Foundations of Finance Homework 3
Prof. Johannes Stroebel Due at the start of class 9
Topic 5: The Capital Asset Pricing Model
1. Assume the risk free rate equals Rf = 4%, and the return on the market portfolio has expectation E [RM ] = 12% and standard deviation σM = 15%. (a) What is the equilibrium risk premium (that is, the excess return on the market portfolio)? (b) If a certain stock has a realized return of 14%, what can we say about the beta of this stock? (c) If a certain stock has an expected return of 14%, what can we say about the beta of this stock? 2. You are given the following two equations: E(Ri ) = Rf + (E(RM ) − Rf )βi E(RM ) − Rf σp E(Rp ) = Rf + σM (1) (2)
) 2. Suppose the price on the North Pole is $18 and the price on the the South Pole is $17? How can you make an arbitrage proﬁt? (Assume no trading costs.) 3. Suppose that the price on the North Pole is $18, that buying or selling on the North Pole costs $2, and that buying or selling on the South Pole is free. What does the No-Arbitrage Condition say about the price on the South Pole? Suppose that there are two securities RAIN and SUN. RAIN pays $100 in there is any rain during the next world cup soccer ﬁnal. SUN pays $100 in there is no rain. Suppose that the world cup soccer ﬁnal is 1 year from today (although this is not true), and suppose that RAIN is trading at a price of $23 and SUN is trading at a price of $70. 1. If you buy 1 share of RAIN and 1 share of SUN, what is your payoﬀ after 1 year, depending on the weather? 2. What does the No-Arbitrage Condition imply about the price of a 1-year zero-coupon bond? (Assume no trading costs.) 3. Suppose that a 1-year zero-coupon bond is trading at $90. Show how you would set up a transaction to earn a riskless arbitrage proﬁt. (Assume no trading costs.) 4. Suppose that trading zero-coupon bonds is costless, but trading RAIN and SUN each cost $2 per $100 face value. Can you still make an arbitrage proﬁt? 2
Topic 7: Equity Valuation
Suppose that the consensus forecast of security analysts of your favorite company is that earnings next year will be E1 = $5.00 per share. Suppose that the company tends to plow back 50% of its earnings and pay the rest as dividends. If the Chief Financial Oﬃcer (CFO) estimates that the company’s growth rate will be 8% from now onwards, answer the following questions. 1. If your estimate of the company’s required rate of return on its stock is 10%, what is the equilibrium price of the stock? 2. Suppose you observe that the stock is selling for $50.00 per share, and that this is the best estimate of its equilibrium price. What would you conclude about either (i) your estimate of the stock’s required rate of return; or (ii) the CFO’s estimate of the company’s future growth rate? 3. Suppose your own 10% estimate of the stock’s required rate of return is shared by the rest of the market. What does the market price of $50.00 per share imply about the market’s estimate of the company’s growth rate? This question requires data collection. You can ﬁnd all numbers on http://ﬁnance.yahoo.com. The questions concern Microsoft (ticker: MSFT). 1. What is the current price and the current price-earnings ratio? 2. What is the current plowback ratio? 3. What is the growth rate of earnings for the next 5 years according to the analysts? Hint: look for annual growth rates under “Analyst Estimates” 4. What is the beta of MSFT? Hint:...