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Style Analysis in Excel
Style analysis has become very popular in the investment management industry and has
spawned quite a few variations on Sharpe’s methodology. Many portfolio managers utilize
Web sites that help investors identify their style and stock selection performance.
You can do style analysis with Excel’s Solver. The strategy is to regress a fund’s rate
of return on those of a number of style portfolios (as in Table 24.5 ). The style portfolios
are passive (index) funds that represent a style alternative to asset allocation. Suppose you
choose three style portfolios, labeled 1–3. Then the coefficients in your style regression
are alpha (the intercept that measures abnormal performance) and three slope coefficients,
one for each style index. The slope coefficients reveal how sensitively the performance of
the fund follows the return of each passive style portfolio. The residuals from this regres-
sion, e ( t ), represent “noise,” that is, fund performance at each date, t, that is independent
of any of the style portfolios. We cannot use a standard regression package in this analysis,
however, because we wish to constrain each coefficient to be nonnegative and sum to 1.0,
representing a portfolio of styles.
To do style analysis using Solver, start with arbitrary coefficients (e.g., you can set
a 5 0 and set each b 5 1/3). Use these to compute the time series of residuals from the
style regression according to
e(t)
5 R(t) 2 3a 1 b
1
R
1
(t)
1 b
2
R
2
(t)
1 b
3
R
3
(t)
4
(24.8)
where
R ( t ) 5 Excess return on the measured fund for date t
R
i
( t ) 5 Excess return on the i th style portfolio ( i 5 1, 2, 3)
a 5 Abnormal performance of the fund over the sample period
b
i
5 Beta of the fund on the i th style portfolio
Equation 24.8 yields the time series of residuals from your “regression equation” with
those arbitrary coefficients. Now square each residual and sum the squares. At this point,
you call on the Solver to minimize the sum of squares by changing the value of the four
coefficients. You will use the “by changing variables” command. You also add four con-
straints to the optimization: three that force the betas to be nonnegative and one that forces
them to sum to 1.0.
Solver’s output will give you the three style coefficients, as well as the estimate of the
fund’s unique, abnormal performance as measured by the intercept. The sum of squares also
allows you to calculate the R -square of the regression and p -values as explained in Chapter 8.
24.6
Performance Attribution Procedures
Rather than focus on risk-adjusted returns, practitioners often want simply to ascertain
which decisions resulted in superior or inferior performance. Superior investment perfor-
mance depends on an ability to be in the “right” securities at the right time. Such timing
and selection ability may be considered broadly, such as being in equities as opposed to
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C H A P T E R
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Portfolio Performance Evaluation
865
fixed-income securities when the stock market is performing well. Or it may be defined
at a more detailed level, such as choosing the relatively better-performing stocks within a
particular industry.
Portfolio managers constantly make broad-brush asset allocation decisions as well as
more detailed sector and security allocation decisions within asset classes. Performance
attribution studies attempt to decompose overall performance into discrete components
that may be identified with a particular level of the portfolio selection process.
Attribution studies start from the broadest asset allocation choices and progressively
focus on ever-finer details of portfolio choice. The difference between a managed port-
folio’s performance and that of a benchmark portfolio then may be expressed as the sum
of the contributions to performance of a series of decisions made at the various levels of
the portfolio construction process. For example, one common attribution system decom-
poses performance into three components: (1) broad asset market allocation choices across
equity, fixed-income, and money markets; (2) industry (sector) choice within each market;
and (3) security choice within each sector.
The attribution method explains the difference in returns between a managed portfo-
lio, P, and a selected benchmark portfolio, B, called the bogey . Suppose that the universe
of assets for P and B includes n asset classes such as equities, bonds, and bills. For each
asset class, a benchmark index portfolio is determined. For example, the S&P 500 may
be chosen as a benchmark for equities. The bogey portfolio is set to have fixed weights in
each asset class, and its rate of return is given by
r
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