Term Glossary

Metrics, Models & Concepts

Jensen's Alpha


Jensen's alpha (ex-post alpha) is a difference between realized excess return of an asset and realized excess return of a market index according to the Single Index Model \begin{equation} \alpha_\text{ex-post} = (E(r) - r_{f}) - \beta E(r_{M} - r_f) \end{equation}

\(r\)
asset return
\(E(r)\)
asset expected return
\(r_f\)
risk-free return
\(\beta\)
beta of asset returns
An intraday version of ex-post alpha could be reduced further by setting a risk-free rate equal to zero: \begin{equation} \alpha_\text{ex-post, intraday} = E(r) - \beta E(r_{M}) \end{equation}

Jensen's alpha could be used to determine how a security or portfolio is doing in comparison to the rest of the market. For example, if returns are higher than predicted by SIM, asset is said to have a positive alpha. Positive (negative) alpha represents abnormaly high (low) returns generated by the asset.


Function Reference
portfolio_jensensAlpha, position_jensensAlpha