The Equal Importance of Asset Allocation and Active Management

AHEAD OF PRINT Financial Analysts Journal Volume 66  Number 2 ©2010 CFA Institute The Equal Importance of Asset Allocation and Active Management James X. Xiong, CFA, Roger G. Ibbotson, Thomas M. Idzorek, CFA, and Peng Chen, CFA What is the relative importance of asset allocation policy versus active portfolio management in explaining variability in performance? Considerable confusion surrounds both time-series and cross-sectional regressions and the importance of asset allocation. Cross-sectional regressions naturally remove market movements; therefore, the cross-sectional results in the literature are equivalent to analyses of excess market returns even though the regressions were performed on total returns. In contrast, time-series analyses of total returns do not naturally remove market movements. Time-series analyses of excess market returns and cross-sectional analyses of either total or excess market returns, however, are consistent with each other. With market movements removed, asset allocation and active management are equally important in determining portfolio return differences within a peer group. Finally, an examination of period-by-period cross-sectional results reveals why researchers using the same regression technique can get widely different results. A portfolio’s total return can be decomposed into three components: (1) the market return, (2) the asset allocation policy return in excess of the market return, and (3) the return from active portfolio management (see, e.g., Bailey, Richards, and Tierney 2007; Solnik and McLeavey 2003). The “total return” of the portfolio or fund is the return net of all expenses and fees. Our measure of the “market return” is the equally weighted return for a given period for all the funds in the applicable universe. The “asset allocation policy return” refers to the static asset allocation (beta) return of the fund; intuitively, the asset allocation policy return in excess of the market return is the static asset allocation (beta) return less the market return. The “active portfolio management return” refers to the remaining returns from security selection, tactical asset allocation, and fees. Of the many studies on the importance of asset allocation policy versus active portfolio management, the one most often cited is the seminal work James X. Xiong, CFA, is a senior research consultant, Thomas M. Idzorek, CFA, is chief investment officer and director of research, and Peng Chen, CFA, is president at Ibbotson Associates, a Morningstar company, Chicago. Roger G. Ibbotson is chairman and chief investment officer of Zebra Capital, Milford, Connecticut; a professor in practice at the Yale School of Management, New Haven, Connecticut; and founder of and adviser to Ibbotson Associates, a Morningstar company, Chicago. March/April 2010 by Brinson, Hood, and Beebower (BHB 1986). The BHB study used the time-series total returns of a portfolio and did not separate the market returns from the total returns. The BHB study found that asset allocation policy has an explanatory power of more than 90 percent for the total return variations. Several later studies pointed out that this high explanatory power is dominated by market movements embedded in the total returns (see, e.g., Hensel, Ezra, and Ilkiw [HEI] 1991; Ibbotson and Kaplan 2000). In other words, market movements dominate time-series regressions on total returns.1 In studying the relative importance of asset allocation policy and active portfolio management within a peer group of portfolios (after removing the overall applicable market return movements), we attempted to answer the question, Why do portfolio returns differ from one another within a peer group? Or, put slightly differently, Is the difference in returns among funds the result of asset allocation policy or active portfolio management? We used both time-series and cross-sectional data to answer these equivalent questions. To remove the dominance of the applicable market returns in the time-series analysis, we used excess market returns. We calculated the market returns and asset allocation policy returns for each month for each portfolio and then ran a time-series regression of the portfolio excess market returns against the asset allocation policy excess market returns.2 Extending AHEAD OF PRINT 1 AHEAD OF PRINT Financial Analysts Journal and clarifying previous studies by Ibbotson and Kaplan (2000) and Vardharaj and Fabozzi (2007), we also conducted cross-sectional analyses. Figure 1 plots the decomposition of total return variations under the two different methodologies of BHB (1986) and of HEI (1991) and Ibbotson and Kaplan (2000). It illustrates their interpretations of the explanatory power of asset allocation policy for total return variations. The two bars on the left depict the BHB (1986) time-series regression analysis for both equity and balanced funds. In contrast, the two bars on the right describe the argument of HEI (1991) and Ibbotson and Kaplan (2000) that market movements dominate time-series regressions on total returns. These two bars enable a more detailed decomposition of the total return into its three components: (1) the applicable market return, (2) the asset allocation policy return in excess of the market return, and (3) the return from active portfolio management. In our study, we did not focus on the debate surrounding the BHB study;3 our goal was to address the relative importance of asset allocation policy versus active portfolio management (after removing the applicable market returns). Data We chose three portfolio peer groups from the Morningstar U.S. mutual fund database: U.S. equity funds, balanced funds, and international Figure 1. equity funds. We used 10 years of return data (May 1999April 2009). We removed duplicate share classes and required that each fund have at least five years of return data. The final sample consisted of 4,641 U.S. equity funds, 587 balanced funds, and 400 international equity funds. Similar to Vardharaj and Fabozzi (2007), we estimated the asset allocation policy return for each fund by using return-based style analysis (see Sharpe 1992). For the U.S. equity mutual funds, we used seven size and style factors: Russell Top 200 Growth Index, Russell Top 200 Value Index, Russell Midcap Growth Index, Russell Midcap Value Index, Russell 2000 Growth Index, Russell 2000 Value Index, and cash. For the balanced funds, we used 11 stock and bond benchmarks. 4 For the international funds, we used eight factors.5 For each peer group, we experimented with other sets of asset classes, all of which led to results that are consistent with the results presented here. Methodology Although the mathematics of our study is unsophisticated, the nature of the discussion requires clearly defined notation. Ri,t = fund total return for fund i in period t Pi,t = policy total return for fund i in period t Decomposition of Time-Series Total Return Variations, May 1999–April 2009 R2 (%) 120 100 80 60 40 20 0 −20 −40 BHB BHB HEI & IK HEI & IK Equity Funds Balanced Funds Equity Funds Balanced Funds Time-Series Regressions Active Management Market Movement Asset Allocation Policy Interaction Effect Note: IK stands for Ibbotson and Kaplan (2000). 2 AHEAD OF PRINT ©2010 CFA Institute AHEAD OF PRINT The Equal Importance of Asset Allocation and Active Management Mt Ri,t – M t Pi,t – Mt Ri,t – Pi,t = market return (e.g., equally weighted return for a peer group) in period t = excess market fund return for fund i in period t = excess market asset allocation policy return for fund i in period t = active management or active return for fund i in period t Time-Series Analysis. In previous timeseries studies, total returns were used in the following regression formula to estimate the explanatory power of asset allocation policy: Ri, t = b0 + b1Pi, t + εi, t . (1) The two regression variables are fund total return (Ri,t ) and policy total return (Pi,t ), b0 and b1 are the regression coefficients, and i, t is the residual return (the difference between the realized fund return and the predicted fund return). Appendix A shows the definition of the coefficient of determination (R2), which measures the explanatory power of the model. As discussed earlier, one problem with the time-series analysis of total returns is that the results are dominated by overall market movement. To further analyze the relative importance of asset allocation policy and active management within a peer group, a more applicable approach is to use excess market returns instead of total returns as the regression variables for the time series. Thus, the regression equation for excess market returns is ( ) Ri, t − M t = b0 + b1 Pi, t − M t + εi, t . (2) When carrying out a time-series analysis of excess market return, Equation 1 is very different from Equation 2 because the market return (M t) varies over time. We refer to Equation 2 as the “excess market return time-series regression.” Cros s- Sec tiona l Analy sis . Unlike timeseries regressions, in which the results are highly dependent on the type of return used (total return or excess market return), cross-sectional regressions on total returns are equivalent to crosssectional regressions on excess market returns. 