Part A:
1. You purchased a share of stock for $120. One year later you received $1.82 as dividend and sold the share for $136. What was your holding period return?
2. Use the following expectations on Stocks X and Y to answer the following questions:
Bear Market Normal Market Bull Market
Probability 0.2 0.5 0.3
Stock X -20% 18% 50%
Stock Y -15% 20% 10%
a. What are the expected rates of return for Stocks X and Y?
b. What are the standard deviations of returns on Stock X and Y?
c. Assume that of your $10,000 portfolio, you invest $9,000 in Stock X and $1,000 in Stock Y. What is the expected return on your portfolio?
3. Given the CAPM, E[ri] - rf = β[E(rM)-rf], answer the following questions:
a. What does βi measure?
b. What is the value of beta for the market portfolio?
c. What is the value of beta for the risk free asset?
d. What is the value of beta for a portfolio with E[ri] = 18%, if E[rf] = 6% and E[rm] = 14%?
4. Use these data for the following questions:
You manage a risky portfolio with expected rate of return of 18% and standard deviation of 28%. The T-bill rate (lending rate) is 8% and borrowing rate is 10%. Your client's degree of risk aversion is A = 3.5.
a. Draw the CAL (capital allocation line with different borrowing and lending rates) on an expected return-standard deviation diagram.
b. Calculate the Sharpe-Ratio (reward-to-variability ratio) of the risky portfolio assuming you can borrow and lend at the same rate, 8%.
c. What proportion, y, of the total investment should be invested in your fund?
d. What is the expected return and standard deviation of the rate of return on your client's optimized portfolio?
Part B: Essay Questions:
1. List any two assumptions of the capital asset pricing model, and discuss how these assumptions relate to the "real world" investment decision process.
2. Discuss concepts covariance and correlation. How do these concepts differ in terms of calculation and interpretation?