a. Fill in the missing values in the table. b. Is the stock of Firm A correctly
ID: 2665094 • Letter: A
Question
a. Fill in the missing values in the table. b. Is the stock of Firm A correctly priced according to the capital-asset-pricing model (CAPM)? What about the stock of Firm B? Firm C? If these securities are not correctly priced, what is your investment recommendation for someone with a well-diversified portfolio?You have been provided the following data on the securities of three firms, the market portfolio, and the risk-free asset:
Security Expected Return Standard Deviation Correlation Beta
Firm A 0.13 0.12 ? 0.9
Firm B 0.16 ? 0.4 1.1
Firm C 0.25 0.24 0.75 ?
The market portfolio (S&P500) 0.15 0.1 ? ?
The risk-free asset (U.S. T-Bill) 0.05 ? ? ?
a. Fill in the missing values in the table.
b. Is the stock of Firm A correctly priced according to the capital-asset-pricing model (CAPM)? What about the stock of Firm B? Firm C? If these securities are not correctly priced, what is your investment recommendation for someone with a well-diversified portfolio?
Explanation / Answer
a. Let bi = the beta of Security i
si = the standard deviation of Security i
sm = the standard deviation of the market
ri,m = the correlation between returns on Security i and the market
(i) bi = (ri,m)(si) / sm
0.9 = (ri,m)(0.12) / 0.10
ri,m = 0.75
(ii) bi = (ri,m)(si) / sm
1.1 = (0.4)(si) / 0.10
si = 0.275
(iii) bi = (ri,m)(si) / sm
= (0.75)(0.24) / 0.10
= 1.8
(iv) The market has a correlation of 1 with itself.
(v) The beta of the market is 1.
(vi) The risk-free asset has 0 standard deviation.
(vii) The risk-free asset has 0 correlation with the market portfolio.
(viii) The beta of the risk-free asset is 0.
b. According to the Capital Asset Pricing Model:
E(r) = rf + b[E(rm) – rf]
where E(r) = the expected return on the stock
rf = the risk-free rate
b = the stock’s beta
E(rm) = the expected return on the market portfolio
Firm A
rf = 0.05
b = 0.9
E(rm) = 0.15
E(r) = rf + b[E(rm) – rf]
= 0.05 + 0.9(0.15 – 0.05)
= 0.14
According to the CAPM, the expected return on Firm A’s stock should be 14%. However, the expected return on Firm A’s stock given in the table is only13%. Therefore, Firm A’s stock is overpriced, and you should sell it.
Firm B
rf = 0.05
b = 1.1
E(rm) = 0.15
E(r) = rf + b[E(rm) – rf]
= 0.05 + 1.1(0.15 – 0.05)
= 0.16
According to the CAPM, the expected return on Firm B’s stock should be 16%. The expected return on Firm B’s stock given in the table is also 16%. Therefore, Firm A’s stock is correctly priced.
Firm C
rf = 0.05
b = 1.8
E(rm) = 0.15
E(r) = rf + b[E(rm) – rf]
= 0.05 + 1.8(0.15 – 0.05)
= 0.23
According to the CAPM, the expected return on Firm C’s stock should be 23%. However, the expected return on Firm C’s stock given in the table is 25%. Therefore, Firm A’s stock is underpriced, and you should buy it.
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