Explaining After-Tax Mutual Fund Performance

Explaining After-Tax Mutual Fund Performance James D. Peterson, Paul A. Pietranico, Mark W. Riepe, and Fran Xu Published research on the topic of mutual fund performance focuses almost exclusively on pretax returns. For U.S. mutual fund investors holding positions in taxable accounts, however, what matters is the after-tax performance of their portfolios. We analyzed after-tax returns on a large sample of diversified U.S. equity mutual funds for the 1981 98 period. We found the variables that determined after-tax performance for this period to be past pretax performance, expenses, risk, style, past tax efficiency, and the recent occurrence of large net redemptions. F or U.S. investors in high tax brackets, aftertax mutual fund returns may differ greatly from pretax returns. For example, U.S. equity fund investors in high tax brackets lost an average of about 2.2 percentage points (pps) annually to taxes in the 1981 98 period. Despite the important impact of taxes on investor returns, we are not aware of any studies, however, about the determinants of after-tax mutual fund performance. We sought to fill that void with this study of the 1981 98 period. Our goal was to identify a concise set of publicly available variables that, together, were useful for explaining subsequent after-tax U.S. equity fund performance. For purposes of comparison, we also studied the effects of fund characteristics on pretax performance and on tax efficiency. Both comparisons help to highlight the unique role that certain characteristics play in determining after-tax returns. In our analysis, we build on research into the determinants of pretax mutual fund performance (e.g., Carhart 1997; Peterson, Pietranico, Riepe, and Xu 2001). Although the results of various prior studies differ in some respects, the common wisdom is that risk, investment style, past pretax performance, turnover, and fund expenses are important determinants of pretax equity fund returns. 1 Therefore, we hypothesized that these characteristics would also be important determinants of after-tax returns. 2 Because our objective was to explain specifically after-tax returns, we also considered the effects of past tax efficiency, net cash flow, and manager turnover on future after-tax returns. 3 James D. Peterson is vice president at Charles Schwab, San Francisco. Paul A. Pietranico, CFA, is director at Charles Schwab, San Francisco. Mark W. Riepe, CFA, is senior vice president at Charles Schwab, San Francisco. Fran Xu, CFA, is senior research analyst at Charles Schwab, San Francisco. Data We sought to identify the determinants of after-tax performance, pretax performance, and tax efficiency over the 1981 98 period by using a sample of 1,170 diversified U.S. equity funds. The mutual fund data source is the December 1998 Center for Research in Security Prices (CRSP) Survivor-Bias Free US Mutual Fund database. Although mutual fund data were available as early as December 1961, our study begins in 1981 because of data limitations described later. Measuring After-Tax s. Mutual funds typically do not distribute capital gains more often than once a year. This practice limited our choice of measurement intervals for after-tax returns to periods of one year or longer. A fairly long time period is important for measuring after-tax returns. To understand why, consider the example of a taxinefficient fund that does not distribute capital gains in a particular year because of some random event, such as abnormally poor performance. If such a fund s after-tax return is measured over a one-year period, the fund will appear to be tax efficient (i.e., its after-tax return will be roughly the same as its pretax return). Moreover, a fund can manage the realization of capital gains and, therefore, taxable distributions and after-tax returns in the short run. Thus, lengthening the measurement period improves the estimate of after-tax return and provides a better chance of rejecting hypotheses about the effect of certain fund characteristics on after-tax returns. Fund managers and investment styles change over time, however, so using a measurement period that is too long is also probably not a good idea. For these reasons, we report results for after-tax returns measured over a threeyear horizon. 4 January/February 2002 75

Financial Analysts Journal CRSP does not report after-tax returns, so we explain in Appendix A the procedure we used to calculate after-tax returns. Fund Characteristics. An important task in this study was to identify fund characteristics that might be significant determinants of after-tax mutual fund returns. Common wisdom suggested that risk, investment style, past pretax performance, expenses, and turnover are important determinants of pretax mutual fund performance. So, these characteristics, among others, are also likely to be important determinants of after-tax fund returns. Therefore, we included these five factors as explanatory variables in our model. A key feature of our analysis is that the characteristics we hypothesized to be important determinants of after-tax performance could actually have been observed by investors prior to investors making their fund selections. Past pretax performance, risk, and style were estimated via a three-factor asset-pricing model similar in spirit to that of Fama and French (1993). Specifically, for each fund included in the sample for a particular three-year period, the following ordinary least-squares (OLS) regression was estimated over the 36-month period prior to the beginning of that three-year period: r i,t r f,t = α i + β i(r m,t r f,t ) + s i SML t + v i VMG t + e i,t, (1) where r i,t = pretax return to individual fund i in period t r f,t = risk-free rate α i = historical risk- and style-adjusted pretax performance of the fund (we included the annualized value of the estimate of α i in our tests) β i = risk parameter to be estimated s i = size parameter to be estimated v i = value growth style parameter to be estimated r m,t r f,t = the market risk premium SML t = return to small-cap stocks minus return to large-cap stocks VMG t = return to value stocks minus return to growth stocks e i,t = regression error term Fama and French constructed their market capitalization and value growth factors by using CRSP and