Thanks @David Harper CFA FRM this is most helpful to understand alpha neutralization. But I am still struggling to understand this statement from Bionic Turtle's note of the same chapter - ".....For instance, if a portfolio's modified alpha has a beta factor of 1.5, then the same value can be brought down to value of 1 by making the Alpha benchmark-neutral. " Is it possible for you provide a numerical example, how by applying the formula active alpha - active beta * benchmark alpha will lead to beta falls to 1?Hi @JesusZ I'm not sure if that's from T9 Grinold (in which case this is maybe helpful https://forum.bionicturtle.com/thre...ha-in-portfolio-construction.23783/post-88532) but you have it in T5. Is it a T5 reference? I will say there is a pattern precedent. If we step down from alpha to CAPM, there is a sense in which we "neutralize" a portfolio's excess return with respect to beta in order to identify its (Jensen's) alpha.
For example, say that while the the riskfree rate = 3.0%, the market's excess return = 5.0%, our portfolio generates an excess return of 8.0% (i.e., 11.0% gross return) with a beta of 1.40. Jensen's alpha = 8.0% - 1.40*5.0% = +1.0%. To rephrase this operation, residual return (aka, alpha) = 8.0% active return - 1.40 beta * 5.0% benchmark return. But we could call the Jensen's alpha a beta-neutralized return because it is an excess return that is neutralized with respect to beta. So, while I don't have the exact context, the pattern in familiar. The difference between mine and yours is, in typical Grinold fashion, yours is breaking down the alpha (aka, residual return) itself into a factor contribution and, perhaps, a pure (skill?) alpha. I don't know why you have in T5, it smacks of Grinold.
So, like I'm just musing here okay? Say the benchmark's alpha = 2.0%, and the active beta = 1.20, while our porfolio's active alpha = 3.0%, then this says the alpha neutral = 3.0% - 2.0%*1.2% = 0.60%. The naïve numerical interpretation is easy: the 3.0% active alpha deconstructs into 2.40% contribution by the benchmark plus 0.60% as "pure" alpha.
That said, I would never write those words myself, for several reasons. For one, "active alpha" is not a term that I myself define precisely; I can think of three attempts to define and one contradiction (in the IR, we typically use either active return or alpha; aka, residual return). So the harder part is interpretation. I hope that's helpful