Derivatives (1) Currency Forward Dr. J. D. Han King’s College University of Western Ontario

1. Derivative in general Definition of Derivatives financial assets whose values depend on underlying assets Uses Hedging (against risk) behaviors beget a series of derivatives Different Kinds of Derivatives 1) Short-selling 2) Forward-related Derivatives: Forwards, Futures, Swaps 3) Options-related Derivatives

2. Organization of Forward Market Buyer and sell (of products) agree to buy or sell something at an agreed price F on the trade date which is now , and deliver/pay later at the settlement date (t+1). Over-the-counter (O. T. C.) transactions = Custom Made through face-to-face talks

3. Players in the Forward FOREX market You are using Forward FOREX market for a certain amount of profits. You are an Arbitrageur. “An arbitrageur is a type of investor who attempts to profit from price inefficiencies in the market by making simultaneous trades that offset each other and capturing risk-free profits”(Investopia). As you have stakes in E t+1 , and are exposed to the FOREX risk of unexpected changes in E t+1 compared to Et . Thus, you want to cover from its risk through forward market by taking the opposite position in F. You are a hedger. 3) Initially you have no business risk to FOREX changes. However, you are now assuming new risks through forward market. You are a speculator.

4. Operation of Forward Contract (itself) A Forward Price/Rate of FOREX or “F” is set between the buyer and the seller now or ‘on the trade date (t)’ for the ‘settlement date (t+1: in the future)’. The settlement date is when the delivery/exchange of FOREX is to be done; The settlement date could be 1 month, 3 months, 6 months, 1 year…3 years…from the trade date.

2) Long Position versus Short Position The Buyer of a Forward Contract is called ‘in the long-position’; -> Byuer will win if Et+1 turns out to be higher than F. The seller of the contract is said to be ‘in the short-position’. -> Seller will win if Et+1 turns out to be lower than F.

**Recall the math:  

3) Settlement could be done by the ‘Margin’ payment, not by actual delivery. A and B buys and sells a currency, agreeing on the Forward FOREX rate (price of a unit of foreign currency) or F for the settlement date. -> The buyer has bought forward at F. On the settlement date, compare the forward rate F and the realized spot FOREX rate St+1 on the very day and the locked forward rate F. If Et+1 >F, the buyer (on long position) ‘wins’ in that he saves Et+1 –F; the seller ‘loses’ in that he potentially loses Et+1 –F; The most cost efficient settlement is that the winner(buyer in this case) get the difference/margin Et+1 – F from the loser(seller in this case); and the winner subsequently buys FOREX from the spot market with his own money of F plus the remittance of Et+1. –F. -> The total cost of buying FOREX is F + Et+1 -F = Et+1,, but his own net cost is only F, the same amount he would use in the Forward Contract. If Et+1 <F, the seller gets the difference/margin.

*Hypothetically, in this case You are forward buyer of GBP. If you will not actually need GBP, you may get the delivery of GBP at F(low) and sell it in the spot market at Et+1(high). (This has an open position, and thus it is not a hedging, though).

*Who wins, and who loses in Forward contract ? Seller of Forward Contract -”Short” with Forward Contractor Buyer of Forward Contract -“Long” with Forward Actual Settlement Et+1>F; This is the case when Et+1 turns out to be higher than F. Loses He has to sell at the lower price F instead of selling at a higher price of St+1 Wins He does not have to pay a higher spot market price St+1, but pays a lower price of F to buyer in forward market. No delivery case: The Winner gets St+1 –F from the loser Forward Buyer gets money of St+1-F from seller, and uses the money to buy at spot market for St+1 (= his own money F + the money from buyer of St+1-F)

In general, For the given Contract Price –locked –up or pre-fixed F(contract price: forward), Et+1(purchase price: futures), which are all fixed by now, Buyer (long) has the following Upward-sloping Payoff Line: Seller (short) has the Downward-sloping Payoff Line:

5. Forward Market for Hedging Hedging is covering yourself from the Initial (FX) Risk due to Uncertainty or Changes between Now and the Future. Hedging is the same as ‘Buying Insurance’.

1) How does it work? Suppose that you are in an International Finance Division at TD. Original Business(International Investment) and Potential Loss Suppose that you are a Canadian, and you have payable of loans GBP (1 million) in one year. You will have to repay in GBP. You have brought the borrowed fund of GBP 1 million, converted it into Canadian dollars at the current Spot rate at E, and to Canada and deposited the converted Canadian dollars in a Canadian bank. You have receivable of investment in Canadian dollars to mature in a year. ->You will have loss if the value of GBP rises against CAN ( E Up). Forward Hedging and Potential Gains To cover yourself form the FOREX risks, you have decided to sell forward CAN and to buy GBP forward. -> if E goes up, then you ‘win’ in forward contract, and use the gains to make up for the potential loss from the original business. Illustrate the risk to which TD bank is exposed, and show how it can hedge through Forward/Derivatives in FX market.

Step 1: Draw the Net Payoff curve for the Initial FOREX Risk from International Investment (GBP-denominated liability and CAN-denominated assets): As Et+1 rises below Et, TD bank loses. + - E (=1) Et+1 -

Step 2. Hedging: Choose the Forward Contract to Offset the above FOREX risk: You should take Forward Hedging, which gives the opposite shape of the initial net payoff curve, so that the red/loss part could be hedged: would it be forward selling or forward buying?

i)Choose ‘Hedging by forward-buying FOREX(=GBP), or forward-selling CAN’. ii)the Pay-off curve for the forward buyer of FOREX is upward sloping: F* “Long” position with FOREX forward: TD will win when Et+1 rises above F.

