# Jensen’s Measure ## What is Jensen’s measure?

Jensen’s measure, or Jensen’s alpha, is a risk-adjusted performance measure that represents the average return on a portfolio or investment, higher or lower than that predicted by the fixed asset pricing model (CAPM). ), taking into account the beta of the portfolio or investment and the average market return. This metric is also commonly called simply alpha.

### Key points to remember

• Jensen’s measure is the difference between a person’s performance and the overall market.
• Jensen’s measure is commonly called alpha. When a manager outperforms the market at the same time as the risk, he “delivers alpha” to his clients.
• The measure takes into account the risk-free rate of return for the period.

## Understanding Jensen’s measure

To accurately analyze the performance of an investment manager, an investor must examine not only the overall return on a portfolio, but also the risk of that portfolio to see if the return on the investment compensates for the risk it takes. . For example, if two mutual funds both have a 12% return, a rational investor should prefer the less risky fund. Jensen’s measure is one way to determine if a portfolio is generating the right return for its level of risk.

If the value is positive, the portfolio generates excess returns. In other words, a positive value for Jensen’s alpha means that a fund manager has “beaten the market” with his stock selection skills.

## Real example of Jensen’s measure

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

Using these variables, the Jensen alpha formula is:

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

or:

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

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

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

B = the beta of the investment portfolio compared to the chosen market index

For example, suppose that a mutual fund returned 15% last year. The appropriate market index for this fund returned 12%. The fund’s beta compared to this same index is 1.2 and the risk-free rate is 3%. The alpha of the fund is calculated as follows:

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

Given a beta of 1.2, the mutual fund should be more risky than the index and thus earn more. A positive alpha in this example shows that the mutual fund manager has earned more than enough return to be compensated for the risk he took during the year. If the OPC returned only 13%, the calculated alpha would be -0.8%. With a negative alpha, the mutual fund manager would not have performed sufficiently given the level of risk he was taking.

## Special consideration: EMH

Critics of Jensen’s measure generally believe in the efficient market hypothesis (EMH), invented by Eugene Fama, and argue that any portfolio manager’s excess returns come from luck or random chance rather than the skill. Given that the market has already integrated all the available information, it is said to be “efficient” and has a precise price, according to theory, preventing any active manager from bringing something new to the table . The theory is also supported by the fact that many active managers fail to beat the market more than those who invest their clients’ money in passive index funds.