1. During the past five years, you owned two stocks that had the following annual rates of return:
Year Stock T Stock B
1 0.19 0.08
2 0.08 0.03
3 -0.12 -0.09
4 -0.03 0.02
5 0.15 0.04
a. Compute the arithmetic mean annual rate of return for each stock. Which stock is most desirable by this measure?
b. Compute the standard deviation of the annual rate of return for each stock. (Use Chapter 1 Appendix if necessary.) By this measure, which is the preferable stock?
c. Compute the coefficient of variation for each stock. (Use Chapter 1 Appendix if necessary.) By this relative measure of risk, which is preferable?
d. Compute the geometric mean rate of return for each stock. Discuss the difference between the arithmetic mean return and the geometric mean return for each stock. Discuss the differences in the mean returns relative to the standard deviation of the return for each stock.
2. A stockbroker calls you and suggests that you invest in the Lauren Computer Company. After analyzing the firm's annual report and other material, you believe that the distribution of the expected rates of return is as follows:
Lauren Computer CO.
Possible Rate of return Probability
-0.60 0.05
-0.30 0.20
-0.10 0.10
0.20 0.30
0.40 0.20
0.80 0.15
Compute the expected return [E (Ri)] on your investment on Lauren Computer stock.
3. During the past year, you had a portfolio that contained U.S. government T-bills, long-term government bonds, and common stocks. The rates of return on each of them were as follows:
U.S. government T-bills 5.50%U.S. government long-term bonds 7.50
U.S. government stocks 11.60
4. Assume that the consensus required rate of return on common stocks is 14 percent. In addition, you read in Fortune that the expected rate of inflation is 5 percent and the estimated long-term real growth rate of the economy is 3 percent. What interest rate you expect on U.S. government T-bills? What is the approximate risk premium for common stocks implied by these date?
5. Someone in the 36 percent tax bracket can earn 9 percent annually on her investments in a tax-exempt IRA account. What will be the value of a one-time $10,000 investment in 5 years? 10 years? 20 years? Suppose the preceding 9 percent return is taxable rather than tax-deferred and the taxes are paid annually. What will be the after-tax value of her $10,000 investment after 5, 10, and 20 years?
6. Someone in the 15 percent tax bracket can earn 10 percent annually on his investments in a tax-exempt IRA account. What will be the value of a one-time $10,000 investment in 5 years? 10 years? 20 years? Suppose the preceding 10 percent return is taxable rather than tax-deferred. What will be the value of a $10,000 investment after 5 years? 10 years? 20 years?
7. Assume that the rate of inflation during all these periods was 3 percent a year. Compute the real value of the two tax-deferred portfolios in problems 5 and 6.
8. You decide to sell short 100 shares of Charlotte Horse Farms when it is selling at its yearly high of $56. Your broker tells you that your margin requirement is 45 percent and that the commission on the purchase is $155. While you are short the stock, Charlotte pays $2.50 per share dividend. At the end of one year, you buy 100 shares of Charlotte at $45 to close out your position and are charged a commission of $145 and 8 percent interest on the money borrowed. What is your rate of return on the investment?
9. You own 200 shares of Shamrock Enterprises that you brought at $25 a share. The stock is now selling for $45 a share. You put in a stop loss order at $40. Discuss your reasoning for this action. If the stock eventually declines in price to $30 a share, what would be your rate of return with and without the stop loss order?
10. Two years ago, you bought 300 shares of Kayleigh Milk Co. for $30 a share with a margin of 60 percent. Currently, the Kayleigh stock is selling for $45 a share. Assuming no dividends and ignoring commissions, compute (a) the annualized rate of return on this investment if you paid cash, and (b) your rate of return with the margin purchase.
11. The stock of the Madison Travel Co. is selling for $28 a share. You put in a limit buy order at $24 for one month. During the month the stock declines to $20, then jumps to $36. Ignoring commissions, what would have been your rate of return on this investment? What would be your rate of return if you had put in a market order? What if your limit order was at $18?
12. Compute the abnormal rates of return for the following stocks during period t (ignore differential systemic risk):
Stock Return for stock iReturn for the aggregated market
B 11.5% 4.0%
F 10.0 8.5
T 14.0 9.6
C 12.0 15.3
E 15.9 12.4
13. Compute the abnormal rates of return for the five stocks in problem 12 assuming he following systemic risk measure (beta):
Stock Beta
B 0.95
F 1.25
T 1.45
C 0.70
E -0.30
14. Compare the abnormal returns in Problems 12 and 13 and discuss the reason for the difference in each case.
15. Look up the daily trading volume for the following stocks during a recent five-day period:
- MerckCaterpillarIntelMcDonald'sGeneral Electric
Randomly select five stocks from NYSE, and examine their daily trading volume for the same five days. (a) What are the average volumes for the two samples? (b) Would you expect this difference to have an impact on the efficiency of the markets for the two samples? Why or why not?
16. Using published sources (for example, the Wall Street Journal, Federal Reserve Bulletin), look up the exchange rates 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.
17. 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 Deviation of returnª
Common stock 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
ªBased on arithmetic mean.
(a)Explain why the Geometric mean and arithmetic mean 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 the most to least desirable, Explain. (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.
18. 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 return of inflation during this period was 3 percent. Compute the real rate of return on these investment alternatives.
19. 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 for diversification? Why or why not?
20. The following are monthly percentage price changes for four market indexes.
Month DJIA S&P Russell 2000 Nikkei
1 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.
21. The standard deviation of Shamrock Corp stock is 19 percent. The standard deviation Cara Co stock is 14 percent. The covariance between these two stocks is 100. What is the correlation between Shamrock and Cara stock?
Discussion
I. Predict the performance of the DOW for the next two years. Provide support for your prediction.
II. Given your predictions, recommend whether or not a risk-adverse person should invest in the DOW index fund. Explain your rationale.
III. Analyze the factors that influence investment decisions at different stages in an investor's life cycle, and make a recommendation at which stage the average investor should consider financial investments. Provide support for your recommendation.
IV. Assess how cultural differences in foreign countries impact investor asset allocations.
V. Analyze how national exchanges around the world are linked and suggest which exchange most significantly impacts the U.S. markets. Explain your rationale.
VI. Assess the factor(s) contributing to the global consolidation of stock, bonds, and derivative exchange. Predict the impact to these exchanges in the future.
VII. Analyze the most significant driver in an efficient market and whether or not you would characterize the U.S. markets as efficient. Provide support for your position.
VIII. Discuss how behavioral finance concepts, such as bias, may impact investor decisions and the efficiency of financial markets.
IX. Construct an argument for the average investor to consider diversifying into international markets.
X. Based on international market performance, predict which foreign market will yield the highest return to investors over the next year. Provide support for your prediction.
XI. Assess the factors that contribute to someone being risk adverse and how risk aversion may be diminished for investors.
XII. Explain how a given investor chooses an optimal portfolio and the most significant driver that determines if a diversified or single asset will be used.