1.   Foreign exchange market (4 marks)

If the Australian dollar-British pound exchange rate is A$1.80 per pound, and the

Australian dollar-euro rate is A$1.53 per euro:

(a) What is the pound-per-euro rate? (2 marks)

Answer: The pound-per-euro rate is (1 / AUD1.80/GBP) × AUD1.53/EUR =

GBP0.85/EUR.

(b) How could you profit if the pound-per-euro rate were above the rate you calculated in part a? What if it were lower? (2 marks)

Answer: If the pound per euro rate were above GBP0.85/EUR, you could profit by     converting Australian dollars to euros, euros to pounds, and then pounds to Australian dollars. For example, if the rate were GBP0.90/EUR and you started with A$153, you could exchange the A$153 for €100. Then you could exchange €100 for £90, and £90 for A$162, making a profit of A$9. If the pound per euro rate were below                    GBP0.85/EUR, you could make a profit by converting Australian dollars to pounds,   pounds to euros, and then euros to Australian dollars.

2.   Interest rate parity conditions (5 marks)

(a) It is often said that interest rate parity is satisfied when the differential between the   interest rates denominated in two currencies equals the forward premium or discount between the two currencies. Explain why this is an imprecise statement when the      interest rates are not continuously compounded. (3 marks)

Answer: Interest rate parity requires the equality of returns from investing directly in the domestic money market versus converting domestic currency into foreign            currency, investing the foreign currency, and selling the foreign currency forward.    Symbolically, we have

1 + i(t,DC) = [1 + i(t,FC)] × [F(t,DC/FC)] / S(t,DC/FC)]

If we divide by [1 + i(t,FC)] on both sides and subtract one from both sides, we get [i(t,DC) − i(t,FC)] / [1 + i(t,FC)] = [F(t,DC/FC) − S(t,DC/FC)] / S(t,DC/FC)

The left-hand side is the interest differential between the domestic and foreign rates adjusted for the denominator term and the right-hand side is the forward premium or discount on the foreign currency in terms of the domestic currency.

(b) Suppose you are the German representative of a company selling washing machines in South Africa. Describe your foreign exchange risk and how you might hedge it    with a money market hedge. (2 marks)

Answer: As a German company, you are interested in euro profits. Selling washing     machines in South Africa will give you South African rand revenues. The euro value   of these South African rand revenues will fall in value if the South African rand           weakens relative to the euro. To offset this loss in value, your company should borrow in South African rands.

3.   Purchasing power parity and real exchange rates (10 marks)

(a) Suppose the Australian dollar-United States dollar exchange rate moves from              AUD1.28/USD to AUD1.42/USD. At the same time, the prices of United States-made goods and services rise 8.3 per cent, while prices of Australian-made goods and          services rise 5. 1 per cent. What has happened to the real exchange rate between the     Australian dollar and the United States dollar? (2 marks)

Answer: The rate of change of the real Australian dollar-United States dollar exchange rate is given by:

rs(t+1,AUD/USD) = [1+s(t+1,AUD/USD)] × [1+π(t+1,USD)] / [1+π(t+1,AUD)] – 1 = [S(t+1,AUD/USD) / S(t,AUD/USD)] × [1+π(t+1,USD)] / [1+π(t+1,AUD)] – 1 =   (1.42/1.28) × (1.083/1.051) – 1 = 0.143 or 14.3%

The real Australian dollar-United States dollar exchange rate has risen by 14.3%.

(b) The same television set costs A$750 in Australia, US$500 in the United States, €450   in France, £300 in the United Kingdom, and ¥100,000 in Japan. If the law of one price holds, what are the AUD/USD, AUD/EUR, AUD/GBP, and AUD/JPY exchange         rates? (2 marks)

Answer: If the law of one price holds, then the AUD/USD exchange rate should be AUD750/USD500 = AUD1.5/USD, the AUD/EUR exchange rate should be           AUD750/EUR450 = AUD1.67/EUR, and the AUD/GBP exchange rate should be  AUD750/GBP300 = AUD2.5/GBP, and the AUD/JPY exchange rate should be      AUD750/JPY100,000 = AUD0.0075/JPY.

(c)  Why might the law of one price fail? (2 marks)

Answer: The law of one price may fail because of transportation costs, tariffs, and technical specifications.

