# Jensen's Measure

## What is the 'Jensen's Measure'

The Jensen's measure is a risk-adjusted performance measure that represents the average return on a portfolio or investment above or below that predicted by the capital asset pricing model (CAPM) given the portfolio's or investment's beta and the average market return. This metric is also commonly referred to as Jensen's alpha, or simply alpha.

## BREAKING DOWN 'Jensen's Measure'

To accurately analyze the performance of an investment manager, an investor must look not only at the overall return of a portfolio, but also at the risk of that portfolio to see if the investment's return compensates for the risk it takes. For example, if two mutual funds both have a 12% return, a rational investor should prefer the fund that is less risky. Jensen's measure is one of the ways to determine if a portfolio is earning the proper return for its level of risk. If the value is positive, then the portfolio is earning excess returns. In other words, a positive value for Jensen's alpha means a fund manager has "beat the market" with his stock picking skills.

## Jensen's Measure Calculation Example

Assuming the CAPM is correct, Jensen's alpha is calculated using the following four variables:

R(i) = the realized return of the portfolio or investment

R(m) = the realized return of the appropriate market index

R(f) = the risk-free rate of return for the time period

B = the beta of the portfolio of investment with respect to the chosen market index

Using these variables, the formula for Jensen's alpha is:

Alpha = R(i) - (R(f) + B x (R(m) - R(f)))

For example, assume a mutual fund realized a return of 15% last year. The appropriate market index for this fund returned 12%. The beta of the fund versus that same index is 1.2 and the risk-free rate is 3%. The fund's alpha is calculated as:

Alpha = 15% - (3% + 1.2 x (12% - 3%)) = 15% - 13.8% = 1.2%.

Given a beta of 1.2, the mutual fund is expected to be riskier than the index, and thus earn more. A positive alpha in this example shows that the mutual fund manager earned more than enough return to be compensated for the risk he took over the course of the year. If the mutual fund only returned 13%, the calculated alpha would be -0.8%. With a negative alpha, the mutual fund manager would not have earned enough return given the amount of risk he was taking.