1. From the information below, compute the average annual return, the variance, standard deviation, and coefficient of variation for each asset.
ASSET ANNUAL RETURNS
A 5%, 10%, 15%, 4%
B 6%, 20%, 2%, 5%, 10%
C 12%, 15%, 17%
D 10%, 10%, 20%, 15%, 8%, 7%
2. Based upon your answers to question 1, which asset appears riskiest based on standard deviation? Based on coefficient of variation?
3. RCMP, Inc. shares rose 10 percent in value last year while the inflation rate was 3.5 percent. What was the real return on the stock? If an investor sold the stock after one year and paid taxes on the investment at a 15 percent tax rate, what is the real after-tax return on the investment?
4. Given her evaluation of current economic conditions, Ima Nutt believes there is a 20 percent probability of recession, a 50 percent chance of continued steady growth, and a 30 percent probability of inflationary growth. For each possibility, Ima has developed an interest rate forecast for long-term Treasury bond interest rates:
ECONOMIC INTEREST RATE
FORECAST FORECAST
Recession 6 percent
Constant growth 9 percent
Inflation 14 percent
a. What is the expected interest rate under Ima's forecast?
b. What is the variance and standard deviation of Ima's interest rate forecast?
c. What is the coefficient of variation of Ima's interest rate forecast?
d. If the current long-term Treasury bond interest rate is 8 percent, should Ima consider purchasing a Treasury bond?
Why or why not?
5. Ima is considering a purchase of Wallnut Company stock. Using the same scenarios and probabilities as in problem 10, she estimates Wallnut's return is -5 percent in a recession, 20 percent in constant growth, and 10 percent in inflation.
a. What is Ima's expected return forecast for Wallnut stock?
b. What is the standard deviation of the forecast?
c. If Wallnut's current price is $20 per share and Wallnut is expected to pay a dividend of $0.80 per share next year, what price does Ima expect Wallnut to sell for in one year?
6. EXCEL Spreadsheets are useful for computing statistics: averages, standard deviation, variance, and correlation are included as built-in functions. Below is recent monthly stock return data for ExxonMobil (XOM) and Microsoft (MSFT). Using a spreadsheet and its functions, compute the average, variance, standard deviation, and correlation between the returns for these stocks. What does the correlation between the returns imply for a portfolio containing both stocks?
MONTH XOM RETURN MSFT RETURN
November 4.6% 10.4%
October 0.1% 13.6%
September 1.9% 10.3%
August 3.3% 13.8%
July 4.4% 9.3%
June 1.6% 5.5%
May 0.7% 2.1%
April 9.4% 23.9%
March 0.1% 7.3%
February 3.2% 3.4%