Question

1. Exchange rate for Turkish Lira (TL) is $2

Exchange rate for Swiss Franc is $4

The cross rate between franc and TL is 3 francs per TL.

Is there an triangle arbitrage opportunity to make profit?

2. Exchange rate for Turkish Lira (TL) is $2

Exchange rate for Swiss Franc is $4

The cross rate between franc and TL is 3 francs per TL.

How much profit would you make at most if you have $100?

Answer 1

Cross rate is the derived currency exchange rate between two countries with respect to a common currency based on which official exchange rates of both the countries are given. Traingular arbitrage refers to a possibility where the cross rate is such that there is a possibility of buying low and selling high. For example, in the question given:

• exchange rate for Turkish Lira (TL) and USD ($) is $2/1TL. (in $/TL)
• exchange rate for Swiss Franc (franc) and USD ($) is $4/1franc. (in $/franc)
• Based on the above two information, the implied cross rate between franc and TL can be derived. Therefore ($/TL) / ($/franc) = ($/TL) * (franc/$) = franc/TL. From our example, the implied cross rate between franc and TL is $2/1TL * 1franc/$4 = 1franc/2TL or 0.5franc/1TL.
• We see that the observed or quoted cross rate between franc and TL is higher than the implied cross rate and is given at 3franc/1TL as opposed to 0.5franc/1TL. This means that there is a scope of triangular arbitrage involving the three countries. Had these two cross rates been the same, then there wouldn’t have been any scope for profit. But since the implied cross rate is lower than the quoted cross rate, there is a scope to buy cheap and sell dear in the foreign exchange market and earn profits. One can buy 1 TL for 0.5 franc and sell that 1TL for 3 francs.
• Thus the picture looks like: Case A: ($2/1TL)        Case B: ($4/franc)         Case C: (3franc/1TL)

Using the same information above, if one has $100 to put to use in the triangular arbitrage scenario, one can find out how much profit can be earned.

• Firstly, using case A to convert $ into TL, $2=1 TL or 1$= 1/2 TL or $100= 100*1/2 = 50 TL
• Secondly, using the observed cross rate, TL is converted into franc. 1 TL= 3 franc or 50 TL= 50* 3= 150 franc.
• Thirdly, using case B, franc is converted back into $. 1 franc= $4 or 150 franc= 150*4=$600.
• Thus, on spending $100 in triangular arbitrage, the revenue earned is $600. Therefore the profit earned through triangular arbitrage is revenue minus cost = $600-$100 =$500.