6 Cross-sectional regressions naturally remove the applicable market movement from the peer group, essentially resulting in the same analysis as using excess market returns. We reiterate this point because in most studies on this topic, researchers performed cross-sectional regressions on total returns and failed to recognize the natural removal of the applicable market movement.7 March/April 2010 For single-period cross-sectional regressions, Equation 1 is intrinsically identical to Equation 2 because the market return (Mt) is a constant in the single period (no matter how long the period is) that is inherent in a cross-sectional regression. This point is critical in correctly interpreting the cross-sectional regression results. Because the market movement is naturally removed during the cross-sectional analysis, the resulting R2 is an indication of the relative importance of detailed asset allocation versus active management after removing market movement. Furthermore, because the market movement is naturally removed in the cross-sectional analysis, to interpret the typical low R2 from a crosssectional analysis as a statement regarding the overall or total importance of asset allocation or as a basis for deciding how much market exposure to take is incorrect. Appendix A provides an additional analysis to demonstrate that cross-sectional regression naturally removes market movement. Results We present our results in three areas: a time-series regression on total returns, a time-series analysis of excess market returns, and a month-by-month cross-sectional analysis. Time-Series Regression on Total Returns. For a complete picture of total return time-series regression analysis, the total return can be divided into its three components—(1) the return related to the overall market, (2) the return related to asset allocation policy deviation from the applicable market, and (3) the return related to active portfolio management in the form of tactical asset allocation or security selection: ( ) ( ) Ri, t = M t + Pi, t − M t + Ri, t − Pi, t . (3) 2 Table 1 shows the average time-series R s of the three components in Equation 3 for all the funds in a given fund universe. It shows the three components’ average contributions to the total return variations for each fund universe. The detailed methodology is described in Appendix A. For all three fund universes, two important observations emerge from Table 1. First, the market movement component accounts for about 80 percent of the total return variations and dominates both detailed asset allocation policy differences and active portfolio management. In other words, market movement dominates time-series regressions on total returns. This observation is consistent with such previous studies as HEI (1991) and Ibbotson and Kaplan (2000). AHEAD OF PRINT 3 AHEAD OF PRINT Financial Analysts Journal Table 1. Decomposition of Time-Series Total Return Variations in Terms of Average R 2s, May 1999–April 2009 U.S. Equity Funds Average R2 International Funds Market movement: Ri,t vs. Mt 83% 88% 74% Detailed asset allocation policy: Ri,t vs. Pi,t – Mt 18 20 19 Active management: Ri,t vs. Ri,t – Pi,t 15 10 26 –16 –18 –19 100% 100% 100% Interaction effect Total Second, we found that excess market asset allocation policy return and active portfolio management have an equal level of explanatory power, with each accounting for around 20 percent. The interaction effect is a balancing term and makes the three return components’ R2s add up to 100 percent. The negative interaction effect comes from the negative covariance between the total return and a residual term, as shown in Appendix A. We then focused on the second observation and investigated the contributions to return variations from both excess market asset allocation policy and active portfolio management after removing market movement. To our knowledge, the literature contains no record of this kind of time-series analysis of excess market returns. Time-Series Analysis of Excess Market Returns. As discussed earlier, a time series of portfolio excess market returns regressed against policy excess market returns explicitly removes the overall market movement seen in the total return regression and, therefore, is more relevant for identifying the explanatory power of asset allocation within a particular peer group or universe of funds. We decomposed fund excess market return into policy excess market return and active return—Ri,t  Mt = (Pi,t  M t) + (Ri,t  Pi,t)—and then regressed the fund excess market returns on the corresponding policy excess market returns and active returns over time. That is, we regressed 120 months of Ri,t  Mt on 120 months of Pi,t  Mt (policy excess market return) and then on 120 months of Ri,t  Pi,t (active return) for each fund. Table 2 summarizes the decomposition