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American University Monetary Comprehensive Exam June 2012 DIRECTIONS: There are two sections to this exam. Please follow the directions for each section. Section 1 Part A. Short Answer Questions Choose any three (3) of the following. For each concept you choose, you must give a definition and discuss the significance of the concept for financial economics. You may include examples if you wish but these do not substitute for the definition and explanation. 1. 2. 3. 4. 5. 6. Covered call option Equity premium Arrow-Debreu security Risk-free rate Certainty equivalent Sharpe ratio Part B. Problems Choose any three (3). Remember to answer all parts of the question. You must show all relevant formulas and calculations in addition to your explanation. You may use a calculator (provided). 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 6% is paid in semi-annual installments. Term to maturity Price Coupon 6 months $94 0 1 year $98 6% (b) Find the profitable arbitrage opportunity if the price of a one-year zero coupon bond in the market is $95. 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)? (d) What does the yield curve in this problem indicate about the market‟s expectation of future 6-month interest rates? Demonstrate and carefully explain the theory you are using. (e) What are the potential limitations of the theory you employed in part (d)? Explain. Page 2 of 5 2. Consider a 2-period CRR (Cox-Ross-Rubinstein) model with an annually compounded interest rate r = .08, S(0) = $110, u = 1.1 and d = .90. The payoff is the European at-themoney call option with strike price K = $110. Let t = 1. (a) Find the projected values of the stock after two periods. (b) Find the payoffs of the call option after two periods. (c) Compute the relevant risk-neutral probabilities and explain their meaning. (d) Find the price of the call option after the first period. (e) Find the price of the call option today (time 0). (f) Explain in words the principles of financial economics you employed in parts (a)-(e). (g) Explain the risks faced by the seller (writer) of the call option. (h) In general, how could the risks faced by the seller be mitigated? Explain. 3. (a) Derive the put-call parity condition (you can use equations or 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 the risk-free security with payoff equal to K. (c) Next, use the parity condition to carefully show how to replicate a European put option. You must demonstrate and explain each step completely (e.g. action taken today, payoffs in the future). 4. Let C(t) and P(t) represent the prices of a European call and put option respectively. K is the strike price of each option, S(t) is the price of a single share of stock, F(t) is the forward price of the stock a year from now, q is the continuously compounded dividend payment and (T-t) = 1. Show that arbitrage profit is possible in the following two cases: (a) C(t) + Ke-r (T-t) > S(t) + P(t) (b) F(t) > S(t) e(r-q) (T-t) Be sure you demonstrate each step and clearly show the profit 5. A firm‟s assets consist only of 8-year zero-coupon bonds and 2-year zero coupon bonds, each with face value of $1,000. Assume the annual interest rate is 6% with a flat yield curve. The firm has liabilities worth $10,000 due in 4 years. (a) How many units of each bond should the portfolio hold if it wants to create a duration-immunizing portfolio? (b) If the interest rate rises to 7% tomorrow, what is the net value of the firm‟s position? Be sure you add a complete explanation for each part Page 3 of 5 6. (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) Suppose you consider investing in mutual fund A that invests 30% of its funds in the risk-free asset at the rate of 5%, and 70% of its funds in a portfolio with a beta equal to .75 and an expected return of 20%. The market has been returning an average of 25% with a standard deviation of 10%. The current price of one share in fund A is $100. What is today‟s theoretical CAPM price of one share in fund A? Is fund A correctly priced according to CAPM? Show all steps. (c) What was the role of the capital market line (CML) and the securities market line (SML) in your answer to part (b)? Explain and demonstrate completely. Provide a carefully labeled graph in each case. (d) How much does the market pay for the specific risk of fund A? Explain. (e) Explain and then evaluate the extension of the CAPM to a multi-factor model by French and Fama. Part C. Essay Answer ONE (1) question. 