Instructions: You must do both sections of this exam. Each section receives equal weight in grading. Make sure you follow the directions in each section carefully.
Choose any two (2) of the following.
1.
Show and explain how a forward contract written on a share of stock with continuous dividends can be replicated and priced.
2. Explain two methods used to measure the riskiness of a portfolio. Discuss the adequacy of each measure.
3. How can the value-additivity principle be used to price an asset? How is value-additivity connected to the no-arbitrage condition? Explain in detail.
4. Explain how writing a call option could benefit or hurt an investor with a long position in a stock.
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.
1.
A corporate bond denominated in dollars has annual coupon payments of 3%, a face value of $1000, and a term to maturity of three years. Three-year bonds of similar quality are currently yielding 5%.
(a) Find the market price of the bond. Does the bond sell at par, at a discount, or at a premium? Explain why in words.
(b) Find the bond’s yield to maturity. Discuss its meaning.

(c) Find the bond’s duration. Discuss its meaning.
(d) Suppose an investor buys the bond today and sells it after one year at a time when the yield to maturity on two-year bonds equals 10%. Find the investor’s realized rate of return over the one-year holding period. Show all calculations.
(e) Are there any conditions under which the initial investor with a one-year holding period would prefer the three-year bond described above to a one-year bond with a yield to maturity of 4%? Make your comparison explicit.
2. (a) Show that the log utility function, U(x) = ln(x), and that the power utility function, U(x) = x
  both display constant relative risk aversion (CRRA).
(b) Suppose an investor owns asset A which pays $10,000 with probability 0.4 and pays
$8,000 with probability 0.6. The investor’s utility function is U(x) = ln(x). Find the investor’s certainty equivalent (CE) and explain its meaning. What should the investor pay for asset A?
(c) Does an investor’s expected utility function play a role in risk-neutral asset pricing?
3. Consider a 2-period CRR (Cox-Ross-Rubinstein) model with an annually compounded interest rate r = .07, S(0) = $110, u = 1.2 and d = .75. The payoff is the European at-the-money call option with strike price K = $100. Let
 t = 1.
(a) Find the projected value 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.

4. (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 a European put option. (c) Next, use the parity condition to carefully show how to replicate a European call option. You must demonstrate and explain each step completely (e.g. action taken today, payoffs in the future).
5. Consider the following bonds with face value equal to $100 and which are free of default risk. The annual coupon of 8% is paid in semi-annual installments.
Term to maturity
6 months
1 year
Price
$95.20
$90
Coupon
0%
0%
1 year $100 8%
(a) Find the profitable arbitrage opportunity (if any) given the information shown above.
Show all steps as well as all cash flows.
(b) Based on the table above, what is the expected future 6-month interest rate on zero coupon bonds according to the pure expectations hypothesis? Show your calculations.
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) Explain in detail how the capital asset pricing model (CAPM) is used to determine the required rate of return on risky assets. Include a discussion of the capital market line and the securities market line. (b) What assumptions are made in the CAPM model? (c) What is the importance of the extension known as the multi-factor model?

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, and accuracy and depth of technical detail. Show me what you know.
Section A . Answer one question .
1. Brazil and QE
Assume that Brazil in 2006 is at the intersection of the internal and external balance curves of the
Swan model. a) By 2009, the United States (a major importer of Brazilian goods) has gone into a serious recession as have many other countries that Brazil exports to. What component of the IS curve is changed because of this change? Why? b) What happens to the trade balance as a result? What happens to output due to this change? c) In response to the financial crisis and deepening recession, the Federal Reserve has lowered interest rates significantly. What happens to the capital account if Brazil does not change interest rates? d) The United States has conducted a policy of quantitative easing since 2009 which has massively expanded the money base. Brazil has not expanded the money supply very much as inflation has been near or above Brazil’s inflation target. Given what you learned from the exchange rate equation of Obstfeld-Rogoff, what happened to Brazil’s exchange rate as a result of these policies? e) Given your answers above, show these changes to Brazil since 2006 on the Swan diagram. f) Let’s say Brazil wants to reduce its interest rates to match those of the United States. What would happen to inflation as result? Why would the central bank object to this policy? Hint:
Brazil is an inflation targeter) g) Let’s say Brazil is experiencing inflation due to capital inflows from the interest rate differential with the United States. Can Brazil reduce inflation by raising interest rates in this case? Why or why not?

