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Corporate Finance Exercise: Correlation and Beta - CAPM

You have been provided the following data about the securities of tree firms, the market portfolio, and risk-free:

Security Expected return Standard deviation Correlation* Beta
Firm A .10 .27 (i) .85
Firm B .14 (ii) .50 1.50
Firm C .17 .70 .35 (iii)
The market portfolio .12 .20 (iv) (v)
The risk-free asset .05 (vi) (vii) (viii)

*With the market portfolio

a) Fill in the missing values in the table. (show workings)

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?

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Solution Preview

(iv) = 1 and (v) = 1. By definition, the correlation of anything with itself is 1, and the market has a beta 1.

(vi) = (vii) = (viii) = 0. The risk free has no risk (hence no std. dev.) and is not correlated with any other assets, including the market.

Next, we recall two forumlae,

Corr(X,Y) = Cov(X,Y)/[std(X)std(Y)], where std denotes the standard deviation and Cov denotes the ...

Solution Summary

Corporate finance: Correlation and Beta - Capital Asset Pricing Model