Question

1. The risk-free rate in the US is 5% and the UK risk-free rate is 8%. The spot quote is $1.80/£ while the one year forward quote is $1.78/£. You can borrow either $1,000,000 or £555,556. According to IRP, is the forward quote correct? If not, what should it be?

If the forward quote is not correct, lay out the steps to implement an arbitrage.

Answer 1

According to IRP ,forward rate should be : spot rate (1+iUS)/(1+iUK)

                              = 1.8(1+ .05)/(1+.08)

                             = 1.8 *1.05/1.08

                            = $ 1.75 Per pound

According to IRP ,forward quote of $ 1.78 per pound is not correct.

2)Today :

Borrow $ 1,000,000 in US and you to repay 1,000,000(1+.05) = 1,050,000 in one year

the borrowed amount should be invested in UK for one year : 555,556 (1+.08)= 600000.48 pound in one year

After one year:

You will get 600000.48*1.78 =$ 1,068,000.8544 by selling the pound .   (by selling 600000.48)

Profit /(loss) = Amount received in $ in one year -amount to repay

              = 1068000.8544-1050000

                = $ 18000.8544