Measuring Performance Without Asset
Pricing Models
(Chapter 12)
 Performance Relative to Market Indices
 Pure-Play Benchmarking
 Performance Relative to Peer Groups
 Tracking Targets
 Performance Based on Portfolio Weight
Selection
Performance Relative to Market Indices
 The most popular method of measuring portfolio
performance is to compare the portfolio’s returns
with the returns on some market index.
 The most popular market index used today is the
S&P 500.
 When a portfolio specializes its investments in
some particular type of stock (e.g., small cap.,
value), some other stylized index may be used.
 There are also a variety of international indices
that may be used as benchmarks.
Some Standard & Poor’s Indices
(October 31, 2001)
Total Capitalization ($bil)
Mean Capitalization ($mil)
Medial Capitalization ($mil)
S&P
500
9,613
19,264
7,400
S&P
MidCap
400
768
1,921
1,567
S&P
Small Cap
600
330
550
438
 The medians are substantially lower than the
means. This indicates that the stocks are
unevenly distributed in size (I.e., a relatively small
number of large stocks may dominate the index –
especially the S&P 500)
Problems Asociated With Using Market
Indices to Measure Portfolio Performance
 Given the propensity of portfolio managers (e.g.,
mutual funds) to diversify among relatively large
numbers of stocks:
 When the largest stocks in the index are
performing well, it is extremely difficult to
outperform the index.
 When the largest stocks in the index are
performing poorly relative to the smaller
stocks in the index, outperforming the index
will be relatively easy.
Barra Growth and Value Indices
(October 31, 2001)
 Barra (a portfolio management firm) divides the S&P
indices into growth and value components that may be
used as benchmarks to evaluate portfolio managers when
they specialize in either growth or value stocks.
 Source: www.barra.com/research/fundamentals.asp
Median Cap $bil
P/E ratio
Div Yield (%)
ROE (%)
Mid
Mid
Small Small
S&P
S&P
Cap
Cap
Cap
Cap
500
500
400
400
600
600
Growth Value Growth Value Growth Value
11.1
6.1
2.2
1.4
0.6
0.4
28
17
23
14
20
13
1.27
2.17
0.51
2.16
0.46
1.54
24.8
13.3
15.2
10.4
15.7
8.4
Pure-Play Benchmarking
 A pure-play benchmark is identical to the portfolio being
evaluated in all aspects affecting returns. Examples of
variables that may impact on returns according to the
author of the text include:
 Market and APT betas
 Liquidity (e.g., bid-asked spread)
 Profitability
 Price to book ratio
 Price to earnings ratio
 Past performance
 Ratings by professional analysts
 Weighting in industrial sectors
 Of course, identifying the “correct” variables is indeed a
difficult task.
Measuring Performance Relative to
Peer Groups
 Another approach to measuring portfolio
performance is to compare the performance of a
particular portfolio manager with the
performance of other portfolio managers that
have similar styles (e.g., the manager’s peers).
 These peers can either be real managers of other
portfolios, or synthetic peer-groups that are
constructed with characteristics similar to the
portfolio manager being evaluated.
 The author provides a rather detailed discussion
of this topic in the text. You may browse through
this discussion to get an feel for the process
involved.
Tracking Targets
 Many investors attempt to create
portfolios with returns that are closely
associated with some target (e.g., stock
market indices, growth or value indices,
pure-play benchmarks, etc.). For example,
you may wish to construct a portfolio that
is highly correlated with the S&P 500
Index, but contains only the 50 stocks that
you feel will have higher than average
returns. Targets can be tracked with either
(1) Index Models, or (2) the Markowitz full
covariance approach.
Using Index Models to Track a Target
 Suppose an indexed mutual fund’s goal is to
match the return on some market index. The
objective would be:
 Identify the appropriate multi-factor model that
minimizes the portfolio’s residual variance. For
example, suppose the following three factor
model is appropriate:
rj,t  A j  βM, jrM, t  βI, jrI,t  βG,jrG,t  ε j,t

The objective would be to construct a portfolio
such that the market index beta was equal to
1.00, and the other factor betas were all equal
to 0.
 Of course, another approach is to buy “the
market.” This approach, however, is often
impractical when money is flowing in on a
regular basis, or the fund is a small one.
