BFW3331 Suggested Solutions for Tutorial 6 Week 7

10Chapter 3: Forward Markets and Transaction Exchange RiskBFW3331 Suggested Solutions for Tutorial 6 Week 7

Tutorial 6: The Foreign Exchange Markets

1. Explain the following terms:i) bid, offer, spread and pipsii) spot rate, forward rate, cross rate, reciprocal rateiii) commodity currency, term currencyiv) direct and indirect quotes

Q.1 (i) Bid rate- the rate at which the quoting bank is willing to buy the commodity currency. Offer rate- the rate at which the quoting bank is willing to sell the commodity currency Spread- the difference between the offer and bid rate Pips- units in the last decimal place to which a particular exchange rate is usually quoted.

(ii) Spot rate- price of exchanging one currency for another which will be made 2 business days from the contract date. Forward rate the rate agreed upon today at which one currency is sold / bought against another for delivery on a specified future date. Cross rate an exchange rate which derives from 2 other exchange rates. Reciprocal rate is the inverse of a conventional quote. (iii) Commodity currency the currency being priced in an exchange rate quotation. Term currency the quoted currency which is expressed in terms of no. units of the other currency; the other currency is known as the term currency.

(iv) Direct quote an exchange rate quoted in terms of the local currency ie no units of local currency which equals one unit of a foreign currency. Indirect quote the local currency is expressed in terms of a foreign currency. i.e. 1 unit of local currency equals no. units of foreign currency.

Bekaert & Hodrick. Chapter 2 page 66 / 67 Problems: 1, 2, 3, 4, 5, and 6.

1. Mississippi Mud Pies, Inc. needs to buy 1,000,000 Swiss francs (CHF) to pay its Swiss chocolate supplier. Its banker quotes bidask rates of CHF1.39901.4000/USD. What will be the dollar cost of the CHF1,000,000?

Answer: The banks bid rate is CHF1.3990/$. That is the price at which the bank is willing to buy $1 in return for CHF1.3990. The bank sells dollars at ask price CHF1.4000/$. Mississippi Mud Pies must sell dollars to the bank to buy CHF. Therefore Mississippi Mud Pies will receive the banks bid rate of CHF1.3990/$. The dollar cost of CHF1 million is consequently = CHF 1 million / CHF1.399/$ = $714,796

2. If the Japanese yenU.S. dollar exchange rate is 104.30/$, and it takes 25.15 Thai bahts to purchase 1 dollar, what is the yen price of the baht?

Answer: To prevent triangular arbitrage, the direct quote of the yen price of the baht (/THB) must equal the yen price of the dollar times the dollar price of the baht (which is the reciprocal of the baht price of the dollar:

104.30/$ 1/(THB25.15/$) = 104.30/$ $0.03976/THB = 4.1471/THB

3. As a foreign exchange trader, you see the following quotes for Canadian dollars (CAD), U.S. dollars (USD), and Mexican pesos (MXN):CAD1.419/USDMXN6.4390/CADMXN8.7535/USDIs there an arbitrage opportunity, and if so, how would you exploit it?

Answer: The direct quote for the cross-rate of MXN6.4390/CAD should equal the implied cross-rate using the dollar as an intermediary currency; otherwise there exists a triangular arbitrage opportunity. The indirect cross rate is MXN8.7535/USD / CAD1.419/USD = MXN6.1688/CAD

This indirect cross rate is less than the direct quote so there is an arbitrage opportunity to exploit between the three currencies. In this situation, buying the CAD with MXN by first buying USD with MXN and then buying the CAD with the USD and finally selling that amount of CAD directly for MXN would make a profit because we would be buying the CAD at a low MXN price and selling the CAD at a high MXN price.

4. The Mexican peso has weakened considerably relative to the dollar, and you are trying to decide whether this is a good time to invest in Mexico. Suppose the current exchange rate of the Mexican peso relative to the U.S. dollar is MXN9.5/USD. Your investment advisor at Goldman Sachs argues that the peso will lose 15% of its value relative to the dollar over the next year. What is Goldman Sachss forecast of the exchange rate in 1 year?

Answer: One way to think of this is to say that the investment advisor is referring to the fact that the Mexican peso price of the dollar will be 15% higher next year. In this case, the forecast of the MXN/USD exchange rate in year 1

MXN9.5/USD 1.15 = MXN 10.925/USD

A 15% loss of value of the Mexican peso versus the U.S. dollar technically means that dollar price of the peso is 15% lower. We know that the current USD price of the peso is1 / (MXN9.5/USD) = USD0.1053/MXN

If this exchange rate falls by 15%, the new exchange rate will be

0.85 USD0.1053/MXN = USD0.0895/MNX

In this case the forecast for the future exchange rate measured in pesos per dollar is 1 / (USD0.0895/MXN) = MXN11.1726/USD

The difference arises because the simple percentage change in the exchange rate depends on how the exchange rate is quoted.

5. Deutsche Bank quotes bidask rates of 0.98500.9855/$ and 104.30-104.40/$. What would be Deutsche Banks direct asking price for yen (/)?

