult to control for. However, this bias will likely be less of a problem in our study as fund managers have more recently begun using tools that enable them to efficiently invest excess cash. For instance, they can temporarily hold positions in stock index futures contracts or use services such as ReFlow Management. The synthetic portfolios do not suffer from this bias because they do not involve any cash flows. A second source of spurious timing ability is the possibility that funds hold portfolios that are more option-like than the market
E. Benos et al. / The Quarterly Review of Economics and Finance 50 (2010) 509–514 Table 3 Daily average raw returns (in %) of actual funds and synthetic portfolios. We sort the actual funds into deciles by their raw returns over their entire life and calculate the decile average daily raw return. We also calculate the average decile raw returns of the corresponding synthetic portfolios. The difference between the two returns is in the third column. Actual fund returns are net of operating expenses whereas synthetic portfolio returns are not. Deciles
Actual funds
Synth. portf.
Difference
(High) 1 2 3 4 5 6 7 8 9 (Low) 10
0.10 0.06 0.05 0.04 0.04 0.03 0.02 0.01 0.00 −0.03
0.12 0.07 0.07 0.07 0.06 0.06 0.06 0.06 0.06 0.04
−0.02 −0.01 −0.02 −0.02 −0.03 −0.03 −0.04 −0.04 −0.05 −0.07
513
proxy portfolio. This point is made in Jagannathan and Korajczyk (1986). To illustrate, consider a fund manager who has no timing ability. If this manager does have the ability to pick stocks with a call-option-like sensitivity to the risk factors, then estimation of model (1) will still yield positive and significant coefficients for the convex terms. This is an upward bias and thus has more serious implications than the cash flow bias. Since the constructed synthetic portfolios mimic the actual funds in terms of their portfolio composition, they exhibit by construction similar “stock selection” behavior (but no “timing ability”) to the actual funds. Thus, they account for the above bias which is induced by the selection of stocks with option-like payoffs.
5. Results We start by reporting in Table 3 the average daily raw returns (in %) of actual fund decile portfolios and of the corresponding synthetic portfolios. When comparing these returns one needs to consider that actual fund returns are net of operating expenses such as management and distribution fees. This reality may explain the
Table 4 Fractions and average timing coefficients of funds with positive (+) and negative (−) timing coefficients as well as significantly positive (++) and negative (− −) timing coefficients. The factor timing coefficients ip are estimated from model (1). We present the results for both the quadratic and the piecewise-linear specifications. Panel A shows fractions and average timing coefficients of the actual funds in our data set. Panel B shows fractions and average timing coefficients for the synthetic portfolios. Panel C shows the fraction of funds for which the difference between the actual and synthetic fund timing coefficients is positive/negative and significantly positive/negative. Significance is at five percent level and is established by the bootstrap. Panel A: Actual funds g(fit ) = fit2 Fraction 1p 2p 3p 4p
4
i=1
ip
Timing coefficient 1p 2p 3p 4p
4
i=1
g(fit ) = fit I[fit ≥0] − 0.30 0.36 0.52 0.50
+ 0.70 0.64 0.48 0.50
ip
++ 0.23 0.25 0.10 0.14
−− 0.06 0.07 0.09 0.15
+ 0.69 0.57 0.55 0.55
− 0.31 0.43 0.45 0.45
++ 0.17 0.08 0.04 0.16
−− 0.06 0.06 0.06 0.10
0.69
0.31
0.24
0.05
0.70
0.20
0.21
0.05
+ 0.99 2.39 3.34 1.63
− −0.88 −2.75 −2.37 −1.40
++ 1.55 3.33 7.25 2.78
−− −1.87 −5.39 −4.00 −2.73
+ 0.06 0.06 0.07 0.07
− −0.05 −0.08 −0.07 −0.06
++ 0.11 0.12 0.22 0.13
−− −0.11 −0.19 −0.13 −0.13
3.45
−3.12
5.41
−5.44
0.11
−0.10
0.18
−0.21
− 0.34 0.33 0.59 0.17
++ 0.20 0.07 0.05 0.42
−− 0.06 0.02 0.08 0.00
Panel B: Synthetic portfolios g(fit ) = fit2 Fraction 1p 2p 3p 4p
4
i=1
i=1
− 0.37 0.20 0.56 0.17
+ 0.63 0.80 0.44 0.83
ip
Timing coefficient 1p 2p 3p 4p
4
g(fit ) = fit I[fit ≥0]
ip
++ 0.25 0.32 0.05 0.34
−− 0.09 0.01 0.10 0.00
+ 0.66 0.67 0.41 0.83
0.82
0.18
0.46
0.01
0.80
0.20
0.41
0.02
+ 1.06 2.53 2.76 1.44
− −0.92 −3.22 −2.52 −1.33
++ 1.51 3.42 6.69 1.93
−− −1.85 −10.44 −3.74 −6.35
+ 0.06 0.05 0.07 0.08
− −0.04 −0.08 −0.08 −0.06
++ 0.10 0.12 0.17 0.11
