# Currency Forward Contracts

I am having a hard time with these types of FRA. I understand the convered interest arbitrage and which currency should be sold or bought but the steps are hard to follow. I don’t follow step 2, can someone please help explain? 1) If fwd price is higher and you sell at mkt price 2) buy 1/(1+rf)^T units of foreign ccy 3) hold position and earn interest 4) at maturity deliver the ccy and get paid the fwd price

steps 2 and 3 combined means you are ending up with 1 Unit of the foreign currency. do you see that? buy 1/(1+rf)^T units of foreign currency. It earns (1+rf)^t of Interest you end up with 1 unit of foreign currency. when you deliver that - in Step 4 - you end up with Forward currency contract amount for the 1 unit of FC.

Thanks CP…i got the unit of foreign ccy. So to calculate the rate of return from this arbitrage, you take the (fwd price/spot price)-1? And is spot price what we got from step 2? Can you please walk me through this question? For example p.54 from text book. Euro trades at \$1.0231, USD risk free is 4% and Euro risk free is 5%. 6 months forward contracts are quoted at \$1.0225. Indicate how you can earn a risk free profite and outline the steps.

Calculated Forward: 1.0231 /euro \* (1.04/1.05)^0.5 = 1.01822 /euro actual forward=1.0225\$ so forward contract is overpriced. So short sell the forward contract . borrow -\>buy Euro at Spot 1=>0.97742 Euro Lend it forward-> 0.97742 * 1.05^0.5 = 1.00156 Euro convert to at the forward rate -\> (real) 1.00156\*1.0225 = 1.02410 your 1\$ which you need to pay back = 1.00 * 1.04^0.5 = 1.0198 so your arbitrage profit = 1.0241-1.0198 = 0.0043 been a long time since I did this. pray tell me I am ok?

CP- i actually used 1eur and got the same answer as you but the book’s answer of return is not factoring in the cost of borrow. So they have (1.0225-.9988)=.0237 as arbitrage profit.

i had the same problem with this EOC and wondered why the arbitrage profit is not 1.0225-1.0182. 1.0182 is the “real” forward rate calculated from the interest rate parity. Can someone please help with this? Thanks!