Single-factor and multi-factor models

Unless stated otherwise, round your answers to two decimal points, and do not round intermediate calculations.

Problem 1.

The following are estimates for two stocks.

Stock

Expected Return

Beta

Firm-Specific Standard Deviation

A

10

%

0.95

35

%

B

17

1.50

45

The market index has a standard deviation of 19% and the risk-free rate is 12%.

a) What are the standard deviations of stocks A and B?

b) Suppose we build a portfolio with the following proportion: 0.35 in stock A, 0.35 in stock B, and 0.3 in risk-free T-bills. Compute the expected return, standard deviation, beta, and nonsystematic standard deviation of the portfolio

Problem 2.

Suppose that the index model for stocks A and B is estimated from excess returns with the following results:

and σM = 29%; R-squaredA = 0.29; R-squaredB = 0.14

Assume you create portfolio P with investment proportions of 0.60 in A and 0.40 in B.

a) What is the standard deviation of the portfolio? [Hint: R-squared is the variance explained by the market risk divided by the variance in the stock .]

b) What is the beta of the portfolio?

c) What is the firm-specific variance of the portfolio? (Round to 3 decimals.)

d) What is the covariance between the portfolio and the market index? (Round to 3 decimals.)

Problem 3.

Consider a security of which we expect to pay a constant dividend of $18.49 in perpetuity. Furthermore, its expected rate of return is 20.1%. Using the equation for present value of a perpetuity, we know that the price of the security ought to be , where D is the constant dividend and k is the expected rate of return. Assume that the risk-free rate is 3%, and the market risk premium is 6.4%. What will happen to the market price of the security if its correlation with the market portfolio doubles, while all other variables, including the dividend, remain unchanged?

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