IRCO 403: Problem Set 1
Due in class Apr 15th
1 Arbitrage in Financial Markets [20 Marks]
1. It costs 12.19 Mexican peso to buy $US1. Interest rates on one year bonds
of the Mexican government are 4.3%. Interest rates on one year bonds of
the US government are 0.13%. How many peso would you expect to be
able to sell for $US1 using a forward contract that settles in one year? [5]
2. What rate of depreciation or appreciation of the Mexican peso against the
US$ must investors be anticipating over the next year, if expected returns
on dollar- and peso-denominated assets are equal, given the facts of part
(1)? [5]
3. Explain the di erence between Covered and Uncovered Interest Parity
Arbitrage. What risks does a US investor face when buying Mexican
government bonds, and trying to exploit these arbitrage strategies? [10]
2 Arbitrage in Goods Markets [20 Marks]
1. What is the di erence between Absolute and Relative PPP? Which theory
requires fewer assumptions? [5]
2. Give two reasons why Absolute PPP might not hold in the short-run. [5]
3. Is there empirical evidence in favour of either Absolute or Relative Pur-
chasing Power Parity, and which has more empirical support? [10]
3 Money and Asset Market Equilibrium [20 Marks]
1. Derive and explain the Fisher E ect. Is the Fisher E ect more likely to
hold in the short-run or the long-run, and explain why. [5]
2. What are the implications of the Fisher E ect for real interest rate di er-
entials between countries? [5]
3. What determines a country's long-run nominal interest rate? [4]
4. Assume that goods prices are sticky in the short-run and can change only
gradually. Explain the initial impact of a doubling of Ms on US nominal
interest rates. What will happen to US nominal interest rates over the
long-run as goods prices react? [6]
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4 Complete Model of Exchange Rates [40 Marks]
1. Derive a long-run model of exchange rate determination, if exchange rates
are determined by Absolute PPP, and goods prices
exibly adjust to bring
about equilibrium in domestic money and nancial markets. [10]
Assume investors use the long-run model you derived in part (1) to form
their forecasts of future exchange rates, Ee, but that in the short-run
goods prices are xed.
2. Refer back to the data on US and Mexican interest and exchange rates
given in section 1, and assume foreign exchange and domestic money mar-
kets are initially in equilibrium. The Federal Reserve unexpectedly an-
nounces a new round of Quantitative Easing, a temporary expansion of
the US money supply: for the next year the US money supply will be 50%
higher, before returning to its initial level after 12 months. Other than
this, no changes are expected in either the US or Mexican economies.
Graph (but do not calculate) the response of US interest rates and the
$-peso exchange rate over the next year, assuming that Mexican mone-
tary policy does not change in response to the Fed's announcement and
that investors believe the Fed's commitment to reverse this increase in the
money supply in one year. [7]
3. A year after the implementation of the Quantitative Easing program, the
Fed announces that in fact it will not reverse its expansion of the money
supply, which will be permanently 50% higher. Repeat your graph from
part (2), extending it forward in time to show the expected response of
US interest rates and the exchange rate over the year following the second
announcement, assuming again that there is no change in Mexican policy,
that the Fed is expected to abide by this new policy, and that US goods
prices are able to gradually adjust. [8]
4. Figures 1 and 2 illustrate the prevailing interest rates in the US, Mexico
and Japan from 1990-1995, along with the peso-dollar and yen-dollar ex-
change rates (measured on the right-hand axis of each graph). For which
exchange rate does the theory of Uncovered Interest Parity appear to hold
most consistently over this period? For that country, does the theory hold
equally well throughout, or is there an episode which seems inconsistent
with the theory? [15]
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Figure 1: The yen-dollar exchange rate, 1990-1995
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US interest rate Mexican interest rate peso/$ (right axis)
Figure 2: The peso-dollar exchange rate, 1990-1995
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