Problem 1

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 Investment A Investment B

2015 5% -5%

2014 -2% -20%

2013 15% 30%

2012 20% 40%

2011 5% 10%

a)Calculate theaverage return and the risk premiumfor eachinvestment.Which investment is likely to be is riskier? Explain.

b)Calculate thestandard deviation foreachinvestment.

Problem2

A stock had the following prices and dividends. What is the average return on this stock?

Year Price (end) Dividends

2017 $24.08 $.33

2016 $22.26 $.31

2015 $22.90 $.30

2014 $22.57 $.29

Problem3

As part of an investment team at a largeCanadian investment company, you are analyzing the returns of two stocks:TD bank and Sobey.You consider fivepossible scenarios for the stocks' returns depending on how good the economy will be over thecoming year.AssumeTD bank has a 0.9 correlation with the market portfolioandSobeyhas 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 Probability Return on TD bank stock Return on Sobey stock

Boom 0.3 30% 8%

Above average 0.2 20% 8%

Average 0.2 10% 10%

Below average 0.2 0% 12%

Recession ?? -20% 15%

a)Calculate the expected returns for each stock.

b)Calculate the standard deviation for each stock.

c)Calculate the correlation between thetwostocksif the covariance of the returns = -35

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.

e) Calculate the beta of each stock?

f) What is the beta of your portfolio in (d)?

g) Ifthe return on the market portfolio = 9%, isTD bank stock is correctly priced today?Show your work.

Problem4

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%

Problem5

You are considering purchasing shares of GreenPro,a supplier of fresh produce. Thestock just paid a dividend of $1.42 and dividends are expected to grow after 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 stock's returns is 0.60 and the standard deviation of the overall market's returns is 0.375. The yield on

T- Bills is 3%, and themarket risk premiumis expected to be8.5%.

a) What should be the price of the stock assuming that the Capital Asset Pricing model is true?

b) Suppose the stock is selling in the market at a price of $14.10, is it over-valued or under-valued? Explain what should happen to the stock price if the market is efficient.