International Bulletin of Business Administration ISSN: 1451-243X Issue 10 (2011) © EuroJournals, Inc. 2011 http://www.eurojournals.com

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The Skills of Active Managers of U.S. Equity Mutual Funds

Samih Antoine Azar

Faculty of Business Administration & Economics, Haigazian University

Mexique Street, Kantari, Beirut, Lebanon

Telefax: +9611349230 E-mail: samih.azar@haigazian.edu.lb

Abstract

This paper aims to examine the timing abilities of the managers of a sample of U.S. equity mutual funds. Three abilities are considered: stock selection (or micro forecasting), market timing (or macro forecasting), and volatility timing. The statistical techniques utilized are constrained pooled regressions and system regressions. The intercept and all slope estimates in these regressions are constrained to be the same across funds. It is found that the managers of the equity mutual funds have significant stock selection, market timing and volatility timing abilities. All coefficient estimates have the expected signs, and are statistically significantly different from zero. Moreover the average systematic risk of these funds is statistically significantly less than +1, implying that fund managers do not pursue market indexing. The originality of this paper is fourfold. The first is that the specification of the econometric models includes volatility timing, besides stock selection and market timing variables, and this is little tested in the literature. The second is that two different market timing variables are considered. One of them necessitates the calculation of the cost of a put option. The third is that the significant volatility timing that is present is interpreted differently from the literature. Fourth, and because of all the above, the intercept which stands for Jensen’s alpha is properly and more precisely estimated. Keywords: Equity mutual fund performance, Jensen’s alpha, Stock selection ability,

Market timing ability, Volatility timing ability, Pooled regressions, System estimation.

JEL Classification Codes: G23, C58, C32.

1. Introduction The performance of U.S. equity mutual funds is an issue that has received a lot of attention in the academic literature. Some research finds no evidence of outperformance, like in the seminal paper of Jensen (1968). Other research finds evidence of overall industry outperformance like in Ippolito (1989). An early summary of the empirical results related to the subject is surveyed in Ippolito (1993). A more recent survey can be found in Al Hourani (2010). The empirical results are contradictory. Some reach the conclusion of outperformance, and others reach the opposite conclusion. This topic is highly important, especially because there are two contrasting theoretical strands, and that one of them needs to be supported. The first strand believes in market efficiency, and the ensuing random walk behavior of stock prices (Fama, 1965, 1970, 1992), and in global financial accounting (French, 2008) whereby stock trading is a zero-sum game. The second strand believes otherwise (Grossman and Stiglitz, 1980). According to the latter information is costly and those who undertake security research,

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like managers of mutual funds, will only do so if there are enough returns to offset this cost. Mutual funds must earn extra profits to cover at least their expenses. The significant growth in mutual fund assets, which occurred with a sharp decrease in individual stock holdings, points in the direction that the second strand of the theoretical literature is on the right track. However, another explanation for this success is that investment in a mutual fund removes appreciably unsystematic or diversifiable risk.

Jensen (1968) pioneered the first estimate of abnormal performance which is rightly called Jensen’s alpha. This measure starts from the first-pass regression of the CAPM, whereby the fund

excess return ( fi RR −) is linearly related to the market excess return ( fm RR −

), with the factor of

proportionality being the systematic risk ( β ):

( ) ( ) itftmtiiftit RRRR εβα +−+=− (1)

Equation (1) is a simple linear regression, and the expected value of iα is zero. If iα is statistically significantly positive then there is outperformance for this particular fund. However, as Ippolito (1989) contends, outperformance should be measured for the whole industry, or, at least, for the whole sample of funds included in the estimation. If the average α divided by its standard error results in a statistically significant and positive t-statistic then there is outperformance.

