National Bank quotes the following for the British pound and the New Zealand dol

Question

National Bank quotes the following for the British pound and the New Zealand dollar:

Quoted Bid Price

Quoted Ask Price

     $1.61

     $1.62

       $.55

       $.56

NZ$2.95

NZ$2.96

Assume you have $10,000 to conduct triangular arbitrage. What is your profit from implementing this strategy?

$77.64.

$15.43.

$111.80.

$197.53.

Quoted Bid Price

Quoted Ask Price

Value of a British pound (£) in $

     $1.61

     $1.62

Value of a New Zealand dollar (NZ$) in $

       $.55

       $.56

Value of a British pound in    New Zealand dollars

NZ$2.95

NZ$2.96

Explanation / Answer

Solution:

Triangular arbitrage - The process of converting one currency to second currency, then converting the second currency to third and then finally converting the third currency to the first currency, in order to earn small profit, is known as triangular arbitrage. This opportunity arises when the exchange rate for the currencies do not exactly match up.

In the above case, by observation we can see that converting US dollar to Pound, then pound to NZ dollar and then NZ dollar to US dollar would be the case of triangular arbitrage.

We have $10,000 to start with.
From USD to British pound - Since the value of british pound in terms of USD is given and we need to buy pound, we would use Ask price for it (GBP/USD = 1.62). Hence Pounds = 10,000 * (1/1.62) = GBP 6,172.84

From GBP to NZD - Since the value of british pound in terms of NZD is given and we need to sell GBP, we would use bid price for it (GBP/NZD = 2.95), Hence NZD = 6,172.84 * 2.95 = NZD 18,209.88

From NZD to USD - Since the value of NZD in terms of USD is given and we need to sell NZD, we would use bid price for it (NZD/USD = 0.55), Hence USD = 18,209.88 * 0.55 = USD 10,015.43

So we finally got $10,015.43 by the process which is higher than $10,000 we started with.

Hence the profit from implementing the strategy is 10,015.43-10,000 = $15.43
Option b is the correct option

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