Tom Max, TMP’s quantitative analyst, has developed a portfolio construction model
about which he is excited. To create the model, Max made a list of the stocks currentlyin the S&P 500 Stock Index and obtained annual operating cash flow, price, and total
return data for each issue for the past five years. As of each year-end, this universe was
divided into five equal-weighted portfolios of 100 issues each, with selection based solely
on the price/cash flow rankings of the individual stocks. Each portfolio’s average annual
return was then calculated.
During this five-year period, the linked returns from the portfolios with the lowest
price/cash flow ratio generated an annualized total return of 19.0 percent, or 3.1 percentage
points better than the 15.9 percent return on the S&P 500 Stock Index. Max also
noted that the lowest price-cash-flow portfolio had a below-market beta of 0.91 over
this same time span.
a. Briefly comment on Max’s use of the beta measure as an indicator of portfolio risk in
light of recent academic tests of its explanatory power with respect to stock returns.
b. You are familiar with the literature on market anomalies and inefficiencies. Against
this background, discuss Max’s use of a single-factor model (price–cash flow) in his
research.
Chapter 6 Problem 1
Compute the abnormal rates of return for the following stocks during period t (ignore differential
systematic risk):
Stock Ri t 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
Chapter 6 Problem 2
Compute the abnormal rates of return for the five stocks in Problem 1 assuming the following
systematic risk measures (betas):
Stock βi
B 0.95
F 1.25
T 1.45
C 0.70
E −0.30
Chapter 6 Problem 3
Compare the abnormal returns in Problems 1 and 2 and discuss the reason for the difference
in each case.
Chapter 7 Question 12
Stocks K, L, and M each has the same expected return and standard deviation. The correlation
coefficients between each pair of these stocks are:
K and L correlation coefficient = +0.8
K and M correlation coefficient = +0.2
L and M correlation coefficient = −0.4
Given these correlations, a portfolio constructed of which pair of stocks will have the
lowest standard deviation? Explain.
Chapter 7 Question 13
A three-asset portfolio has the following characteristics.
Asset
Expected
Return
Expected
Standard
Deviation Weight
X 0.15 0.22 0.50
Y 0.10 0.08 0.40
Z 0.06 0.03 0.10
The expected return on this three-asset portfolio is
a. 10.3%
b. 11.0%
c. 12.1%
d. 14.8%
Chapter 7 Problem 3
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
_R
i 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?
Chapter 7 Problem 7
Month DJIA S&P 500 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.
