# Mock -- Beta and RFR?

Okay, I have what may be the stupidest question ever. One that maybe should go on the L-I board…but at the risk of getting summarily ejected from the forum, here goes: On one of the mock questions (#46) they calculate a forecast portfolio value by simply multiplying the portfolio’s beta by the market return. What happened to the risk-free rate? Last I looked that was part of CAPM, right? We’re given the RFR (actually a nice sampling of them) in the fact pattern, but it plays no role in their calculation of portfolio performance. What gives? Have I been looking at this stuff so long that I’ve just gone bonkers. Probably… Ended up getting the Q right by figuring that must be the calc they wanted…but I’m afraid I’m missing something very, very basic here…

Market return already factors in the risk free rate. I think you’re getting confused with the equity risk premium (ERP), to which you then would add the Rf. To get portfolio return you need to adjust it by the beta of portfolio times market return.

But then you saying that expected return = beta x market return How is that consistent with: expected return = RFR + (beta x ERP), given that market return = RFR + ERP?

It is consistent, if I understand you correctly. Beta is needed because the portfolio is not exactly as market. You’re calculating expected portfolio return right?

yes. i certainly understand the concepts of beta, ERP and all that. but i still don’t understand the logic of saying that: forecast equity portfolio return = equity market return x portfolio beta. this certainly doesn’t equate to CAPM on an algebraic basis unless the RFR is assumed to be zero, which it was not in the mock exam problem. so what am i missing?

Ok, I see your point, the math does not add up. I wish I could enlighten you on this one. The formulas seem right though.

The only thing I can add is perhaps they’re not using the CAPM predicted return. But you have a very good question. Technically, I agree that multiplying beta*market return is correct, since we obtain beta by regressing the portfolio return against the market return, not the ERP. So, this math should be fine.

no matter what it’s regressed against, it’s only beta 'cause there’s an alpha first…can’t forget the alpha

Seriously, nobody else found it strange that in two problems on the Mock, expected portfolio return was calc’d as portfolio beta x market return? nobody? what the he!! am i missin’ here?

okay, so it came to me over dinner – beta of portfolio regressed against benchmark and we assume alpha is zero… i guess.

Ok MaxTheDog, it’s you and me, I guess. Yeah, assume alpha is zero. I think it’s a fair assumption over a shorter period though. I don’t know what the period was in the question.

yeah; it was a very short period – 90 days i think. that’s definitely the logic and it makes sense. don’t know why i had such a mental block about it. way, way, way too much time studying this stuff. not even sure why any more. cfa charter does zip for me. just can’t not finish after starting… thanks for working this one through with me. best of luck on sat.

i am puzzled by it too… and how do we supposed to know that we need to assume that alpha is zero if we can calculate ER w/o alpha by using Rf+b(Rm-Rf)?

yeah, i completely don’t get how any of this works into CAPM. but given that i think CAPM is an absolute load of academic nonsense and that i’ve made a nice career simply ignoring it, i’m just going to tuck this away into that “cfa way” file and hope i don’t get tripped up by it on exam day. i tell you, though, i must’ve spent at least 15 minutes on the mock banging my head against the desk trying to fit this into a capm framework. especially since (if i remember correctly) they give you both short-term and long-term risk-free rates in the problem… rrrrgggghhhh…