Answer: The direct asking price of euro per yen (/) is the price at which the bank will sell yen for euros. The bank would want this to be the same as the price at which it sells euros for dollars (the banks ask price) times the price at which it sells dollars for yen. This latter price is the reciprocal of the price at which the bank buys dollars for yen, which is the banks bid price of yen per dollar. Thus, the ask price of euros per yen should be

0.9855/$ [1 / (104.30/$)] = 0.009449/

6. Western Mining of Australia has called Mitsubishi Tokyo Financial to get its opinion about the Japanese yenAustralian dollar exchange rate. The current rate is 67.72/A$, and Mitsubishi thinks the Australian dollar will weaken by 5% over the next year. What is Mitsubishis forecast of the future exchange rate?

Answer: If the Australian dollar weakens by 5% over the next year, it will take 5% fewer Japanese yen to purchase the Australian dollar. Thus, the forecast is

67.72/A$ (1 0.05) = 64.334/A$

Bekaert & Hodrick. Chapter 3 page 114 / 115 Questions: 1 and 2. Problems: 1, 4, and 5a

Q1. What is a forward exchange rate? When does delivery occur on a 90-day forward contract?

Answer: The forward exchange rate is a price quoted today for the exchange of currencies at the maturity of the forward contract. To find the delivery date for a 90-day forward contract, one first finds the spot value date, which is typically two business days in the future relative to the day that the contract is made. Then, to find the forward value date, one goes to the calendar date in three months corresponding to the calendar date of the spot value date. If that calendar dates in three months is a legitimate business day in both countries, that date is the forward value date. If the banks in one of the countries are closed on that date, because it is a weekend of holiday, the forward value date is the next available business day without going out of the month. If going forward in time would take you out of the month, you go backward in time. This rule is followed except when the spot value day is the last business day of the current month, in which case the forward value day is the last business day in both countries in three months (this is referred to as the end-end rule).

Q2.If the yen is selling at a premium relative to the euro in the forward market, is the forward price of EUR/JPY larger or smaller than the spot price of EUR/JPY?

Answer: When the yen is selling at a premium in the forward market, the euro price of the yen in the forward market, EUR/JPY, would be larger than the spot price of EUR/JPY.

P1.If the spot exchange rate of the yen relative to the dollar is 105.75, and the 90-day forward rate is 103.25/$, is the dollar at a forward premium or discount? Express the premium or discount as a percentage per annum for a 360-day year?

Answer: When the forward rate of yen per dollar is less than the spot rate of yen per dollar, the dollar is said to be at a discount in the forward market. The magnitude of the discount is expressed in percentage per annum by dividing the difference between the forward rate and the spot rate by the spot rate and multiplying by reciprocal of the fraction of the year corresponding to the maturity of the forward contract (360/N days) and by 100. Thus, the annualized forward discount is 9.46% because

Notice that the word discount implies that the forward rate is less than the spot rate.

P4.Consider the following spot and forward rates for the yeneuro exchange rates:

Spot30 days60 days90 days180 days360 days

146.30145.75145.15144.75143.37137.85

Is the euro at a forward premium or discount? What are the magnitudes of the forward premiums or discounts when quoted in percentage per annum for a 360-day year?

Answer: The forward rates of yen per euro are lower than the spot rates. Therefore, the euro is at a discount in the forward market. The annualized forward premium or discount for the N day forward contract is

If the value of this calculation is negative, say -2%, we say there is a 2% discount. Therefore, the discounts are 4.51% for 30 days, 4.72% for 60 days, 4.24% for 90 days, 4.01% for 180 days, and 5.78% for 360 days.

P5a.As a currency trader, you see the following quotes on your computer screen

Exch. RateSpot1-month2-month3-month6-month

USD/EUR1.0435/4520/2552/6275/9097/115

JPY/USD98.75/8512/1020/1625/1945/35

USD/GBP1.6623/3330/3562/7595/110120/130

Answer: The spot bid and ask quotes for USD/EUR are 1.0435/45. These quotes mean that the bank buys euros with dollars spot at $1.0435/, and the bank sells euros for dollars at $1.0445/. Because the forward points at the 3-month maturity are 75/90, we know that we must add the points to get the outright forward bid and ask rates. Adding the points makes the bid-ask spread in the forward market larger than the bid-ask spread in the spot market. Consequently, the forward bid rate is $1.0435/ + $0.0075/ = $1.0510/, and the forward ask quote is $1.0445/ + $0.0090/ = $1.0535/.

Q 4 Consider the following US$1 against SFR exchange rates quoted by 3 banks in different centres.Bank XYZ1.7140/50 in TokyoBank ABC1.7153/63 in SingaporeBank Win1.7150/55 in Melbourne

i) Is there any arbitrage opportunity? If yes, how would you take advantage of this arbitrage?ii) How much profit (in SFR term) would you make on a principal amount of US$ 10 million?

Answer

Arbitrage Profiti)a) Buy US$1 against SFR from Bank XYZ in Tokyo at 1.7150b) Sell US$1 against SFR to Bank ABC in Singapore at 1.7153c) Arbitrage profit is 0.0003 SFR per US$

ii) US$10,000,000*0.0003= SFR 3000

6Monash University Malaysia: BFW3331, S1 20141