Wharton MBA for Executives FNCE 731
Fall 2009
Professor Gordon Bodnar
Due WED Oct 14 11:59pm EDT
(email to bodnar@jhu.edu)
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-currency
Expected
the FC against the JPY
nominal interest rate
inflation [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.
2.
Interest Rate Parity Calculations
The following are a set of information for the USD and the GBP.
Spot rate: S(USD/GBP) = 1.6565
Horizon
90 days
365 days
USD interest rate (APR)
2.65%
3.15%
GBP interest rate (APR)
4.25%
F(USD/GBP)
1.6262
Using the exact formula, determine:
a. The 90 day forward rate, F(USD/GBP)t,90, that is consistent with no arbitrage.
b. The GBP 365 day interest rate (APR) that is consistent with no arbitrage.
c. The 2 year forward rate, F(USD/GBP)t,2YR, that is consistent with no arbitrage.
3.
2 years
3.75%
5.65%
-
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).
a.
Complete the missing entries using the exact formulas for 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 Year
5 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)
0.7047
0.6754
Forward rate (CHF/USD)
ii.
iv.
b.
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)
c.
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).
FNCE 731 Problem Set #2
Fall 2009
p. 1
4.
d.
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?
e.
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.)
CIP Arbitrage
Suppose you saw the following rates in the London interbank money market:
FX:
CAD spot
1.1085 / 91
90 day swap points
60 / 50
Euro-rates:
CAD 90 day rates
3 3/16 – 3 %
USD 90 days rates
5 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).
5.
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 #2
Fall 2009
p. 2