of excess market return variations for the three peer groups, again in terms of average R2s. Table 2. Overall, excess market asset allocation policy and active portfolio management have about an equal amount of explanatory power after removing the applicable market effect. For the U.S. equity funds, asset allocation policy excess market return accounts for 48 percent of the excess market return variations for the average equity funds; active portfolio management accounts for 41 percent. The residual 11 percent is a result of the interaction effect. For the balanced funds, policy excess market return and active portfolio management account for 36 percent and 39 percent of the excess market return variations, respectively. The results are very similar for the international funds. Thus, this analysis also indicates that excess market asset allocation policy has about the same explanatory power for excess market return variations as active portfolio management within a peer group. Month-by-Month Cross-Sectional Analysis. Cross-sectional regressions are run for a single period, which is typically defined as either one month or one year. We ran the analysis 120 times, once for each of the possible 120 monthly periods. Again, cross-sectional analysis naturally removes the average applicable market return and attempts to determine the excess market return relationship within a given universe of funds. The cross-sectional sample variance is the excess market return variance whether one uses the total returns or the excess market returns. In other words, the R2 of the cross-sectional regression between (Ri,t  Mt) and (Pi,t  Mt) is the same as the R2 of the crosssectional regression between Ri,t and Pi,t. Not surprisingly, one would find more variability in the policy excess market return (Pi,t  Mt) if one studied an eclectic universe of funds. Decomposition of Time-Series Excess Market Return Variations in Terms of Average R 2s, May 1999–April 2009 Average R2 U.S. Equity Funds Balanced Funds International Funds Excess market asset allocation policy: Ri,t – Mt vs. Pi,t – Mt 48% 36% 49% Active portfolio management: Ri,t – Mt vs. Ri,t – Pi,t 41 39 45 Interaction effect Total 4 Balanced Funds AHEAD OF PRINT 11 25 6 100% 100% 100% ©2010 CFA Institute AHEAD OF PRINT The Equal Importance of Asset Allocation and Active Management In discussing these period-by-period crosssectional regression results, we will use the results from the peer group of 4,641 U.S. equity funds as the primary peer group. The other two peer group analyses produced similar results. Figure 2 and Figure 3 show the results of the 120 separate cross-sectional analyses for the 120 monthly returns from May 1999 to April 2009. Because we ran the cross-sectional regressions month by month, the horizontal axis has 120 points. For each month, we regressed fund returns (Ri,t) on their corresponding policy returns (Pi,t). In Figure 2, the cross-sectional fund dispersion is defined as the standard deviation of crosssectional fund returns (Ri, t). It is very volatile. The residual error is the standard deviation of the Figure 2. regression residual—  in Equation A1 (see Appendix A). Note that the residual error is relatively stable, with 68 percent of the values falling between 1 percent and 2.3 percent. The relatively low and stable residual errors imply that the multifactor model that describes fund returns (i.e., the return-based style analysis used to estimate the funds’ policy portfolio) works well. Figure 3 shows the rolling cross-sectional R2s, which range from 0 percent to 90 percent. From Equation A1 (the R2 formula in Appendix A), we can see that the volatility of the cross-sectional R2 in Figure 3 is primarily the result of the volatility of the cross-sectional fund return dispersion in Figure 2 (y in Equation A1). Rolling Cross-Sectional Regression Results for U.S. Equity Funds, May 1999–April 2009 Monthly Dispersion (%) 12 Fund Dispersion 10 8 6 4 2 Residual Error 0 May/99 Figure 3. Sep/00 Jan/02 May/03 Sep/04 Jan/06 May/07 Sep/08 Rolling Cross-Sectional R 2s for U.S. Equity Funds, May 1999– April 2009 R2 (%) 100 80 60 40 20 0 May/99 Sep/00 Jan/02 May/03 Sep/04 Jan/06 May/07 Sep/08 Note: Each point represents a cross-sectional regression for a single month. March/April 2010 AHEAD OF PRINT 5 AHEAD OF PRINT Financial Analysts Journal A wider cross-sectional return dispersion was observed among both individual stocks and equity mutual funds during the internet bubble from 1999 to 2001. De Silva, Sapra, and Thorley (2001) showed that the wider dispersion in funds was primarily the result of wide individual security return dispersions and had little to do with changes in the range of portfolio