question about CAPM

[JamesVU2000]

why is correlation included to solve the problem? I cant see anything in the notes when we multiply the two terms x correlation?

Beta (i,M) = covariance(i, M)/variance(M) = 24%*15%*0.70/15%^2 = 1.12 <<- must know all of these steps! CAPM: E[R(i)] = Rf + Beta (i,M)*[R(M) - Rf] = 3% + 1.12*(8%-3%) = 8.60% PV (annual compounding) = $100/(1.086) + $100/(1.086)^2 = $176.87
thanks james

 

[David Harper CFA FRM]

HI @JamesVU2000 You've not sourced this so I don't have the context (@Nicole Seaman can you please move this thread once we know to what it refers?).

A fundamental, essential identity is that covariance(x,y) = correlation(x,y) * StandardDeviation(x) * StandardDeviation(y) such that "correlation is a standardized version of the covariance" per correlation(x,y) = covariance(x,y)/[StandardDeviation(x) * StandardDeviation(y)]. In the CAPM, β(i,M) = covariance(i, M)/σ^2(M) which, because covariance(i, M) = ρ(i, M)*σ(i)*σ(M), equivalently means that β(i,M) = [ρ(i, M)*σ(i)*σ(M)]/σ^2(M) = ρ(i, M)*σ(i)/σ(M). Because β(i,M) = ρ(i, M)*σ(i)/σ(M) we say "beta is correlation multiplied by (aka, scaled by) cross-volatility." Thanks,

 

[JamesVU2000]

David- its from the study note from Elton

 

[David Harper CFA FRM]

@JamesVU2000 Thank you. CAPM is found in three places in P1.T1 (Elton, Amenc, and Bodie) so it wasn't obvious to me. Each morning, Nicole and I hustle to answer questions, many of which can be moved to prior discussions (because most do not use search, as much as we try), so it saves us time if we have a direct reference. I typically do not have time to sift thru our notes to look for the match! Thanks,

 

[JamesVU2000]

I will put a specific reference from now on, David.

 

[JamesVU2000]

This is from the study notes from Elton
Apply the CAPM in calculating the expected return on an asset. Assume that the following assets are correctly priced according to the security market line. Derive the security market line. What is the expected return on an asset with a Beta of 2.0 (Elton Question 13.1)? = 6%, = 0.5, = 12%, = 1.5 Answer: 12% = + 1.5 6% = + 0.5 6% = ⇒ = 3% and the implied CAPM model is given by = % + × %. So that = 2.0, = 3% + 6%(2) = 15%

What does the MRP mean and what is R1 and R2? I cant see anything in the notes that helps me understand the problem. thanks!


I dont understand what the

 

[David Harper CFA FRM]

@JamesVU2000 R(1) and R(2) are returns, ERP = equity risk premium. Please see https://forum.bionicturtle.com/threads/using-capm-to-calculate-expected-return.10193/post-48122 i.e.,

Hi @omar72787 Given (Rm-Rf) = 6%, we can plug that back into 6% = Rf + .5*(Rm-Rf):
Rf + .5*(Rm-Rf), but we know Rm-Rf = 6% so that
6% = Rf + .5*6% -->
6% = Rf + 3% -->
Rf = 6% - 3%.

This is solving for two variables with two equations, so there is more than one way to approach it. For example, if we wanted to solve for Rf first (instead of the equity risk premium first), we could do this be seeking to eliminate (Rm_Rf) in a subtraction. Noticing that the second .5(Rm-Rf) is one-third the first 1.5(Rm-Rf), would could triple it as follows:

• 12% = Rf + 1.5(Rm-Rf)
• [6% = Rf + .5(Rm-Rf)]*3; i.e., multiply both sides by three with the goal of equalizing the (Rm-Rf).

which gives us:

• 12% = Rf + 1.5(Rm-Rf)
• 18% = 3*Rf + 1.5(Rm-Rf)

swap them so the second is first and vice versa

• 18% = 3*Rf + 1.5(Rm-Rf)
• 12% = Rf + 1.5(Rm-Rf)

and then subtract the second from the first:

• 18% = 3*Rf + 1.5(Rm-Rf)
• -[12% = Rf + 1.5(Rm-Rf)]
• 6% = 2*Rf; so now we can see Rf = 3%, which then can be used to solve (Rm-Rf). I hope that help!

 

[JamesVU2000]

Thanks David