What Is Jensen's Measure (Alpha), and How Is It Calculated?

What Is the Jensen's Measure?

Jensen's measure is a risk-adjusted performance measure that represents the average return on an investment above or below that predicted by the capital asset pricing model (CAPM). Put simply, it measures an investment's abnormal or excess returns compared to its estimated returns. Jensen's measure can used to determine returns for any asset, including stocks and bonds, as well as entire financial portfolios. It takes into account the beta and the average market return of the portfolio or the investment.

Formula and Calculation of Jensen's Measure

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

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

Where:

• 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
• B = the beta of the investment portfolio related to the chosen market index

Calculating this metric using the formula above can result in one of three possible outcomes:

• Positive: If the alpha is positive, it means that the asset outperforms the market or benchmark.
• Negative: A negative alpha means that the security is underperforming the market or benchmark.
• Zero: This happens when the alpha is neutral. As such, it performs consistently with or tracks the market or benchmark.
  

Understanding Jensen's Measure

Jensen's measure was developed by economist Michael Jensen in 1968 as a way to calculate investment returns while taking risk into account. As noted above, Jensen's measure is a financial performance metric that adjusts for risk. Investors and investment professionals can use the formula above to calculate the excess returns of an investment or portfolio's expected returns.

The expected returns are measured using the CAPM. This is a model that is used to calculate an investment's expected rate of return. Investors and investment professionals can determine whether the price of an asset, such as a stock, bond, or other security, conforms to its expected return by factoring in things like risk and the time value of money (TVM).

Jensen's measure can also be used to accurately analyze the performance of an investment manager. To do so, an investor must look at the overall return of a portfolio in addition to the risk of that portfolio. The goal is 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 less risky fund. 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 beats the market with their stock-picking skills.

Criticism of Jensen's Measure

Critics of Jensen's measure generally believe in the efficient market hypothesis (EMH), which was invented by Eugene Fama. EMH is a theory that suggests that an asset's price trades at its fair value and accounts for all variables, including risk. As such, people who follow EMH believe that investors can consistently beat the market.

As such, critics argue that any portfolio manager's excess returns derive from luck or random chance rather than skill. Because the market already prices in all available information, it is said to be efficient and accurately priced. Further supporting the theory is the fact that many active managers fail to beat the market any more than those who invest money in passive index funds.

Example of Jensen's Measure

Here's a hypothetical example to show how Jensen's measure works. Let's assume that a mutual fund's realized return was 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. As such, it is expected to 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 taken over 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 they were taking.

The Bottom Line

Investing comes with both risks and rewards. While you may not be able to guarantee the outcome, several tools can help you along the way like Jensen's measure. This is a performance metric that can help you determine any excess returns for an investment compared to its expected returns while factoring in risk. Keep in mind that this isn't a foolproof method so you should do your due diligence whenever you make any financial decisions.