manager talent. They believed that the information embedded in cross-sectional fund return dispersion, as well as the information on the market mean return, is useful in performance evaluation. They suggested that active fund return (realized return minus policy return) be adjusted by a period-specific dispersion statistic from the peer group for which the manager is being evaluated. The wide and varying fund dispersion in Figure 2 demonstrates that analyses performed for different periods can lead to very different results. This finding explains the wide range of cross-sectional results reported in the literature. Period-by-period cross-sectional R2s are unstable, leading to the differences in previously reported R2s. For example, Vardharaj and Fabozzi (2007) studied a group of large and small U.S. equity funds. They reported that the R2 ranged from 15 percent for 10-year (19952004) compounded cross-sectional fund returns to 72 percent for the 5-year (20002004) period. They attributed the variability in R2 to fund sector or style drift over the 10-year period. But our analysis, which pertains to partially overlapping periods, suggests that the primary reason is the wider dispersion of cross-sectional fund returns and that sector or style drift over the 10-year period is more likely a secondary factor.8 Figure 4. Figure 3 shows that the average of the 120 crosssectional R2s is 40 percent. Thus, on average, the excess market asset allocation policy explains about 40 percent of the cross-sectional excess market return variances for the U.S. equity fund universe. This result is consistent with the time-series analysis of excess market return results reported in Table 2. Figure 4 summarizes the distributions of R2s for the 4,641 U.S. equity funds under two different regression techniques: (1) time-series regressions of fund excess market returns on policy excess market returns and (2) cross-sectional regressions of fund total returns on policy total returns (as noted, this technique is equivalent to cross-sectional regressions of fund excess market returns on policy excess market returns). The frequency in the vertical axis is rescaled for 4,641 time-series regressions and 120 cross-sectional regressions so that the cumulative distribution adds up to 100 percent for both sets of regressions. We can see from the two R2 distributions that the results are consistent. These results confirm our earlier finding that cross-sectional regression is consistent with excess market timeseries regression. Conclusion Our study helped identify and alleviate a significant amount of the long-running confusion surrounding the importance of asset allocation. First, by decomposing a portfolio’s total return into its three components—(1) the market return, (2) the asset allocation policy return in excess of the market return, and (3) the return from active portfolio Distribution of R 2 for Cross-Sectional and Excess Market TimeSeries Regressions for U.S. Equity Funds, May 1999–April 2009 Frequency 0.25 0.20 0.15 0.10 0.05 0 0 10 20 30 40 50 60 70 80 90 100 R2 (%) Excess Market Time Series Cross Sectional Note: We ran 120 cross-sectional regressions and 4,641 excess market time-series regressions. 6 AHEAD OF PRINT ©2010 CFA Institute AHEAD OF PRINT The Equal Importance of Asset Allocation and Active Management management—we found that market return dominates the other two return components. Taken together, market return and asset allocation policy return in excess of market return dominate active portfolio management. This finding confirms the widely held belief that market return and asset allocation policy return in excess of market return are collectively the dominant determinant of total return variations, but it clarifies the contribution of each. More importantly, after removing the dominant market return component of total return, we answered the question, Why do portfolio returns differ from one another within a peer group? Our results show that within a peer group, asset allocation policy return in excess of market return and active portfolio management are equally important. Critically, this finding is not the result of a mathematical truth. In contrast to the mathematical identity that in aggregate, active management is a zero-sum game (and thus, asset allocation policy explains 100 percent of aggregate pre-fee returns), the relative importance of both asset allocation policy return in excess of market return and active portfolio management is an empirical result that is highly dependent on the fund, the peer group, and the period being analyzed. The key insight that ultimately enabled us to conclude that asset allocation policy return in excess of market return and