Jensen's Measure

Exploration Essay

The Jensen's measure, or Jensen's alpha, is a performance instrument that represents the average return on a portfolio or investment, above or below the average market return. This metric is also commonly referred to as simply alpha. 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 returns make sense for the risk it takes. For example, if two funds both have a 12% return, a good 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. There is a certain formula in order to figure out Jensen’s measure: Alpha = R(i) - (R(f) + B x (R(m) - R(f))). R(i) is the realized return of the portfolio or investment. R(m) is the realized return of the appropriate market index. And R(f) is the risk-free rate of return for the time period. For example, let’s say that a mutual fund had a return of 15% last year but the 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%. Due to a beta of 1.2, the mutual fund is expected to be riskier than the index, and earn more. A positive alpha in this example shows that the mutual fund manager earned more than enough return to justify the risk they 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 they were taking. Some people disagree with Jensen's measure because they believe that any portfolio manager's extra returns come from luck or random chance rather than skill. The value of alpha can range from positive, negative, or zero. ● Positive Alpha: Outperformance ● Negative Alpha: Underperformance ● Zero Alpha: Neutral Performance (Tracks Benchmark) Now, let’s move to another example of calculating Jensen’s Measure, with these numbers: ● Beginning Portfolio Value = $1 million ● Ending Portfolio Value = $1.2 million ● Portfolio Beta = 1.2 ● Risk-Free Rate = 2% ● Expected Market Return = 10% If we divide $1.2 million by $1 million and subtract one, we get 20% for the portfolio return. Next, the portfolio beta was stated as 1.2 while the risk-free rate is 2%, so we have all the necessary inputs. In closing, the estimated alpha for our example scenario is equal to 8.4%