Compustat data. We constructed our series by using data from Ibbotson Associates. (We use slightly different notation from that of Fama French to help distinguish these series.) Exhibit 1 contains these variables and the relevant Ibbotson Associates data series. Because we required three years of historical data to estimate Equation 1 and the value growth series became available to us only beginning in 1978, our analysis of fund returns begins in 1981. Exhibit 1. Time-Series Data for Risk and Style Estimates Variable r f r m r f SML VMG Ibbotson Associates Series U.S. 30-day T-bill total return U.S. equity risk premium U.S. small-stock premium [(Wilshire large-cap value Wilshire large-cap growth) + (Wilshire small-cap value Wilshire small-cap growth)]/2 The time-series regression equation (Equation 1) was estimated once for each three-year return observation in the sample. For example, consider a fund s after-tax return observed for the three-year period 1981 1983. In this case, Equation 1 was estimated from 36 months of fund pretax return data beginning in January 1978 and ending in December 1980. The annualized estimate of α i obtained from estimating Equation 1 for this period is an estimate of the fund s historical risk- and style-adjusted pretax performance, and it is associated with the aftertax return observed for the 1981 83 period. The estimates of β i, s i, and v i represent estimates of the risk and style variables associated with this return. Keep in mind that after-tax returns may be related to the beta measure of risk for reasons other than compensation for bearing systematic risk. Financial theory dictates that securities with high systematic risk should have high pretax returns. For this reason, studies of pretax returns typically include a measure of systematic risk, such as beta, as an explanatory variable. The argument is that investors are not rewarded for bearing unsystematic risk because this type of risk can be diversified away. Total risk, or variance, which is a measure of systematic plus unsystematic risk, may affect after-tax mutual fund returns because high-variance funds are more likely than low-variance funds to have capital losses to offset capital gains. Because mutual funds tend to be well diversified, however, beta and variance/standard deviation are highly correlated. 5 Two factors remain that have been identified as important for pretax returns and may be important for after-tax returns: turnover in the fund s stock holdings and fund expenses. Turnover, which is computed by taking the lesser of purchases or sales and dividing by average monthly net assets, is a measure of the fund s trading activities. Expenses are measured by the fund s reported 76 2002, AIMR

Explaining After-Tax Mutual Fund Performance expense ratio, which is the percentage of fund assets paid for operating expenses and management fees, excluding brokerage costs. In addition to these factors, we needed measurements of three factors that may have particular effects on after-tax returns tax efficiency, cash flows (inflows and outflows), and manager turnover. Tax efficiency may be affected by a fund s turnover in stock holdings or vice versa. Some analysts have argued that high-turnover funds are tax inefficient because selling a security that has appreciated in value causes the fund to realize a capital gain. Tax-efficient funds may have the higher turnover, however, because their managers seek to offset such gains with capital losses. Therefore, turnover may not be a good proxy for tax efficiency. As an alternative to turnover, we considered the fund s return lost to taxes (RLT), which we measured as follows: aftertax 1 + r i RLT t = --------------------------------- 1, pretax 1 + r i pretax where denotes absolute value and r i and aftertax r i are the annualized pretax and after-tax returns on fund i measured over the 36-month period ending just prior to the period for which the returns being studied were measured. The hypothesis we tested is that funds that were tax efficient (inefficient) in the past subsequently had higher (lower) after-tax returns. Note that the RLT measure is similar to Morningstar s tax-efficiency measure. Morningstar computes tax efficiency as r i /ri. This aftertax pretax measure of tax efficiency is applicable, however, only when both pretax and after-tax returns are positive. If pretax returns are negative, the taxefficiency ratio is greater than or equal to 1, but a tax-efficiency ratio greater than 1 implies that aftertax returns are bigger than pretax returns. This cannot be the case for a mutual fund, however, because mutual fund losses cannot be passed through to the investor to reduce the investor s income. Therefore, a tax-efficiency ratio is not reported unless it is between 0 and 1. In an extended down market, the tax-efficiency ratio is not likely to fall in this range. Yet, tax efficiency is an important consideration even when pretax returns are negative, because after-tax returns may be even more negative. Our calculation of RLT in Equation 2 is applicable for either positive or negative values for both pre- and after-tax returns. After-tax performance may also be affected by cash flows into or out of a fund. Managers faced with large cash redemptions may be forced to sell (2) appreciated shares, which results in a capital gains distribution. Managers faced with large net cash inflows may add higher-cost-basis shares to existing positions. For those funds that specifically identify the shares they sell for tax purposes, selling the high-cost-basis shares first can minimize taxable distributions. Net cash flow is defined as follows: pretax NA i, t NA i, t 1 1 + r i, t 1 NCF i, t = ------------------------------------------------------------------------, (3) NA i, t 1 where NA i,t is the net assets of fund i at time t. Fund managers can usually accommodate small net redemptions and small net inflows without any tax ramifications. Thus, to consider large net cash flows only, we constructed two dummy variables: LgnegNCF was set to 1 if the fund s cash flow was in the bottom 25 percent in terms of net cash flow for all funds with NCF less than 0 in the year prior to the period in which the returns being studied were measured and set to 0 otherwise; LgposNCF took on a value of 1 if the fund s cash flow was in the top 25 percent in terms of net cash flow for all funds with NCF greater than or equal to 0 in the prior year and took on the value of 0 otherwise. 