Leonard N. Stern School of Business

Global Financial Markets - Additional Problems, Solved

A supplement to Global Financial Markets, a guide to the workings of the world's currency, money and capital, commodities and derivatives markets.

by Ian H. Giddy, Stern School of Business, New York University

Chapter 2 - The Foreign-Exchange and Eurocurrency Markets

1. Christiana Bank provides the following quotation to Norway Oil Co. for the Swedish krone: 6.3140-6.3200 krone per dollar. How many dollars would Norway Oil Co. receive if it made a 50-million-krone investment in the United States?

Norway Oil Co.'s 50-million-krone investment in the U.S. effectively means that the company needs to convert Swedish krone to U.S. dollars. The quotation is receives from Christiana Bank is 6.3140-6.3200. The bid rate is SKr6.3140/$ and the offered rate is SKr6.3200/$. Since Norway Oil Co. needs to buy U.S. dollars, the appropriate rate is the bank's offered rate, SKr6.3200/$. Thus Norway Oil Co. would receive 50,000,000/6.3200=7,911,392.4$

2. Siemens, wishing to buy 15,000 British pounds, receives a quotation of US$1.6205-1.6245. How many U.S. dollars would the sterling cost the company? (Remember that the pound is quoted in dollars per pound sterling)

Siemens wishes to buy 15,000 British pounds. The quotation from the bank is US$1.6205-1.6245. Thus the bid rate (i.e., rate at which the bank is willing to purchase British pounds) is US$1.6205/GBP and the offered rate (i.e., rate at which the bank is willing to sell British pounds) is US$1.6245/GBP. Thus the appropriate rate for Siemens is the offered rate. Thus the 15,000 British pounds would cost the company treasurer 1.6245x15,000=24,367.5$

3. Hongkong Bank quotes bid-asked rates of SF2.6550-2.6600/$ and Y252-253/$. What Y/SF bid and asked cross rates would the bank quote?

The bid rate would be the rate at which HSBC is willing to buy SF, paying yen, and the offered rate is the rate at which HSBC is willing to sell SF in exchange for yen. HSBC is being asked to quote bid and offered rates for SF in terms of yen. Thus the cross rates can be obtained by dividing the offered rate for the yen by the bid rate for the SF and vice-versa:

(253Y/US$)/(2.6550SF/US$)=95.2919 (Offer rate: HSBC buys yen, sells SF)

(252Y/US$)/(2.6600SF/US$)=94.7368 (Bid rate: HSBC sells yen, buys SF)

4. Yin & Yang Bank in HongKong needs to fund a U.S.-dollar loan. It obtains the following quotations: 3-month Eurodollars 5 1/4-5 1/8, 3-month Euroyen 2 3/4-2 11/16, Y/$ spot 105.55-105.65, 3 month forward points 0.049-0.052. Which is the cheapest way of funding the loan? Explain carefully how it would be done.

YinYang needs to fund a U.S.-dollar loan. It could do this in two ways: (1) Borrow directly in the Eurodollar market at 5.25 percent or (2) Borrow in the Eurocurrency (here, Euroyen) market and then swap it into dollars. Let us investigate the second option a little further:

The bid rate on the 3-month Euroyen is 2.75 percent (i.e., YinYang can borrow yen at 2.75 percent).

(a) The forward premium can be calculated as swap points/spot rate=0.052/105.65

(b) Effective cost of yen funding
=[(1+foreign interest rate)(1+forward premium)]-1
= [(1+5.25/4)(1+0.052/105.65)]-1
=5.4495 percent.

Thus, it is cheaper for YinYang to simply borrow directly in the Eurodollar market at 5.25 percent.

5. West LB Bank in London is currently quoting 8% on 12-month Eurodollars deposits. It is also quoting 5.20FF/$ and 5.45FF/$ for spot and 12-month forward French francs, respectively. If a customer asks for a quote on depositing French francs, what interest should the bank quote?

Intuitively, the dollar is worth more French francs in the forward market, so the Eurodollar interest rate should be lower than the Euro-French franc interest rate. Roughly, the interest differential equals the forward premium. The forward premium is .25/5.2=4.81%, so the French rate is about 5% higher than the U.S. dollar rate.