1. (a) Explain two concepts from behavioral finance: “prospect theory” and “ambiguity aversion.” (b) Discuss a specific example of how each concept can help us understand some of the deviations from the principles of traditional finance that are often observed in financial markets. 2. (a) The efficient markets hypothesis (EMH) served as a bedrock of neoclassical finance for many decades. Explain the rationale behind the EMH. (b)What factors contributed to the reevaluation of this theory by many financial economists? Provide three specific examples. (c) Explain how noise traders can undermine the crucial role of arbitrageurs in neoclassical finance. Page 4 of 5 Part 2 Instructions: Answer one question from Section A and one question from Section B. Make sure to read the questions carefully, and answer what is asked. Answers are judged on clarity of exposition and intuition, command of the relevant literature, and accuracy and depth of technical detail. Section A. Answer one question. 1. Cash-in-advance models a. Explain how the cash-in-advance model differs from the money-in-the-utility function approach. b. What are the two constraints that households face in their optimization problem? c. At the optimal level of consumption, what does its marginal utility need to equal? d. What relationships define the capital-labor ratio and the level of consumption in the steady state? e. Is money neutral in the CIA model? Is it superneutral? f. What is the welfare-maximizing rate of inflation in the simple CIA model? Explain, and compare this result to that of Sidrauski‟s MIU model. Does this finding hold up in other versions of the CIA model? 2. New Keynesian models a. Describe how the set-up of the New Keynesian model differs from that of the classical rational-expectations/real-business-cycle model, making sure to refer to (a) whether businesses and consumers optimize, (b) whether markets are perfectly competitive, and (c) the flexibility of wages and prices. b. Why is stickiness a problem for adjustment to adverse shifts in aggregate demand? c. Do micro data support the New Keynesian model‟s maintained hypothesis of considerable stickiness in prices at the firm level? Explain. d. If the New Keynesian model takes people to have rational expectations (so that they do not have „money illusion‟), what is it that gives monetary policy its power to offset fluctuations in real economic activity? Explain, making reference to the MIU model with a lagged wage adjustment laid out by Walsh. e. Write out the Taylor rule and explain its components. a. Is this a descriptive or prescriptive framework? Explain. b. What do empirical estimates of Taylor rule parameters say about cross-country variations in monetary-policy reaction functions: are these functions highly similar or quite different across countries? Page 5 of 5 Section B. Answer one question. 1. Friedman and the equation of exchange a. Was Milton Friedman in favor of using monetary policy to stabilize business cycles? Explain his views and his reasoning. b. How did Friedman think that monetary policy should be conducted? Use the quantity equation („equation of exchange‟) to explain. c. What does the evidence of de Grauwe and Polan suggest: Is Friedman right that “inflation is everywhere and all the time a monetary phenomenon?” d. What is the difference between income velocity and transactions velocity? e. Explain how Mbiti and Weil attempt to quantify how the M-Pesa system affected patterns of financial transactions and real economic activity in Kenya. f. Conceptually, how has the introduction and phenomenal expansion of the M-Pesa system affected the money supply and the conduct of monetary policy in Kenya? Explain. 2. Monetary policy in financial crisis a. Why is it said that monetary policy becomes ineffective if the central bank lowers the policy interest rate to zero – and is this actually right? Explain, using the forward-solution to output as a function of future expected interest rates to illustrate your argument. b. Discuss what three means the central bank can use to try to affect the public‟s expectations of future real costs of borrowing, even if the nominal interest rate is already at the zero bound. c. What was the liquidationist view of the Great Depression, and how did it condition the actions the Fed did or did not take following the stock market crash of 1929 and ensuing recession? d. In the Friedman-Schwartz view, why should the Fed be seen as having played a major role in turning the 1929-1930 recession into the Great Depression? e. In the view of Ben Bernanke, bank failures played a critical role in turning the downturn of 1929-30 into the Great Recession of 1929-33. Explain his argument and the econometric evidence he presented to support it.