Question

If the current 1-year risk free rate in US is 6%, the current 1-year risk free rate in Switzerland (currency symbol: CHF) is 9%, and the current spot rate between USD and CHF is CHF 1.2550/USD.

(1) If interest rate parity holds, what should be the appropriate one year forward rate?   

(2) You find out the actual quote from your bank on the one year forward contract is CHF 1.2850 /USD, what would be your covered interest arbitrage profits if you can borrow USD $1,000,000 in US at the risk free rate? To get full credits, you need to include step by step instructions on how to carry out this strategy.

Answer 1

1. If interest rate parity holds,the appropriate one year forward rate will be

Forward rate=( Spot rate *(1+domestic country interest rate))/(1+ foreign currency interest rate)

domestic country interest rate= USD =6%

foreign currency interest rate =CHF= 9%

Spot rate= I CHF= 1.2550USD

Forward rate = 1.2550USD*(1+6%)/1+9%)= 1.2204 USD

i.e I CHF= 1.2204 USD

2. Covered interest arbitrage profits if I can borrow USD $1,000,000 in US at the risk free rate (6%) and invest in CHF

Step 1 borrow USD $1,000,000 at 6% at spot rate I CHF= 1.2550USD

So we will receive= $1,000,000/1.2550 = 796812.75 CHF

Step 2 Invest 796812.75 CHF at 9% so we receive =796812.75*(1+9%)=868525.89 CHF

Step 3 Sell 868525.89 CHF at the forward rate agreed with bank CHF= 1.2850 USD so at the end of the year we will receive = 868525.89 *1.2850 =1116055.77 USD

Step 4 Repay the boroowings in usd = $1,000,000*(1+6%)=1060000 USD

Step 5 Balance =1116055.77 USD-1060000USD= 56055.776 USD is the Covered interest arbitrage profits