All interest rates are given as p.a. You must ajust to the period. Take money an

Question

All interest rates are given as p.a. You must ajust to the period. Take money and interest rates to four decimals before rounding.

You observe that the interest rate on 90-days treasury billis is 4-percent p.a in the U.S (1.0-percent total interest for 3 months) and an annual 6 percent in the U.K. If the spot exchange rate between the pound and the dollar is $1.40£ today:

A) Using one of the parity conditions, what would you expect the spot $/£ rate to be in 3 months? What relationship did you use for that answer?

B) If the 90-days foward rate is $1.38/$ today, using the ineterest rates given, could one make an arbitrage profit? Use numbers to justify your answer.

C) Prove your answer to b. using a nominal amount of 10,000 units of the currency you would borrow. Show all the steps.

Explanation / Answer

A) Using Covered Interest Rate parity relation, 90 days=3 months

Use relation,forward rate($/£)(T days)= spot exchange rate*{((1+(R$*T/360))/(1+(R£*T/360))}($/£)

90-days forward rate($/£)= ($1.40/£)*{((1+(.04*90/360))/(1+(.06*90/360))}

90-days forward rate($/£)= ($1.40/£)*{((1+.01)/(1+.015)}

90-days forward rate($/£)= ($1.40/£)*(1.01)/(1.015)

90-days forward rate($/£)=1.39

B,C)Yes the interest rate relationship implied forward rate=1.39($/£) is different from given 90-days forward rate is $1.38/£ today thus we could make arbitrage profit. Steps for arbitrage

1)Borrow 10,000 £ at  6-percent p.a in the U.K and convert it into $ using  spot exchange rate  $1.40/£. so that total $= 10,000 £*( $1.40/£),

2)Invest converted $ at annual 4 percent in the U.S for 3 months so that at end of period investment becomes 10,000 £*( $1.40/£)*(1+.04*90/360),simultaneously enter into a forward contract to sell $ at 90-days forward rate of $1.38/£

3)Now recover US $ investment after 3 months and convert it into £ using the forward contract, so value obtained is 10,000 £*( $1.40/£)*(1+.04*90/360)/$1.38/£=£10246.377

4) Pay the borrowed amount in £ at end of 3 months of Investment in UK= 10,000 £*(1.015)=£10150

5)Profit from the net amount £10246.377-£10150=£96.377 is the risk less arbitrage profit made.

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