Jensen Measure

The Jensen measure is the ratio of your portfolio’s return less the portfolio’s expected return as determined by the capital asset pricing model, or CAPM. The CAPM is an economic theory that describes the relationship between risk and the pricing of assets. The CAPM theory suggests that the only risk that is priced by investors is risk that cannot be diversified away. The CAPM in its most simple form shows that the expected return of a security or a portfolio is equal to the rate on a risk-free security plus the asset’s risk premium multiplied by the asset's beta.

The Jensen’s measure incorporates the CAPM into its calculation. The Jensen measure is calculated as follows:

a_p = r_p – [ r_f + ß_p (r_m – r_f) ]

In this equation, a_p = the alpha for the portfolio, or the return over and above your benchmark; r_p = the average return on the portfolio; ß_p = the weighted average beta of the portfolio; r_f = the average risk-free rate; and r_m = the average return on the market index. This measure is the ratio of the portfolio’s performance (r_p) less the expected portfolio return as determined by CAPM or [ r_f + ß_p (r_m – r_f) ].

Note that this measure by itself is also sufficient to determine risk-adjusted performance. Since we know the market’s beta is 1.0 (by definition), and since we both add and subtract the risk-free rate, the CAPM return is just the market return. So if the Jensen’s measure is positive, the asset has outperformed on a risk-adjusted basis.