# Jensen's measure

Jensen’s measure, or Jensen’s alpha, developed by Michael Jensen in 1968, is used to calculate the return on a portfolio in excess of its theoretical expected return. The theoretical expected return is based on a market model, usually the Capital Asset Pricing Model (CAPM). The CAPM provides a model for the risk-adjusted return on an investment. Any investment that performs better than its projected risk-adjusted return is said to have a positive alpha. Alpha is a measure of return over and above that explained by the securities market line and the investment’s beta (volatility).

Jensen’s measure is used to evaluate investment managers’ performance, since a positive measure of alpha shows that the portfolio has outperformed the benchmark.

### How is it calculated?

Jensen’s measure is a measure of alpha $a$. It takes into account the excess return on the portfolio in relation to its beta and the return on the market as a whole.

• Return on portfolio, ${R}_{p}$.

• Return on a risk-free investment, ${R}_{f}$.

• Expected return on the market as a whole, ${R}_{m}$.

• Portfolio volatility, ${a}_{p}$. Jensen’s measure uses beta as a measure of volatility. This is the systematic risk or market risk to which the investment is subject.

##### Example

Looking at an investment portfolio manager, let us assume that he has made a return of 20%. The rate of return on a risk-free investment is 3%, and the market as a whole experienced a return of 8%. The beta of the investment manager’s portfolio is 1.4.

• $a=17-7$

The investment portfolio manager achieved alpha of 0.1, meaning that the portfolio outperformed the market by 10%.

### Efficient market hypothesis

Investment managers are constantly striving for alpha. When developing his measure, however, Jensen discovered in his research that no funds really ever did achieve alpha. The few that did, he attributed to random chance. In fact, Jensen’s findings strongly correlated with the efficient market hypothesis.

The efficient market hypothesis was developed by Eugene Fama as a model for market performance. If the prices in a market reflect all available information, that market is said to be ‘efficient’. This means that any external information investors may consider when making investment decisions has already been considered in the pricing of stocks. This effectively negates speculative trading and suggests that an actively managed portfolio may perform no better than a passively managed, or index, fund.

Jensen’s measure is an important tool for treasurers who will want to achieve the best possible return on any investment, whether that means achieving alpha or not. Jensen’s measure may be used, in association with other metrics, to make predictions on the potential of a particular investment to outperform another, thus assisting treasurers in their investment decisions.