# Jensen’s Alpha

Jensen’s Alpha, also known as the Jensen’s Performance Index, is a measure of the excess returns earned by the portfolio compared to returns suggested by the CAPM model. It represents by the symbol α.

The value of the excess return may be positive, negative, or zero. The CAPM model itself provides risk-adjusted returns, i.e., it takes into account the risk of the security. So, if the security is fairly priced, its actual returns will be same as CAPM. The Alpha in this case will be 0. If, however, the security earns even more than the risk-adjusted returns, it will have a positive Alpha. Negative alpha indicates that the portfolio has not earned its required return. A higher Alpha is always desirable by portfolio managers.

Jensen’s alpha focuses only on non-diversifiable, relevant risk by using beta and CAPM. It assumes that the portfolio has been adequately diversified.

The Jensen’s Alpha can be calculated using the following formula:

$\alpha =R_{P}-\left ( R_{f}+\beta \left ( R_{M} -R_{f}\right ) \right )$

Where:

- R
_{p}= Returns of the Portfolio - R
_{f}= Risk-free rate - β = Stock’s beta
- R
_{m}= Market return

Jensen’s alphas are reported in a percentage format, indicating the percentage by which the portfolio over-or-under-performed the market on a risk-adjusted basis.

Let’s take the example of XYZ stock. If the daily return based on CAPM is 0.15% and the actual stock return is 0.20%, then Jensen’s alpha is 0.05%, which is a good indicator.

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