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

2. 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

3. 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

4. 3. Players in the Forward FOREX market
1) As you have stakes in S t+1 , and are exposed to the FOREX risk of unexpected changes in S t+1 compared to St . Thus, you want to cover from its risk through forward market by taking the opposite position in F. You are a hedger.
2) Initially you have no business risk to FOREX changes. However, you are now assuming new risks through forward market. You are a speculator.

5. 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)’.

6. 2) Long Position versus Short Position
The Buyer of a Forward Contract is called ‘in the long-position’; and the seller of the contract is said to be ‘in the short-position’.

7. 3) Actual Settlement by the ‘Margin’
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.
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 St+1 >F, the buyer (on long position) wins and get the difference St+1 – F from the seller (on short position).
If St+1 <F, the seller gets the difference.

8. Who wins and who loses in forward contract ?
depend on the comparison between F (in contract) and St+1 (to be realized in the spot market).
Seller of Forward Contract
-”Short” with Forward Contractor
Buyer of Forward Contract
-“Long” with Forward
Actual Settlement
St+1>F;
when (Spot) Price goes up.
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)
St+1<F

9. In general,
For the given Contract Price –locked –up or pre-fixed F(contract price: forward), pre-fixed X(exercise price: option) or St+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:

10. 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’.

11. 1) How does it work?
Suppose that TD bank invests on U.S. $1 million Bonds at the current FX rate with Cdn $ 1 million, and the bonds will mature in one year.
There is no guarantee of how much the bank would get back in Cdn $ for U.S. $1 million.
The TD bank is exposed to FX Market Risk.
Illustrate the risk to which TD bank is exposed, and show how it can hedge through Forward/Derivatives in FX market.

12. Step 1: Draw the Net Payoff curve of TD Bank’s Initial Banking/Bond Trading Business Risk from FX rate changes:
As St+1 falls below St, TD bank loses. + -
St (=1)
St+1 -
Case 1. TD bank is to receive U.S. $ 1 m in the future; how much it would be in Cdn $?

13. Step 2. Hedging: Choose the Forward Contract to Offset the above FOREX risk: TD bank 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?

14. Choose ‘Hedging by Selling FOREX Forward’, which, as you may recall, has the down-ward sloping Pay-off line: F
“Short” position with FOREX forward: TD will win when St+1 falls below F.

15. * The applied General principle of hedging is, “In insurance, you bet on the worst possibility”.
If you hates “the depreciation of the U.S. dollar in your business” (as your business is hurt in such a case).
Thus in insurance, you should bet on the worst for you, that is, the depreciation of the U.S. dollar.
In Forward Market, he should sell(be long on) U.S. dollars.

16. Step 3: combining the above two graphs, we get the ‘zero’ net:
Whether the Future spot FOREX rate St+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 1.Initial FOREX Risk before Hedging + +
Zero profit line -
Now Step 3. Net profit/loss= 0 at all times -
From Step 2. Forward Hedging: “Short Position” (with FOREX)

17. Step 3’: Alternatively, if TD manages to get the higher F, the better it would be for its profits:
If TD bank manages to get a forward buyer which agrees on F quite high to the right(>St), then the profits from the forward contract exceed the loss from the actual business (of bond trading). The net profit will be always positive.
1.Initial FOREX Risk
3.Now the New Net/Combined profit/loss positive at all times + + F
Zero profit line St - -
2. Forward Hedging

18. Step 3’’: Alternatively, F can be lower than St, and then there will be always net cost for hedging. Still this is cost for Hedging or Peace of Mind.
If TD bank can only get a forward buyer which agrees on F (<St). Then, at any realized St+1, the loss from the actual business (of bond trading) would not be fully hedged. The net profits will be always negative(net loss).
1.Initial FOREX Risk + F +
Zero profit line St -
3.Net profit/loss= negative at all times -
2. Forward Hedging

19. Suppose that initially, St =1, and
* The same above Example of Forward Hedging with some specific numbers:
Suppose that initially, St =1, and
Asset: TB bank has a receivable of US $1 million coming from a maturing bond in 1 year.
Liabilities: TD bank has payables of Canadian $1 million for wages, salaries, and expenses in Canada. You need Canadian dollars. i

