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Gray Matters
Asset Allocation Is King
By 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.
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
28 Morningstar Advisor April/May 2010
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
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.
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
Return ‘Levels’ Versus Return ‘Variations’
Monthly 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.
12%
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.
Residual Error
Fund Dispersion
10
8
6
4
2
May–99
Sep–00
Jan–02
May–03
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.”
Relative Importance of Asset Allocation
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).
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,
Before our new article, researchers and
investors misinterpreted the results of
cross-sectional regressions. Historically, these
cross-sectional regressions have been
Sep–04
Jan–06
May–07
Sep–08
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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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.
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.
Rolling Cross-Sectional R-Squareds for U.S. Equity Funds*
R^2
R^2
Average
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
30 Morningstar Advisor April/May 2010
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.
Market Movement
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.
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.
Time Series and Cross-Sectional R-Squared Distributions
Frequency
Excess-Market Time-Series
Cross-Sectional
0.25
0.2
0.15
0.1
0.05
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
R^2
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).
Decomposition of Total-Return Variations
Asset-Allocation Policy
Market Movement
Investment Strategy
Excess-Market Asset-Allocation Policy
Interaction Effect*
R-Squared
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 management, 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.
References
Brinson, Gary P., L. Randolph Hood, and Gilbert L.
Beebower. 1986. “Determinants of Portfolio
Performance.” Financial Analysts Journal, July/August,
pp. 39–44.
120%
100
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.
80
60
Ibbotson, Roger G., 2010. “The Importance of Asset
Allocation.” Financial Analysts Journal, March/April.
40
20
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.
0
–20
BHB Equity Funds
BHB Balanced Funds
HEI & IK Equity Funds
Time-Series Regressions
HEI & IK Balanced Funds
Vardharaj, Raman and Frank J. Fabozzi. 2007. “Sector,
Style, Region: Explaining Stock Allocation Performance,”
Financial Analysts Journal, May/June, pp. 59–70.
*The interaction effect is a balancing term that makes the three return components of R-squared add up to 100%.
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.
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