Question

A US investor sees an arbitrage opportunity in the currency markets. The spot exchange rate between the Swiss Franc and US Dollar is 1.0404 ($ per CHF). Assume the continuously compounded interest rates in the US and Switzerland are 0.25% and 0%, respectively. The 3-month currency forward price is 1.0300 ($ per CHF).\

a) What is the theoretically correct forward price?

b) What is the investor’s total profit (in CHF), assuming she begins by borrowing 1,000 CHF?

Answer 1

Spot Rate = CHF = USD 1.0404

Fwd Rate = SPot rate * COmpound int in Home country / Compound Int rate in Foreign country

= $ 1.0404 * e^rt / ert

= $ 1.0404 * e^0.0025*3/12 / e⁰

= `$ 1.0404 * 1.000625 / 1

= $1.0404

Actual Price is 1 CHF = $ 1.0300

Is under Priced. Hence purchase.

Part B:

Borrow CHF 1000

COnvert it into USD using spot rate

= 1000 * 1.0404

= $ 1040.40

depsoit that in US

& Realize the matured amount

= 1040.40 * 1.000625

= $ 1041.05

COnvert that amount in to CHF

= 1041.50 / 1.03

= CHF 1010.73

Repay the loan along with Int: (Int "0")

repay loan of CHF 1000

Book Prtofit of 10.73 CHF ( 1010.73 - 1000 )