The Fama measure of net selectivity is then found by subtracting this return from the
actual return on the portfolio:
70.60 – 74.47 = - 3.87%.
Again the two measures (Jensen and Fama’s net selectivity) give opposite results. The
reason for and the interpretation of this divergence is exactly the same as that for the
divergence between the Sharpe and Treynor measures. In other words, Fama’s net
selectivity measure is appropriate in cases where the portfolio under question is the total
portfolio of the investor. Jensen’s measure is appropriate when we are looking at sub-
portfolios of a larger (well-diversified) portfolio.
The Fama approach can be used to give a complete break-up of the observed return in
terms of its various components. For P’s portfolio, this break-up will be as follows:
- Risk-free return 12.00%
- Compensation for systematic risk(beta)
1.121 (41.40 – 12.00) 32.95% - Compensation for inadequate diversification 29.52%
Return mandated by CML 74.47%
Less return mandated by SML 44.95%
Net selectivity - 3,87%
Total Actual Return 70.60%
The Jensen measure can be recovered from this break-up by adding together the last two
elements (viz., the net selectivity and the compensation for inadequate diversification) to
give 29.52 – 3.87 = 25.65%.
From evaluation to Correction.
As we noted in the very beginning of this chapter, one important reason for doing
performance evaluation is to help us in correcting our errors and improving our
performance over a period of time. (If we are evaluating somebody else and not
ourselves, this is not relevant; the corrective action may simply consist of replacing the
portfolio manager). How do the performance evaluation measures discussed so far
provide us with a basis for such an exercise of self improvement?
The Fama framework provides a very convenient tool for this purpose. A simple
comparison of the return on P’s portfolio (70.60%) with that of the market (41.40%)
would indicate that P has significantly outperformed the market. Fama’s measure of net
selectivity indicates that, on the contrary, the return was 3.87% less than what it should
have been. The Fama analysis indicates what has gone wrong. The first two components
of the Fama decomposition specified above tell us what the position was in terms of
systematic risk. The beta of P (1.121) was a little higher than that of the market (1.00)