Treynor and Mazuy (1966) have derived a non-linear version of the CAPM. If investors expect an upturn they will increase the beta of the portfolio to take advantage of the higher return. Therefore at high rates of return the beta is also significantly higher, producing approximately a quadratic CAPM:

( ) ( ) ( ) itftmtiftmtiiftit RRRRRR εγβα +−+−+=− 2 (2)

The expected sign of γ is positive. If the average γ is positive and statistically significant, then mutual fund managers are able to time the market or to forecast the macro economy. If the average α is positive and statistically significant, then these managers are able to pick and select stocks profitably, or to forecast the micro economy.

Treynor and Mazuy did not find support for their relation in equation (2). They do not report Jensen’s alphas. Using equation (2) Stevenson (2004) finds no significant stock selection and market

timing abilities for Irish funds. The average estimate of α and γ are all negative contrary to expectations. With this same equation, Chander (2006) finds an average market timing coefficient of -0.0063 for the Indian capital market, but he does not report a significance test for this coefficient. In his

Exhibit 1 (p. 320) 7 estimates of γ are negative and statistically significant, contrary to what is expected. Chu and McKenzie (2008) follow the same testing procedure. They find that using equation (2) there is no evidence of market timing, and little evidence for an abnormal average Jensen’s alpha in the Hong Kong financial market. Do et al. (2009) find little evidence for market timing among Australian hedge fund managers. Their average estimates of α are all positive and they conclude that these managers have some stock selection ability.

Another model of market timing is proposed by Merton (1981), Henriksson and Merton (1981) and Henriksson (1984). They add a term in their parametric tests of market timing which is the realization of a put option, which takes the following form:

],0[ mtft RRMax − (3)

Merton (1981) provides an estimate for the price of such a put at $ 0.08. He assumes the strike

price to be ( )ftR+1

, and the underlying asset to have a value of $ 1. The total model specification becomes:

( ) itmtftiftmtiiftit RRMaxRRRR εδβα +−+−+=− ],0[ (4)

Henriksson (1984) find little evidence of stock selection and market timing abilities using

equation (4). Stevenson (2004) finds no fund with a statistically significant and positive δ . Chander

(2006) finds an average δ of 0.00564, which has the correct positive sign, but he does not report a significance level. Chu and Mckenzie (2008), using equation (4), find for Hong Kong an average

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Jensen’s alpha of 0.0007 having a t-statistic of 2.4232, and an average δ of -0.0173, having a t-statistic of -1.0826. Hence stock selection seems to be possible for their sample but not market timing or macro forecasting. Ferruz et al. (2010) estimate a pooled regression on equation (4). They argue that the cost of the put should be accounted for in the Merton/Henriksson model. When they do that their estimate of equation (4) shows better statistical results, with a positive pooled and statistically significant market timing effect, and with a positive and statistically highly significant pooled Jensen’s alpha.

A final model adds volatility timing to the specification. If volatility is high fund investors will cut on their exposure to risky assets. It can be shown that this effect will show up as a cubic term in the Treynor and Mazuy (1966) model, i.e. equation (2) in this paper:

( ) ( ) ( ) ( ) itftmtiftmtiftmtiiftit RRRRRRRR ελγβα +−+−+−+=− 32 (5)

In the literature, the expected sign on λ is negative. I do not agree. If investors reduce their exposure because of higher volatility, then stock prices must fall as investors sell these stocks, and hence returns will rise. In other terms, higher volatility implies a higher required excess return. That is

why the expected sign on λ should be positive and not negative. Stevenson (2004) estimates equation

(5) for the Irish capital market, and he obtains 5 out of 35 funds with positive λ , the rest being

negative, and 5 out of 35 with a negative and statistically significant λ . Do et al. (2009) conclude that, with equation (5), there is little evidence of volatility timing for Australian funds but some evidence of that timing for US funds. Holmes and Faff (2004) estimate a cubic regression with and without a

conditional beta. They find a positive selectivity timing and a negative λ for the majority of funds. In addition they find that the cubic relation is stable across sub-periods and during up and down market conditions. However, they find an anomalous seasonal effect, especially for July.

