Question

Suppose the pound is pegged to gold at 5 pound per ounce, whereas the German Mark is pegged to gold at 15 Mark per ounce.

Currently the market exchange rate is 2.5 Mark per pound.

1. What is the implied exchange rate between German Mark and pound? Answer: 1 pound = German Mark (Please write your answer in whole German Mark. Enter just the number without the currency unit).

2. Which of the following strategy will take advantage of this situation? Suppose you are a UK investor and start with 1,500 pound.

3.What is your arbitrage profit (in pound)? Suppose you are a UK investor and start with 1,500 pound Please round your answers to whole pound.

Answer 1

Question 1:

The implied exchange rate would be 1 pound = 3 German Marks (meaning 3 Marks per pound)

Explanation: Both the currencies are defined by per ounce, so we can easily equate them, by saying that if it costs 5 Pound per ounce, and 15 Mark per ounce, then the equilibrium exchange rate would be 15 Marks/5 Pounds = 3 Marks per pound.

Question 2:

Investment value = 1,500 pounds

An arbitrage strategy can be adopted here, since the Mark is underpriced in the direct foreign exchange market as compared the implied exchange rate determined.

Suppose you need to buy German marks, if you buy it directly in the foreign exchange market, it will cost 2.2 Marks per pound, giving us only 3,300 German Marks (Calculation: 1500 pounds*2.2).

Alternatively, you can first buy an ounce of gold for 5 pounds, which will give total ounces of gold = 300 ounces of gold (Calculation: 1500 Pounds/5 Pounds per ounce).

You can convert this gold into German marks, by selling it at the rate of 15 Marks per ounce of gold, giving 4,500 marks (Calculation: 300 gold ounces*15 German marks = 4,500 german marks)

We can sell these german marks in the foreign exchange market, for 2.2 Mark per pound, giving you, 2,045 pounds. (Calculation: 4500/2.2 = 2,045.45 pounds)

Question 3:

The arbitrage profit will be 2,045 pounds - 1,500 pounds = 545 pounds.