h) It appears Brazil is somewhat stuck. Let’s say the central bank complains to the Brazilian
Treasury that it is unable to meet the inflation target alone. Can the fiscal authority help through fiscal policy? (Assume that a budget deficit crowds out private investment thus increases interest rates. Also assume that a higher deficit tends to fuel inflation by overheating the economy.) i) Even if the Brazilian Treasury can help the central bank, can you see why they might not want to? Why or why not?
2. Phillips Curve a) Define the Phillips curve and graph a sample Phillips curve. b) Solow and Samuelson thought the Phillips curve represented an opportunity for policymakers who want to affect output/unemployment and inflation. What was that opportunity? c) Over Thanksgiving dinner, your mother asks about the Phillips curve in the early 60s. What do you tell her? d) Over Thanksgiving dinner, your mother then asks about the Phillips curve in the 70s. What do you tell her? e) Assuming Lucas believes his model to be an accurate representation of reality, what would
Lucas predict would happen to unemployment and inflation in response to a significant tightening of monetary policy that is announced ahead of time? f) How accurate would his prediction for unemployment and inflation be on what actually happened to unemployment and inflation when monetary policy became tight in the early 1980s? g) Imagine if Friedman also made a prediction in 1968 based on the Friedman expectationaugmented Phillips curve for what would happen to unemployment and inflation if Volcker tried to disinflate. What would that prediction be and how accurate would his prediction be for what actually happened 1979 to 1987? (Hint: Money was tightened from 1979-1982 and then monetary policy was not tight or loose but neutral from 1982-1987, so you can consider that as a one-time monetary tightening shock. Unemployment was rising 1979-1982 as inflation was falling. Inflation was roughly steady 1982-1987 and unemployment returned its 1979 level by
1987.) h) Imagine if a Keynesian had made a prediction in 1975 based on the IS-LM model and the
Samuelson-Solow interpretation of the Phillips Curve for what would happen to unemployment and inflation if Volcker tried to disinflate. What would that prediction be and how accurate would his prediction be for what actually happened 1979 to 1987? (Hint: Don’t forget to distinguish between the shock period 1979-1982 and the neutral period 1982-1987.)

Section B. Answer one question.
1. In this question you will show your knowledge about two things: Keynes’ monetary theory in the General Theory , and what we can learn about monetary economics from Keynes’ theory. a) Who are the classicals? b) What does Keynes argue is the classical position regarding wage flexibility? Is wage flexibility stabiling or destabilizing for the classicals? c) Does Keynes believe that the classicals consider the possibility or wage rigidities? Are wage rigidities stabilizing or destabilizing for the classicals? d) Does Keynes argue anywhere in Chapter 19 that wages have a tendency to be sticky, due to the standard ``Keynesian’’ factors governing wage rigidities like resistance to wage cuts, union wage bargaining, long-term contracts, and so on? e) Does Keynes think wage flexibility is stabilizing or destabilizing? By that, I mean, does more age flexibility mean that fluctuation in output will be greater or smaller than relative to less flexible wages? f) Does increasing wage flexibility (less wage stickiness) reduce deviations in output in the
Fisher, Taylor, and Rotemberg formulation of price stickiness? g) Keynes writes: “It is probable that the general level of prices will not rise very much as output increases, so long as there are available efficient unemployed resources of every type. But as soon as output has increased sufficiently to begin to reach the “bottlenecks”, there is likely to be a sharp rise in the prices of certain commodities.” i) Create a graph with unemployment and inflation on each axis. Label three portions of a curve, High, medium, and low unemployment, and chart what you think will happen to inflation in these three regions. ii) Draw the same chart but replace unemployment with output. If you have drawn this chart correctly, it should look like an (Old) Keynesian Aggregate supply curve.

2. a) How is the loss function in the Barro Gordon model different from the other loss functions we have seen in the course? b) Why is k>1 in the Barro Gordon model? c) What are the three cases we studied in the Barro Gordon model? Explain each case. d) What is true about expectations for each case? What is true about the central bank’s inflation target for each? e) Graph all three cases on a graph with axes of output and inflation with ellipses showing the loss functions for each. f) What is the inflation bias? g) Why does it matter? h) How serious of a problem do you think inflation bias is in the real world? i) Define discretionary monetary policy. j) Define rule-based monetary policy. k) Do you think that discretion or rules are a better way to conduct monetary policy? Or a mix of the two? Explain your answer.