In a previous post I introduced two forms of the differential return equation that are included in the CIPM curriculum at the Principles Level:
- differential return using standard deviation
- differential return using beta
If it seems that the differential return formula is just another confusing formula to memorize, it may help to recognize that the formula for differential return using beta is equivalent to the formula for Jensen’s alpha (also known as regression alpha, or Jensen’s performance measure).
Recall the equation for differential return using beta:
But, recall hat the beta of the market is 1.0, thus, we can simplify:
And now, a simple algebraic rearranging of terms gives us the ex-post form of the Jensen’s alpha equation:
Thus, if you know the formula for Jensen’s alpha, then you know the formula for differential return (using beta)! One less formula to memorize!