20. (1) (FX) Risk of Business of Bond Trading In one year, St+1 may be different from St. U.S. $1 million bond may bring less or more of Cdn $ than Cdn$1 m.
Possiblity 2: St+1 = 0.90
US. $1 m -> Cdn $ 0.9 m
‘Unexpected’ Loss
from FOREX: - C $ 0.10 m
(risk needs to be hedged)
Suppose Now (St=) 1.0 i
Zero profit line
St+1
Possibility 1: St+1 = 1.10
U.S. $1 m -> Cdn $1.10 m
‘Windfall’ Gains
from FOREX: C$ 0.10 m
(no need to worry)

21. (2) Now how to do ‘Forward Hedging’ for Risk: You as TD bank’s risk 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)?

22. * The General principle of hedging is, “In insurance, you bet on your (possible) loss”.
You hate ‘the depreciation of the U.S. dollar’ or falling St+1 as your receivables are in U.S. dollars.
Thus in forward hedging(=buying insurance), you should bet on the falling U.S. dollar or a lower St+1.
Thus, if the U.S. dollar depreciates, (although you may lose in primary business/bond trading) you may win in the financial/forward contract. The gain from the forward contract offsets the loss in business.
<- You should (buy/sell) U.S. dollar Forward. – *circle your answer. ** Hint: You can sell something only when you get it.

23. With numbers: Taking a position in the Forward FOREX Market
Suppose that you have succeeded in getting the forward rate F =1.0
Do you have to be a seller or buyer at this rate?
-You are afraid that at FOREX St+1 turns out to be equal, say, to 0.9, you may lose C$ 0.1 for every U.S. $1.
-You should position in such a way that in the forward contract, under this circumstance, you win C$ 0.1.
- The only way to make profit is to buy low and to sell high. – Given the spot rate 0.9, and the forward rate 1.0: You have to be a buyer at the spot market and to be a seller at the forward market.

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

25. Is this ‘selling forward (at F)’ or ‘buying’ forward (at F)? .
Three ways to figure out:
Easy way: As the TD bank will have U.S. $, it will have to sell US $ forward for hedging.
Graphic Way: we recall that a buyer’s payoff curve is upward sloping and a seller’s payoff curve is downward sloping.
Logical Reasoning: When you are committed to sell at F in forward market: If St+1 falls below F, the forward seller will have gains. He can sell U.S. $ at F(higher) in forward contract; if the bank has to sell on spot, it will have to sell (US $) at St+1(lower).
* Even one has no US $ coming at t+1, he will buy US $ spot at St+1(lower) and turn around and sell at F in his forward contract.

26. Elaboration of the last “Logical” reasoning for Forward Hedging: Suppse now he can get one-year ‘Forward Sell U.S. dollars’ at F = What will be his pay-off one year later? F
Zero profit line
St+1
Possibility 1: St+1 turns out to be below F (=1.0)
For instance, St+1 = 0.90
Hedging: As you buy U.S. dollar at St+1 (0.9) at the spot and deliver it at F (1.0) And the forward contact will bring you C $0.10 million of profits.
Profit from Hedging: C $0.10 m

27. Forward Hedging (continued; can be skipped): Suppse now he can get one-year ‘Forward Sell U.S. dollars’ at F = What will be his pay-off one year later? F
St+1
Zero profit line
Possibility 2: St+1 turns out to be above F
For instance, St+1 = 1.10
Hedging: As you could U.S. dollar at St+1 (1.10) at the spot, but have to sell it at F (0.9) in forward contract. The forward contact will bring you - C $0.10 million (loss)
Loss from Hedging: - C $0.10 m

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

29. The alternative result with a ‘Better’ Hedging Deal:
If TD manages to get a forward contract partner(forward buyer) agreeing on F which stands above S:
(b)
Ffixed
Stfixed
(a)
St+1stochastic
Draw the net profit curve.