## Term Glossary

### 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 $$\alpha_\text{ex-post} = (E(r) - r_{f}) - \beta E(r_{M} - r_f)$$

$r$
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: $$\alpha_\text{ex-post, intraday} = E(r) - \beta E(r_{M})$$

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