(d) Can purchasing power parity help predict short-term movements in exchange rates? Why or why not? (2 marks)

Answer: Purchasing power parity does not hold on a day-to-day basis – or even on a month-to-month or year-to-year basis. It tells us how exchange rates will move over long periods like decades. In the short run, exchange rates can deviate substantially  from their purchasing power parity levels. In the short run, exchange rates are          determined by a host of factors affecting supply and demand for currencies and are  effectively unpredictable.

(e) If the price (measured in a common currency) of a particular basket of goods is 10 per cent higher in the United Kingdom than it is in Australia, which country’s currency is undervalued, according to the theory of purchasing power parity? Why? (2 marks)

Answer: According to the theory of purchasing power parity, the real exchange rate    should equal 1. If we look at the ratio of the cost of the basket of goods in Australia to the cost in the United Kingdom, that ratio (which is the real exchange rate taking        Australia to be the home country), is less than one. The Australian dollar is therefore  undervalued. If the Australian dollar were to strengthen, the Australian dollar price of the United Kingdom basket of goods would fall, bringing the real exchange rate back towards 1.

4.   Foreign currency swaps (5 marks)

The swap desk at Macquarie Bank is quoting the following rates on 5-year swaps versus 6-month Australian dollar BBSW:

Australian dollars: 6.85% bid and 6.95% offered

Swiss francs: 4.25% bid and 4.35% offered

You would like to swap out of Swiss franc debt with a principal of CHF50,000,000 and into fixed-rate Australian dollar debt.

(a) At what rates will Macquarie Bank handle the transaction? (2 marks)

Answer: Because you want to swap out of Swiss franc debt, you want Macquarie      Bank to pay you Swiss francs and you want to pay Macquarie Bank Australian         dollars. Macquarie Bank pays Swiss francs at 4.25%, and it receives Australian         dollars at 6.95%. When you receive Swiss francs, you pay 6-month Australian dollar BBSW on the equivalent Australian dollar amount, and when you pay Australian      dollars, you receive 6-month Australian dollar BBSW on that same Australian dollar amount. Thus, the floating rate Australian dollar cash flows cancel, and you would   just make the fixed rate Australian dollar payment and would receive the fixed rate   Swiss franc payment.

(b)  If the current exchange rate is AUD1.46/CHF, what would the cash flows be? (3 marks)

In the beginning of the currency swap, you would give the Swiss franc principal of CHF50,000,000 to Macquarie Bank who would give you AUD1.46/CHF ×             CHF50,000,000 = AUD73,000,000.

You would then make semi-annual Australian dollar payments of 0.5 × 6.95% × AUD73,000,000 = AUD2,536,750.

You would receive semi-annual Swiss franc payments of 0.5 × 4.25% × CHF50,000,000 = CHF1,062,500.

At the end of 5 years, you would also pay the principal of AUD73,000,000 and you would receive the CHF50,000,000.

5.   A monopolist with imported costs (8 marks)

Suppose you are a monopolist who faces a domestic demand curve given by Q = 1,000 – 2P. Your domestic cost of production involves domestic costs per unit of 300 and a         foreign cost per unit produced of 150.

(a) If the real exchange rate is 1. 1, what would be the price you would charge and the quantity you would sell? (4 marks)

Answer: The monopolist will operate where marginal revenue equals marginal cost. Price is (1,000 – Q) / 2, and total revenue is P × Q = (1,000Q – Q2) / 2. Marginal     revenue is therefore (1,000 – 2Q) / 2 = 500 – Q.

Marginal cost has a domestic component of 300 and a foreign component of RS ×     150. The initial real exchange rate is 1.1. Therefore, marginal cost is 300 + 1.1 × 150 = 465. Equating marginal revenue to marginal cost gives the optimal production:

500 – Q = 465 Q = 35

To sell a quantity of 35, the monopolist must charge P = (1,000 – 35) / 2 = 482.5.

(b)  How does the price you would charge and the quantity you would sell change when the real exchange rate increases by 10%? (4 marks)

Answer: If there is a 10% real appreciation of the foreign currency, the new real        exchange rate is 1.1 × (1 + 10%) = 1.21. Marginal cost increases to 300 + 1.21 × 150 = 481.5, and the optimal quantity falls to:

500 – Q = 481.5

Q = 18.5

The relative price in the domestic market increases to P = (1,000 – 18.5) / 2 = 490.75.

