Morningstar Advisor April/May 201028

Gray Matters

The importance of asset allocation has been the subject of considerable debate and misunderstanding for decades. What seems like an easy question or topic on the surface is actually quite complicated and filled with nuance. In the recent article I wrote with my fellow Ibbotson Associates’ James Xiong, Roger Ibbotson, and Peng Chen, “The Equal Importance of Asset Allocation and Active Management” (published in the March/April issue of Financial Analysts Journal), we pinpoint one of the primary sources of confusion surrounding the importance of asset

allocation. Before presenting the key insights of our new paper, let’s briefly recap the debate and put our new contribution into context.

BHB Starts the Debate

The seminal work on the importance of asset allocation, the catalyst of a 25-year debate, and unfortunately the source of what is arguably the most prolific misunderstanding among investment professionals, is the 1986 article “Determinants of Portfolio Performance,” by Gary Brinson, Randolph Hood, and Gilbert Beebower (BHB). BHB regressed the time

series returns of each fund on a weighted combination of indexes reflecting each fund’s asset-allocation policy. In one of the many analyses that BHB carried out (and probably one of the least important ones), they found that the policy mix explained 93.6% of the average fund’s return variation over time (as measured by the R-squared of the regression)—the keyword being variation.

Unfortunately, this 93.6% has been widely misinterpreted. Many practitioners incorrectly believe the number means that 93.6% of a

Asset Allocation Is KingBy Thomas M. Idzorek

Forget about that 90% number. After removing the market movement, asset allocation and active management are equally important in explaining return variations.

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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’

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

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,

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

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 cross-sectional 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 impor-tantly, that the R-squared from a cross-section-

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.

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12%

May–99 Sep–00 Jan–02 May–03 Sep–04 Jan–06 May–07 Sep–08

Fund DispersionResidual ErrorMonthly Dispersion

Rolling Cross-Sectional Regression Results on U.S. Equity Funds

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Gray Matters

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-sec-tional 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 cross-sectional 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 cross-sectional 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 regres-sions so that the cumulative distribution adds up to 100% for both sets of regressions.

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

Market Movement

Finally, returning to that dreaded “90 percent” number that comes from a time-series regression on total returns, some research-ers—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 asset-allocation 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 decomposi-tion 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.

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

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.

R^2

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100%

May–99 Sep–00 Jan–02 May–03 Sep–04 Jan–06 May–07 Sep–08

AverageR^2

Rolling Cross-Sectional R-Squareds for U.S. Equity Funds*

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Long Live Asset Allocation

Investors understand that asset allocation is important, but the answer to the question of how important is tricky. Unfortunately, BHB’s landmark article unintentionally created the fallacy that 90% of return levels come from asset allocation. Investors would do well to forget the 90% number. In aggregate, 100% of return levels come from asset allocation. Return variations are dominated by the common market factor embedded in the funds being analyzed. After removing this common market factor, on average for typical funds about half of the return variations comes from detailed asset-allocation decisions in excess of the market movement and about half of the return variations comes from active manage-ment, although this 50/50 result dramatically changes from one period to the next. Our research clarifies the contribution of each and highlights the significant contribution from market movement. For aggregate return levels, asset allocation is king! K

Thomas M. Idzorek, CFA, is chief investment officer at Ibbotson Associates, a Morningstar company.

ReferencesBrinson, Gary P., L. Randolph Hood, and Gilbert L. Beebower. 1986. “Determinants of Portfolio Performance.” Financial Analysts Journal, July/August, pp. 39–44.

Hensel, Chris R., D. Don Ezra, and John H. Ilkiw. 1991. “The Importance of the Asset Allocation Decision.” Financial Analysts Journal, July/August, pp. 65–72.

Ibbotson, Roger G., 2010. “The Importance of Asset Allocation.” Financial Analysts Journal, March/April.

Ibbotson, Roger G., and Paul Kaplan, 2000. “Does Asset Allocation Policy Explain 40, 90, or 100 Percent of Performance?” Financial Analysts Journal, January/February, pp. 26–33.

Vardharaj, Raman and Frank J. Fabozzi. 2007. “Sector, Style, Region: Explaining Stock Allocation Performance,” Financial Analysts Journal, May/June, pp. 59–70.

Xiong, James X., Roger G. Ibbotson, Thomas M. Idzorek, and Peng Chen, 2010. “The Equal Importance of Asset Allocation and Active Management,” Financial Analysts Journal, March/April.

Exhibit 3 Consistent Answers: By placing time series and cross-sectional regressions on equal footing, asset-allocation decisions in excess of market movement and active management are about equally important at explaining return variations.

Cross-SectionalExcess-Market Time-SeriesFrequency

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0.1

0.15

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0.25

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%R^2

Time Series and Cross-Sectional R-Squared Distributions

Exhibit 4 Market Movement Dominates: BHB attributed the bulk of total return variations to asset-allocation policy (left two bars). In contrast, HEI & IK argue that market movement dominates (right two bars).

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BHB Equity Funds BHB Balanced Funds HEI & IK Equity Funds HEI & IK Balanced FundsTime-Series Regressions

R-Squared

Interaction Effect*Asset-Allocation Policy Market Movement

Excess-Market Asset-Allocation PolicyInvestment Strategy

Decomposition of Total-Return Variations

*The interaction effect is a balancing term that makes the three return components of R-squared add up to 100%.