Financial Portfolio Benchmarks
Most investors are interested in evaluating portfolio managers in order to know to whom to entrust their funds. For that purpose, it is necessary to rank portfolio managers in terms of some appropriate bench mark.
There are three main possibilities. The first is the naively selected portfolio with a risk approximately equal to that of the actual portfolio. The use of "naive" models or bench marks is a familiar technique in economics, meteorology, and perhaps elsewhere. In economics, it is now ordinary practice to evaluate economic forecasts by reference to naive forecasts such as would be produced by assuming that next year will be like this year or that next year will be different from this year by the same percentage that this year differed from last, fn meteorology, it is commonplace to evaluate weather forecasts by reference to such naive models as one which postulates that the next day will be like the current day or one that selects a forecast for the next day at random with probabilities proportionate to the historic relative frequency of different kinds of weather.
A second bench mark is obviously provided by the average performance of the group of actual portfolios which are considered comparable. For example, it would be appropriate to judge the performance of each mutual fund having capital appreciation as its objective with the average performance of all other such funds. In the Jensen study, it would have been possible to draw a regression line to represent the relationship between risk and rate of return for the mutual funds actually studied.
The line PT is the regression line fitted to the fund observations. Its slope, in this instance, is flatter than that of the capital market line RfQ. The ranking can be based on deviations of each fund from PT in much the same way that funds could be ranked according to their deviations from Sharpe's capital market line. Rankings by one method may differ from those by the other because of differences in the slopes of the two regression lines. For example, fund A in the diagram is superior to fund B when compared to the capital market line, but inferior to fund B when compared to the regression line for fund returns alone.