Page 328 - DCOM504_SECURITY_ANALYSIS_AND_PORTFOLIO_MANAGEMENT

Unit 13: Portfolio Performance Evaluation

Differential Return (Jensen Measure) Notes

Jensen’s measure is an absolute measure of performance, adjusted for risk. This measure assesses
the portfolio manager’s predictive ability. The objective is to calculate the return that should be
expected for the fund given the risk level and comparing it with the actual return realized over
the period.
Jensen Measure of differential return with risk measured by Beta: The Jensen measure of differential
returns for portfolios p and p is
1 2
The model used is; R + R + a + + (R – R ) + e 1
jt ft 1 j mt ft
Or Rp – Rp = [R + (R – R ) p ] – [R + (R – R ) p ],
1 2 F M F 1 F M F 21
which simplifies to
= Rp – Rp = (R – R ) ( p – p ).
1 2 M F 1 21
Or (R – R ) = [R – R( )] + [R( ) – R ]
A F A A A F
The variables are expressed in terms of realized return and risk.
R — Average return on portfolio for period t
jt
R — Risk-free rate of interest for period t
ft
a — Intercept that measures the forecasting ability of the portfolio manager
1
— A measure of systematic risk
j
R — Average return on the market portfolio
mt
e —Error term.
In both Sharpe and Treynor models, it is assumed that the intercept is at the origin. In the Jensen
model, the intercept can be at any point, including the origin.
If the intercept has a positive value, it indicates that the superior return has been earned due to
superior management skills.
a = 0 indicates neutral performance.
j

!
Caution The manager has done as well as an unmanaged randomly selected portfolio with
a buy-and-hold strategy. If intercept has negative value it indicates that the managed
portfolio did not do as well as an unmanaged portfolio of equal systematic risk.

Applying the Jenson Measure
This requires that you use a different risk-free rate for each time interval during the sample
period. You must subtract the risk-free rate from the returns during each observation period
rather than calculating the average return and average risk-free rate as in the Sharpe and Treynor
measures. Also, the Jensen measure does not evaluate the ability of the portfolio manager to
diversify, as it calculates risk premiums in terms of systematic risk (beta). For evaluating
diversified portfolios (such as most mutual funds) this is probably adequate. Jensen finds that
mutual fund returns are typically correlated with the market at rates above 0.90.

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