The 10% increase in the real exchange rate causes marginal cost to increase by 3.55% from 465 to 481.5. The price of the product increases by a smaller percentage, 1.71%, from 482.5 to 490.75. Thus, pass-through from the change in the exchange rate to the product price is less than one-for-one.

6.   International debt financing (6 marks)

(a) What is the difference between a foreign bond and a Eurobond? (2 marks)

Answer: One segment of the international bond market is the foreign bond market,   where a foreign issuer issues bonds in a particular domestic bond market, subject to  local regulations. The other segment is the Eurobond market, where bonds are issued simultaneously in various markets, outside the specific jurisdiction of any country.    Hence, these bonds are not subject to the regulations of any particular country.

(b) Why are Eurocredits not extended by one bank but by a large syndicate of banks? (2 marks)

Answer: Eurocredits are typically very large so that banks appreciate the opportunity to share the risk of default on the loan with other banks.

(c)  Should corporations issue bonds in countries where they face the lowest credit

spreads? Be specific about the concept of credit spread you use. (2 marks)

Answer: The answer here is potentially yes. When expressed in a multiplicative sense (by dividing one plus the interest rate the company faces by one plus the rate on a      comparable risk-free government bond), lower credit spreads do indeed translate into lower borrowing costs, provided the company can cheaply hedge the cash flows         involved into its desired borrowing currency.

7.   Risk and return of international investments (12 marks)

Suppose a Singaporean investor wishes to invest in a British firm currently selling for £80 per share. The investor has S$20,000 to invest, and the current exchange rate is S$2/£ .

(a) How many shares can the investor purchase? (2 marks)

Answer: S$20,000/2 = £10,000

£10,000/£80 = 125 shares

(b) Fill in the table below for rates of return after one year in each of the nine scenarios (three possible share prices denominated in pounds times three possible exchange   rates). (3 marks)

Price per

share (£)

£70

£80

£90

Pound-               Singaporean dollar-denominated return for

denominated                    year-end exchange rate (%)

return (%)         S$1.80/£           S$2.00/£           S$2.20/£

Answer: To fill in the table, we use the relation r(t+1,S$) = [(1 + r(t+1,£)] × [S(t+1) / S(t)] − 1.

Price per

share (£)

£70

£80

£90

Pound-               Singaporean dollar-denominated return for

denominated                  year-end exchange rate (%)

S$2.20/£

−3.75%

10.00%

23.75%

(c) If each of the nine outcomes is equally likely, find the standard deviation of both the pound-denominated and Singaporean dollar-denominated rates of return. (2 marks)

Answer: The standard deviation of the pound-denominated return (using 3 degrees of freedom) is 10.21%. The Singaporean dollar-denominated return has a standard         deviation of 13. 10% (using 9 degrees of freedom), greater than the pound-                  denominated standard deviation. This is due to the addition of exchange rate risk.

(d) Now suppose the investor also sells forward £10,000 at the forward exchange rate of S$2. 10/£ . Recalculate the dollar-denominated returns for each scenario. (3 marks)

Answer: First we calculate the Singaporean dollar value of the 125 shares of stock in each scenario. Then we add the profits from the forward contract in each scenario.

Price per share (£)

£70

£80

£90

Profit on forward exchange

Singaporean dollar value of stock at given exchange rate

S$2.20/£

19,250

22,000

24,750

−1,000

Profit on forward exchange = 10,000 × [2. 10 − S(t+1)]

Price per share         Total Singaporean dollar proceeds at given exchange rate

(£)                              S$1.80/£                   S$2.00/£                   S$2.20/£

£70                          18,750                     18,500                     18,250

£80                          21,000                     21,000                     21,000

£90                          23,250                     23,500                     23,750

Finally, calculate the Singaporean dollar-denominated rate of return, recalling that the initial investment was S$20,000:

Price per share

(£)

£70

£80

£90

Rate of return at given exchange rate (%)

S$1.80/£                  S$2.00/£                  S$2.20/£

−6.25%                     −7.50%                     − 8.75%

5.00%                          5.00%                          5.00%

16.25%                      17.50%                      18.75%