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.




Compute the abnormal rates of return for the following stocks during period t (ignore differential systematic risk):

Stock                             Rit                            Rmt

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

Rit = Return for stock i during period t

Rmt = Return for the aggregate market during period t



Compute the abnormal rates of return for the five stocks in Problem 1 assuming the following systematic risk measures (betas):

STOCKS                          βi

B                                    0.95

F                                    1.25

T                                    1.45

C                                    0.70

E                                   -0.30


Compare the abnormal returns in Problems 1 and 2 and discuss the reason for the difference in each case.


Look up the daily trading volume for the following stocks during a recent five-day period:

  • Merck
  • Caterpillar
  • Intel
  • McDonald’s
  • General Electric

Randomly select five stocks from the NYSE, and examine their daily trading volume for the same five days.

  1. What are the average volumes for the two samples?
  2. Would you expect this difference to have an impact on the efficiency of the markets for the two samples? Why or why not?




Using published sources (for example, The Wall Street JournalBarron’sFederal 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.



The following information is available concerning the historical risk and return relationships in the U.S. capital markets:


Investment                                                       Arithmetic        Geometric        Standard Deviation

Category                                                             Mean                Mean                    of Returna

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

aBased on arithmetic mean

  1. 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.
  2. 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.
  3. 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.



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. Comput

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