active portfolio management are equally important is the realization that cross-sectional regression on total returns is equivalent to cross-sectional regression on excess market returns because cross-sectional regression naturally removes market movement from each portfolio. We believe that this critical and subtle fact has not been clearly articulated in the past and has been overlooked by many researchers, especially when interpreting cross-sectional results visà-vis the overall importance of asset allocation. The insight that cross-sectional regression naturally removes market movement leads to the notion that removing market movement from traditional total return time-series regression is necessary should one want to put the time-series and crosssectional approaches on an equal footing. After putting the two approaches on an equal footing, we found that the values of R2 for the excess market time-series regressions and the cross-sectional regressions (on either type of return) are consistent. Finally, by examining period-by-period crosssectional results and highlighting the sample period sensitivity of cross-sectional results, we explained why different researchers using the same regression technique can get widely different March/April 2010 results. More specifically, cross-sectional fund dispersion variability is the primary cause of the period-by-period cross-sectional R2 variability. The authors thank William N. Goetzmann of the Yale School of Management and Paul Kaplan and Alexa Auerbach of Morningstar for their helpful comments. This article qualifies for 1 CE credit. Appendix A. Regression Analyses Coefficient of Determination The coefficient of determination, R2, is defined as the fraction of the total variation that is explained by the univariate regression between dependent variable y and independent variable x. Formally, R 2 = b12 = 1− σ2x σ2y σε2 σ2y (A1) , where b1 = the regression’s slope coefficient 2x = the variance of x 2y = the variance of y 2 = the unexplained or residual variance Variances for Time-Series and Cross-Sectional Regressions Under the single-factor market model, the fund return for fund i is Ri, t = αi, t + βi M t + εi, t , (A2) where i,t = average return to fund i that is not related to the market return in period t i = the sensitivity of fund i to the return on the market Mt = market return in period t i,t = an error term Traditional or Total Return Time-Series Variance. We take a variance operator on Equation A2 to get the time-series variance for fund i: σi 2 = βi 2 σ M 2 + σε,i 2 , (A3) where ,i2 is the variance of the residual amount (i + i). AHEAD OF PRINT 7 AHEAD OF PRINT Financial Analysts Journal The first component is the systematic risk, and the second component is the fund-specific risk. Assuming that the monthly standard deviation of the market return is 5 percent and the beta of the fund relative to the market is 0.9, the estimated systematic (i.e., market) risk is βi 2 σ M 2 = 0.9 2 × 5% 2 ≈ 0.002 . σi, excess 2 = ( βi − 1)2 σ M 2 + σε, i 2 . (A5) The excess market return variance is typically much less than the total return variance because with total returns, i is close to 1 for a typical fund. With excess market returns, i  1 is typically closer to 0 than it is to 1. This result can be seen by continuing with our example based on commonly observed values and comparing the following estimate with Equation A4: (βi − 1) 2 σ M = ( 0.9 − 1) × 5% 2 2 ≈ 0.00003. (A6) Cross-Sectional Variance. We can show that the cross-sectional variance, t 2 , is conditional on a realized market return of Mt . In a given period t, the cross-sectional variance is σt 2 = σβ, t 2 M t 2 + σε, t 2 , (A7) where ,t 2 is the cross-sectional variance of fund betas. Equation A7 assumes that the fund-specific risk, ,t 2, is the same for all the funds (hence, no fund subscript). Assuming that the monthly market return and standard deviation of fund betas are 1 percent and 0.3, respectively, an estimate of the first term in Equation A7 is 9 σβ, t 2 M t 2 = 0.32 × 1% 2 ≈ 0.00001. (A8) Comparing Equations A4, A6, and A8, we can see that the time-series variance is much higher than both the excess time-series variance and the cross-sectional variance. Note that Equation A5 is comparable to Equation A7, which indicates that excess market time-series and cross-sectional regressions are on the same footing, and that market movement is removed from both. 8 AHEAD OF PRINT To determine the contributions to total return variations from the three components, we need to modify Equation 3 as follows: ( Ri, t = b1M M t + b1P Pi, t − M t ( ) ) (A9) + b1S Ri, t − Pi, t + εi, t , (A4) Excess Market Time-Series Variance. On the basis of Equations