Response to the following problems:
1. Using published sources (for example, The Wall Street Journal, Barron's, Federal Reserve Bulletin), look up the exchange rate for U.S. dollars with Japanese yen for each of the past 10 years (you can use an average for the year or a specific time period each year). Based on these exchange rates, compute and discuss the yearly exchange rate effect on an investment in Japanese stocks by a U.S. investor. Discuss the impact of this exchange rate effect on the risk of Japanese stocks for a U.S. investor.
2. The following information is available concerning the historical risk and return relationships in the U.S. capital markets:
U.S. CAPITAL MARKETS TOTAL ANNUAL RETURNS, 1990-2011
|
Investment Category
|
Arithmetic Mean
|
Geometric Mean
|
Standard Deviationof Return'
|
|
Common stocks
|
10.28%
|
8.81%
|
16.9%
|
|
Treasury bills
|
3.54
|
3.49
|
3.2
|
|
Long-term government bonds
|
5.10
|
4.91
|
6.4
|
|
Long-term corporate bonds
|
5.95
|
5.65
|
9.6
|
|
Real estate
|
9.49
|
9.44
|
4.5
|
Based on arithmetic mean.
a. Explain why the geometric and arithmetic mean returns are not equal and whether one or the other may be more useful for investment decision making.
b. For the time period indicated, rank these investments on a relative basis using the coefficient of variation from most to least desirable. Explain your rationale.
c. Assume the arithmetic mean returns in these series are normally distributed. Calculate the range of returns that an investor would have expected to achieve 95 percent of the time from holding common stocks.
3. You are given the following long-run annual rates of return for alternative investment instruments:
U.S. Government T-bills 3.50%
Large-cap common stock 11.75
Long-term corporate bonds 5.50
Long-term government bonds 4.90
Small-capitalization common stock 13.10
The annual rate of inflation during this period was 3 percent. Compute the real rate of return on these investment alternatives.
4.The following are the monthly rates of return for Madison Cookies and for Sophie Electric during a six-month period.
|
Month
|
Madison Cookies
|
Sophie Electric
|
|
1
|
-0.04
|
0.07
|
|
2
|
0.06
|
-0.02
|
|
3
|
-0.07
|
-0.10
|
|
4
|
0.12
|
0.15
|
|
5
|
-0.02
|
-0.06
|
|
6
|
0.05
|
0.02
|
Compute the following.
a. Average monthly rate of return for each stock
b. Standard deviation of returns for each stock
c. Covariance between the rates of return
d. The correlation coefficient between the rates of return
• What level of correlation did you expect?
• How did your expectations compare with the computed correlation?
• Would these two stocks be good choices for diversification? Why or why not?
5.The following are monthly percentage price changes for four market indexes.
|
Month
|
DJIA
|
S&P 500
|
Russell 2000
|
Nikkei
|
|
I
|
0.03
|
0.02
|
0.04
|
0.04
|
|
2
|
0.07
|
0.06
|
0.10
|
-0.02
|
|
3
|
-0.02
|
-0.01
|
-0.04
|
0.07
|
|
4
|
0.01
|
0.03
|
0.03
|
0.02
|
|
5
|
0.05
|
0.04
|
0.11
|
0.02
|
|
6
|
-0.06
|
-0.04
|
-0.08
|
0.06
|
Compute the following.
a. Average monthly rate of return for each index
b. Standard deviation for each index
c. Covariance between the rates of return for the following indexes: DJIA-S&P 500 S&P 500-Russell 2000 S&P 500-Nikkei Russell 2000-Nikkei
d. The correlation coefficients for the same four combinations
e. Using the answers from parts (a), (b), and (d), calculate the expected return and standard deviation of a portfolio consisting of equal parts of (1) the S&P and the Russell 2000 and (2) the S&P and the Nikkei. Discuss the two portfolios.
6. The standard deviation of Shamrock Corp. stock is 19 percent. The standard deviation of Cara Co. stock is 14 percent. The covariance between these two stocks is 100. What is the correlation between Shamrock and Cara stock?