D. Triangular Arbitrage & Cross Exchange Rates - Cross exchange rates are exchange rates between two currencies (bilateral) - Daily cross rates are available between all major currencies - Given the exchange rate between two currencies and a third, you can calculate the exchange rate between those two currencies. Sa/c/Sb/c = Sa/b Or Sa/c = Sa/b x Sb/c Or 1.0 = Sa/b x Sb/c x Sc/a this is called the no-arbitrage condition (NOC) - If this condition is violated, then traders can make a risk-free profit by trading currencies. - Trading currencies to exploit temporary violations of the no-arbitrage condition is called triangular arbitrage. - Triangular arbitrage will hold all currencies in equilibrium and enforce the NOC Example: Triangular Arbitrage & Spot Exchange Rates Given: SDm/$ = Dm1.908/$ A/B S$/FFr = $.1563/FFr B/C What is the equilibrium rate of Dm per FFr? SDmFFr = 1.908 x .1563 = .2982 = Dm.2982/FFr A/C No-arbitrage condition: Sa/b x Sb/c x Sc/a = 1.00 1.908 x .1563 x 1/.2982 = 1.0 Sa/b x Sb/c = Sa/c = .2982 1.908 x 1.563 = .2982 Choosing the action to take in triangular arbitrage: No-arbitrage condition: Sa/b x Sb/c x Sc/a = 1.00 Arbitrage opportunity: Sa/b x Sb/c x Sc/a > 1.00 Buy the numerator Sa/b x Sb/c x Sc/a < 1.00 Buy the denominator Example: Identify if an arbitrage opportunity exists and how to exploit it! S$/Dm = $.524/DM Price of Dm in U.S. dollars SDm/C$ = Dm1.298/C$ Price of Canadian dollars in Dm SC$/$ = C$1.30/$ Price of U.S. dollars in Canadian dollars S$/Dm x SDm/C$ x SC$/$ = .524 x 1.298 x 1.30 = .8842 Checking the NOC What action do you take? Buy the denominator Take $ and buy Dm: $1/$.524 = Dm1.9084 Take Dm and buy C$: Dm1.9084/Dm1.298 = C$1.4703 Take C$ and buy $: C$1.4703/C$1.30 = $1.131 You started with $1 and made an arbitrage profit of 13%! Suppose that you started with: SC$/$ = C$1.50/$ What would you do?
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