I am very sorry that I am disturbing you as of this crucial moment. However reading more about the formula of Alpha has confused me to greater lengths than it should have. Hence I wanted a conceptual clarity on the formula of Alpha.

__1.__Now as I understand it we get Alpha as the value by Regressing the following Equation

(rp-rf) =α + β (rb-rf)

Thus solving for the above shouldn't we get

**α = (rp - rf) - β (rb-rf) ...........(1)**

However in various posts, the general formula seems to be as

**α = rp - β (rb)**

**2.**- Further, what does the

**β**in the Equation (1) interpret aside from the fact that it is the slope coefficient ?

- How would it relate to the actual

**β**(ie. the one under CAPM - Systematic factor of Risk) ?

- Next, would the beta in the regression equation 1 have the same value as it would have under CAPM if our benchmark portfolio was the same as Market Portfolio (ie

**β(p,m)=1**) ?

- Also how would the calculation differ if the benchmarked portfolio was not a market portfolio ?

__3.__Also, wrt illustration that you drafted here, (which honestly helped a lot to understand)

(Link: https://www.bionicturtle.com/forum/...n-ratio-formula-garp16-p2-72.1933/#post-45232)

Imagine the riskfree-rate is 1.0% and the benchmark return is 4.0% such that the benchmark's excess return = 3.0%. Now imagine a portfolio with a beta of 0.80 returns 4.60%, such that the portfolio's excess return is 3.60%.

- The active return is the difference in excess returns = 3.60% - 3.00% = +0.60%; or just the difference in returns, 4.60% - 4.00% = +0.60%; i.e.,
activereturn is the portfolio's return relative to the benchmark- The residual return = 3.60% - 3.0%*0.80 = 1.20%, or in this single-factor model, (jensen's) alpha = 4.60% - (3.00%*0.80) - 1.0% Rf = + 1.20%; i.e.,
residualreturn is the portfolio's excess return relative to (beta*benchmark excess return).

- In the above equation what exactly does the beta of 0.80 refer to (ie. Is it the Beta value under regression equation (ie regressed with benchmark), or is it

**β**value under CAPM ie when regressed with market) ?

- Further assuming that the

**β**in the above question corresponds to that under CAPM (ie.

**) , if the benchmark is different from market and has a**

**β(p,m)****or say**

**β(b,m) =1.25****β(b,m) = 0.7.**How would we proceed in the above case ?

I realize that my foundation concepts are very weak, and genuinely apologize for being not able to understand this.

*I've also skimmed through all the articles in this forum which have been tagged as Alpha, however none of them address my points.*

Hence, I would really appreciate if you could help me out on this, as I am unable to move forward on my curriculum without getting a grasp of these concepts.