Question

Question 3: Suppose that on January 1st the annual cost of borrowing in Swiss Francs and US dollars are 5% and 7% respectively (R-swiss=5% and R-us=7%). The spot rate of USD on January 1st is CHF0.98 (or USD/CHF0.98) per USD.

Question 3a: Suppose one year forward rate was quoted as CHF 0.95 per dollar (or USD/CHF0.95). Given you have a credit of $10M to mobilize, is there any CIA (Covered Interest Arbitrage) opportunity? If so, how much is the CIA profit?

Question 3b: Suppose the expected one year spot rate is CHF 0.98 per dollar (or USD/CHF0.98). Given you have a credit of $10M to mobilize, is there any UIA (Uncovered Interest Arbitrage) opportunity? If so, how much is the UIA profit?

Answer 1

Covered interest arbitrage gives us the following equation

F/S = [ 1 + i (f)] / [ 1 + i (d)]

F = 0.98 * ( 1.05 / 1.07)

= 0.96

we see that the forward rate is not equal to the actual forward rate of CHF 0.95 / USD. So a arbitrage opportunity exists.

We shall follow the below steps :

a) We shall invest USD 10 M in Swiss Franc @ 5%

So amount invested = 10 * 0.98 = CHF 9.8 M

So amount received after 1 year with interest = 9.8 * 1.05 = CHF 10.29 M

b) Borrow USD 10 M in US dollars @ 7%

Amount to be paid after 1 year = 10 *1.07 = USD 10.70 M

c) We shall pay back the amount borrowed with the invested funds received

So amount refunded back in USD =10.29 / 0.95 = 10.8316

So arbitrage profit = 10.8316 - 10.70 = USD 0.1316 M

3b)

An unhedged currency exchanges happen to earn higher return in UCP.

There exists a arbitrage opportunity as we have calculated below as the estimated stock price is not equal to the expected spot price

E/S = [ 1 + i (f)] / [ 1 + i (d)]

E = 0.98 * ( 1.05 / 1.07)

= 0.96

a) We shall borrow USD 10 M in Swiss Franc @ 5%

So amount borrowed = 10 * 0.98 = CHF 9.8 M

So amount paid after 1 year with interest = 9.8 * 1.05 = CHF 10.29 M

b) Invest USD 10 M in US dollars @ 7%

Amount to be received after 1 year = 10 *1.07 = USD 10.70 M

c) We shall pay back the amount borrowed with the invested funds received

So amount refunded back in USD =10.29 / 0.98 =USD 10.5 M

So arbitrage profit = 10.70 - 10.50 =$0.20 M