Suppose an investor receive the following spot quotes from the bank for the Aust

Question

Suppose an investor receive the following spot quotes from the bank for the Australian dollar & the euro:

Is triangular arbitrage profitable for an Australian investor with AUD 1million to apply toward arbitrage? Show the work to support the answer. If arbitrage is profitable, how would one expect the quotes to adjust? Would the result change if the investor making the investment was an American investor with US$1million?

Bid Ask AUD 1.3775/USD AUD 1.3785/USD $ 1.1638/euro $ 1.1645/euro AUD 1.6063/euro AUD 1.6073/euro

Explanation / Answer

1

The triangular arbitrage is not profitable for an Australian investor with AUD 1million

Step 1 is to sell AUD @1.6063 = 1000000/1.6063 = Euro 622,548.7144

Step 2 is to buy USD @1.1645 = 622548.7144*1.1645 = USD 724957.978

Step 3 is to sell USD @1.3775 = 724957.978*1.3775 = AUD 998629.6146

So in this triangular arbitrage we started with AUD 1 mn and ended with lesser amount AUD 998,629

Arbitrage loss = AUD (1,000,000 - 998629.6146) = 1370.385358

2

If arbitrage is to profitable, the quote needs to adjust minimum by 20 basis points for bid price - that is increase from AUD 1.3775/USD to AUD 1.3795/USD

At bid price of AUD 1.3795/USD, the step 3 above will result in AUD =724957.978*1.3795 =1000,079.531 AUD

Arbitrage Profit = AUD (1,000,079.531 - 1,000,000) = 79.531

3

Yes. The triangular arbitrage  is profitable for an American investor with USD 1million

Step 1 is to sell USD @1.1638 = 1000000/1.1638 = Euro 859254.1674

Step 2 is to buy AUD @1.6073 = 859254.1674*1.6073 = AUD 1381079.223

Step 3 is to sell AUD @1.3775 = 1381079.223/1.3775 = USD 1,002,598.347

Arbitrage Profit = USD 1,002,598.347 - 1,000,000 = 2598.347

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