Exchange rate theory, Exercises for Financial Market
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Ak.waka

Exchange rate theory, Exercises for Financial Market

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Tutorials for exchange rate theory
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International Bond and Currency Markets C39SM1 Tutorial Problem Set 7 Solutions

1. The main difference is that currency market is an inter-banking market without any single institution organizing it (e.g. stock exchange like in the case of the stock market). 2. A direct quote is the price of foreign currency in terms of the domestic currency. An indirect quote is the other way around: the price of domestic currency in terms of foreign currency. (a) Hence from the standpoint of a US investor, since the prices in the table give USD/unit of foreign currency, these are direct quotes. (b) To buy one USD we need 1/1.0219 = 0.9786 Euros; or 1/0.00798 = ¥125.31; or 1/1.5566 = £0.6424 (c) Let EUR = Euro, JPY = Yen, GBP = pound sterling, USD = US dollar. Then the rates given in the table are essentially USD/EUR, USD/JPY, USD/GBP. The required cross rates are JPY/EUR, EUR/GBP and JPY/GBP (putting these rates in the way they are usually quoted). Then, JPY/EUR = (USD/EUR) / (USD/JPY) = 1.0219 / 0.00798 = 128.06 Similarly for the two other cross rates: EUR/GBP = (USD/GBP) / (USD / EUR) = 1.5566 / 1.0219 = 1.5232 JPY/GBP = (USD/GBP) / (USD / JPY) = 1.5566 / 0.00798 = 195.06. 3. Let CAD = Canadian dollar, GBP = pound sterling, USD = US dollar, then: USD/CAD = 0.63, USD/EUR = 1.02, EUR/CAD = 0.67. Consider starting with 1 USD, converting it to Canadian dollars, then to Euros, then back to USD. We end up with: (1/0.63) x 0.67 x 1.02 = $1.08476. Hence by going round this loop we end up 8 cents richer. Alternatively:

1) Sell USD and buy CAD (USD 1,000,000  CAD 1,587,301) 2) Sell CAD and buy EUR (CAD 1,587,301  EUR 1,063,492) 3) Sell EUR and buy USD (EUR 1,063,492  USD 1,084,761)

So, yes, triangular arbitrage is possible, and starting with USD 1 million, we end up with a profit of $84,761. But in principle this is not the end of the story, as nothing is to stop us from going round the loop repeatedly – however does this mean we could earn an infinite amount? Comment: As soon as this sort of behaviour appears possible, the markets will adjust to make it unprofitable, e.g. via small adjustments to exchange rates. 4. The bid/ask spread is the difference between the buying and selling prices (e.g. 1.2511 – 1.2518). Yes, the bid/ask spread can lead to the disappearance of the arbitrage profit (the bid/ask spread is, essentially, the measure of the trading cost in the currency market). 5. Let F = forward currency rate and S = spot currency rate. When F<S, then there is a discount, while when F>S then there is a premium. 6. Spot rate of Hungarian Forint is 389.138 HUF/GBP. One month forward premium (annualised) is -6.2%. Hence, one-month forward exchange rate, F, is derived from the formula: AFP = {(F - S)/S} x 12 x 100%. In this case, F - S = - 6.2 x 389.138 / 1200 = - 2.011 HUF. Hence F = 387.127 HUF.

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