# Forward Contracts

Should we expect questions about calculating the payments at settlement of forward contracts on stock indices, or on interest rates? I can not understand when long pays short and what amount he pays…

What does the LOS say?

In 2007 it said expect to calculate, not sure about the 2008 LOS. Also know what the 2 x 4, 3 x 6 etc. for the forward contract means. As for the calculation part --> this is how I remember this: Interest amount = Nominal * (Rate at settlement - Contract Rate ) / 100 * Length of the forward contract Long pays short. If amount is +ve --> Short pays Long. Length of contract --> is something like 90/360 or 180/360. and is determined by the 2 x 4, 4 x 6 etc. CP

i think this is a pretty good example from wikipedia of how forward contracts work. Example of how the payoff of a forward contract works Suppose that Bob wants to buy a house in one year’s time. At the same time, suppose that Andy currently owns a \$100,000 house that he wishes to sell in one year’s time. Both parties could enter into a forward contract with each other. Suppose that they both agree on the sale price in one year’s time of \$104,000 (more below on why the sale price should be this amount). Andy and Bob have entered into a forward contract. Bob, because he is buying the underlying, is said to have entered a long forward contract. Conversely, Andy will have the short forward contract. At the end of one year, suppose that the current market valuation of Andy’s house is \$110,000. Then, because Andy is obliged to sell to Bob for only \$104,000, Bob will make a profit of \$6,000. To see why this is so, one needs only to recognize that Bob can buy from Andy for \$104,000 and immediately sell to the market for \$110,000. Bob has made the difference in profit. In contrast, Andy has made a loss of \$6,000.  Example of how forward prices should be agreed upon Continuing on the example above, suppose now that the initial price of Andy’s house is \$100,000 and that Bob enters into a forward contract to buy the house one year from today. But since Andy knows that he can immediately sell for \$100,000 and place the proceeds in the bank, he wants to be compensated for the delayed sale. Suppose that the risk free rate of return R (the bank rate) for one year is 4%. Then the money in the bank would grow to \$104,000, risk free. So Andy would want at least \$104,000 one year from now for the contract to be worthwhile for him - the opportunity cost will be covered. Bob, as any other buyer would, will seek the lowest price he can for the contract - although as we’ve seen, there is an invisible lower limit of \$104,000 that Andy will not go below. As a result, the contract price would be at least \$104,000 or it will not happen at all. http://en.wikipedia.org/wiki/Forward_contract

i just realized i was talking about fra and not forward contracts, in general.

A forward contract on an interest rate would usually be an FRA so your answer was fine.

Thank you for your answers. I have checked, and the LOS only requires the calculation for FRA, not the others… My problem is I can not understand the logic of the FRA. For example (CFAI question, slightly changed): The treasurer of Company A expects to receive a cash flow of \$15 milllion in 90 days. He expects short-term interest rates to fall during the 90 days. To hedge, he decides to use an FRA that expires in 90 days and is based on 180-day LIBOR. The FRA is quoted at 5%. At expiration, LIBOR is 4.5%. The notional principal is \$15 mil. Should treasurer short or long the rate? How much is his gain? I know how to solve the question mechanically, but I do not understand the logic. My questions are: - When the treasurer shorts the rate, then what does it mean? Will he start to get 5% interest on his money after 90 days for a duration of 180 days? - If he is long the rate, then how do the answers to my questions above change? Thanks!

When you short anything, you want it to go down. So this Treasurer is going to get money in 90 days. His risk is that interest rates go down so he will not collect as much interest on the money as he would like. So he enters into a derivative that will pay him if the thing he doesn’t like comes to pass. That means he shorts an FRA, i.e., locks in the lending rate of 5%. When the FRA expires, he gets what he agreed to - the opportunity to lend money at 5% for 180-days. That comes in a backwards way though. The counterparty to the FRA doesn’t borrow the money. The counterparty pays him the amount of cash that if he deposited it along with the notional amount of the FRA at current LIBOR would give him the 5% interest rate he was locking in. Remember that you can always lend money at LIBOR by making a Eurodollar deposit (call up any bank in any developed foreign country with safe banks and ask them what the rate is on \$1M and you get a LIBOR deposit).

Thank you very much. It is kind of swap then actually…