Portfolio Theory

Portfolio Theory.

The problem sets must be submitted via Canvas by 12:30pm on Monday, 12th October.
Answers will be posted on Canvas later on the same day.
Question 1
The common stock of Leaning Tower of Pita, Inc., a restaurant chain, will generate the
following payoffs to investors next year:
State Dividend Stock Price
Boom $5 $195
Normal Economy $2 $100
Recession 0 0
The company goes out of business if a recession hits. Calculate the expected rate of return
and standard deviation of return to Leaning Tower of Pita shareholders. Assume for
simplicity that the three possible states of the economy are equally likely. The stock is selling
today for $90.
Note 1: The formulas for computing an expectation and a standard deviation of a random
variable can be found in Appendix 3 of Lecture 3.
Note 2: A return on a stock is defined as follows. Consider buying a stock at time 0 at price
P0 and holding it between years 0 and 1. Next year’s price is P1 and next year’s dividend is
D1. Your return is
Question 2
Sassafras Oil is staking all its remaining capital on wildcat exploration off the Cote d’Huile.
There is a 10% chance of discovering a field with reserves of 50 million barrels. If it finds oil,
it will immediately sell the reserves to Big Oil, at a price depending on the state of the
economy. Thus, the possible payoffs are as follows:
Value of Reserves,
per Barrel
Value of Reserves,
50 Million Barrels
Value of Dryholes
Boom $4.00 $200,000,000 0
Normal economy $5.00 $250,000,000 0
Recession $6.00 $300,000,000 0
Is Sassafras Oil a risky investment for a diversified investor in the stock market —
compared, say, to the stock of Leaning Tower of Pita in the exercise above? Explain. (Note
that the answer to this question is of a qualitative and not quantitative nature).
0
1 1 0 ( )
P
D P P R + − =
Finance I, Autumn 2020
2 out of 2
Question 3
Here are some historical data on return and risk characteristics of Boeing and Polaroid.
Boeing Polaroid
Expected return 16.24% 18.08%
Yearly standard deviation of return 21% 26%
(a) The correlation coefficient of Boeing’s return versus Polaroid’s is 0.37. What is the
standard deviation of a portfolio invested half in Boeing and half in Polaroid?
(b) What is the standard deviation of a portfolio invested one-third in Boeing, one-third in
Polaroid, and one-third in Treasury bills? (Note: Treasury bills are risk-free assets.)
Question 4
“The expected return from a portfolio of securities is the average of the expected returns of
the individual securities that make up the portfolio, weighted by the value of the securities in
the portfolio”
“The expected standard deviation of returns from a portfolio of securities is the average of the
standard deviations of returns of the individual securities that make up the portfolio, weighted
by the value of the securities in the portfolio”
Are these statements correct?
Question 5 (challenge – optional)
Suppose Mrs. Qureshi can invest all her savings in shares of Ihser plc., or all her savings in
Resque plc. Alternatively she could diversify her investment between these two. There are
two possible states of the economy, growth or recession, and the returns on Ihser and
Resque depend on which state will occur.
State of the
Economy
Prob. of state
occurring
Ihser return (%) Resque return (%)
Boom 0.7 30 15
Recession 0.3 -10 20
a) Calculate expected return, variance and standard deviation for each share
b) Calculate the expected return, variance and standard deviation for the following
diversifying allocations of Mrs. Qureshi’s savings:
a. 50% in Ihser, 50% in Resque;
b. 11% in Ihser, 89% in Resque.
c) Explain the relationship between risk reduction and the correlation between individual
financial security returns.

Sample Solution

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Portfolio Theory