Calculating expected return with beta = 1

[MMonk4392]

Hi, I came across this question in the 2024 GARP materials (P1.T1.C5, question 5.3) and am curious of GARP's logic in these answer choices.

In the CAPM, what is the expected return for a stock with a beta of 1?
A. E(Ri)
B. E(RM) - r
C. r + (E(RM) - r)
D. E(RM)

They indicate that the correct answer is C, which makes sense when you plug Bi=1 into the formula for expected return, E(Ri)= r + Bi(E(RM) - r).

However, once you further simplify the above, wouldn't the risk-free rates cancel each other out to give you E(RM) (choice D)? Additionally, BT materials explain that "by definition the market portfolio has a beta of 1.0", so I would think the implication is that the return for an asset with beta=1 would be the same as that of the market portfolio, i.e. E(RM). I understand why choice C is correct, but am I wrong in thinking that D would also be correct?

 

[Clay Carter]

Hi, I came across this question in the 2024 GARP materials (P1.T1.C5, question 5.3) and am curious of GARP's logic in these answer choices.

In the CAPM, what is the expected return for a stock with a beta of 1?
A. E(Ri)
B. E(RM) - r
C. r + (E(RM) - r)
D. E(RM)

They indicate that the correct answer is C, which makes sense when you plug Bi=1 into the formula for expected return, E(Ri)= r + Bi(E(RM) - r).

However, once you further simplify the above, wouldn't the risk-free rates cancel each other out to give you E(RM) (choice D)? Additionally, BT materials explain that "by definition the market portfolio has a beta of 1.0", so I would think the implication is that the return for an asset with beta=1 would be the same as that of the market portfolio, i.e. E(RM). I understand why choice C is correct, but am I wrong in thinking that D would also be correct?

Hi @MMonk4392 ,

Both C and D are mathematically equivalent. However, I believe the more conceptually accurate answer is D since it represents the simplified and final form of the equation where the expected return E(Ri) equals the expected return of the market portfolio E(RM).

As David has said before, I don't always understand the questions and answers that GARP comes up with, but in instances like this, it is better to attribute the answer to an oversight rather than to some deeper meaning.

I hope this helps,

CC