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Unformatted text preview: University of Toronto, Department of Economics, ECO 204 Summer 2009 S. Ajaz Hussain ECO 204 Summer 2009 S. Ajaz Hussain Practice Problems 24 Please help improve the course by sending me an email about typos or suggestions for improvements For these problems, it'll be helpful to remember these formulas for expected value, expected variance, expected covariance, expectation of a sum and variance of a sum: E[Rp] = (1 )RF + E[RM] E[2] = i=1:n pi(xi EV[x])2 E[cov(x,y)] = i=1:n pi (xi EV[x])(yi EV[y]) E[a x + b y] = a E[x] + b E[y] (a and b are constants) Var(a x + b y) = a2 Var(x) + b2 Var(y) + 2 a b cov(x,y) (a and b are constants) Always express returns and standard deviation in % terms. Question 1 Suppose you invest $1,000 in a mutual fund: the price of a share today is $100. After extensive research, you believe that a year from now the share price will be: State of the Economy Boom Normal Recession Probability 0.25 0.50 0.25 Stock Price $140 $110 $80 You expect the dividend to be $4 (in finance, this would correspond to a dividend yield of 4% = 1 University of Toronto, Department of Economics, ECO 204 Summer 2009 S. Ajaz Hussain $4/$100, where dividend yield is defined as dividend income per dollar invested in the stock at the start of the period). (a) What is the expected return of the stock? Hint: Calculate the return for each state of the economy and compute EV. Assume there is zero inflation. (b) What is the risk of this stock's return? (c) In your calculation of risk, are a boom and recession economy treated "equally"? Why might this be troubling for some investors? Question 2 After graduating from U of T, you are hired by a nonprofit organization The "Save the Economists" foundation. The foundation has an endowment one half of which is in "Goolab Jammins" stocks (Goolab Jammins makes hip Indian fusion desserts) and the other half is in 3 month Canadian bonds. The price of Goolab Jammins stocks is sensitive to the price of sugar: at times, when the Caribbean sugar crop fails, the price of sugar spikes up and Goolab Jammins suffers significant losses. The "Save the Economists" board of directors gives you the following table with the Goolab Jammins' rate of return Probability Rate of Return Normal Year Bullish Stock Market 0.5 25% Bearish Stock Market 0.3 10% Abnormal Year Sugar Crisis 0.2 25% Suppose the return on 3month Central Bank of Canada bonds is 5%. (a) What is the expected rate of return on Goolab Jammins stock? (b) What is the expected risk of Goolab Jammins stock? (c) What is the expected return of "Save the Economists" foundation's portfolio? (d) What is the expected risk of "Save the Economists" foundation's portfolio? 2 University of Toronto, Department of Economics, ECO 204 Summer 2009 S. Ajaz Hussain Thanks to ECO 204, you're an expert in the economics and finance of portfolios. You notice that in years of a sugar crisis in the Caribbean, a Hawaiian company "Brown Sugar" reaps massive profits. You investigate further and discover that "Brown Sugar" returns are: Probability Rate of Return Normal Year Bullish Stock Market 0.5 1% Bearish Stock Market 0.3 5% Abnormal Year Sugar Crisis 0.2 35% (e) What is the expected return for "Brown Sugar"? (f) What is the expected risk for "Brown Sugar"? (g) Is "Brown Sugar" a candidate investment for diversifying "Save the Economists" portfolio? Why? (h) Consider the following 3 portfolios: (1) 100% of portfolio in Goolab Jammins stock (2) 50% in bonds,50% in Goolab Jammins (3) 50% in Goolab Jammins, 50% in Brown Sugar Do you notice anything interesting about these portfolios? Hint: Examine the expected return and risk of each portfolio. Question 3 (Actual CFA Level 1 question). You manage an equity fund with an expected risk premium of 10% and an expected standard deviation of 14%. The rate of TBills is 6%. Your client chooses to invest $60,000 of portfolio in your equity fund and $40,000 in a TBill money market fund. What is the expected return and standard deviation of your client's portfolio? By the way, the "risk premium" in finance is the difference between the returns of a risky and a risk free asset. Question 4 (20072008 Final Exam Question) The following table gives the expected return and standard deviation for returns of stocks A and B: 3 University of Toronto, Department of Economics, ECO 204 Summer 2009 S. Ajaz Hussain Stocks A B Expected Return (R) 10% 15% Standard Deviation () 5% 10% The covariance of stock A and B returns is 50. What is the risk free rate? You may find following formulas helpful: ax + bx + c = 0 2  b b 2  4ac x = 2a Rp = RX + (1 )RY 2p = 22X + (1 )22Y + 2 (1 ) cov(RX,RY). Question 5 (20072008 Test Question) As an equity analyst for AJax Investment Bank (Motto: "We Don't Know How to Count, But We Do Know How to Invest"), you analyze the % rate of return for two stocks: "Canada Rules!" and "USA Rules!". The two charts below give the number of times rates of returns have been observed over the last 200 trading periods (Note: Xaxis = Rate of Return (%) Yaxis = # of observations) 4 University of Toronto, Department of Economics, ECO 204 Summer 2009 S. Ajaz Hussain Will purchasing these two stocks reduce AJax's risk? Show calculations clearly and give a one sentence explanation. Question 6 (20072008 Test Question) You are an asset manager at "Etorre" Investments. Jane Murdock is your client. Recently, she borrowed money from your company and invested the borrowed amount plus her portfolio ($100,000) in risky assets. While trying to balance the books, you discover to your horror that you forgot to note how much she borrowed. You start to panic but then think back to ECO 204: given the following data, can you figure out how much she borrowed? Rf = 5%, 2m = 100, Risk premium = 25%, Rp = 42.5% 5 ...
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This note was uploaded on 05/02/2011 for the course ECO 204 taught by Professor Hussein during the Fall '08 term at University of Toronto Toronto.
 Fall '08
 HUSSEIN
 Economics, Microeconomics

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