Economic Question - Arbitrage, Market Equilibrium and Exchange Rate

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 difference 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 difference 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 Effect. Is the Fisher Effect more likely to hold in the short-run or the long-run, and explain why. [5]

2. What are the implications of the Fisher Effect for real interest rate differ- 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 flexibly adjust to bring about equilibrium in domestic money and financial 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 fixed.

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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Figure 2: The peso-dollar exchange rate, 1990-1995

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