How is the Jensen's alpha calculated?

Jensen's alpha is a measure used in finance to assess the performance of an investment portfolio or a specific security. It helps determine whether the investment has outperformed or underperformed the market.

To calculate Jensen's alpha, the following steps are involved:

1. Determine the expected return of the investment or portfolio. This can be done by using a suitable benchmark, such as a market index like the S&P 500. The expected return is the return that would be anticipated based on the risk and return characteristics of the investment.

2. Calculate the actual return of the investment or portfolio over a specific period. This can be done by subtracting the initial value from the final value and dividing it by the initial value.

3. Calculate the expected return of a risk-free investment, such as a government bond, over the same period. This represents the return that could have been earned without taking any risk.

4. Calculate the beta of the investment or portfolio. Beta measures the sensitivity of the investment's returns to the overall market returns. It can be calculated by regressing the historical returns of the investment against the returns of the benchmark.

5. Use the Capital Asset Pricing Model (CAPM) to calculate the expected return of the investment or portfolio based on its beta. CAPM is a widely used model that relates the expected return of an investment to its beta and the expected return of the market.

6. Finally, Jensen's alpha is calculated by subtracting the risk-free rate of return from the actual return of the investment or portfolio, and then subtracting the expected return based on CAPM. The formula for Jensen's alpha is:

Jensen's alpha = Actual Return - (Risk-Free Rate + Beta * (Expected Market Return - Risk-Free Rate))

A positive Jensen's alpha indicates that the investment or portfolio has outperformed the market, while a negative alpha suggests underperformance. It is important to note that Jensen's alpha is just one measure of performance and should be used in conjunction with other metrics to assess the overall risk and return characteristics of an investment.