Page 270 - DCOM304_INDIAN_FINANCIAL_SYSTEM

Unit 13: Mutual Funds and Insurance Services

denominator). If we had a fully diversified portfolio, then both the Sharpe and Treynor measures Notes
will give us the same ranking. A poorly diversified portfolio could have a higher ranking under
the Treynor measure than for the Sharpe measure.

Differential Return (Jensen Measure)

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 model used is; R + R +  +  + (R - R ) + e  1
jt ft 1 j mt ft
The Jensen measure of differential return for portfolio p and p is
1 2

which simplifies to

Or, (RARB) = [RA - R (A) I + [R (A) - RF]
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
 – 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
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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