Measuring Performance Without Asset Pricing Models (Chapter 12)

1
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

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Performance Relative to Market Indices

• The most popular method of measuring portfolio
  performance is to compare the portfolios returns
  with the returns on some market index.
• The most popular market index used today is the
  SP 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.

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Some Standard Poors Indices(October 31, 2001)
Total Capitalization (bil) Mean Capitalization (mil) Medial Capitalization (mil) SP 500 9,613 19,264 7,400 SP MidCap 400 768 1,921 1,567 SP 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 SP 500)

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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.

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Barra Growth and Value Indices(October 31, 2001)

• Barra (a portfolio management firm) divides the
  SP 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 () SP 500 Growth 11.1 28 1.27 24.8 SP 500 Value 6.1 17 2.17 13.3 Mid Cap 400 Growth 2.2 23 0.51 15.2 Mid Cap 400 Value 1.4 14 2.16 10.4 Small Cap 600 Growth 0.6 20 0.46 15.7 Small Cap 600 Value 0.4 13 1.54 8.4
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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.

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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 managers 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.

8
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 SP 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.

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Using Index Models to Track a Target

• Suppose an indexed mutual funds goal is to match
  the return on some market index. The objective
  would be
• Identify the appropriate multi-factor model that
  minimizes the portfolios residual variance. For
  example, suppose the following three factor model
  is appropriate
• 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.

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Using the Markowitz Full Covariance Approach to
Track a Target

• To illustrate the Markowitz full covariance
  approach to tracking targets (e.g., tracking the
  SP 500 Index), the following information was
  generated using historical data

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• Next, the following efficient set was created
  using the Markowitz Mean-Variance 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.

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• Note Since ?p ?p,M ?(rp)/ ?(rM), ?p,M
  ?p ?(rM)/ ?(rp)

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Beta
Beta
Beta Versus Variance
Beta Versus Standard Deviation
Variance
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.

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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
  SP 500 index).
• Note For your browsing information, the author
  discusses the procedures for identifying the
  above portfolios.

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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)

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Portfolio Change Measure (PCM)(Continued)

• For each stock in the portfolio, multiply the
  stocks 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.

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Portfolio Change Measure (PCM)(Continued)

• While PCM has some promising possibilities,
  several problems cloud its use. See the authors
  extended discussion in the text.
• For example, PCM measures the portfolio managers
  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.

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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.