Download Problem Set #1 - Wharton Finance Department

Merrill Lynch Investment Banking Institute
August 2005
International Finance Sessions
Professor Gordon Bodnar
Problem Set #1
Some of the problems require that you obtain the data file: ps1data.xls from my program web page at
http://finance.wharton.upenn.edu/~bodnarg/ml/outline. The data file is an MS Excel file and contains nominal
exchange rates (all in USD/FC), and various price indexes for several countries over the period January 1973 –
May/June 2004. Download the file by clicking on it and following the prompts.
1.
Exchange Rate Games
a. The following is a table of exchange rates. Based upon the provided information fill in the missing values.
Express rates as S(Currency in Top Row/ Currency in First Column)
S(top row/first col)
USD
EUR
JPY
GBP
USD
1.00
108.25
0.5518
EUR
1.2075
JPY
GBP
CAD
0.7518
b.
You are told that the rates for exchanging currencies are:
JPY 108.25 = USD1
USD 1.2075 = EUR 1
CAD
USD 1.8123 = GBP 1
Please state the following spot prices as S(·/·) (mathematical quotaion) :
i.
the price of yen in terms of dollars
ii. the dollar price of euros
iii. the number of pounds per dollar
2.
c.
Suppose the USD strengthened relative to the JPY but weakened relative to the EUR and GBP. Which
way would the following exchange rates move (up or down)?
i. S(USD/JPY)
ii. S(USD/EUR)
iii. S(GBP/USD)
d.
Suppose you see the following rates on an FX board at a airport currency exchange desk
Japanese Yen
S(JPY/USD)
123.965 / 128.025
British Pounds
S(USD/GBP)
1.4025 / 1.4735
i. At what price could you sell the yen that you have left over from your last trip to Tokyo for
US dollars?
ii. At what price can you buy British pounds for your upcoming trip to London with US dollars?
iii. Suppose you had £1,000 and you needed yen. How many yen would you have when you left
the counter?
Effective XR Index
Consider a US firm with operations in the UK, Mexico, and Brazil. Ps1data.xls contains monthly data on
exchange rates for these three countries.
a.
Suppose the firm has 50% of its foreign sales in the UK, 35% in Mexico, and 15% in Brazil.
Determine the effective exchange rate index for the firm for the period January 2000 – May 2004.
Choose January 2000 as the base year for the index.
b.
Determine whether the effective FC value of the US dollar for the firm has appreciated or depreciated
between January 2000 and May 2004. Determine the percentage change in the USD value (USD/FC)
of this weighted foreign currency index.
ML Investment Banking Institute: August 2005
Problem Set #1
p. 1
3.
Parity Conditions
The following table shows interest rates and exchange rates for the United States dollar (USD) and the Danish
Krone (DKR). The current spot exchange rate for DKR is 6.7317 (DKR.USD).
a.
Complete the missing entries using the exact formulas (ratios) whenever possible for the parity conditions.
Horizon
3 Months
6 Months
1 Year
USD interest rate (annual)
1 3/32 %
1 5/32 %
v.
iii.
2 3/8%
DKR interest rate (annual)
2 1/4 %
Forward rate (DKR/USD)
i.
iv.
6.7981
Forward premium on DKR, (annual %/yr)
ii.
-1.05 %
vi.
b.
If expected US inflation for the next year is 1.0% and we assume the International Fisher condition holds,
what it is the equilibrium real rate of interest for one year and what is inflation expected to be in Denmark
over the coming year? (use exact formulas)
c.
Suppose you expected the 12-month ahead spot rate to be DKR 7.00/USD. Explain how you could take a
position and expect to make an arbitrage profit using the 12-month forward contract.
d.
Suppose the current 5-year DKR Danish government note has an annualized yield to maturity of 5.15%
while the equivalent maturity US Treasury (USD) note had a yield to maturity of 4.37%. Determine the
future exchange rate (DKR/USD) for 5 years from now that is consistent with no speculative profits.
Complete the following questions and attach a graph and a small table of the relevant numbers to support your answers.
4.
5.
6.
British Pound Real Exchange Rates
Calculate and graph a real exchange rate index (with a base period of June 1973) based upon consumer prices
(CPI), for USD/GBP exchange rate.
a.
In September 1992, the GBP left the exchange rate mechanism of the European Monetary System and
depreciated sharply. Discuss the size of this devaluation (by February 1993) in terms of PPP for the
GBP versus the USD.
b.
Based upon PPP, is the USD expected to appreciate or depreciate in real terms against the GBP in the
future? For May 2004, determine the percentage under/overvaluation of the USD against the GBP. (be
careful about the size and sign)
Mexican Peso Inflation Adjusted Exchange Rates
Mexico devalued their currency in December of 1987. Assume that the exchange rate at the end of January
1988 is a good approximation of an equilibrium rate (benchmark for APPP).
a.
Using both the CPI and WPI data, plot the inflation-adjusted exchange rates for the MXP/ USD
exchange rate and the actual nominal exchange rates from January 1988 onward.
b.
Using the plot, discuss the size of the nominal peso devaluation in mid December 1994 (between Nov
and Dec 1994 data) in terms the inflation-adjusted exchange rates. How did the devaluation size
compare (roughly speaking) with the predictions of APPP?
c.
Identify the inflation adjusted exchange rate levels using WPI for May 2004. Compare this with the
nominal rate at this time. Determine the % over or under valuation for the nominal exchange rate.
(% overvaluation of MXP = [NXR(USD/MXP) – IAXR(USD/MXP))/IAXR(USD/MXP)]
Compare this value to the extent of overvaluation in November 1994 just prior to the last devaluation.
What does PPP say about the possibility of another devaluation of the peso?
Exchange Rate Behavior
On June 30, the FED raised US interest rates by 25 basis points. Simple economic reasoning would suggest
that the higher US interest rates should attract foreign capital into the US and raise the FC value of the USD.
However, in response to the rate increase, the value of the dollar fell slightly against all major currencies.
Foreign central banks did not alter their interest rates on that day. Offer a rational economic explanation for
this apparently illogical behavior of the exchange rate in response to the US interest rate increase.
ML Investment Banking Institute: August 2005
Problem Set #1
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