In Forward Market, he should buy(be long on) GBP. * The applied General principle of hedging is the same as the “In insurance where you bet on the worst possibility”. If you hate “the appreciation of GBP in your international investment business” (, which increases your liabilities in CAN). Thus in insurance, you should bet on the worst for you, that is, the appreciation of GBP. In Forward Market, he should buy(be long on) GBP.

Now, let’s combine the two, the initial Risk and the forward Hedging

The alternative result with a ‘Better’ Hedging Deal: If TD manages to get a forward contract partner(forward buyer) agreeing on F which below E: (a) Ffixed Etfixed (b) Et+1stochastic Draw the net profit curve.

Still, you can get only the following Hedging Deal: If TD can only get a forward contract partner(forward buyer) agreeing on F which stands above E: (a) Etfixed Ffixed (b) Et+1stochastic Draw the net profit curve.

Step 3: combining the above two graphs, you may get the ‘zero’ net or something close if you can get F close to E: Whether the Future spot FOREX rate Et+1 falls or rises, the net profits will be constant all the time, being equal to the implicit insurance premium he has paid (=C $ 0.01 million). From Step 2. FOREX Hedging + + Zero profit line - Now Step 3. Net profit/loss= 0 at all times - From Step 1. Initial Risk

Step 3’: Alternatively, you can manage to get F lower than Et, and then there will be always net profits for hedging. Still this is cost for Hedging or Peace of Mind. If you can only buy forward buyer at F quite low (<Et). Then, at any realized Et+1, there will always be net profits with initial business and hedging. 1.Initial FOREX Risk + 3.Net profit/loss= negative at all times + F Zero profit line Et - - 2. Forward Hedging

Step 3’’: Alternatively, if you can only get a higher F, there will be net negative profit: 2. Forward Hedging F + + Zero profit line Et - 3.Now the New Net/Combined profit/loss positive at all times - 1. Initial Business FOREX Risk

Suppose that initially, Et =1, and * The same above Example of Forward Hedging with some specific numbers: Suppose that initially, Et =1, and Asset: TB bank has a receivable of CAN $1 million coming in 1 year. Liabilities: TD bank has payables of loans of GBP 1 million i

(1) (FX) Risk of Business of Bond Trading In one year, Et+1 may be different from Et. GBP 1 million may bring require a lot more than CAN 1.75 million Possiblity 2: Et+1 = 2.00 GBP 1 million -> CAN 2 million ‘Unexpected’ additional burden from FOREX: - CAN 0.25 m (risk needs to be hedged) Suppose Now (Et=) 1.75 i Zero profit line Et+1 Possibility 1: Et+1 = 1.50 GBP 1 m -> CAN 1.50 m ‘Windfall’ Gains from FOREX: CAN 0.25 m (no need to worry)

(2) Now how to do ‘Forward Hedging’ for Risk: You as TD bank’s manager are “risk-averse”, and willing to pay for the elimination of the risk of having the loss through Forward FOREX transactions. What position(buy- Long or sell-Short) should he take with respect which currency(U.S. or Canadian dollars)?

* The General principle of hedging is, “In insurance, you bet on your (possible) loss”. You hate ‘the appreciation of GBP’ or Et+1 Up as your payables are in GBP. Thus in forward hedging(=buying insurance), you should bet on the rising GBP or Et+1 UP. Thus, if GBP appreciates, (although you may lose in primary business/international investment) you may win in the financial/forward contract. The gain from the forward contract offsets the loss in business. <- You should (buy/sell) GBP Forward. – *circle your answer. ** Hint: You can sell something only when you get it.

With numbers: Taking a position in the Forward FOREX Market Suppose that you have succeeded in getting the forward rate F =1.75 Do you have to be a seller or buyer at this rate? You are afraid of Et+1 Up; Position yourself to win as Et+1 Up. You have to be Forward Buyer of GBP You are afraid that FOREX Et+1 may turn out to be higher than1.75, say, 2.0. When it happens, then you may gain CAN 0.25 for every GBP $1 in Forward Contract

Forward Hedging should look like: Zero profit line Et+1 Is this a payoff curve for a seller(short) or a buyer(long)?

Is this ‘selling forward (at F)’ or ‘buying’ forward (at F)? . Three ways to figure out: Easy way: As you as a TD manager will need GBP in a year, you have to buy GBP forward for hedging. Graphic Way: In forward contract, you want a upward profit line. We recall that a buyer’s payoff curve is upward sloping and a seller’s payoff curve is downward sloping. Thus you have to be a forward buyer of GBP. Logical Reasoning: When you are committed to buy GBP at F in forward market: If Et+1 rises below F, the forward buyer will have gains: you will pay only F, not Et+1. You get the remittance of Et+1-F from the seller, and add it to your F and buy GBP at the rate of Et+1.

Elaboration of the last “Logical” reasoning for Forward Hedging: Suppse now he can get one-year ‘Forward Sell U.S. dollars’ at F =1.75. What will be his pay-off one year later? F Zero profit line Et+1 Possibility 1: Et+1 turns out to be above F (=1.75) For instance, Et+1 = 2.00 Hedging: As you buy GBP forward at F (1.75), and sell it Spot at Et+1 (2.00). Profit from Hedging: CAN 0.25 m