6 If funds with large net redemptions incur more taxes than funds with small net redemptions, then funds with large negative net cash flows should subsequently underperform comparable funds on an after-tax basis. Conversely, if large net inflows lead to lower taxes, then funds with large positive net cash flows should subsequently outperform comparable funds on an after-tax basis. Large net cash flows may have implications for future fund returns that are not entirely tax related. For example, many analysts argue that large net inflows lead to lower performance, particularly for small-cap funds. Therefore, multiple cash flow effects may neutralize each other in after-tax returns. Recent manager turnover may also have implications for subsequent after-tax fund returns. New managers may trade extensively to implement their own investment plans, potentially triggering large capital gains distributions. To include this consideration, we used the date the manager took control of the fund (as identified in the CRSP database) and set a variable Mgrturn to 1 if the current manager took control within the previous year and to 0 otherwise. If manager turnover leads to higher taxes, then funds with recent manager turnover should subsequently underperform comparable funds on an after-tax basis. 7 Using a sample of 492 managers, Chevalier and Ellison (1999) found, among other things, that manager age was an important determinant of mutual fund returns in the 1988 94 period. We do not have January/February 2002 77

Financial Analysts Journal data on manager age, but our manager turnover variable could be related to manager age (i.e., a manager with short tenure is more likely to be young). To further control for a manager age/tenure effect, we established the variable Tenure, which was set to 1 if the fund s manager had responsibility for managing the fund for at least five years and 0 otherwise. Therefore, funds with Tenure = 1 are funds whose managers have had a long tenure; funds with Mgrturn = 1 are funds whose managers have had a short tenure. We conducted the tests involving manager tenure information for a shorter time period (1992 1998) than for other tests because the CRSP database does not report the date the current manager took control of the fund prior to 1992. Finally, investment style is an important determinant of pretax returns, and therefore, style is almost surely an important determinant of after-tax returns for reasons that have nothing to do with taxes. In addition, fund style may have unique implications for after-tax returns. For example, value funds may be less tax efficient than growth funds because of the former s tendency to hold higher-dividend-paying stocks. Small-cap funds may sell high-performing stocks to avoid style drift, which could force a capital gains distribution. The stocks held in small-cap funds tend to exhibit more overall risk, however, than those held in large-cap funds. So, small-cap managers are much more likely to have capital losses to offset capital gains, which promotes tax efficiency. Methodology Our primary objective was to measure the marginal effects of the characteristics identified in the previous section on after-tax mutual fund performance; other objectives were to measure the effects of the characteristics on pretax performance and on tax efficiency. To fully investigate the importance of investment style to after-tax returns, we also extended the analysis of the characteristics effects to four subsamples of the full sample based on size and value orientation versus growth orientation. A common approach to estimating the marginal effects of variables on return is the two-step estimation technique developed by Fama and MacBeth (1973). 8 In the first step of the Fama MacBeth technique, a cross-sectional regression is estimated for each period (typically monthly) in the sample. In studies of mutual fund returns, the dependent variable in this regression is a measure of fund return for a particular period and the independent variables are the fund characteristics potentially associated with that return. In the second step, the time-series averages of the regression coefficient estimates obtained from the first-step regressions are computed. The average associated with a particular characteristic is interpreted as an estimate of the average premium in fund returns associated with that characteristic. A large number of time-series observations are required in the second step of the Fama MacBeth method to obtain precise estimates of the average premiums. For this reason, most applications of the Fama MacBeth technique use monthly data. For reasons discussed in the previous section, we measured after-tax returns over long holding periods in particular, six consecutive three-year holding periods beginning in 1981 and ending in 1998. Unfortunately, six time-series observations are not enough to draw reliable inferences from the data. Therefore, we used a slightly different technique. The estimation technique we used has features that are similar to the Fama MacBeth approach. The Fama MacBeth technique accommodates time variation in estimates of the premiums in returns. The premium in returns associated with a specific mutual fund characteristic may or may not be expected to vary over time. For example, the fact that stock market investments are risky implies that the stock market risk premium will vary with changing economic conditions (i.e., in some years, investors will be rewarded for taking on stock market risk; in other years, taking on risk will be costly). Similar arguments suggest that investment-style premiums might also vary over time. Therefore, like the Fama MacBeth approach, the estimation technique we used had to accommodate variation in estimates of risk and style premiums. There is no reason to expect that the true premiums associated with non-risk-related and non-style-related characteristics, such as the expense ratio, will vary over time. Therefore, pooling the cross-sectional and time-series data for such traits so that a single regression is estimated, instead of one regression for each period in the sample, is beneficial. 9 Pooling the data potentially increases the precision of the regression coefficient estimates for those coefficients that are not expected to vary over time. Because the estimated premiums on some of the characteristics in our analysis are expected to vary over time and some are not, our approach was to pool the time-series and cross-sectional data and to model time-series variation in the estimated premiums when doing so was appropriate. Specifically, the average premiums in after-tax returns were estimated via the following pooled time-series and cross-sectional OLS regression: 78 2002, AIMR

