Jensen’s measure

Jensen’s measure, also known as Jensen’s alpha or the Jensen index, is a risk-adjusted performance measure used in finance to assess the excess return generated by an investment relative to its expected return based on a specific benchmark. It was developed by Michael Jensen, an economist and finance professor.

Jensen’s measure is calculated by subtracting the risk-free rate of return from the actual return of the investment and subtracting the expected return of the investment based on the Capital Asset Pricing Model (CAPM). The formula for Jensen’s measure is as follows:

Jensen’s Measure = Portfolio Return – (Risk-Free Rate + Beta * (Benchmark Return – Risk-Free Rate))

where:

• Portfolio Return is the actual return of the investment portfolio.
• Risk-Free Rate is the rate of return on a risk-free investment, such as a government bond or Treasury bill, which represents the minimum return expected without taking on any additional risk.
• Beta is a measure of the investment’s sensitivity to systematic risk, as estimated by the CAPM.
• Benchmark Return is the expected return of a specific benchmark, such as a market index, which represents the return expected from a comparable investment with similar systematic risk.

Jensen’s measure helps investors evaluate whether an investment has outperformed or underperformed its expected return based on the CAPM and the specific benchmark. A positive Jensen’s alpha indicates that the investment has generated excess returns beyond what would be expected given its systematic risk, while a negative Jensen’s alpha suggests underperformance.

Jensen’s measure is commonly used in evaluating the performance of actively managed investment portfolios, such as mutual funds or hedge funds. It helps assess the value added by the portfolio manager in generating excess returns after accounting for the systematic risk.