Wharton MBA for Executives FNCE 731 Due WEDOct 1411:59pmEDTFall 2009 (email to )

Professor Gordon Bodnar

Problem Set #2: Interest Rate Parity and Exchange Rate Behavior

  1. Parity Linkages Across Countries

The 360 day nominal interest rate on JPY in the London interbank market is 1.0% (one percent) and the expected rate of inflation for the yen over the coming year is –1.0% (deflation). Based upon this information and assuming the international parity conditions (Purchasing Power Parity, Fisher Effect, Interest Rate Parity, etc.), determine the missing entries for the table. (Use the linear approximation formulas in this question).

Annualized forward premium on

Currency 360 day Euro-currencyExpected the FC against the JPY

nominal interest rateinflation[F(JPY/FC) - S(JPY/FC)]/S(JPY/FC)

Swiss Franc SFR 1.50%a.b.

Russian Rouble RUB c.d.-12.50%

Korean Won KRW e.0.50%f.

  1. Interest Rate Parity Calculations

The following are a set of information for the USD and the GBP.

Spot rate: S(USD/GBP) = 1.6565

Horizon90 days365 days2 years

USD interest rate (APR)2.65%3.15%3.75%

GBP interest rate (APR)4.25% -5.65%

F(USD/GBP) - 1.6262 -

Using the exact formula, determine:

  1. The 90 day forward rate, F(USD/GBP)t,90, that is consistent with no arbitrage.
  2. The GBP 365 day interest rate (APR) that is consistent with no arbitrage.
  3. The 2 year forward rate, F(USD/GBP)t,2YR, that is consistent with no arbitrage.
  1. Parity Calculations

The following table shows some interest rates and exchange rates for the US dollars (USD), Australian dollar (AUD), and the Swiss Franc (CHF) The current spot exchange rate for AUD is 0.7250 (N.B. USD/AUD) and for the CHF is 1.1263 (N.B. CHF/USD).

  1. Complete the missing entries using the exact formulasfor interest rate parity calculations. Determine interests rates (k 365 and N = 5Yr) and forward rates to 4 placed after the decimal (annualization factor is 360 days)

Horizon 1 Year5 year

k = 365 n = 5

AUD interest rate (annual)3.0875% iii.

CHF interest rate (annual)0.4035%2.0015%

USD interest rate (annual) i.3.0875%

Forward rate (USD/AUD)0.70470.6754

Forward rate (CHF/USD) ii. iv.

  1. If you expect Australian inflation for the next year (365 days) to be 2.1% and assume the Fisher Effect holds internationally, what it is the common expected global real rate of interest (annualized) and what is expected inflation in Switzerland and the US over the same period? (use the full ratio form of the equations and truncate your answers to one spot after the decimal point as this is the precision of the inflation forecast)
  2. If inflation in Australia is expected to average 2.1% per year over the next 5 years and inflation in Switzerland is expected to average the rate you determined in part b per year over the next 5 years, determine the expected future exchange rate Et(S(CHF/AUD)t+5Y) based upon Relative Purchasing Power Parity (use ratio form of equation and provide answer to four decimal places).
  3. Suppose you expected the 365 day ahead spot rate for AUD to be USD 0.6000/ USD. Explain how you could take a position today in the 365 day forward contract and expect to make a speculative profit (not guaranteed). What would your expected profit be in AUD if you took a speculative position with a present value of USD1M?
  4. Given the 5 year interest rates for the USD and CHF, use the linear form of long horizon Interest Rate Parity (or International Fisher Effect) to determine a set of annual exchange rate forecasts for years 1 – 5.

(Hint: use the implied annualized forward premium from this rate to project out exchange rates into years1–5.In other words, connect the spot rate with the implied forward rate 5 years out and determine the annual estimates along that line.)

  1. CIP Arbitrage

Suppose you saw the following rates in theLondon interbank money market:

FX: CAD spot 1.1085 / 9190 day swap points 60 / 50

Euro-rates: CAD 90 day rates3 3/16 – 3 %USD 90 days rates5 1/8 –5 %

Note: euro-market quotes are annualized interest rate, with the offer (lending) rate then the bid (deposit) rate

Demonstrate that there is not an arbitrage opportunity in either direction (borrowing dollars and investing

in CAD or borrowing CAD and investing in dollars).

(Hint: borrow USD1 and invest in CAD and repay USD loan – is there any profit? Then do the other direction. Remember to de-annualize and be sure to state the interest rates as decimals).

  1. Exchange Rate Behavior

On June 30, 2004, the FED raised US interest rates by 25 basis points. Simple economic logic would suggest that the higher US interest rates should raise real interest rates in the short term and attract foreign capital into the US and thereby lead to an immediate (but temporary) rise in the FC value of the USD. However, in response to the rate increase, the value of the dollar fell against all major currencies. Foreign central banks did not alter their interest rates on that day. Offer an explanation for this behavior of the exchange rate in response to the US interest rate increase based upon the asset pricing model of exchange rates in which exchange rates are forward looking prices and contain all expected future economic conditions.

FNCE 731 Problem Set #2Fall 2009p. 1