Explaining After-Tax Mutual Fund Performance r i, t r f, t = µ 0 + where T J λ m D m + δ j x i, j, t 1 m =2 j =1 J T K + w j, m x i, j, t 1 D m γ k x i, J + k, t 1 + ε + i, t, j =1 m =2 k =1 µ 0 = regression intercept D m = (for m = 2,..., T) indicator, or dummy, variables that take on the value of 1 if m = t and 0 otherwise λ m = (for m = 2,..., T) regression parameters associated with the intercept dummy variables δ j = (for j = 1,..., J) regression parameters associated with the J risk and style variables x i,c,t 1 = value of characteristic c for fund i observed prior to period t (e.g., if characteristic c is a fund s expense ratio, then x i,c,t 1 is the actual value of the expense ratio for fund i observed prior to period t) ω j,m = (for j = 1,..., J, m = 2,..., T) regression parameters associated with the slope dummy variables on the risk and style variables γ k = (for k = 1,..., K) regression parameters associated with the K variables that are not risk or style related ε i,t = regression error term The first summation term in Equation 4 is for the T 1 dummy variables included to allow the intercept estimate to vary over each period t, t = 1,..., T, in the sample. The results we present are for the case in which t is three years long. In this case, µ 0 represents the regression intercept for the first three-year period in the sample, 1981 1983. The intercepts for each of the five remaining three-year periods in the 1981 98 sample are given by µ 0 + λ m, for m = 2,..., 6. The second summation term in Equation 4 is for the J risk and style variables in the regression (i.e., β, s, and v). The next (double) summation term is for the J(T 1) terms included to allow the estimated premiums on the risk and style variables to vary by period. When t is three years long, δ j represents the premium associated with risk or style variable j for the first three-year period in the sample, 1981 1983. The premiums for each of the five remaining three-year periods in the 1981 98 sample are given by δ j + ω j,m, for m = 2,..., 6. The average of the six estimated premiums for variable j represents the average premium for that variable over the sample period. 10 (4) The final summation term is for the remaining K fund characteristics those that are neither risk nor style related (i.e., past performance, expenses, turnover, past tax efficiency, large net redemptions, large net inflows, tenure, and manager turnover). The estimated premiums on these variables were not allowed to vary over time. We consider a variable a determinant of returns if the estimated average premium associated with that variable is (statistically) significantly different from zero. For purposes of comparison, we also estimated Equation 4 with pretax returns (less the risk-free rate) as the dependent variable. The results from this exercise serve as a benchmark for comparison with results for after-tax returns. In addition, we compared our results with those obtained from a similar analysis of return lost to taxes, our measure of tax efficiency. Both comparisons help to highlight the unique role that certain characteristics play in determining after-tax returns. Results As Table 1 indicates, correlations between the explanatory variables are near zero. Thus, the regression results do not suffer from a multicollinearity problem. Full Sample of Funds. The estimated average annualized premiums in pretax returns, aftertax returns, and return lost to taxes associated with the fund characteristics discussed previously are in Table 2. Results for the entire 1981 98 period do not include average premium estimates for manager turnover and tenure, which are given for the shorter, 1992 98, time period. Determinants of pretax returns. Table 2 shows that, as expected, the estimated premium on fund expenses in pretax returns is negative and statistically significant. The estimated value of 1.60 percent implies that for the 1981 98 period, funds with expense ratios that were 1 pp higher than comparable funds had pretax returns that were on average 1.6 pps lower than comparable funds on an annualized basis. The estimated α premium (historical risk- and style-adjusted pretax performance) of 0.11 percent is also statistically significant. This result suggests that for the 1981 98 sample period, funds with superior risk-adjusted and style-adjusted performance in one period of 36 months, as measured by α in Equation 1, performed better, on average, in the next 36 months. 11 The estimated average premium associated with β risk in future pretax returns in our time period (4.4 percent a year) is also statistically January/February 2002 79

Financial Analysts Journal Table 1. Correlation Matrix of Explanatory Variables RLT Turnover Tenure Mgrturn LgnegNCF LgposNCF Expense Ratio α β v s RLT 1.00 Turnover 0.14 1.00 Tenure 0.07 0.14 1.00 Mgrturn 0.08 0.14 0.30 1.00 LgnegNCF 0.02 0.04 0.03 0.06 1.00 LgposNCF 0.13 0.03 0.04 0.02 0.11 1.00 Expense ratio 0.26 0.12 0.02 0.00 0.04 0.07 1.00 α 0.12 0.02 0.09 0.07 0.19 0.26 0.22 1.00 β 0.09 0.00 0.05 0.00 0.02 0.00 0.05 0.14 1.00 v 0.17 0.11 0.02 0.02 0.03 0.07 0.07 0.24 0.08 1.00 s 0.08 0.09 0.05 0.02 0.02 0.13 0.21 0.01 0.30 0.16 1.00 Note: Correlations were estimated for the 1981 98 period with the exception of correlations involving manager tenure and manager turnover, which were estimated for the 1992 98 period. Table 2. Determinants of Fund Performance (except where otherwise noted, parentheses indicate t-statistics) Explanatory Variable Pretax Annualized Average Premium Estimates (percent) 1981 98 1992 98 After-Tax Lost to Taxes Pretax After-Tax Lost to Taxes Expense ratio 1.60* 1.38* 0.18* 1.71* 1.46* 0.20* ( 8.96) ( 7.81) ( 4.85) ( 6.75) ( 5.72) ( 3.81) α 0.11* 0.10* 0.01 0.01 0.04 0.04* (4.28) (4.03) (1.22) ( 