IBF Chs 4 and 5

# IBF Chs 4 and 5 - L3: (Ch4) The International Parity...

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L3: (Ch4) The International Parity Conditions The Law of One Price The law of one price also known as purchasing power parity (PPP) implies: Equivalent assets sell for the same price The implication for multinational finance is that an asset must have the same value regardless of currency in which value is measured. Arbitrage Profit Strictly defined as a profitable position obtained with; no risk and no net investment . Arbitrage opportunities are quickly exploited and quickly disappear as arbitrageurs drive prices back towards equilibrium. Let P d denote the price of an asset in the domestic currency and P f denote the price of the asset in an foreign currency the spot rate of exchange must equate the value in the foreign currency to the value in the domestic currency. P d / P f = S d/f  P d = P f S d/f If this equality does not hold arbitrage opportunities!! Note: Seldom holds for non-traded assets Can’t compare assets that vary in quality May not hold precisely when there are market frictions I.e. suppose gold sells for P \$ = \$400/oz in New York and P £ = £250/oz in London . The no-arbitrage condition requires that the value of gold in the dollars must equal the value of gold in pounds, so; S \$/£ = P \$ /P £ = (\$400oz)/( £250/oz) = \$1.6000/£ Or S £/\$ = 1/(S \$ / £ ) = £0.6250/\$

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Arbitrage Profit when transaction costs exist Whether PPP holds depends on the extent of which market frictions restrain arbitrage from working its magic. Fees are charged for; providing information, providing a market, transporting or delivering an asset. Other barriers are imposed by government authorities ; trade barriers, taxes and financial market controls. I.e. FX dealer: \$1.599/£ bid and \$1.601/£ ask Gold Dealer A: £250.25/oz Offer and £250.00/oz Bid Gold Dealer B: \$401.40/oz Offer and \$401.00/oz Bid To buy low and sell high; in this case I would buy from dealer A and sell to dealer B . Specifically, I can buy form dealer A at £250.25/oz Offer price and sell to dealer B at \$401.00/oz Bid price . Procedure Buy 1mil oz from dealer A: - £250,250,000 Simultaneously sell 1mil oz to dealer B: + \$401,000,000 Buy £ ’s with \$’s at the \$1.601/ £ ask price Working : 1 / (\$1.601/£) = £0.62461/\$ [for every \$ I can get £0.624610 (£0.62461/\$)(\$401,000,000) = £250,468,457.20 Arbitrage profit = £218,500 [or if I convert back to \$] (\$1.599/£) (£218,500) = \$348,582 notice that we now must transfer money back through the FX dealer at the bid price.
Cross Rates and Triangular Arbitrage An exchange rate that does not involve the domestic currency is called a cross exchange rate or simply a cross rate . Suppose you are given bilateral exchange rates for currencies d, e and f. The

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## IBF Chs 4 and 5 - L3: (Ch4) The International Parity...

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