Morningstar Advisor - April/May 2010 - 30

Gray Matters

Exhibit 2 Rolling R-Squareds: The average of these rolling cross-sectional regression R-squareds is 40% (blue line), meaning that variations in asset allocation explain approximately 40% of excess-market return variations.
Rolling Cross-Sectional R-Squareds for U.S. Equity Funds*
R^2 R^2 Average

Empirically, after adjusting for the overall movement of the market, detailed assetallocation decisions and active management are about equally important, although this result varies significantly over time.
Market Movement

100% 80 60 40 20 May–99 Sep–00 Jan–02 May–03 Sep–04 Jan–06 May–07 Sep–08

* Each point represents a cross-sectional regression for a different rolling period.

al regression is never a statement about the overall importance of asset allocation.
Why Results May Vary

Building upon this clarification related to the “40%” number associated with cross-sectional analysis, our article makes two additional important contributions. First, by running a series of rolling cross-sectional regression analyses (in which the return of each fund in question is regressed against its corresponding asset allocation policy) and graphing the residual error, the cross-sectional fund return dispersion, and the resulting R-squared at each point in time, we pinpoint that dramatic changes over time in crosssectional fund return dispersion explain why different researchers may get very different cross-sectional results. Most researchers have simply run one cross-sectional regression and present the corresponding regression results, rather than a series of cross-sectional regressions results. In Exhibit 1, we link each of these separate cross-sectional regession results. The green line represents the cross-sectional fund return dispersion at each

point in time for U.S. equity funds. The blue line represents the standard deviation in the unexplained residual returns. Taking the information in Exhibit 1 and recalling that the formula for R-squared is 1 minus the variance in the unexplained residual returns divided by the cross-sectional fund return variance, we plot the rolling cross-sectional regression R-squareds in Exhibit 2. The average of the rolling regressions is around 40% (blue line), indicating that variations in asset allocation in excess of market movement explain 40% of the excess-market return variations. Next, in Exhibit 3, by performing a time-series analysis on excess-market returns, we put time-series regression analysis and crosssectional regression analysis on an even playing field for the first time. The R-squareds from a time-series regression on excess-market returns and cross-sectional regression on either type of return (total or excess-market) give us consistent answers. 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% for both sets of regressions.

Finally, returning to that dreaded “90 percent” number that comes from a time-series regression on total returns, some researchers—especially our own Roger Ibbotson— think that it is important to recognize that much of the “90 percent” in return variations comes from the market’s overall movement, while a much smaller amount comes from the return variations coming from the granular assetallocation decisions. This was an important contribution from Ibbotson and Kaplan (2000) that was largely overlooked, and it is a point made even more clear by our new research. The “90 percent” number comes from a time-series regression, typically on multiple asset-class factors. Switching from a somewhat granular list of asset-class factors to a single explanatory variable, such as the S&P 500 (single factor regression), typically leads to only a minor decrease in the average R-squared. In Exhibit 4, the left two bars illustrate the BHB time-series regression analysis for both equity and balanced funds in which the bulk of the return variations are attributed to what is usually identified as asset-allocation policy. In contrast, the right two bars illustrate the arguments put forth in Hensel, Ezra, and Ilkiw (1991) and Ibbotson and Kaplan (2000) (HEI & IK)—that market movement dominates time-series regressions on total returns. The two right bars give a more detailed decomposition of total return and its parts: the applicable market return, asset-allocation policy return in excess of the market return, and the return from active portfolio management. Taken together, market return and asset-allocation return in excess of market return dominate active portfolio management. This affirms that market return plus asset-allocation return in excess of market return are the dominant determinants of total return variations.

30 Morningstar Advisor April/May 2010
Morningstar Advisor - April/May 2010

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