Question

With the aid of appropriate illustrations discuss the concept of international arbitrage and scenario necessary for it to be plausible under the following headings.

(i)Locational arbitrage

(ii)Triangular arbitrage

Use specific numerical examples to illustrate the various arbitrage types. Additionally, you are free to use derivations/equations, tables, diagrams/figures etc.

Answer 1

Traingular Arbitrage:

Triangular arbitrage is the result of a discrepancy between three foreign currencies that occurs when the currency's exchange rates do not exactly match up. These opportunities are rare and traders who take advantage of them usually have advanced computer equipment and/or programs to automate the process. The trader would exchange an amount at one rate (EUR/USD), convert it again (EUR/GBP) and then convert it finally back to the original (USD/GBP), and assuming low transaction costs, net a profit.

Example of Triangular Arbitrage

As an example, suppose you have $1 million and you are provided with the following exchange rates: EUR/USD = 0.8631, EUR/GBP = 1.4600 and USD/GBP = 1.6939.

With these exchange rates there is an arbitrage opportunity:

1. Sell dollars for euros: $1 million x 0.8631 = €863,100
2. Sell euros for pounds: €863,100/1.4600 = £591,164.40
3. Sell pounds for dollars: £591,164.40 x 1.6939 = $1,001,373
4. Subtract the initial investment from the final amount: $1,001,373 - $1,000,000 = $1,373

From these transactions, you would receive an arbitrage profit of $1,373 (assuming no transaction costs or taxes).

1. Local Arbitrage (One good, one market)

It sets the price of one good in one market. Law of one price: the same good should trade for the same price in the same market.

Example: Suppose two banks have the following bid-ask FX quotes: Bank A Bank B

USD/GBP 1.50 1.51 1.53 1.55

Taking both quotes together, Bank A sells the GBP too low relative to Bank B’s prices. (Or, conversely, Bank B buys the GBP too high relative to Bank A’s prices). This is the pricing mistake!

Sketch of Local Arbitrage strategy:

(1) Borrow USD 1.51 (<= No own capital!)

(2) Buy a GBP from Bank A (at ask price SA t,ask = USD 1.51)

(3) Sell GBP to Bank B (at bid price SB t,bid = USD 1.53)

(4) Return USD 1.51 and make a π = USD .02 profit (1.31% per USD 1.51 borroweed

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