Download Monetary Economics Exam: Zero Coupon Bonds, European Put Options, and Efficient Markets and more Exams Economics in PDF only on Docsity! 1 American University Department of Economics Comprehensive Exam June 2009 Eco 013 Monetary Economics Page 1 of 4 DIRECTIONS: There are two parts to this exam. Be sure you follow the directions for each part. Part 1 SECTION A. Answer TWO questions. Remember to answer all parts of the question. You must show all relevant formulas and calculations in addition to your explanation. 1. (a) Construct a synthetic one-year zero coupon bond using the information in the table. All bonds are free of default risk and have face value equal to $100. The annual coupon of 7% is paid in semi-annual installments. Term to maturity Price Coupon 6 months $97 0 1 year $101 7% (b) Find the profitable arbitrage opportunity if the price of a one-year zero coupon bond in the market is $92. Be specific in your answer (e.g. show all cash flows). (c) What conditions are necessary for arbitrage to enforce the price calculated in part (a)? 2. Consider a 2-period CRR (Cox-Ross-Rubinstein) model with a continuously compounded interest rate r = .10, S(0) = $200, u = 1.20 and d = .80. The payoff is the European put option with strike price K = $200. Let Δt = 1. (a) Find the projected value of the stock after two periods. (b) Find the payoffs of the put option after two periods. (c) Compute the relevant risk-neutral probabilities and explain their meaning. (d) Find the price of the put option after the first period. (e) Find the price of the put option today (time 0). (f) Describe the arbitrage profit if the current price of the put option equals $5. (g) Why might the seller of the put option want to hedge the risk? What steps should be taken (in general) to create the hedge? 2 Page 2 of 4 3. (a) Derive the put-call parity condition (you can use graphs for this) and explain in detail how it relies on the value additivity condition. (b) Use the parity condition to carefully show how to replicate a European call option. (c) Next, use the parity condition to carefully show how to replicate a risk-free bond. You must demonstrate and explain each step completely. 4. Consider a one-period binomial model for a European call option with strike price K = 100. The underlying model is: Su = 150 Sd = 50 Let the interest rate r = .20. S(0) = 100. The call option was sold for C(0). (a) Describe the risk faced by the seller of the call option. Is the risk unlimited? (b) Find the replicating portfolio and solve for δ0 and δ1. (c) Explain the meaning of δ1 and find C(0). (d) The seller of the call option wants to hedge the risk. Compare the profit or loss with hedging to the profit or loss without hedging. Suppose that at maturity, S(T) = 200. (e) Would you recommend that the risk be hedged in this specific case? How about in the general case? SECTION B. Answer ONE question. Be sure your answers are responsive to the questions. 1. A prominent economist summarizes the theoretical basis for the efficient markets Hypothesis (EMH) by claiming it relies on rational investors and “market forces.” (a) Do you agree with this description? Explain why or why not. (b) Describe two anomalies that call the validity of the EMH into question. (c) How can the presence of “noise traders” and “investor sentiment” help us understand the anomalies? 2. (a) What are the main assumptions of the Capital Asset Pricing Model (CAPM)? Are these assumptions realistic in your view? Does this affect the usefulness of the model? (b) How does the CAPM price the market risk of asset j? How much does the market pay for the specific risk of asset j? (c) Explain why CAPM is an example of an equilibrium model. (d) Explain and then evaluate the extension of the CAPM to a multi-factor model by French and Fama.
