The economy next year is either in a boom or in a recession. The probability of a boom is 0.75 while the probability of a recession is 0.25. The current value of the stock market is £100. In a boom, the stock market goes up to £120 while in a recession it falls to £80. There is also a risk-free bond, which earns a net risk-free return of Rf= 0%.
1 What is the expected stock market return? What is the variance of this return?
2 Now consider a put option on the stock market with a strike price of £81 and expiry next year. What are the payoffs from the put in the two states of the world next year? Construct a portfolio of stocks and bonds that replicates the put. Under no arbitrage, what is the price of the put today?
3 What is the expected net return from investing in the put? How does it compare to the risk-free return, Rf?
4 What is the covariance of the return on the put with the return on the stock market? What is the beta of the put with respect to the market return? [Hint: the beta of an asset ‘x’ with respect to the market ‘m’ is ]
5 In a CAPM world, what should be the expected return of the put? Does this match your answer to part c above? Does CAPM appear to hold?
