Homework AD 717 Week 4
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Homework AD 717
Week 4 – 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 |
|||||
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:
RA = 3.00% + 1.05RM + eA
RB = -1.20% + 1.20RM + eB
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?
2023-02-22