2. The Models Two general models will be estimated: Model 1 and Model 2. Model 1 is equation (4) generalized to include a cubic term and the future cost of the put:

( ) ( ) ( ) itftmtimtftiftmtiiftit RRRRMaxRRRR ελδβα +−+−−+−+=− 309190645.0],0[ (6)

In equation (6) the next-period cost of the put is $ 0.09190645, assuming a $ 1 value of the underlying, a $ 1.0305782 for the strike price, i.e. exp(0.03012), a riskless return of 3.012%, and a volatility of 22.4007%, which represent respectively the average T-bill yield and the standard deviation of the log returns of the S&P 500 with this paper’s sample.

Model 2 is simply equation (5). These two models incorporate all the variables identified in the literature in order to avoid any problem of omitted variables, and in order to estimate the intercept, which is Jensen’s alpha, properly. Another problem is the econometric bias in the slope when the same

variable ( )ftR

appears on both sides of the regression. That is why the average of ftR for the sample

(i.e. 3.012%) will replace its time-varying substitute. See Al Hourani (2010) and Azar and Al Hourani (2010) for further details. Hence Model 1 becomes:

( ) ( ) ( ) 03012.009190645.0]03012.0,0[ 03012.003012.0 3itmtimtimtiiit RRMaxRR ελδβα +−+−−+−+=− (7)

Moreover, the actual regressions performed, whether by pooling or system analysis, constrain the estimators to be the same across funds. The final Model 1 is:

( ) ( ) ( ) itmtmtmtit RRMaxRR ελδβα +−+−−+−+=− 303012.009190645.0]03012.0,0[ 03012.003012.0 (8) And the final Model 2 is:

( ) ( ) ( ) ( ) itmtmtmtit RRRR ελγβα +−+−+−+=− 32 03012.003012.003012.003012.0 (9)

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3. The Data The source of the data is from the Vanguard website. It is a reliable source of all needed data and information on all Vanguard funds and on the 5,831 funds of other companies that investors can invest through Vanguard portal “Fund Access”. The information is free and is accessible to everyone. All in all 26 equity mutual funds out of the 200 Vanguard mutual funds and 174 equity mutual funds out of the 5,831 funds of other companies are selected. These funds are of different categories. Some are for large, others for median and still others for small cap. They are for different stock styles: value, growth and blend. The focus is on the domestic equity mutual funds only. Mutual funds that are of age less than ten years, bond funds and international funds are excluded. The sample is the same as in Al Hourani (2010) and Azar and Al Hourani (2010).

The selection process is alphabetical. It is implicitly assumed that the first letter of the names of the funds is randomly distributed. The sample covers the period 2000 to 2009 annually. Mutual fund rates of return fluctuate with market conditions. For that reason, it is helpful to examine performance over a relevant time period. Annual data for 10 years provides a lengthy and appropriate observation period. It is reasonable to believe that performance measurement over 10 years will result in adequate and more stable estimates of average returns and betas. Annual data has much less noise than quarterly

or monthly data. The analysis is based on logarithmic ( )Ln annual returns using the following equation

where tP stands for the net assets of the individual mutual fund at time t:

( ) ( ) ( )/1 1return Ln P Ln P Ln P Pt tt t= − =− − (10)

The index selected is the S&P 500. This index is weighted by market value, and its performance is thought to be representative of the stock market as a whole. The index provides a broad snapshot of the overall U.S. equity market. In fact, over 70% of all U.S. equities are tracked by the S&P 500. The index provider selects the included companies based upon their market size, liquidity, and sector. Most of the companies in the index are solid mid-cap or large-cap corporations. Most experts consider the S&P 500 one of the best benchmarks available to judge overall U.S. market performance.

