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?)

Thanks in advance for your help!!

*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?

  • $\begingroup$ You should use Tex and make the formulas more clear. $\endgroup$
    – Richi W
    Oct 7, 2014 at 8:06

1 Answer 1


a) The formula for Beta is:


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


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.

  • $\begingroup$ My book says Beta(j)=σ(j,M)/σ(M)^2 :-( $\endgroup$
    – Mark
    Oct 4, 2014 at 14:23
  • $\begingroup$ @Mark yes correct sry, I will edit it. $\endgroup$
    – emcor
    Oct 4, 2014 at 14:38
  • $\begingroup$ 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.) $\endgroup$
    – Mark
    Oct 4, 2014 at 23:53
  • $\begingroup$ @Mark Are you sure your numbers are correct? Please express everything in "normal" numbers to have same basis and doublecheck with your book. $\endgroup$
    – emcor
    Oct 5, 2014 at 0:08
  • 1
    $\begingroup$ 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 ??? $\endgroup$
    – Mark
    Oct 5, 2014 at 1:55

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