Comprehensive Examination
Monetary Economics
American University
Department of Economics
January 2014
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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.
SECTION 1
Part A. Short Answer Questions
Choose any two (2) 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.
Value additivity
Index of investor sentiment
Covered call
Portfolio insurance
Equity premium
Value-at-risk (VaR)
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.
1. A corporate bond denominated in dollars has annual coupon payments of 5%, a face
value of $1000, and a term to maturity of three years. Three-year bonds of similar quality
are currently yielding 3%.
(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 current yield and yield to maturity. Discuss the difference between these
two concepts.
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(c) 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 8%. Find the investor’s realized rate of return
over the one-year holding period. Show all calculations.
(d) 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 firm’s assets consist only of 20-year zero coupon bonds and 1-year zero coupon bonds.
Each individual bond has a face value of $1000. Assume the annual interest rate is 6% with a flat
term structure. The firm has liabilities worth $100,000 payable in 5 years.
(a) Explain the concepts of duration and of duration immunization.
(b) How many units of each bond should the portfolio hold if the firm wants to create a duration
immunizing portfolio? Show and explain.
(c) If the market interest rate increases to 12% tomorrow, is the net value of the firm’s
position positive or negative? Show this.
(d) Suppose instead that the firm decides to hold all assets in 20-year zero coupon bonds and the
market interest rate increases to 12% tomorrow. Show and explain the impact on the firm’s
balance sheet. Compare this result to the result in part (b).
3. Consider a 2-period CRR (Cox-Ross-Rubinstein) model with an annually compounded interest
rate r = .07, S(0) = $140, u = 1.2 and d = .80. The payoff is the European at-the-money put
option with strike price K = $140. Let t = 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) 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 put option.
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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 share of stock. (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
Price
Coupon
6 months
$97.20
0%
1 year
$98.20
0%
1 year
$103.70
8%
(a) Find the profitable arbitrage opportunity (if any) given the information shown above.
Show all steps as well as all cash flows.
(b) Are there factors which can limit the role of arbitrage in this sort of situation? Explain.
(c) 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.
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) Explain in detail how the capital asset pricing model (CAPM) is used to determine the
required rate of return on risky assets. (b) Discuss the assumptions necessary for the validity
of the CAPM approach. (c) What is the importance of the extension known as the multifactor model?
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Section 2
Instructions: Answer one question from Part A and one question from Part 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.
Part A. Answer one (1) question.
1.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)
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2.a) Define the Phillips curve relationship 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) Draw a graph showing Friedman’s expectations-augmented Phillips curve
d) Label on this graph 3 points- one with an initial point (point A), one after a monetary shock
[short run] (point B), and one for the long-run (point C).
e) Explain why and how an economy would move from point A to point to point C (Basically
describe how the Friedman Phillips curve works).
f) Assume an economy where there are random aggregate monetary shocks. Would an
econometrician observe a Phillips curve in a Lucas islands monetary model?
g) What will happen to the Phillips curve in the Lucas monetary model economy if the central
bank tries to exploit the Phillips curve and choose a persistently simulative monetary policy to
get lower unemployment?
i) According to Lucas, what happens if the central bank flips a coin, heads increase the money
supply, and tails decrease the money supply?
h) What happens in a Lucas model if the central bank tries to increase the monetary growth rate
during a recession to increase output?
Part B. Answer one (1) question.
1. This question is about the Baumol-Tobin model. For this question, state your answers in
terms of income (Y), money holdings (M), interest (i), Number of trips to the bank (N), and cost
of trips to the bank (F) over a single period.
a) What are average money holdings in the Baumol-Tobin model?
b) How much interest is foregone by holding money in the Baumol-Tobin model?
c) What are the costs of visits to the bank in the Baumol-Tobin model?
d) What is the total cost of money management in the Baumol-Tobin model?
e) What is the cost minimizing number of trips to the bank?
f) What are average money holdings?
g) What happens to money demand if income increases by a factor of 9?
Continued on next page
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h) What happens to money demand if the interest rate quadruplues (x4)?
i) What happens to money demand if the fixed cost of trip to the bank is reduced by 75%?
j) Assume the price level (P) equals one. Velocity is defined as Y/M. What is velocity in the
Baumol-Tobin Model?
k) What happens to velocity if the fixed cost of trip to the bank is ¼ of its previous value?
l) In the early 1980s the behavior of M1 and M2 changed dramatically, especially the velocity of
M1 and M2 (the ratio of M1 and M2 to the money base). One explanation that was given for this
change was the introduction of automatic teller machines which made withdrawing money much
more convenient. Given your knowledge of the Baumol-Tobin model, do you think it is
reasonable to think that this technological change would affect broader monetary aggregates like
M1 and M2?
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?
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.