4. The Empirical Results Two general statistical and econometric specifications are carried out: pooled regressions, and system estimation. The statistical package that is employed (Eviews7) provides three estimation procedures for the coefficients in the pooled regressions: OLS, White (1980) consistent standard errors, and Newey and West (1987) consistent standard errors. Table 1 presents the results. In Models 1 and 2, i.e. equations (8) and (9), the constants, or Jensen’s alphas, are positive and highly significant statistically. They are respectively 6.6634% and 4.2763%. These figures are gross of expenses. Management fees and expenses for 2009 represent a ratio on total assets of 1.2413%, with a standard error of 0.0610204%. In French (2008) the expense ratios are estimated to be 2.08% in 1980 and 0.95% in 2006, estimates that are close to my estimate. Comparing, with an F-test, the square of the expense ratio standard error to the square of the standard errors on the intercept, obtained from the three kinds of estimators for the two pooled regressions, results in rejecting the null hypothesis of equality at very low marginal significance levels. Therefore it is inferred that the two populations of the expense ratio and Jansen’s alpha, have different standard errors (see the last row in Table 1). Because of this the t-statistics and the degrees of freedom of these net alphas are calculated according to Keller (2009, p. 442). The tests that these alphas are statistically significant and positive net of expenses are carried out in Table 2 Panel A. For the three cases of each model the t-statistics of these net alphas are quite high, the lowest being 7.626. This shows that the funds in the sample have managed to earn net and positive abnormal profits. This means that the active managers of these funds have indeed stock selection and micro forecasting abilities.

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For the pooled regressions, the first variable in Model 1 produces a pooled beta of 1.061905, which seems to be statistically different from +1 in 2 cases out of the three. The same first variable in Model 2 produces a pooled beta of 0.875838, which is statistically different from +1 in all three cases. From this one can infer that mutual funds do not own the market portfolio, that they have less than market risk, and that they are not index funds.

The second variable in Model 1, i.e. the future value of the put option net of cost, has also a positive and highly significant coefficient. This coefficient is 0.328163. The three standard errors, OLS, White, and Newey and West, produce a minimum t-statistic of 5.026. Therefore the managers of these funds have shown market timing abilities.

Finally, the coefficient on the last independent variable, which is the cubic term, and which measures volatility timing, is positive and not negative and is highly significant statistically for both models. The lowest t-statistic is 6.223. This means that fund managers show volatility timing abilities. In Model (2) the Treynor and Mazuy (1966) variable, i.e. the quadratic term, is positive and highly significant statistically. The lowest t-statistic is 4.649. In addition, The pooled adjusted R-Squares are all relatively high, i.e. around 79%.

Table 1: Pooled multiple linear regressions.

Coefficient Estimates & their t-statistics

Variable Model (1) Model (2)

Constant 0.066634 0.042763 t-statistic(1) 19.443 10.872 t-statistic(2) 17.957 13.876 t-statistic(3) 13.299 13.8975

(Rmt – 0.03012) 1.061905 0.875838 t-statistic(1) 26.835 40.223 t-statistic(2) 34.656 33.64 t-statistic(3) 38.065 27.142

(Rmt – 0.03012)2 0.652961 t-statistic(1) 4.649 t-statistic(2) 5.592 t-statistic(3) 6.089

( )0 , 0 .0 3 0 1 2m t

M a x R− − 0.09190645 0.328163

t-statistic(1) 5.026 t-statistic(2) 6.221 t-statistic(3) 5.780

(Rmt – 0.03012)3 1.303482 2.081566 t-statistic(1) 9.029 7.162 t-statistic(2) 7.720 7.426 t-statistic(3) 6.223 6.676

P-value for the hypothesis that the slope on (Rmt – 0.03012) is +1: OLS 0.1177 < 0.0001 White 0.0434 < 0.0001 Newey and West 0.0265 0.0001

Pooled Adjusted R-Square 0.7918 0.7915 Pooled Durbin-Watson statistic 1.5351 1.5230 Pooled sample size 2000 2000 P-value for an F-test on the equality of standard errors < 0.0001 < 0.0001

Notes: t-statistic(1) is produced by OLS (Ordinary Least Squares), t-statistic(2) is estimated by White (1980) consistent standard errors, and t-statistic(3) is estimated by Newey and West (1987) consistent standard errors. The test on the equality of standard errors is a test on whether the square of the standard error of the Jensen’s alpha, i.e. the constant, is higher than the square of the standard error of the mean expense ratio. This test is an F-test. The comparisons for all three estimated standard errors of the Jensen’s alpha, by OLS, White, and Newey and West, produce the same p-value (< 0.0001). The standard error of the mean expense ratio is 0.000610204.

