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portfolio’s return level (for example, a fund’s 10-year annualized return) comes from a fund’s asset-allocation policy. Not true. The truth is that in aggregate 100% of portfolio return levels comes from asset-allocation policy.
Return ‘Levels’ Versus Return ‘Variations’

Exhibit 1 Dramatic Changes: The wide range in cross-sectional fund return dispersion (green line) explains why researchers get different results when gauging the relative importance of asset allocation.
Rolling Cross-Sectional Regression Results on U.S. Equity Funds
Monthly Dispersion Residual Error Fund Dispersion

It is imperative to distinguish between return levels and return variations. In the big picture, investors care far more about return levels than they do return variation. The often-cited 93.6% says nothing about return levels, even though that is what so many practitioners mistakenly believe. It is possible to have a high R-squared, indicating that the return variations in the asset-class factors did a good job of explaining the return variations of the fund in question, yet see the weighted-average composite asset-allocation policy benchmark produce a significantly different return level than the fund in question. This is the case in BHB’s study. Despite the high average 93.6% R-squared of their 91 separate time-series regressions, the average geometric annualized return of the 91 funds in their sample was 9.01% versus 10.11% for the corresponding policy portfolios. So even though 93.6% is the number that seems to be stuck in everyone’s mind, 112% (10.11% divided by 9.01%) of return levels in the study’s sample came from asset-allocation policy. To put it bluntly, when it comes to returns levels, asset allocation is king. In aggregate, 100% of return levels come from asset allocation before fees and somewhat more after fees. This is a mathematical truth that stems from the concept of an all-inclusive market portfolio and the fact that active management is a zero-sum game. This fundamental truth is somewhat boring; therefore, it is often lost in the debate, even though it is by far the most important result.
Relative Importance of Asset Allocation

12% 10 8 6 4 2 May–99 Sep–00 Jan–02 May–03 Sep–04 Jan–06 May–07 Sep–08

what causes certain funds to underperform and others to overperform? In contrast with the “100% number” that stems from a mathematical identity, the answer to this question is an empirical one. This also brings us back to our new article, “The Equal Importance of Asset Allocation and Active Management.” To help answer the relative importance of asset allocation among funds as it pertains to return variations, researchers use cross-sectional regression rather than a time-series regression. For example, in Roger Ibbotson and Paul Kaplan’s 2000 article, “Does Asset Allocation Policy Explain 40, 90, or 100 Percent of Performance?” the “40%” number comes from a cross-sectional regression, the “90%” comes from a time-series regression, and the “100%” comes from the ratio of realized policy return to fund return. More recently, in a 2007 article, Raman Vardharaj and Frank Fabozzi performed a series of cross-sectional regressions in which the ensuing R-squareds varied widely (a result they inaccurately attribute mostly to style drift). Before our new article, researchers and investors misinterpreted the results of cross-sectional regressions. Historically, these cross-sectional regressions have been

This discussion leads us to a much more interesting question for most investors—even if in the bigger picture of realized return levels it is far less important. Among funds in a particular peer group and over a time period,

performed on total returns; because of this, some may have mistakenly interpreted the R-squared as a statement about total returns and the overall importance of asset allocation. We show that a cross-sectional regression performed on total returns is equivalent to a cross-sectional regression performed on “market-excess” returns, because the crosssectional regression procedure naturally removes the common “market” return that is inherent in the peer group of funds being analyzed. I use the term “market” loosely to describe the peer-group-specific common return, but the results would not change significantly with a more-generic market definition. After we identify the inherent market return as the weighted average return of the funds being analyzed, we convert total returns into market-excess returns by subtracting the peer-group-specific market return. When one performs a cross-sectional regression, it doesn’t matter which type of returns one uses—total returns or excess-market returns. The beta coefficient and R-squared from the cross-sectional regressions are the same; only the intercepts are different. This is proof that a cross-sectional regression naturally removes the common market factor and, more importantly, that the R-squared from a cross-section-

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Morningstar Advisor - April/May 2010

Table of Contents for the Digital Edition of Morningstar Advisor - April/May 2010