Using the Markowitz Full Covariance
Approach to Track a Target
 To illustrate the Markowitz full covariance approach
to tracking targets (e.g., tracking the S&P 500
Index), the following information was generated
using historical data:
S&P 500 Index
Commonwealth Edison
Sears Roebuck & Co.
Value Line Inc Fund
Century Shares Trust
Franklin Utilities
Mean
Return (%)
16.321
18.500
19.491
14.933
14.900
13.568
Standard
Deviation
12.160
16.122
34.254
11.010
13.765
14.124
Beta
.048
.688
.523
.369
.085
 Next, the following efficient set was
created using the Markowitz MeanVariance Program. Note that the beta has
replaced the traditional position of
average return on the vertical axis.
Because the beta of a portfolio relative to
the target is (as with expected or mean
return) the weighted average of the betas
of the combined securities, the shape of
the efficient set is identical to that of the
conventional Markowitz efficient set. Also
note that either standard deviation or
variance can be placed on the the
horizontal axis.
Portfolio
MVP
2
3
4
5
6
7
8
9
10
Beta
.265
.449
.633
.816
1.000
1.184
1.367
1.551
1.735
1.918
Standard
Deviation
8.674
9.350
11.134
13.596
16.463
19.487
22.666
25.925
29.237
32.586
Variance
75.238
87.422
123.966
184.851
270.142
379.743
513.748
672.106
854.802
1061.847
Note: Since p = p,M (rp)/ (rM),
Correlation*
With S&P 500
.372
.584
.691
.730
.740
.739
.733
.727
.722
.716
p,M = p (rM)/ (rp)
Beta
2.5
Beta Versus Variance
Beta
2.5
Beta Versus Standard Deviation
2
2
1.5
1.5
1
1
0.5
0.5
0
0
0
500
1000
Variance
1500
0
20
40
Standard Deviation
 Note: For any given target beta, portfolios in the
efficient set will have the smallest variances of
return. Of course, this also implies that for any
given target beta, portfolios in the efficient set
will have the smallest residual variances as well.
Three Unique Alternative Portfolios on the
Efficient Set That Could be Reasonably
Selected as the Tracking Portfolio
 The portfolio with a beta of 1.00 and the lowest
possible residual variance (portfolio #5 in the
example).
 The maximum correlation portfolio (portfolio #5
in the example).
 The minimum volatility of differences portfolio is
the one that minimizes the differences between
the periodic returns to the tracking portfolio and
the returns to the target (in this case the S&P 500
index).
 Note: For your browsing information, the author
discusses the procedures for identifying the
above portfolios.
Performance Based on Portfolio Weight
Selection
 Given the controversies regarding the CAPM and
APT, the author presents “a possible alternative”
of measuring portfolio performance that does not
rely on asset pricing models.
 Portfolio Change Measure (PCM)
m
PC M 
r
J,t (w J,t  w J,t 1 )
j1
rJ,t  th erate of re tu rnon stock(J) du rin gpe riod(t)
w J,t  th eportfoliowe igh tof stock(J) at th e
be gin n ingof pe riod(t)
w J,t-1  th eportfoliowe igh tof stock(J) at th e
be gin n ingof pe riod(t-1)
Portfolio Change Measure (PCM)
(Continued)
 For each stock in the portfolio, multiply
the stock’s return by the change in
portfolio weight in the previous period.
Then, sum all the products to get PCM. If
the sum is positive, the manager of the
portfolio has tended to increase the
weights in relatively good performing
stocks and has tended to decrease the
weights in relatively poor performing
stocks.
 Whereas a positive sum would indicate
good performance, a negative sum would
tend to indicate poor performance.
Portfolio Change Measure (PCM)
(Continued)
 While PCM has some promising
possibilities, several problems cloud its
use. See the author’s extended discussion
in the text.
 For example, PCM measures the
portfolio manager’s timing abilities
relative to the group of stocks they have
chosen to invest in. It is possible that a
particular group of stocks can
underperform the market while at the
same time provide the manager with
high PCM scores.
Final Thought Concerning Portfolio
Performance
 “To sum up, considering the current
state of the art, you may well have a
right to scream and yell if you ever
get fired on the basis of poor
portfolio performance.”