−− −0.09 −0.27 −0.17 0.00
4.08
−5.04
5.05
−25.39
0.13
−0.13
0.18
−0.46
Panel C: Difference in timing coefficients g(fit ) = fit2
g(fit ) = fit I[fit ≥0]
Fraction 1p 2p 3p 4p
+ 0.52 0.36 0.54 0.27
− 0.48 0.64 0.46 0.73
++ 0.13 0.02 0.07 0.03
−− 0.13 0.13 0.05 0.27
+ 0.51 0.41 0.57 0.26
− 0.49 0.59 0.43 0.74
++ 0.08 0.02 0.04 0.02
−− 0.10 0.06 0.02 0.27
ip
0.35
0.65
0.04
0.21
0.35
0.65
0.04
0.20
4
i=1
514
E. Benos et al. / The Quarterly Review of Economics and Finance 50 (2010) 509–514
systematic negative difference in returns across deciles9 but it also suggests that overall and over long horizons fund managers possess no timing ability. Otherwise, some of the differences would be zero or positive; remember, the synthetic portfolios match the actual funds by risk exposure and any differences to their raw returns cannot be attributed to risk. Table 4 shows the estimates of the timing coefficients of model (1). In Panel A, we show (ala BB (2001)) the fraction of positive/negative and significantly positive/negative timing coefficients of the actual funds as well as their simple averages. We estimate these coefficients for both the quadratic and piecewiselinear specifications. In Panel B we show the same results for the synthetic funds which by construction exhibit no timing ability. Thus, the fraction of significantly positive and negative timing coefficients in Panel B is the benchmark percentage of significant coefficients under the null hypothesis of no timing ability. Interestingly, under the null, 20–25% of funds are expected to have positive and significant market timing coefficients depending on the specification. A simple inspection of Panels A and B shows that the actual funds have neither a higher fraction of significantly positive timing coefficients nor higher coefficients on average. In fact, for the timing coefficients of the market, size and B/M premia, the fractions are almost the same. Regarding momentum, synthetic funds have higher fractions of significantly positive timing coefficients; this is the opposite of what one would expect had managers been able to time the momentum factor. We should bear in mind that the estimated coefficients of the actual funds are subject to the cash flow bias discussed earlier. We are in no position to assess the magnitude of the bias and thus to conclude if, absent the bias, the actual fund coefficients would have differed appreciably. One potential way around this problem is to more frequently adjust the synthetic fund coefficients. By doing so, one could perhaps model a fund’s changing holdings and style as money flows in and out of the fund. We leave this for future research. In Panel C we show the percentage of funds whose coefficients are lower/higher and significantly lower/higher than those of their synthetic counterparts. The significance of the difference of the two coefficients is established by the standard error of the difference: (difference) =
2 (ˆ actual ) + 2 (ˆ synthetic )
where (ˆ actual ) and (ˆ synthetic ) are the bootstrap standard deviations of the actual and synthetic fund coefficients. If fund managers did exhibit timing ability one would expect the fraction of funds with significantly higher timing coefficients than their synthetic counterparts to be greater than the fraction of funds with significantly lower timing coefficients. As one can see in Panel C however, these fractions are either very similar or lower for the actual funds. For example, for the quadratic specification and the market factor, 13% of funds have significantly higher coefficients than their synthetic counterparts but the exact same fraction of funds has significantly lower coefficients. For the other risk factors too, these fractions are either similar or more synthetic funds have greater timing coefficients than do actual funds. These results suggest that no market or other risk factor timing ability is persistent and lasts long enough so as to be captured by the timing model in Eq. (1). This does not necessarily mean that timing ability does not exist at all. If managers only occasionally time the market, then a model that uses data from the entire lifetime of a
9 The differences are also larger for the bottom deciles. This is consistent with the well-established fact that poorer performers charge higher fees.
