Problem 1 (14 marks):
Consider the following historical returns on two investments A and B. The average
risk-free rate during the 2011-2015 period was equal to 3%.
Annual return (%)
Year
2015
2014
2013
2012
2011
Investment A
5%
-2%
15%
20%
5%
Investment B
-5%
-20%
30%
40%
10%
a) Calculate the average return and the risk premium for each investment. Which
investment is likely to be is riskier? Explain. (6 marks)
b) Calculate the standard deviation for each investment. (8 marks)
Problem 2 (11 marks):
A stock had the following prices and dividends. What is the average return on this stock?
Year
Price (end)
Dividend
2017
$24.08
$.33
2016
$22.26
$.31
2015
$22.90
$.30
2014
$22.57
$.29
Problem 3 (34 marks):
As part of an investment team at a large Canadian investment company, you are
analyzing the returns of two stocks: TD bank and Sobey. You consider five possible
scenarios for the stocks returns depending on how good the economy will be over
the coming year. Assume TD bank has a 0.9 correlation with the market portfolio
and Sobey has a -0.5 correlation with the market portfolio. The market portfolio
has a standard deviation of 10%. The risk-free rate is equal to 4%.
Economy scenario
Boom
Above average
Probability
0.3
0.2
Return on TD bank stock Return on Sobey stock
30%
8%
20%
8%
1
Average
Below average
Recession
0.2
0.2
??
10%
0%
-20%
10%
12%
15%
a) Calculate the expected returns for each stock. (4 marks)
b) Calculate the standard deviation for each stock. (8 marks)
c) Calculate the correlation between the two stocks if the covariance of the
returns = -35 (2 marks)
d) Assume you have a portfolio with $5,000 invested in TD bank and $15,000
invested in Sobey. Calculate the expected return and standard deviation of returns
for this portfolio. How well does diversification work in this case? Comment on why
or why not diversification works. (10 marks)
e) Calculate the beta of each stock? (4 marks)
f) What is the beta of your portfolio in (d)? (2 marks)
g) If the return on the market portfolio = 9%, is TD bank stock is correctly priced
today? Show your work. (4 marks)
Problem 4 (6 marks):
For each stock state whether it is overvalued, undervalued or correctly priced if
the risk-free rate of return is 3.2% and the market risk premium is 8.4%. Also
state your investment strategy (buy, sell, or hold).
Stock Beta Expected Return
A
0.72
8.62%
B
1.46
15.79%
Problem 5 (10 marks):
You are considering purchasing shares of GreenPro, a supplier of fresh produce.
The stock just paid a dividend of $1.42 and dividends are expected to grow after
2
that at an annual rate of 2%, forever. The stock has a correlation with the overall
market of 0.70. The standard deviation of the stocks returns is 0.60 and the
standard deviation of the overall markets returns is 0.375. The yield on
T- Bills is 3%, and the market risk premium is expected to be 8.5%.
a) What should be the price of the stock assuming that the Capital Asset
Pricing model is true? (7 marks)
b) Suppose the stock is selling in the market at a price of $14.10, is it overvalued or under-valued? Explain what should happen to the stock price if the
market is efficient. (3 marks)
3
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