Question

You are a trader in Tokyo in Japan and observe the following quotes on the trading screen for the Japanese Yen (JPY), Australian dollar (AUD), and US dollar (USD):

AUD per USD (AUD/USD) 1.3618 – 1.3762 JPY per AUD (JPY/AUD) 77.95 – 78.78 JPY per USD (JPY/USD) 105.29 – 105.82

Suppose that you have 200,000 JPY in your trading account and interest rates are 0. Can you identify any positive arbitrage opportunities by using these quotes? Explain and show your working clearly and completely. Give your final answers in JPY.

Answer 1

Given Quotes

Quote-1 AUD/USD = 1.3618/1.3762

Quote-2 JPY/AUD = 77.95/78.78

Quote-3 JPY/USD = 105.29/105.82

Let us calcuate the syntetic rates for JPY using the first quote

AUD/USD * JPY/AUD = 1.3618*77.95/1.3762*78.78

Hence JPY/USD = 106.1523/108.417

JPY/USD * USD/AUD = (105.29/1.3762)/(105.82/1.3618)

JPY/AUD = 76.5077/77.706

Here clearly we can see Arbitrage opportunity as the quotations are different from the synthectic rates

Arbitrage profit

We have 2,00,000 JPY we will covert this into USD using the third quote

= 2,00,000 * 105.82 ( We will buy USD) = 1890 USD

Now we will convert USD into AUD = 1890*1.3618 = 2573.805( We will sell USD or Buy AUD)

Now we will convert AUD into JPY using the second Quote = 2573.805*77.95 = 200628.1

Hence we will get an amount of 200628.1 after using all the convertions but we have used only 2,00,000

Accordingly the arbitrage profit is 628.1 RS