Under the classic Gold Standard, British pound is pegged to gold at £4.2474 = 1

Question

Under the classic Gold Standard, British pound is pegged to gold at £4.2474 = 1 ounce of gold, and Japanese yen is pegged to gold at ¥41.47 = 1 ounce of gold. (a) What is the implied exchange rate between British pound and Japanese yen under the Gold Standard? (b) If market rate is £1=¥ 10, is there an arbitrage opportunity? How much profit can you make? Will the market stay at this rate? Why? c) If market rate is £1= ¥9.5, is there an arbitrage opportunity? How much profit can you make? Will the market stay at this rate? Why? Assume you have £100 or Japanese yen of equivalent value.

Explanation / Answer

.(a)Implied exchange rate

1Ounce of gold=

£         4.2474

1Ounce of gold=

¥      41.47

£                         4.2474 =

¥      41.47

Implied exchange rate :

1 £    =(41.47/4.2474) ¥=9.7636201¥

Implied exchange rate:

¥ 9.7636201/£

.(b)Arbitrage Opportunity:

£1=¥ 10,

Yes,There is arbitrage opportunity since the Yen is cheaper

Step1.Convert £100 to yen .

You will get (100*10) =¥ 1,000

Step2.Purchase gold:

Amount of gold purchased with 1,000Yen=(1000/41.47) Ounce=24.113817 Ounce

Step 3.Sell 24.113817 Ounce of gold to get £ (24.113817*4.2474) =£102.42

Amount of profit=(£102.42-£100)= £2.42

.(c) Arbitrage Opportunity:

£1=¥ 9.5

Yes,There is arbitrage opportunity since the Pound is cheaper

Step1.Available Yen=100*9.7636==¥976.36

Convert Yen to Pound

You will get =976.36/9.5=£102.77

Step2.Purchase gold:

Amount of gold purchased with £102.77=(102.77/4.2474) Ounce=24.1971Ounce

Step 3.Sell 24.1971 Ounce of gold to get =¥ (24.1971*41.47)= =¥ 1003.45

Amount of profit=(¥ 1003.45- ¥976.36)= ¥27.09

1Ounce of gold=

£         4.2474

1Ounce of gold=

¥      41.47

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