A2 and A3, we can show that the excess market time-series variance for fund i is 2 Return Variations Decomposition where b1M, b1P, and b1S are the univariate regression coefficients between Ri,t and M t , between Ri,t and (Pi,t – Mt), and between Ri,t and (Ri,t – Pi,t), respectively—that is, b1M = b1P = b1S = ( cov Ri, t , M t var ( M t ) ( ), cov Ri, t , Pi, t − M t ( var Pi, t − M t ( ) cov Ri, t , Ri, t − Pt ( var Ri, t − Pi, t ) ) , and (A10) ). Note that Equation A9 is not a standard multiple regression equation. We chose b1M, b1P, and b1S in this particular way because we needed to decompose R2 into its three components. Taking a covariance with Ri,t on both sides of Equation A9, we obtain ( ) ( cov Ri, t , Ri, t = b1M cov M t , Ri, t ) ( ) (A11) + b1SS cov ⎡⎣( Ri, t − Pi, t ) , Ri, t ⎤⎦ + cov ( εi, t , Ri, t ) . + b1P cov ⎡⎣ Pi, t − M t , Ri, t ⎤⎦ Combining Equations A10 and A11 and the first part of Equation A1, we obtain 2 RM + RP2 + RS2 + Rε2 = 1, (A12) 2 , R 2 , and R 2 are the R2s of the univariate where R M P S regressions between Ri,t and Mt, between Ri,t and (Pi,t – Mt), and between Ri,t and (Ri,t – Pi,t), respectively. R 2 is a balancing term and is proportional to the covariance between i,t and Ri,t; we call it “interaction effect” in Table 1. The same methodology can be applied to Table 2. ©2010 CFA Institute AHEAD OF PRINT The Equal Importance of Asset Allocation and Active Management Notes 1. 2. 3. 4. 5. 6. 7. See Ibbotson (forthcoming 2010) for a detailed review. We calculated the market return as the equally weighted return for all the funds in the applicable fund universe (e.g., U.S. equity funds or balanced funds). Dollar-weighted returns produced similar results. For those interested in the debate, see Nuttall (2000). The 11 asset classes are Russell 1000 Growth Index, Russell 1000 Value Index, Russell 2000 Growth Index, Russell 2000 Value Index, FTSE NAREIT Equity Index, MSCI EAFE Index, MSCI Emerging Markets Index, Barclays Capital High Yield Index, Barclays Capital 13 Year Government/ Credit Index, Barclays Capital Long-Term Government/ Credit Index, and cash. The eight factors are S&P 500 Index, MSCI Canada Index, MSCI Japan Index, MSCI AC Asia ex Japan Index, MSCI United Kingdom Index, MSCI Europe ex UK Index, MSCI Emerging Markets Index, and cash. Technically, the intercept of the regression is different, but the remaining regression coefficients and R2 are the same. This key observation was also made by Solnik and Roulet (2000), who stated that the cross-sectional method looks at relative returns. In our context, the relative return is the excess market return. 8. To verify this finding, we attempted to duplicate the Vardharaj and Fabozzi (2007) results by decomposing the R2. Using what we believed to be a similar universe of U.S. equity funds, we calculated the 5-year (20002004) and 10-year (19952004) annually compounded cross-sectional fund dispersions (8.39 percent and 3.13 percent for the 5-year and 10-year compounded returns, respectively). We estimated the residual dispersion to be 4.44 percent for the five-year compounded return, and thus, the R2 is about 72 percent (⬇ 1  4.442 /8.392). We estimated the residual dispersion to be 2.88 percent for the 10-year compounded return, and thus, the R 2 is about 15 percent (⬇ 1  2.882/ 3.132 ). The residual dispersions do not differ much (2.88 percent to 4.44 percent), but the fund dispersions differ considerably (3.13 percent to 8.39 percent). Therefore, the wide fund dispersion explains the widely distributed R 2s in Vardharaj and Fabozzi (2007). 9. For the universe of U.S. equity funds, the cross-sectional beta volatility,  t , is about 0.3, which is estimated from the Morningstar mutual fund database. References Bailey, Jeffery V., Thomas M. Richards, and David E. Tierney. 2007. “Evaluating Portfolio Performance.” In Managing Investment Portfolios: A Dynamic Process. 3rd ed. Edited by John L. Maginn, Donald L. Tuttle, Dennis W. McLeavey, and Jerald E. Pinto. Hoboken, NJ: John Wiley & Sons. Ibbotson, Roger G., Paul D. Kaplan. 2000. “Does Asset Allocation Policy Explain 40, 90, or 100 Percent of Performance?” Financial Analysts Journal, vol. 56, no. 1 (January/February):26–33. Brinson, Gary P., L. Randolph Hood, and Gilbert L. 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Forthcoming 2010. “The Importance of Asset Allocation.” Financial Analysts Journal, vol. 66, no. 2 (March/April). Vardharaj, Raman, and Frank J. Fabozzi. 2007. “Sector, Style, Region: Explaining Stock Allocation Performance.” Financial Analysts Journal, vol. 63, no. 3 (May/June):59–70. March/April 2010 Nuttall, John. 2000. “The Importance of Asset Allocation.” Working paper. AHEAD OF PRINT 9