0.16) (0.92) ( 4.31) β 4.40* 4.10* 0.16 10.38* 10.56* 0.36* (F = 43.83) (F = 38.50) (F = 1.44) (F = 177.41) (F = 179.50) (F = 5.04) v 0.98* 0.78* 0.15 0.69 0.45 0.19 (F = 7.90) (F = 5.24) (F = 3.75) (F = 1.74) (F = 0.40) (F = 3.19) s 2.83* 2.41* 0.35* 6.12* 6.17* 0.15 (F = 31.37) (F = 23.03) (11.01) (F = 86.19) (F = 85.40) (F = 1.19) Turnover a 0.04 0.01 0.03 0.38 0.45* 0.05 (0.26) ( 0.07) (1.04) ( 1.79) ( 2.06) (1.06) RLT 0.01 0.41* 0.35* 0.09 0.39* 0.40* ( 0.11) (-4.39) (17.77) (0.59) ( 2.44) (12.68) LgnegNCF 0.50 0.72* 0.19* 0.56 0.79 0.22* ( 1.51) ( 2.20) (2.87) ( 1.12) ( 1.57) (2.12) LgposNCF 0.55 0.01 0.48* 0.20 0.19 0.35* ( 1.52) (0.02) ( 6.37) ( 0.42) (0.41) ( 3.63) Tenure NA NA NA 0.71* 0.85* 0.13* ( 2.39) ( 2.85) (2.17) Mgrturn NA NA NA 0.79 0.59 0.14 (1.61) (1.20) (1.37) R 2 49 50 30 40 39 17 NA = not available. a The average premium numbers displayed in the table for the turnover variable are the actual values multiplied by 10 2. *Significantly different from zero at the 5 percent level. 80 2002, AIMR

Explaining After-Tax Mutual Fund Performance significant, which implies that mutual fund investors received a positive premium for bearing market risk. The estimated average premium associated with the value growth variable, v, of 0.98 percent a year indicates that, on average, value funds outperformed growth funds in the 1981 98 period. Moreover, the estimated average premium associated with the market capitalization variable, s, of 2.83 percent suggests that, on average, largecap funds outperformed small-cap funds in this time period. Unreported regression results revealed that the estimated risk, value growth, and market-cap premiums varied dramatically from period to period. For example, in the first nine years of the sample, the value growth premium was positive, but in the last nine years, it was negative. The propensity for these premiums to switch back and forth between positive and negative values over time highlights the importance of diversifying among investment styles. Although the argument is often made that high turnover reduces pretax returns, we found that the average premium associated with turnover in subsequent pretax returns was not significantly different from zero over this sample period. 12 Not surprisingly, the average premiums on the variables introduced to capture tax effects were not statistically significant when regressed against pretax returns. In addition to finding no significant premium associated with turnover in subsequent pretax returns, we found that the average premium on past tax efficiency, as defined by RLT, in the 1981 98 period was near zero. The signs of the average premiums on large negative and large positive cash flow are negative, but neither is statistically significant. In the 1992 98 period (studied separately because tenure and manager turnover could be measured only for this period), the estimated average premium in pretax returns associated with the Tenure variable, 0.71 percent, is statistically significant, which implies that managers having at least five years of experience with their funds underperformed managers with less experience by an estimated 0.71 pps a year over the 1992 98 period. This result suggests that newer, and possibly younger, managers outperform their more seasoned counterparts and is reminiscent of Chevalier and Ellison s finding that young managers outperform older managers. The estimated average premium associated with the manager turnover variable, Mgrturn, is positive (i.e., funds that have recently changed managers do better in the future on a pretax basis) but not statistically significant. Determinants of after-tax returns. Consistent with the full-period pretax results reported in Table 2, fund expenses, style, past risk- and styleadjusted performance, and beta were important determinants of future after-tax returns. The estimated premiums in after-tax returns associated with these variables are similar to those reported for pretax returns. We found no evidence of a relationship between turnover and future after-tax returns for the 1981 98 time frame. Our results suggest that RLT was a better proxy for future after-tax returns than turnover was during the full period. When we excluded RLT from the regressions entirely (results not shown), we still found no relationship between turnover and future after-tax returns. The relationship between RLT and future aftertax performance is negative and, unlike the relationship for pretax returns, statistically significant. The estimated premium of 0.41 percent implies that an annualized RLT of 1 percent over the prior 36-month period was associated with an annualized 41 bp reduction in after-tax return over the next 36-month period during the full sample period. This result suggests that past tax efficiency as measured by RLT is a useful indicator of future after-tax returns. We also found no evidence of a relationship between large net cash inflows and future after-tax returns over the 1981 98 time period, but large net redemptions were associated with lower subsequent after-tax returns over this period. The estimated premium of 0.72 percent on LgnegNCF implies that funds in the bottom quartile in terms of net redemptions in the prior year subsequently underperformed comparable funds by 0.72 pps on an annualized basis in the 1981 98 period. Further analysis (results not shown) revealed that small net redemptions and small net inflows had no effect on future after-tax performance. Consistent with the results for pretax returns over the 1992-98 period, the average premium in after-tax returns associated with the Tenure variable is negative and statistically significant. This result suggests that managers who have at least five years of experience with their funds underperformed managers with less experience in terms of both pretax and after-tax returns. Investigation of the hypothesis that manager turnover hurts future after-tax performance was hindered by the short sample period we could use. For a period as short as 1992 1998, finding statistically significant results is unlikely because of the statistical noise inherent in the estimated premiums. The fact that the estimated average premium on LgnegNCF is more negative than it was for the full January/February 2002 81