fund will likely fail to detect this occasional market/factor timing. The results do imply however that even if timing ability exists it is either sporadic (i.e. very few managers possess it) and/or fund managers do not exhibit timing ability for prolonged periods. In light of findings suggesting that some managers do exhibit timing abilities over a short term (e.g. Benos & Jochec, 2009; Bollen & Busse, 2004), we interpret these results as evidence that timing ability generally does not persist over longer horizons. Overall, using a similar procedure as BB (2001) on a larger and more recent sample, our findings conflict with theirs. Our data includes the late 1990s equity boom and bust which means that fund managers had ample opportunity to use the timing skills that they might possess and thereby generate substantial abnormal returns. Thus, if at least market timing ability existed and were persistent for some funds in our sample, it should have been detected. Our results are consistent with much of the rest of the mutual fund literature that fails to detect timing ability in longer horizons and in a persistent manner. 6. Summary and Conclusion We use data for a large recent set of mutual funds in order to explore whether they exhibit market and other risk factor timing abilities. As demonstrated by BB (2001), the existence of spuriousness, does not allow one to simply rely on the statistical significance of estimated coefficients in timing models. Instead, one needs to know the cross-sectional distribution of timing coefficients under the null hypothesis of no timing ability. We obtain this distribution by constructing synthetic funds that match the actual ones in terms of their investment style but which by construction have no timing ability. The percentages and average values of the positive and statistically significant timing coefficients of the two types of funds suggest that managers generally do not possess factor timing abilities. Given however evidence that there are some fund managers who do possess short-term timing abilities (e.g. Benos & Jochec, 2009; Bollen & Busse, 2004), we interpret these results as evidence that timing ability does not persist over long time horizons. References Benos, E. & Jochec, M. (2009). Short term persistence in mutual fund market timing and stock selection abilities. Working Paper, University of Illinois. Bollen, N., & Busse, J. (2001). On the timing ability of mutual fund managers. Journal of Finance, 56, 1075–1094. Bollen, N., & Busse, J. (2004). Short-term persistence in mutual fund performance. The Review of Financial Studies, 18, 569–597. Brown, K., Harlow, W. V., & Starks, L. (1996). Of tournaments and temptations: An analysis of managerial incentives in the mutual fund industry. Journal of Finance, 51, 85–110. Carhart, M. (1997). On persistence in mutual fund performance. Journal of Finance, 52, 57–82. Chang, E., & Lewellen, W. (1984). Market timing and mutual fund investment performance. Journal of Business, 57(1, pt. 1), 57–72. Cooper, M., Gulen, H., & Vassalou, M. (2001). Investing in size and book-to-market portfolios using information about the macroeconomy: Some new trading rules. Working Paper. Fama, E., & French, K. (1993). Common risk factors in the returns on stocks and bonds. Journal of Financial Economics, 33, 3–56. Henriksson, R. (1984). Market timing and mutual fund performance: An empirical investigation. Journal of Business, 57(1, pt. 1), 73–97. Jagannathan, R., & Korajczyk, R. (1986). Assessing the market timing performance of managed portfolios. Journal of Business, 59, 217–235. Lakonishok, J., Shleifer, A., & Robert, V. (1994). Contrarian investment extrapolation and risk. The Journal of Finance, 5, 1541–1578. Treynor, J., & Mazuy, K. (1966). Can mutual funds outguess the market? Harvard Business Review, 44, 131–136. Warther, V. (1995). Aggregate mutual fund flows and security returns. Journal of Financial Economics, 39, 209–235.