Ex post alpha

M

mwvt9

New member
Joined
Jun 18, 2026
Messages
0
Reaction score
0
I know this is easy stuff, but….
Why is a simple regression needed to calculate ex post alpha? Is it just to get the ex post beta coefficient that leads to expected returns over the period (which can then be compared to actual returns)?
 
I’m guessing here, but perhaps in an ex post setting the model is respecified including betas to account for the effect that parameters do shift over time.
 
Actually, when I first read the post, I thought, “That is interesting, I’m not sure what the answer is, maybe if I wait mwvt9 will answer it.” Then I looked at the author and immediately lost hope.
 
Ex post alpha = Actual Portfolio return - (Rf +B(Rm-Rf))
Does that help?
 
Black Swan Wrote:
——————————————————-
> I’m guessing here, but perhaps in an ex post
> setting the model is respecified including betas
> to account for the effect that parameters do shift
> over time.
This is my thinking too. Since you are comparing your account from T0–>T10 you want the actual beta from T0–>T10 so you do an ex post regression to get it, comparing stock or portfolio returns to the return on the market over the time period.
Then compare the actual return to the output of the ex post SML (line from Rf to M portfolio).
 
hh Wrote:
——————————————————-
> Ex post alpha = Actual Portfolio return - (Rf
> +B(Rm-Rf))
>
> Does that help?
I get the formula hh, I was looking for confirmation as to why a regression had to be run, but I think I get it.
To get the term on the right side of your portfolio you have to know the actual beta for the performance period you are measuring. So you don’t use the expected beta, but the actual (the output from the regression).
Then you compare using your formula to see if you did any good.
I think…..
 
Yeah, that’s what I figure. Essentially ex ante you’re using a model you specified over a historical time period in an out of sample setting. Then ex post you would be regress and respecify the model on the actuals to achieve an in sample model.
 
besides that the formula is using actual return which is post, so beta would have to be post as well
the problem here is that you are comparing Actual return to Return required by actual risk , but actual risk does not represent the ante risk when the decision was made. ( use ex post risk as ex ante proxy) In this way you could have positive alpha but adjusted to ante risk, no alpha.
 
mwvt9 Wrote:
——————————————————-
> I know this is easy stuff, but….
>
> Why is a simple regression needed to calculate ex
> post alpha? Is it just to get the ex post beta
> coefficient that leads to expected returns over
> the period (which can then be compared to actual
> returns)?
How else would you do it? Returns for a portfolio come from three sources
1) Time value of money (that’s the RFR)
2) The return expected because of embedded market risk (that’s Beta*MRP)
3) The return that comes from other non-market factors (that’s alpha, unless your model has other risk factors that are expected to yield returns)
So something like CAPM is really just an expression of the build-up model for returns:
E(R) = RFR + Return for market risk + alpha
When you do a regression, you will get an equation:
E(R) = Beta*(market return) + Intercept
But Intercept <> Alpha. That’s because CAPM says
E(R) = Beta* (Market Return - RFR) + RFR + Alpha
Rearranging, you realize that
E(R) = Beta * (Market Return) - Beta*RFR + RFR + Alpha
and
Intercept = RFR - Beta*RFR + Alpha
or…
Alpha = Intercept - RFR * (1 - Beta)
—-
Now, if you compute market returns as (MktRet - RFR), then you can just interpret the intercept as (alpha + RFR)
 
Bchad, I think the question was why run another regression rather than using the same beta you had for expected returns. We then figured you had to run the regression to respecify actual beta for that time period rather than historic beta or whatever you had used in your forecast.
 
You must log in or register to reply here.
Back
Top