Specifically, the link between spot and forward rates and Eurocurrency rates is given by the interest-rate-parity theorem:

(1+RUS)n = Spot(1+RFF)n/Forward

Solving for the Euro-French franc interest rate:

RFF = [(1+RUS)n.Forward/Spot-1](1/n) = [(1+.08)1.(5.45/5.20)-1]1 = 13.19%

Chapter 3 - Interest Rates in the Global Money Market

1. If the U.S. 3-month bank deposit rate is 7%, the reserve requirement is 2.5% and FDIC fees are 0.20%, (a) what would you expect the Eurodollar rate to be? (b) What will happen if the reserve requirement increases by 0.2 percentage point?

(a) The efffective cost of a domestic deposit is

= (IUS + FDIC fees) / (1 - reserve requirements)

= (7% + 0.20%) / (1 - 2.5%)

= 7.3846%

Thus the additional cost of the reserve requirements and FDIC fees is 38 basis points and this is the extra amount the bank can afford to pay on Eurodollar deposits to achieve the same cost of funds. Competition will generally drive the Eurodollar rate to the level that equates the cost of funds to banks in the two markets, that is, to 7.38%.

(b) If the reserve requirement increases to 2.7%, the Eurodollar rate will be:

= (IUS + FDIC fees) / (1 - reserve requirements)
= (7% + 0.20%) / (1 - 2.7%)
= 7.3998%

2. The U.S. bank deposit rate is now 5.15%, and the Eurodollar deposit rate 5.45%. Assuming that the entire differential is attributable to the Fed's reserve requirement on bank deposits, what is likely to happen to the Eurodollar rate if the U.S. rate rises by one percentage point?

IE$ = 5.45%
IUS = 5.15%

Banks arbitrage their funding costs between the domestic and the Eurodollar market, so that in equilibrium:

Cost of Eurodollar deposit = Cost of domestic deposit
IE$ = (IUS + FDIC fees) / (1 - reserve requirement)

Assuming the differential is entirely attributable to reserve requirements, we can set FDIC fees=0 and then IE$ = (IUS + 0) / (1 - reserve requirement)

Reserve requirement = 1- (IUS/IE$) = 1-(5.15%/5.45%) = 5.50%.

3. Based on the Eurocurrency interest rates in Figure 3.2 (GFM book, p.48), which currencies might be expected to fall against the French franc?

The interest-rate parity theorem holds that,

F / S (Eurocurrency X/FFr) = (1 + IX) / (1 + IFFr)
F = S (1 + IX) / (1 + IFFr)

Thus, F > S only if IX > IFFr. So, any Eurocurrency with interest rate higher than the EuroFFr interest rate is expected to depreciate in value relative to the FFr. If we look at Table 3.2, the table of Eurocurrency interest rates, we can see that the British pound, Canadian dollar, Italian lira and the Danish krone are expected to depreciate against the French franc.

4. Credit Suisse in Zurich is currently quoting 9.48% on 12-month Eurodollar deposits. It is also quoting 4.85 FF/$ and 5.05 FF/$ for spot and 12-month forward French francs respectively. If a customer asks for a quote on depositing French francs, what interest rate should the bank quote?

The interest-rate parity theorem gives us the theoretical value of the forward premium (or discount) as follows:

F / S (FFr/$) = (1 + IFFr) / (1 + I$) 5.05 / 4.85 = (1 + IFFr) / (1 + 9.48%)

IFFr = 14%

5. The central bank of Indonesia, Bank Negara, invests its reserves in US and German treasury bills. On one day in early 1996, the US Dollar and Deutsche Mark rates shown below were quoted on the Reuters screen. Where should Negara invest its spare cash? Can you identify a covered interest rate differential, in other words a deviation from interest-rate parity? What factors might account for this deviation from parity?

3-month interest rates Treasury-bill rate  
New York (US dollar) 5 7/16 - 5 5/16  
Frankfurt (Deutsche mark) 3 7/16 - 3 1/4  
Exchange rates against dollar Spot 3-month forward points
Deutsche mark 1.4769-1.4777 DM/$ 0.73-0.69 pfennigs discount

The outright forward rates on the DM are 1.4696-1.4708. The bid-side forward premium is (0.0073/1.4769)*4=1.9771%

A quick-and dirty calculation suggests it pays to buy US bills at 5.3125%. In dollar terms, a covered investment in German bills gets Negara roughly 3.25% + 1.9771% = 5.2271% per annum--an inferior return.