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As a general conclusion for the pooled regressions the managers of the equity funds have shown stock selection, market timing and volatility timing abilities. The market timing ability is significant with the two different specifications. Table 2: Testing the hypothesis that the difference between the estimated Jensen’s alphas and the mean

expense ratio is zero. This is a test of the ability of the managers of U.S. equity mutual funds to select or pick stocks profitably, and hence to earn net abnormal returns after expenses.

Panel A: Pooled estimation

t-statistic Degrees of freedom

Model (1):

OLS 15.577 2106 White 14.339 2093 Newey and West 10.685 2054

Model (2):

OLS 7.626 2084 White 9.66 2125 Newey and West 9.675 2126

Panel B: System estimation

t-statistic Degrees of freedom

Model (1):

OLS 15.577 2106 WLS(1) 16.924 2177 WLS(2) 5.998 1027

Model (2):

OLS 7.626 2084 WLS(1) 8.726 2151 WLS(2) 3.644 1279

Notes: The mean expense ratio is 1.2413%, and has a standard error of 0.0610204%. WLS stands for Weighted Least Squares. WLS(1) uses a linear estimation after a one-step weighting matrix. WLS(2) uses a simultaneous weighting matrix and coefficient iteration. For more details see the notes under Table 1.

The system regressions are reproduced in Table 3. There are three econometric procedures:

OLS, Weighted Least Squares (WLS(1)) with a one-step weighting matrix, and WLS(2) with a simultaneous weighting matrix and coefficient iteration. The OLS system results are typically the same as the pooled OLS results in Table 1. Therefore there are only two specifications for each model. The average R-Squares are all relatively high.

Before any tests on the intercepts, the same F-test as before is undertaken to find out whether the square of the standard error of the intercept is higher than the square standard error of the expense ratio. In all cases the hypothesis that the former is higher than the latter is supported (Table 3, last row). Moreover, in all four models the constant, which is the average Jensen’s alpha, is positive and statistically significant at low marginal significance levels. Table 2 Panel B presents tests on the net of expenses returns. In all four specifications, the net returns are significantly different from zero and are positive, implying ability to pick or select stocks profitably, i.e. having proper micro forecasting.

The coefficients on the first variable included in the WLS(1) and WLS(2) regressions, and which indicates the systematic risk held by mutual funds, is statistically no different from +1 in one case out of the four. There is hence little evidence that these funds were indexed on the market.

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Table 3: System multiple linear regressions.

Variable

Coefficient Estimates (t-statistics in parenthesis)

Model (1) Model (1) Model (1) Model (2) Model (2) Model (2)

OLS WLS(1) WLS(2) OLS WLS(1) WLS(2)

Constant 0.06663 0.053668 0.018222 0.042763 0.036660 0.016262 (19.443) (22.742) (24.233) (10.872) (13.525) (18.871)

03012.0−mtR 1.061905 1.02343 1.037186 0.87584 0.895461 1.023297 (26.835) 37.559) (119.46) (40.223) (59.676 (214.493)

( )203012.0−mtR

0.65296 0.435540 0.058757 (4.649) (4.499) (1.909)

( )mtRMax −03012.0 ,0 -0.09190645 0.328163 0.235249 0.023928

(5.026) (5.233) (1.670)

( )303012.0−mtR

1.30348 0.94732) -0.096802) 2.081566 1.423390 -0.018749 (9.029) (9.53) (-3.056) (7.162) (7.107) (-0.294)

P-value for the hypothesis that the

slope on (03012.0−mtR

) is +1 0.1177 0.3898 < 0.0001 < 0.0001 < 0.0001 < 0.0001

Adjusted R-Square: Average 0.65627 0.65743 0.60172 0.65479 0.65528 0.60171 Standard error 0.03278 0.03127 0.03562 0.03283 0.03148 0.03563

