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## Wednesday, April 13, 2016

### Jensen's Portfolio Performance Measure

Jenson Model
Jenson's model proposes another risk adjusted performance measure. This measure was developed by Michael Jenson and is sometimes referred to as the Differential Return Method. This measure involves evaluation of the returns that the fund has generated vs. the returns actually expected out of the fund given the level of its systematic risk. The surplus between the two returns is called Alpha, which measures the performance of a fund compared with the actual returns over the period. Required return of a fund at a given level of risk (b) can be calculated as:

Rt – R = a + b (Rm – R)
Where, Rt = Portfolio Return
R = Risk less return
a = Intercept the graph that measures the forecasting ability of the portfolio manager.
b = Beta coefficient, a measure of systematic risk
Rm = Return of the market portfolio

Thus, Jensen’s equation involves two steps:
(i) First he calculates what the return of a given portfolio should be on the basis of b, Rm and R.
(ii) He compares the actual realised return of the portfolio with the calculated or predicted return. Greater the excess of realised return over the calculated return, better is the performance of the portfolio.

Limitation of this model is that it considers only systematic risk not the entire risk associated with the fund and an ordinary investor can not mitigate unsystematic risk, as his knowledge of market is primitive.

Graphic representation of Jensen’s model is a given in the following figure:

The figure shows three lines showing negative, neutral and positive values. The negative line shows that the management of the performed portfolio is inferior. The positive line shows that superior quality of management of funds. The neutral value shows that the performance of the fund is similar to the performance of the market portfolio.

A comparison between the three models shows that the intercept of the line is Sharpe and Treyner models is always at the origin, where as Jensen’s model it may be at the origin (a = 0), above the origin (a > 0) and even be below the origin indicating a negative value (a < 0). The risk adjusted measures have been criticized for using a market surrogate instead of the true market portfolio. These measures have been unable to statistically distinguish luck or change from skill except over very long period of time. Moreover, these models rely heavily on the validity of CAPM. If in estimating the measures the analyst assumes the wrong from of the CAPM in the market place, he will get based measure of performance, usually in favour of low risk portfolios.