# CAPM (SML) Problem

I got 1.3636 for beta for the problem below(165/121). But I became so unsure about the answer when I solved (c) because then the market risk becomes larger than the variance of Stock A. Beta^2*σ(M)^2=224.98> σ(A)^2=220

Am I making a mistake? Or if my solution is correct,how do I interpret this result?(all the variance of the Stock AS is all due to the Market?)

*By 165%^2 and 220 %^2, I mean percent-squared. A variance of 165%^2 equals 165/10,000. Thanks.

Suppose that the riskless rate of return is 4% and the expected market return is 12%. The standard deviation of the market return is 11%. Sup- pose as well that the covariance of the return on Stock A with the market return is 165%^2. (a) What is the beta of Stock A? (b) What is the expected return on Stock A? (c) If the variance of the return on Stock A is 220%^2, what percentage of this variance is due to market risk?

• You should use Tex and make the formulas more clear.
– Ric
Oct 7 '14 at 8:06

a) The formula for Beta is:

$$\beta_i=\frac{\sigma_{i,M}^2}{\sigma_M^2}=\frac{0.165^2}{0.11^2}=2.25$$

b) So by the CAPM equation, the expected return for the asset is:

$$E(R_i)=r_f+\beta(R_M-r_f)=0.04+2.25(0.12-0.04)=0.22=22\%$$

c) If the variance of the stock is $0.22^2$, since this variance was multiplied by $\beta=2.25$, we get:

$$1-(0.22^2/2.25)/(0.22^2)=55.55\%$$ of asset variance explained by market variance.

• My book says Beta(j)=σ(j,M)/σ(M)^2 :-(
– Mark
Oct 4 '14 at 14:23
• @Mark yes correct sry, I will edit it. Oct 4 '14 at 14:38
• Thanks emocor. But I'm still bit confused.If Beta(j)=σ(j,M)/σ(M)^2, isn't it 0.0165(=165/10000)/(0.11^2)=1.3636??? (Sorry if you missed it but I added "By 165%^2 and 220 %^2, I mean percent-squared. A variance of 165%^2 equals 165/10,000" to the question.)
– Mark
Oct 4 '14 at 23:53
• @Mark Are you sure your numbers are correct? Please express everything in "normal" numbers to have same basis and doublecheck with your book. Oct 5 '14 at 0:08
• I have been confused with the units, I admit. But, as far as I read the problem; r(f)=0.04, r(M)=0.12, σ(M)=0.11, σ^2(M)=0.0121,σ(A,M)=0.0165 ???
– Mark
Oct 5 '14 at 1:55