Durbin-Watson statistic: Average 1.28654 1.27227 1.2714 1.27514 1.26284 1.26945 Standard error 0.04533 0.0472 0.05166 0.04474 0.04660 0.05158

P-value for an F-test on the equality of standard errors

< 0.0001 < 0.0001 0.0001 < 0.0001 < 0.0001 < 0.0001

Notes: OLS means Ordinary Least Squares. WLS stands for Weighted Least Squares. WLS(1) uses a linear estimation after a one-step weighting matrix. WLS(2) uses a simultaneous weighting matrix and coefficient iteration. The test on the equality of standard errors is a test on whether the square of the standard error of the Jensen’s alpha, i.e. the constant, is higher than the square of the standard error of the mean expense ratio. This test is an F-test. The standard error of the mean expense ratio is 0.000610204.

The first model with a WLS(1) estimation, which includes the put variable, finds a coefficient

on the put variable that is positive and significantly different from zero. However the same model with WLS(2) estimation finds that the coefficient on the put variable is statistically insignificant. Not only this but the third variable, i.e. the cubic term, has a coefficient that is statistically significant with WLS(1) but negative and statistically significant with WLS(2). The Eviews User Guide II (2009) mentions, on page 448, that WLS estimation is inappropriate when there is evidence of serial correlation of the residuals. In fact there is such evidence. For the pooled regressions (Table 1), the limits of the Durbin-Watson statistic for a significance level of 1% are 1.643-1.704. The two actual statistics are below the lower limit, implying that serial correlation of the residuals is present. For the system regressions the 1% limits on the Durbin-Watson statistic are 0.340-1.733. Most actual statistics fall in the indeterminate region, i.e. within the limits. As a result the findings using WLS, and especially WLS(2), may not be robust.

The second model with a WLS(1) estimation, which includes the quadratic term, finds a coefficient on the quadratic variable that is positive and significantly different from zero. However the same model with WLS(2) estimation finds that the coefficient on the quadratic variable is marginally statistically significant. Not only this but the third variable, i.e. the cubic term, has a coefficient that is positive and statistically significant with WLS(1) but negative and statistically insignificant with WLS(2). It was argued above that the results of the WLS estimations, especially WLS(2), may not be reliable. Hence, there is strong evidence that the coefficient on the volatility timing is not only positive, as expected, but also statistically significant. This implies that the managers of these funds do require higher excess returns when volatility is high.

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5. Conclusion The aim of this paper is to examine the timing abilities of the managers of equity mutual funds in the United States. A sample of 200 funds is selected as randomly as possible. There are three different timing abilities. The first is the ability to pick up or select stocks profitably. This ability is measured by Jensen’ alpha, and is often called micro forecasting. The second is the ability to time the market, or macro forecasting. There are two functional forms for this last ability. Both are included separately in the analysis. The final one is the ability to time the volatility of the portfolio.

The originality of this paper is to include the above three abilities together in the same regression. Two general models are estimated one for each market timing variable. Estimation is done by pooled regressions, and by system estimation. The first estimation approach takes into consideration the importance of using consistent standard errors while the second approach takes into consideration the fact that weighted least squares may improve the statistical results. In all estimations the return on the S&P 500 stock market index is included. The estimated coefficient on this variable measures the systematic risk. There is strong evidence that equity mutual funds do not index their assets to the market. The evidence also supports the hypothesis that the systematic risk of these funds is lower than average.

The findings are as follows. There is a significant abnormal return, or Jensen’s alpha, for the stock selection ability, both gross and net of expenses. The two forms of market timing produce evidence of a high ability of macro forecasting or market timing. There is strong evidence that volatility timing is present. It can be inferred from all of this that the active managers of the population of U.S. equity mutual funds have all three kinds of market timing abilities. As such they are highly skillful.

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