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Stock 1: E(R) = 10%, SD = 10% ; Stock 2: E(R) = 20%, SD = 30% ; The correlation between Stock 1 & 2 = 0.5. The risk-free return of 5% is avaliable in T-bills.

A investor invested all of his $10,000 net worth in Stock 1.

(a) Is there any portfolio that can be formed with Stock 1, 2 and risk-free security that can make the investor better off? What is it? Assume that no short-selling of stocks is allowed. And also explain why the portfolio is better than investing Stock 1 alone.

(b) Based on the answer in (a), The investor is advised to invest in that portfolio but he asks if the investment in this portfolio can be guaranteed and will not regret with the portfolio one year from now. Can the advisor assure the investor that there will be no regrets and it is guaranteed? Why or why not? Explain in words.

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Deanna Hettinger
Deanna HettingerLv2
28 Sep 2019

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Consider Ford stock (F) with a current price of $20 per share and a standard deviation of returns of 15%.

General Motors (GM) stock has an expected return of 12% and a standard deviation of returns of 16%.

a) An investor expects to sell Ford stock in one year at $21 per share and expects the firm to pay a dividend of $1 per share at the end of the year. What is the expected total return and what is the dividend yield?

b) An investor holds a portfolio of F and GM with 80% of the portfolio in Ford. What is the standard deviation of this portfolio if Ford and GM have a correlation of -1?

c) Given the correlation of Ford and GM stock, can an investor construct a zero variance portfolio? If so, what are the weights on F and GM in this portfolio? If not, explain why?

d) Given your answer in c), what is the risk-free rate? Why?

1. Here are some characteristics of two securities:

Security 1 E(R1) = .10 σ 2 1 = .0025

Security 2 E(R2) = .16 σ 2 2 = .0064

Answer the following questions:

(a) Suppose the investor can only hold a single stock.

(i) Which security should she choose if she wants to maximize expected returns only?

(ii) Which security should she choose if she wants to minimize risk only?

(b) Suppose the correlation of returns is -1.0, what fraction of the investor’s net worth should be held in security 1 and in security 2 in order to produce a zero risk portfolio?

(c) What is the expected return on the portfolio in (c)? How does this compare with the riskless return on Treasury Bills of 10%? Would an investor who is risk averse and likes high expected return want to invest in Treasury Bills?

Stock X and Stock Z both have an expected return of 10%. The standard deviation of the expected return is 8% for Stock X, and 12% for Stock Z. Assume that these are the only two stocks available in a hypothetical world.

A. Assume that the correlation between the returns of the two stocks is +1.

• What is the expected return and standard deviation of a portfolio containing 50% X and 50% Z?

• What is the optimal amount of Stock Z for an investor to hold in a portfolio (if the correlation is +1)?

B. Assume that the correlation between the returns of the two stocks is +0.1.

• What is the expected return and standard deviation of a portfolio containing 50% X and 50% Z?

• What is the optimal amount of Stock Z for an investor to hold in a portfolio (if the correlation is +0.1)?

C. Assume that the correlation between the returns of the two stocks is –1.

• What is the expected return and standard deviation of a portfolio containing 50% X and 50% Z?

• What is the optimal amount of Stock Z for an investor to hold in a portfolio (if the correlation is –1)?

D. If the Capital Asset Pricing Model is true, explain why it is possible for the two stocks to have the same expected return even though the standard deviation of the expected return is 8% for Stock X, and 12% for Stock Z. (What must be true about the types of risks facing the two companies for the given numbers to make sense?).

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