The Capital Asset Pricing Model:
1. Assume the risk free rate equals Rf = 4%, and the expected return on the market portfolio is E [RM] = 12% and standard deviation σM = 15%.
(a) What is the equilibrium market risk premium (that is, the expected return on the market portfolio minus the risk free rate)?
(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. Apple stock has an average return of 12% and a beta of 1.1. Google stock has an average return of 14% and a beta of 1.2. The risk free rate is 5% and the expected return on the market is 10%. If you can only pick one stock to buy, which one would you pick? Explain your answer.
Arbitrage :
3. The stock PolarBear.com trades on both the South Pole Stock Exchange and the North Pole Stock Exchange
(a) Suppose the price on the North Pole is $18. What does the No-Arbitrage Condition say about the price on the South Pole? (Assume no trading costs.)
(b) 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.)
(c) Suppose that the price on the North Pole is $18, that the cost of shorting is $2 and the cost of buying is $0 on both poles. What does the No-Arbitrage Condition say about the price on the South Pole?
4. All zero coupon bonds have a face value of $100. A one-year zero-coupon bond trades at $95. A two-year zero-coupon bond trades at $96. A three-year zero-coupon bond trades at $97. Answer the following questions:
(a) Construct a replicating portfolio from the three zero-coupon bonds above to replicate cash flows of a 7% annual coupon bond with a face value of $100.
(b) What is the equilibrium price of the 7% annual coupon bond given in part (a)?
(c) If the 7% annual coupon bond is trading at a price of $110, show how you can make an arbitrage profit