Question

A currency speculator expects the spot rate of British Pounds (GBP) to change from $2.00 to $2.20 in 6-months. Assume the speculator has access to credit lines of USD 20,000,000 in the US and GBP 10,000,000 in UK. The annual borrowing and lending rates are 6 percent in US and 4 percent in UK. If his forecast turns out be to true, at the end of the 6-month period, the speculator’s expected profit will be:

  

A currency speculator expects the spot rate of Euros to change from $1.20 to $0.80 in one year. Assume the speculator has access to credit lines of USD 12,000,000 in the US and EUR 10,000,000 in Europe. The annual borrowing and lending rates are 6 percent in US and 8 percent in Europe. If his forecast turns out be to true, at the end of the one-year period, the speculator’s expected profit will be:

  

  

Answer 1

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Answer:

1)

The Steps are as follows -

Today

The speculator should borrow in USD, convert into GBP at Spot rate, Invest in GBP for 6 months and then convert back to USD

Calculations:

Borrowings USD 20,000,000

Convert into GBP = 20,000,000/2 = GBP 10,000,000

Invest for 6 months and get 10,000,000*(1+4%*6/12) = GBP 10,200,000

Convert back into USD 10,200,000*2.20 = $22,440,000

Repay Loan 20,000,000*(1+6%*6/12) = $20,600,000

Arbitrage profit = $1,840,000

2)

The Steps are as follows -

Today

1. Take EUR 10000000 in Europe at 8% for six month

2. Convert it into dollar through current spot rate of $1.20, therefore E10000000*1.20 = $12000000

3. Invest it in US at 6% for six months, therefore 12000000(1+0.06/2) = $12360000

After six month

4. After six months loan value become E12000000(1+.08/2) = E12480000

5. Convert it into dollar through spot rate of $0.8, therefore E12480000*0.8 = $99840000

6. Pay $99840000 from $12360000 to settle the loan

Profit = $12360000 -$99840000 = $2376000