Question

Using the CME Group prices, evaluate the 3 month price (F0) for arbitrage in the EUR/USD futures contract. Assume the risk-free rate in the U.S. is 1.8% (annualized) and the risk-free rate in Europe is -.8% (annualized).

(a) show the arbitrage profits that you can make with one contract (125,000 euros)

(b) show that you earn the same profits at time t (a) if ST = $1.10 on the street in three months as you would if ST = $1.50 on the street

Answer 1

Spot Price ( from CME ) : EUR/USD = 0.9090

3 month Future ( from CME ) : EUR/USD= 0.9063

As per Interest Rate Parity Theory : Future ( USD/EUR ) = spot price * (1+USDr/1+EURr)

By putting values, we get Future Price = 0.9090*(0.998/1.0045) = 0.9031

So it means, future is trading cheap so buy Future.

a). At t=0, Borrow 125000 Euro and convert it into USD and get $137513.75

At, t=3 get $137513.75*1.0045 = $138132.56 and convert it into EUR at future i.e $138132.56*.9063 = EUR 125189.54.

Now, EUR to be repaid = 125000*0.998 = 124750

So arbitrage profit = EUR 125189.54-124750 = EUR 439.54

b).As we have purchased future contract of EUR/USD @ 0.9063 so actual spot price at t=3 will not affect our profit.