CHAPTER 6: PROBLEM SOLVING

Problem 1 (15 points)Suppose you have invested in three stocks: A, B and C. You expect that returns on the stocks depend on the following two states of the economy, with the probabilities to happen given below.

State ofEconomy

Probability ofState Occurrence

Return onstock A

Return onstock B

Return onstock C

Boom 0.70 7% 15% 33%Bust 0.30 3% 3% -6%

a. (5 points) What is the expected return of an equally weighted portfolio of these three stocks?

b. (5 points) What is the expected return of a portfolio invested 20 percent each in A and B, and 60 percent in C?

c. (5 points) What is the standard deviation of a portfolio invested 20 percent each in A and B, and 60 percent in C?

Problem 2 (15 points)Based on the following information, calculate the expected return and standard deviation of each of the following stock. Assume each state of the economy is equally likely to happen. What are the covariance and correlation between the returns of the two stocks?

State of Economy Rate of Return on stock A Rate of Return on stock BBear 6.3% -3.7%Normal 10.5% 6.4%Bull 15.6% 25.3%

a. (5 points) What is the expected return on stock A and stock B? b. (5 points) What is the variance and standard deviation for stock A and stock B?c. (5 points) What are the covariance and correlation between the returns of the two

stocks?

Problem 3 (15 points)Based on the following information calculate the expected return and the standard deviation for the two stocks.

State ofEconomy

Probability ofState of Economy

Rate of Return on stock A

Rate of Return on stock B

Recession 0.10 6% -20%Normal 0.60 7% 13%Boom 0.30 11% 33%

a. (5 points) What is the expected return on stock A and stock B? b. (5 points) What is the variance and standard deviation for stock A and stock B?c. (5 points) What is of the standard deviation of an equally weighted portfolio of these

two stocks if the correlation is 0.2?

Problem 4 (15 points)Consider the possible rates of return that you might obtain over the next year. You can invest in stock U or stock V.

State ofEconomy

Probability ofState of Economy

Rate of Return on stock U

Rate of Return on stock V

Recession 0.20 7.0% -5.00%Normal 0.50 7.0% 10.0%Boom 0.30 7.0% 25.0%

a. (5 points) Determine the expected return, variance, and the standard deviation for stock U and V.

b. (5 points) Determine the covariance and correlation between the returns of stock U and stock V.

c. (5 points) Determine the expected return and standard deviation of an equally weighted portfolio of stock U and stock V.

Problem 5 (10 points)Security A has an expected return of 8 percent with a standard deviation of 1.5 percent. Security B has an expected return of 12 percent with a standard deviation of 2.4 percent. The two securities have a correlation coefficient of 0.20. If you invest 40 percent of your funds in Security A and 60 percent in Security B, calculate the expected return and standard deviation of the portfolio. (Note: change the calculator to 6 decimals)