Financial Analysts Journal period but is no longer statistically significant is evidence of the estimates inherent imprecision. If manager turnover causes future taxable distributions, then the estimated premium on Mgrturn should be negative. Yet, the estimated premium is positive, although not statistically significant. Thus, we provide no evidence supporting a systematic manager turnover effect in after-tax returns. Determinants of tax efficiency. We now turn to an analysis specifically of tax efficiency the Lost to Taxes columns in Table 2. To understand why this analysis is useful, recall that a characteristic can affect pretax returns and tax efficiency in opposing ways. Therefore, some variables may affect tax efficiency in one way but have an opposite or neutral effect on after-tax returns. Given the after-tax return results reported in Table 2 for the 1981 98 period, it is not surprising that past tax efficiency, as measured by RLT, and past large net redemptions, as measured by LgnegNCF, were important descriptors of future tax efficiency. More interesting is that large cash inflows, LgposNCF, were associated with lower return lost to taxes (i.e., higher tax efficiency) in this period. This result provides support for the claim that large cash inflows promote tax efficiency, but it does not imply that taxable investors should concentrate their investments in funds with large cash inflows. To understand why, note that the estimated large-cash-inflow premium in pretax returns shown in Table 2 is 0.55 percent, implying that funds with large net inflows subsequently underperformed on a pretax basis (although this effect is not statistically significant). The estimated large-cash-flow premium in return lost to taxes is 0.48 pps, implying that large net inflows were associated with less return lost to taxes (greater tax efficiency). In after-tax returns, these two effects neutralize each other. This result highlights the dangers of focusing strictly on tax efficiency. Investors who do so may minimize return lost to taxes, but they would be better off focusing on maximizing after-tax returns (for their chosen risk tolerance). When other variables were controlled for, results for the s variable show that small-cap funds were more tax efficient over the full sample time period. This result is consistent with the hypothesis that managers of small-cap funds are likely to have more opportunities to offset capital gains with capital losses than are their large-cap counterparts. This tax efficiency is an extremely small part of the overall effect, however, that market cap has on after-tax returns. High-expense funds also appear to have been more tax efficient in the 1981 98 period. A possible reason is that expenses are deducted from portfolio income, so a high-expense fund has a smaller income distribution. Of course, the data could result from random error, or the expense ratio may proxy for measurement error in one or more of the other explanatory variables; for example, highexpense funds are more likely to be small cap and the s variable may be measured with error. Another possibility is that expenses proxy for some variable important for determining return lost to taxes that we did not include in our analysis. For the 1992 98 period, Table 2 shows an estimated premium on Tenure that is positive and statistically significant, which indicates that the funds of managers with more than five years of tenure are less tax efficient than the funds of less-tenured managers. But the estimated premium of 0.13 pps is economically small. The results shown in Table 2 for the 1992 98 period indicate that manager turnover also is positively related to return lost to taxes, but the effect is not statistically significant. Results by Investment Style. In this section, we contrast the results for the sample broken into four subsamples large-cap value, large-cap growth, small-cap value, and small-cap growth to results for the full sample. To categorize a fund by style at a specific point in time, we first used the prior 36 months of return data to compute the correlation of the fund s returns with the returns on the relevant Wilshire index. We then categorized each fund s style as the style of the Wilshire index exhibiting the highest correlation with the fund s returns. Table 3 provides the results from the analysis of after-tax returns and return lost to taxes for the full 1981 98 period. 13 Although the estimated α premiums in after-tax returns are positive for all four style subsamples, they are not statistically significant in the two value categories. This result suggests that performance persistence was limited to growth funds in the 1981 98 period. (Our analysis of pretax returns, not shown, yielded the same conclusion.) Carhart found that momentum investing largely accounts for performance persistence in pretax mutual fund returns. Therefore, a plausible explanation for this result is that the investing strategies of growth fund managers are more consistent with momentum strategies than are the strategies of value fund managers. Note that the relationship between past tax efficiency, as measured by RLT, and future after-tax returns is negative for all four style subsamples, but it is not statistically significant for the two small-cap categories. RLT is significantly positively related to future tax efficiency, however, for all four style subsamples. 82 2002, AIMR

