Stock A has an expected return of 13 percent and a 25 percent volatility. Stock

Question

Stock A has an expected return of 13 percent and a 25 percent volatility. Stock B has an expected return of 9 percent and a 30 percent volatility. An investor can only purchase one of the two stocks.

a. The investor bought stock A. What is her attitude toward risk?

b. The investor bought stock B. What is his attitude toward risk?

c. What is the expected return on stock B that would make a risk-neutral investor buy it?

d. What is the volatility of Stock B that would make a risk-averse investor buy it?

Stock A has an expected return of 8 percent and an 18 percent volatility. Stock B has an expected return of 16 percent and a 30 percent volatility. The correlation coefficient between the returns of stock A and stock B is 0.30.

a. What is the expected return of portfolio P1 with 25 percent of funds in stock A and the balance in stock B?

b. What is the covariance between the returns of stock A and those of stock B?

c. What is the volatility of the portfolio P1?

d. What are the expected return and volatility of the minimum-risk portfolio?

e. Portfolio P2 has an expected return of 14 percent and a 25 percent volatility. Is it an efficient portfolio? Explain. What expected return should portfolio P2 offer to be efficient?

You invest one-third of your wealth in each of three stocks. The expected return and standard deviation of each individual stock is 10 percent and 20 percent respectively. Each stock has a pairwise correlation of 0.50 with the returns of the two other stocks.

a. What is the expected return of the portfolio?

b. What is the risk reduction of investing in the portfolio containing the three stocks relative to investing in only one stock?

Explanation / Answer

As per Utility theory,

U = Er – ½ A * ^2

Where U is the utility function let’s assume it 1 for our calculation purpose

Er is the expected return of the portfolio

A is the measure of the risk tolerance

is the standard deviation of the portfolio

For portfolio A

1 = 0.13 - ½ A * (.25)^2 A = -27.84

For portfolio B

1= 0.09 – ½ A * (.3)^2 A = - 20.22

Investor in stock A is risk averse as measure of risk tolerance is high

b.    The investor bought stock B. What is his attitude toward risk?

Investor in stock B is risk taker as measure of risk tolerance is low

c.    What is the expected return on stock B that would make a risk-neutral investor buy it?

Return on stock B for risk-neutral investor 13/25 = return of B /30

Return on B = 15.6%

d. What is the volatility of Stock B that would make a risk-averse investor buy it?

Volatility of B for risk averse investor 13/25 = 9 / volatility of B

volatility of B = 17.31%

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