# Investments

For Kim Woods

Week 3 Problems (Need each tab in Excel)

Chapter 6 Question 23

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.

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