Explaining After-Tax Mutual Fund Performance Table 3. Results by Investment Style (except where otherwise noted, parentheses indicate t-statistics) Explanatory Variable Annualized Average Premium Estimates (percent) Large-Cap Growth Large-Cap Value Small-Cap Growth Small-Cap Value After-Tax s Lost to Taxes After-Tax Lost to Taxes After-Tax Lost to Taxes After-Tax Lost to Taxes Expense ratio 1.44* 0.05 1.14* 0.12 1.22* 0.25* 1.15 0.07 ( 6.67) ( 0.88) ( 2.87) ( 1.15) ( 3.87) ( 4.30) ( 1.78) ( 0.60) α 0.25* 0.00 0.03 0.02 0.15* 0.01 0.10 0.01 (6.58) (0.42) (0.30) ( 0.85) (3.59) (1.45) (1.03) (0.71) β 3.83* 0.42 3.07 0.57 4.28* 0.16 4.45 0.84 (F = 18.75) (F = 2.82) (F = 2.36) (F = 1.25) (F = 11.48) (F = 0.49) (F = 2.54) (F = 2.77) v 0.61 0.06 4.84 2.21 1.41* 0.29* 1.60 1.77* (F = 1.00) (F = 0.11) (F = 2.51) (F = 7.89) (F = 4.58) (F = 5.87) (F = 0.14) (F = 5.35) s 2.18 0.06 10.64* 0.95 4.09* 0.56* 2.69 0.94 (F = 2.94) (F = 0.02) (F = 17.82) (F = 2.18) (F = 14.16) (F = 7.95) (F = 0.77) (F = 2.89) Turnover a 0.01 0.06 0.06 0.25* 0.00 0.00 0.01* 0.04 (0.03) (1.23) ( 0.17) (2.37) ( 0.00) ( 0.09) ( 2.00) (0.47) RLT 0.65* 0.42* 0.97* 0.65* 0.10* 0.23* 0.10 0.32* ( 5.79) (12.93) ( 4.49) (11.87) ( 0.62) (7.38) ( 0.24) (4.74) LgnegNCF 0.18 0.12 1.80* 0.66* 0.29 0.19 1.43 0.05 ( 0.51) (1.22) ( 2.76) (3.96) ( 0.47) (1.73) (0.98) (0.21) LgposNCF 0.19 0.33* 0.16 0.08 0.54 0.62* 2.29 0.02 ( 0.51) ( 3.16) ( 0.26) ( 0.50) ( 0.93) ( 5.84) ( 1.86) (0.07) R 2 74 34 67 50 37 24 40 53 a The average premium numbers displayed in the table for the turnover variable are the actual values multiplied by 10 2. *Significantly different from zero at the 5 percent level. Table 3 indicates that a relationship between large cash outflows and future returns is restricted to large-cap value stocks. A possible explanation may lie in the empirical observation that value funds, particularly large-cap value funds, tend to turn over their investments less frequently than other funds. For example, the average turnover during the 1981 98 sample period for the large-cap value funds in our sample was 56 percent, whereas the average turnover for large-cap growth, smallcap growth, and small-cap value was, respectively, 65 percent, 82 percent, and 74 percent. (The differences between the average turnover for large-cap value funds and the average turnover for each of the other three categories are statistically significant.) To satisfy requests for large redemptions, a manager of a fund with low turnover may have to sell lower-cost-basis shares than would a manager of a fund with higher turnover, which would result in higher capital gains distributions and lower after-tax returns for the low-turnover fund. Conclusions and Implications The main findings from our analysis of after-tax returns for the 1981 98 period are as follows: After we controlled for other factors, funds that were historically tax efficient outperformed comparable funds on an after-tax basis, funds that experienced large net redemptions, particularly large-cap value funds, subsequently underperformed comparable funds on an after-tax basis, risk, investment style, past pretax performance, and expenses were important determinants of after-tax and pretax returns, and turnover did not appear to be related to future after-tax returns. When we analyzed mutual fund tax efficiency in the 1981 98 period, we found, after controlling for other factors, that funds that did not experience recent large cash redemptions, did experience recent large cash inflows, were historically tax efficient, were classified as small capitalization, or had high expense ratios tended subsequently to be more tax efficient. But although funds with large cash inflows, high expense ratios, or an emphasis on small-cap stocks tended to be more tax efficient in the sample period, they also tended to have lower pretax returns. In fact, for all three variables, the negative influence on pretax return was at least January/February 2002 83

Financial Analysts Journal as great as the positive influence on tax efficiency implying a neutral or negative net effect on aftertax returns. These results suggest that taxable investors should not make investment decisions with tax efficiency as their sole focus. Instead, they should emphasize maximizing after-tax returns (for their chosen risk tolerance). Moreover, U.S. equity investors should diversify across investment styles (large small, value growth). When choosing equity funds for a taxable account, investors should focus on funds with good past pretax performance, low expenses, and high past tax efficiency (i.e., low return lost to taxes) that have not recently experienced large net redemptions. Our results suggest that the benefits of being a taxaware investor are substantial. The authors wish to thank Terry Banet, Kimberly LaPointe, Mark Sheridan, and Gordon Fowler for helpful comments and suggestions. Remaining errors are our responsibility. Appendix A. Construction of Tax- Adjusted s CRSP reports key data for each distribution capital gain, income, or split over the life of each fund in its database. We used this information, together with information on short- and long-term tax rates (to be discussed), to construct a monthly after-tax return series for each fund in the CRSP database. We obtained after-tax returns for longer frequencies by compounding the monthly return data. For each month t, we identified the total number of distributions N that occurred in that month for a fund. Assuming an arbitrary $1 investment in the fund at the closing net asset value (NAV) from the prior month, the number of shares invested in a fund at the beginning of month t is given by 1 S 0,t = NAV t 1 --------------------, (A1) where NAV t 1 is the fund s net asset value at the end of month t 1. An updated share amount was computed following each distribution i = 1,..., N, sorted by date, within the month as follows: If the distribution was income or capital gains, XAMT S i, t = S i 1,t 1 + i -----------------------, (A2) RENAV i where XAMT i is the per share dollar amount of the income or capital gains distribution and RENAV i is the reinvestment net asset value on the close of the pay date of the income or capital gains distribution, including reinvestment of the distribution. If the distribution was a stock split, S i,t = S i 1,t SFACTOR i, (A3) where SFACTOR i is the split factor (e.g., 2 for 1). The taxes on capital gains and income distributions within a given month t were calculated as N Taxes t = i =1 (A4) where XAMT D i = dollar amount of the dividend XAMT C i = dollar amount of the capital gains distribution T d = ordinary income tax rate T c = tax rate on capital gains Table A1 lists the tax rates on ordinary income and capital gains used in this article for each year in the sample. Although income taxes are a function of an individual investor s personal tax rate, we could not, of course, calculate each individual s rate. For years prior to 1993, the ordinary income tax rates we used to compute taxes correspond most closely to the rates of high-tax individuals as determined by Dickson and Shoven (1993). For 1993 forward, the ordinary income tax rate is the maximum U.S. federal marginal tax rate. Table A1. Tax Rates S i, t [ XAMTD ( i )( T d ) + XAMTC ( i )( T c )], Year Income Tax Rate Capital Gains Tax Rate 1981 63.2% 25.0% 1982 50.0 20.0 1983 50.0 20.0 1984 49.0 19.6 1985 49.0 19.6 1986 49.0 19.6 1987 38.5 28.0 1988 33.0 28.0 1989 33.0 28.0 1990 33.0 28.0 1991 31.0 28.0 1992 31.0 28.0 1993 39.6 28.0 1994 39.6 28.0 1995 39.6 28.0 1996 39.6 28.0 1997 39.6 28.0 1998 39.6 20.0 Note: For years prior to 1993, tax rates are from Dickson and Shoven. For 1993 1998, the ordinary income tax rate is the maximum federal marginal tax rate. 84 2002, AIMR