Let's check it out. The transaction would be:

Buy US bills at 5 5/16%, getting an effective return of 5.3840% (remember T bills are quoted on a discount basis)


Convert the dollars to DM at the spot rate of 1.4769

Invest in German treasuries at 3 1/4%, earning an effective return of 3.2766%

In 3 months, change the DM back into US dollars at the forward rate of 1.4708

This gives a return of 4.9492%.

Why does this arbitrage opportunity persist? Because T-bill arbitrage is only quasi-arbitrage: Treasury bill investors are not generally permitted or able to do it. The forward premium or discount is determined by Eurocurrency rates, not T-bill rates. Indeed, T-bills are not necessarily equivalent--they bear sovereign risk. See "Tea in Canada," a similar example.

Chapter 4 - Exchange-Rate Systems

1. A reversal of the U.S. trade deficit must involve:

(a) a reduction of the U.S. government budget deficit (including state- and local-government budgets).

(b) an increase in the growth of domestic output.

(c) an increase in the U.S. personal savings rate (plus a reduction in the U.S. personal-consumption rate).

(d) all of the above.

(e) any of the above.

The national income equation is defined as follows:


and the individual income-allocation equation is:


Rearranging the terms, we get:


Current account surplus = Net private-sector savings - Net government deficit.

Therefore, a reversal of the U.S. trade deficit should involve an increase in the right-hand side of the last equation. That is, an increase in the savings rate and/or a reduction in the government budget deficit.

2. Due to the massive strikes that hurt France in December 1995, Prime Minister Juppé, concerted with Président Chirac and his fellow European colleagues, has no other choice but to devalue the French franc within the ERM. Along with this realignment, the other participating currencies would be revalued upward. Beginning 1996, the central rates were as follows:

CurrencyCurrency/ECU (before)Currency/ECU (after)
Verify that FF/DM rate would change by about 5.5%. How does this percentage change compare to percentage changes in ECU central rates?

DM/ECU central rate: before, 1.91007; after, 1.906638. DM has risen 0.1797% (ECU has fallen 0.1797%).

FF/ECU central rate: before, 6.40608; after, 6.758414. FF has fallen 5.2133% (ECU has risen 5.2133%).

FF/DM central rate: before, 3.353846; after, 3.544676. FF has fallen 5.3836% (DM has risen 5.3836%).

Chapter 5
Exchange Rates, Interest Rates and Inflation Rates: An Integrated Framework

1. The annualized interest rates in the U.K. and Switzerland are 6.5% and 2% respectively, and the current spot rate for the Swiss franc is £0.556.
(a) What is the 90-day forward rate if interest-rate parity holds?
(b) You observe that the 90-day Swiss franc is being quoted at £0.5601. Is there an arbitrage opportunity? Specify the steps you would take to undertake such an arbitrage.

IBP = 6.5%
ISFr = 2%
S(£/SFr) = 0.556
If the interest-rate parity holds, F/S = (1+IBP)/(1+ISFr)
Therefore, F = 0.556*(1+6.5%/4)/(1+2%/4)
= 0.5622 £/SFr

Now, if there is a dealer willing to quote £0.5601, there must be an arbitrage opportunity. Since the quoted rate is below the theoretical equilibrium rate, we want to buy SF at £0.5601 and sell at £0.5622. We do this as follows:

(1) Borrow SF at 2%
(2) Change into pounts at spot rate of 0.556 per SF
(3) Invest the pount at 6.5%
(4) Sell £ (buy SF) forward at $0.5622.

2. In the course of one year, inflation in Peru has been 14.5% while in the U.S. inflation has been 1.7%. On the basis of relative PPP, what would you expect the currencies to do?

On the basis of the PPP, the rate of change of the exchange rate expressed in Peruvian sol per U.S. dollar will be given by the following relation:

(IPeru-IUS)/(1+IUS) = (14.5%-1.7%)/(1+1.7%)=12.59%.

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