Jensen's alpha calculator



The expected return of portfolio P %

The risk-free rate %

The Beta

The expected return of Market portfolio %

Jensen's alpha calculator helps calculating the Jensen's alpha.

What is Jensen's alpha?

The Jensen's alpha was developed by Michael Jensen in 1968.

The Jensen's alpha, also known as Jensen's Performance Index or ex-post alpha, is used to determine the abnormal return of a security or portfolio of securities over the theoretical expected return. It is a version of the standard alpha based on a theoretical performance index instead of a market index.

The Formula of Jensen's alpha

Jensen's alpha (α₀) = E(r_p) - [ r_f + β_p × ( E(r_M) - r_f ) ]

where:

E(R_p) is an expected return of portfolio p

r_f is a risk-free rate

β_p is a nondiversifiable or systematic risk of portfolio p

E(R_M) is an expected Market's portfolio return

Interperating Jensen's alpha

This is based on the concept that riskier assets should have higher expected returns than less risky assets. If an asset's return is even higher than the risk adjusted return, that asset is said to have "positive alpha" or "abnormal returns". Investors are constantly seeking investments that have higher alpha.

Example of Jensen's alpha

For example: if the expected return of portfolio P equals to 20.00%, the risk-free rate equals to 4.00% and the Beta equals to 0.50,

The Treynor Ratio equals to 32.00%:

20 - 4

0.5