Editing Jensen's alpha (section)

==Calculation==

:<math>\overset\text{Jensen's alpha}{\alpha_J} = \overset\text{portfolio return}{R_i} - [\overset\text{risk free rate}{R_f} + \overset\text{portfolio beta}{\beta_{iM}} \cdot (\overset\text{market return}{R_M} - \overset\text{risk free rate}{R_f})]</math>

In the context of CAPM, calculating alpha requires the following inputs:
* <math>R_i</math>: the [[market portfolio|realized return]] (on the portfolio),
* <math>R_M</math>: the [[market portfolio|market return]],
* <math>R_f</math>: the [[risk-free rate]] of return, and
* <math>\beta_{iM}</math>: the [[Beta coefficient|beta]] of the portfolio.

An additional way of understanding the definition can be obtained by rewriting it as:

:<math>\alpha_J = (R_i - R_f) - \beta_{iM} \cdot (R_M - R_f)</math>

If we define the excess return of the fund (market) over the risk free return as <math>\Delta_R \equiv (R_i - R_f) </math> and <math> \Delta_M \equiv (R_M - R_f)</math> then Jensen's alpha can be expressed as:

:<math>\alpha_J = \Delta_R - \beta_{iM} \Delta_M </math>