American University
Monetary Comprehensive Exam
January 2013
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.
Portfolio insurance
Value-at-risk
Martingale pricing models
Value additivity
Replicating portfolio
Home bias
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 8% is paid in semi-annual installments.
Term to maturity
Price
Coupon
6 months
$92
0
1 year
$95
8%
(b) Find the profitable arbitrage opportunity, if any, when the price of a one-year zero
coupon bond in the market is $90. Be specific in your answer (e.g. show all cash flows).
(c) Find the duration of each bond in part (a) and explain its meaning.
(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 drawbacks to the theory you employed in part (d)? Explain.
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2. Consider a 2-period CRR (Cox-Ross-Rubinstein) model with an annually compounded
interest rate r = .05, S(0) = $115, u = 1.2 and d = .80. The payoff is the European at-themoney call option with strike price K = $115. 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) What are the possible strategies to reduce the risk in part (g)? Explain in words.
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 a risk-free bond. (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). (d) Can a risk-free bond
be created using Arrow-Debreu securities? If so, demonstrate.
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) A given stock trades at $70 and, in six months it will pay a dividend of $5.50. The oneyear continuously compounded interest rate is 6% and the six-month continuously
compounded interest rate is 4% (quoted on an annualized basis). Find the one-year forward
price of the stock. Explain your steps carefully.
(b) Show the arbitrage profit when F(t) equals $80. You must show and explain each step carefully to
receive credit.
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6.(a) What are the main assumptions of the Capital Asset Pricing Model (CAPM)? Are
these assumptions realistic in your view? Explain. Does this affect the usefulness of the
model? Explain.
(b) The expected return and standard deviation of the market portfolio are 10% and 15 %
respectively. The expected return on security A is 7%. The standard deviation of security
B is 20% and its specific risk is (5%)2. A portfolio that invests ¼ of its value in A and ¾
in B has a beta of 1. According to CAPM, what are the values of the risk-free rate and the
expected return on B?
(c) Show how the graphs of the CML and SML could be used in part (b).
(d) Explain why CAPM is an example of an equilibrium model.
(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.
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Section 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.
CONTINUED ON NEXT PAGE
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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?
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.