1. Homework # 2
Finc 335
Due: Feb. 23, 2021
1. Consider the three stocks in the following table. Pt represents price per share at time t,
and Qt represents shares outstanding at time t (in millions).
P0 Q0 P1 Q1
A 50 100 55 100
B 50 200 45 200
C 100 200 110 200
For the …rst period (t = 0 to t = 1), compute rates of return on:
(a) a price-weighted index of the three stocks;
(b) a market value-weighted index of the three stocks;
(c) an equally weighted index of the three stocks;
(d) Suppose at t = 0, you started a portfolio consisting of $2,500 in stock A, $2,500 in
stock B and $5,000 in stock C. Suppose also that you did not change your positions
during the time period from t = 0 to t = 1: How many shares of each stock (A B
and C) did you have in your portfolio? What is the rate of return of your portfolio
for this period? Is your portfolio’
s return re‡
ected by the return of one of the indices
from (a), (b) and (c)? Which one? Give an explaination based on the proportion of
money invested in each stock in your portfolio.
(e) Suppose instead, at time t = 0, you want to invest a total of $14,000 in the three
stocks. You want your portfolio to mimic the return of the market value weighted
index in the period from t = 0 to t = 1: How many shares of each stock would you
have in your portfolio and why?
2. Consider information regarding the following two stocks. The probability of each state of
the economy is 1/3. No dividends are paid.
Ending Price in
Stock Initial Price Boom Normal Bust
A 40 60 50 25
B 25 20 25 35
(a) What is the expected value and the standard deviation of the rate of return of each
stock?
(b) Which stock is the better investment for you? Why?
3. Consider a risky portfolio. The end-of-year cash ‡
ow derived from the portfolio will be
either $50,000 with probability 0.6 or $150,000 with probability 0.4. The alternative
riskless investment in T-bill pays 5%. This risky portfolio is currently selling (asking
price) for $80,000
2. (a) If you require a risk premium of 10% to be interested in investing in this portfolio,
will you pay the asking price for this portfolio? Explain. (Hint: you can …rst …gure
out how much the portfolio is worth to you now as in our example from the lecture)
(b) If your friend is willing to pay the asking price for this portfolio, what is her expected
return? What can you say about her risk attitude compared to yours? Is she more
risk averse or less risk averse than you?
4. You manage a risky portfolio with an expected return of 17% and a standard deviation of
27%. The T-bill rate is 5%.
(a) Your client chooses to invest 70% of a portfolio in your fund and 30% in a T-bill
money market fund. What is the expected value and standard deviation of the rate
of return on your client’
s portfolio?
(b) Suppose that your risky portfolio includes the following investments in given propor-
tions:
Stock A: 27%
Stock B: 33%
Stock C: 40%
What are the investment proportions in your client’
s overall portfolio including the posi-
tion in T-bills?
(c) What is the Sharpe (reward-to-volatility) ratio of your risky portfolio? Your client’
s?
(d) Suppose your client decides to invest in your portfolio a proportion y of the total
investment budget so that the overall portfolio will have an expected rate of return of
15%. What is the proportion y? What is the standard deviation of the rate of return
on your client’
s portfolio?
5. Suppose Merck stock o¤ers an expected rate of return of 12% and a standard deviation of
25%. The risk-free rate is 5%.
(a) Graph the Capital Allocation Lines (CAL) for Merck stock.
(b) What is the Sharpe (reward-to-volatility) ratio of Merck stock.
(c) If you have a portfolio of $15,000 with $5,000 invested in a risk free security and
$10,000 in Merck stock, what is the expected rate of return of your portfolio? What
is your portfolio’
s standard deviation? What is the reward-to-volatility ratio (Sharpe
ratio) of your portfolio?
(d) If your friend is more risk averse than you are and that she also has a portfolio of
$15,000 invested in a risk free asset and Merck stock. Do you think she has more or
less than $10,000 in Merck stock? Why?
6. Suppose Southwest Airlines’stock o¤ers an expected return of 10% and a standard de-
viation of 20%. Suppose American Airlines’stock o¤ers an expected return of 8% and a
standard deviation of 16%. The risk-free rate is 5%.
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3. (a) Graph Capital Allocation Lines (CAL) for Southwest and American.
(b) If one can only invest in one of the airlines along with the risk-free security, which
airline stock will a risk averse investor choose? Why?
(c) If you are less risk averse than the person in (b), which airline stock will you choose
to invest along with the risk-free security? Why?
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