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

2. 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.

3. Some Standard & Poor’s Indices(October 31, 2001) • 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)

4. 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.

5. 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

6. 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.

7. 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.

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 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.

9. 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: • 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.

10. 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:

11. 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.

12. Note: Since p = p,M(rp)/ (rM), p,M = p(rM)/ (rp)

13. Beta Beta Beta Versus Variance Beta Versus 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. Variance Standard Deviation

14. 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.

15. 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)

16. 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.

17. 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.

18. 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.”