Back in CFA Level I, we learned the formula for Jensen’s Alpha which is as follows:
Alpha = Rp - [Rf + Beta of Portfolio * (Rm - Rf)]
where
- Rp = Portfolio Return
- Rf = Risk-Free Rate
- Rm = Market Benchmark Return
However, the CFA II reading appears to give a different formula for alpha.
Alpha = Rp - Beta of Portfolio * Rm
My questions are as follow:
- Are the above alpha formulas synonymous? If so, please show me a mathematical proof.
- If they’re indeed different, are the two alpha formulas designed with different purposes in mind? In other words, which one should we use in which scenario?
Any insight you may have would be much appreciated. Thanks!
Where in the Level 2 curricullum did you see that formula?
From what i remember alpha Rp - Rm…
I don’t have the CFA books under my eyes, but this link might help you
https://en.wikipedia.org/wiki/Jensen's_alpha#Calculation
In fact, the first formula is
Jensen’s alpha = Portfolio Return − [Risk Free Rate + Portfolio Beta * (Market Return − Risk Free Rate)]
with, by implicit definition of CFA level 1,
_ Portfolio Return = _ Rp
_ Market Return = _ Rm
The second formula may be
_ Jensen’s alpha = NewPortfolio Return - Portfolio Beta * NewMarket Return _
with, by implicit definition of CFA level 2,
_ NewPortfolio Return = Portfolio Return − Risk Free Rate = _ Rp
_ NewMarket Return = Market Return − Risk Free Rate = _ Rm
Ah perfect, thanks pivpomars! I felt like the reference to the alpha formula in CFA II reading (Portfolio Management section) was somewhat misguiding. Good to know. 