Explaining After-Tax Mutual Fund Performance Given an initial investment amount of $1, we calculated the after-tax monthly return as aftertax r t = S N, t NAV t Taxes t 1. (A5) Several assumptions are inherent in these calculations. First, taxes are assumed paid at the end of each month, although in reality, they are typically paid on an annual basis. This assumption has only a minor impact on the calculation of after-tax returns. Second, the capital gains of an investor are not offset by any capital losses of that investor. Third, all capital gains are taxed at the longterm capital gains rate. To assume otherwise would require information about the investor s holding period and personal tax situation. Accounting for capital gains taxes individually would change our estimate of the magnitude of returns lost to taxes our estimate of tax efficiency. But because the estimated premiums are essentially a covariance between the characteristic, such as past RLT, and future after-tax returns, a change in the level of return lost to taxes that is driven by a change in the investor s tax rate would not have a big impact on our results. Fourth, no state taxes are considered. State taxes depend on the individual and will increase the amount of return lost to taxes. Again, an increase in the amount of return lost to taxes does not imply that the estimated premium will change. Fifth, the calculations ignore any additional taxes resulting from the liquidation of the fund at the end of the period. So, the after-tax returns correspond most closely to those earned by long-term buy-and-hold investors. To assume otherwise, we would have to make assumptions regarding the holding period of each individual investor. Notes 1. Past performance is not a guarantee of future results. Principal value and investment returns fluctuate with changes in market conditions, so an investor's shares when redeemed may be worth more or less than their original cost. Smallcapitalization funds are subject to greater volatility than funds following other style strategies. For more complete information on a fund s past performance including management fees, charges, and expenses investors should obtain and read the prospectus carefully before investing. 2. Prior studies of mutual fund performance did not uniformly conclude that all of these characteristics are important determinants of pretax returns, but each characteristic was identified in numerous studies as an important determinant of pretax returns. Many analysts believe that assets under management and/or net cash flow may be important determinants of pretax performance, but the literature contains little evidence to support such a claim. 3. The potential capital gains exposure of a fund might also be an important determinant of future after-tax returns. Unfortunately, data on capital gains exposure were available to us only for the last year of our sample period. We did perform tests for this restricted period and found no relationship between potential capital gains exposure and subsequent after-tax returns. Because of the short sample length, these results are only suggestive, and we thus leave them for future research. 4. Although we do not report results for the case in which returns were measured annually, we did carry out such measurements and found the results to be qualitatively similar to those reported later in this article. 5. In tests not reported, we estimated regressions that included past standard deviation together with and in lieu of β and found that past standard deviation did not provide any additional explanatory power beyond that already provided by β. Also, in a test not reported, we tested the hypothesis that funds with a great deal of style purity are less tax efficient than less-pure funds. Our measure of style purity was the standard deviation of the regression error term in Equation 1. After controlling for other factors, we found no evidence to suggest that style purity affects aftertax returns or tax efficiency. 6. Measuring NCF over the prior quarter did not alter the conclusions drawn from our analysis. Monthly net asset figures are not available in the CRSP database for the entire 1981 98 sample period, so we did not perform tests using NCF measured over monthly intervals. 7. We also used a six-month cutoff to define Mgrturn and obtained similar results to those reported here. 8. For an example of application of this technique in the mutual fund performance literature, see Carhart. 9. See Malkiel (1995) and Chevalier and Ellison for examples of studies that used pooling in the process of estimating the marginal effects of mutual fund characteristics on return. 10. The average premiums associated with the risk and style variables are a function of more than one regression coefficient. So, the test statistic for the hypothesis that the average premium is 0 is distributed as an F random variable. For those non-risk-related and non-style-related variables for which the premium was not allowed to vary over time, the average premium is a function of one regression coefficient. In those cases, the test statistic is t distributed. When reporting the results of our tests, we provide the appropriate test statistic. 11. A positive premium on past performance could be the result of performance persistence among the poorest performing funds only. We checked for this possibility and found that performance persisted for both poor performers and good performers. 12. For all funds in 1991, turnover was reported as zero by CRSP. We used turnover in 1990 to proxy for turnover in 1991. 13. We also estimated average premiums for the 1992 98 time period, for which data on tenure and manager turnover became available. The results of this analysis, not shown, are qualitatively similar to those reported here. January/February 2002 85