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Derivatives of Foreign Exchange Markets(1): FOREX Forward

Dr. J. D. Han

King’s College

University of Western Ontario

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1. Derivative in general

• Definition of Derivatives financial assets whose values depend on underlying assets

• UsesHedging (against risk) behaviors beget a series of derivatives

• Different Kinds of Derivatives1) Short-selling 2) Forward-related Derivatives: Forwards, Futures, Swaps 3) Options-related Derivatives

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2. Organization of Forward Market

• Buy a currency at an agreed rate on the trade date which is now , and deliver/pay later at the settlement date.

• The intervals or Value dates are 1, 2, 3, 6, or 12 months, or 30 days, 60 days, 90days, 180 days, or 360days: Ft+1 , Ft+2 , Ft+3 … Ft+6 …. Ft+12

• Over-the-counter (O. T. C.) transactions = Custom Made through face-to-face talks

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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.

4. Operation of Forward Contract (itself)1) A Forward Rate of FOREX is set between

the buyer and the seller on the trade date (t) for the settlement date (t+i)

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2) Long Position versus Short Position

• The Buyer of a Forward currency is in the long-position; and the seller is in the short-position.

3) Relationship of the Forward Rate with the present spot rate St and the corresponding spot rate St+1

• With St

F – St >0, we say ‘There is Forward Premium by F – St / St

• With St+1

When the St+1 turns out to be higher than F, the buyer (on the long-position) wins.

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4) Winner and Loser in the Forward Contract

• F is set through the Forward Contract

• St+1 will turn out to be:

(1)If St+1 >F, the Buyer of Forward FOREX wins.

(2)Vice versa.

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5) Actual Settlement by the ‘Margin’

A and B buys and sells a currency, agreeing on the Forward FOREX rate or F for the settlement date.

When the settlement date comes, compare the forward rate F and the spot FOREX rate St+1 on that day.

If St+1 >F, the buyer A (on long position) wins and get the difference St+1 – F from the seller B (on short position).

6) Exposition of the ‘Game Play’

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Hedging itself creates the following in the T accounts for the Buyer of FOREX (U.S. dollar);

Assets

(receivable)

Liabilities

(payable) US $1 mil C $1 mil x F

Assets

(receivable)

Liabilities

(payable) C $1 mil x F US $1 mil

And for the Forward Seller

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A Detailed T accounts for the forward Buyer of forward FOREX:

Assets

(receivable)

Liabilities

(payable) Net Profit

US $1 mil C $1 mil x F

Conversion in C $

$ 1 mil x St+1

$ 1 mil x F St+1 - F

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*Numerical Example 1: A Detailed T accounts for the Buyer:F = 1.00; St+1 turns out to be 1.2

Assets

(receivable)

Liabilities

(payable) Net Profit

US $1 mil C $1 mil x F(=1.0)

Conversion in C $

$ 1 mil x St+1 (=1.2)

$ 1 mil x F (=1.0) St+1 – F =0.2*

*He pays C $1 m for U.S. $1 m through Forward contract, and can sell it for C $ 1.2 m in the spot market.

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*(continued) Numerical Example 1: A Detailed T accounts for the Seller of FOREX(U.S.):F = 1.00; St+1 turns out to be 1.2

Assets

(receivable)

Liabilities

(payable) Net

C $1 mil x F US $1 mil.

Conversion in C $

$ C $1 x F (=1.0)

$ 1 mil x St+1 (=1.2) St+1 – F = - 0.2

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*(continued) Numerical Example 1: A Detailed T accounts for the Seller of FOREX(U.S.):F = 1.00; St+1 turns out to be 1.2

Assets

(receivable)

Liabilities

(payable) Net

C $1 mil x F US $1 mil.

Conversion in C $

$ C $1 x F (=1.0)

$ 1 mil x St+1 (=1.2) St+1 – F = - 0.2*

He has to sell U.S. $1 m for C $1 m, but could instead get C $ 1.2 m if he were to sell it in the spot market.

*(continued) Numerical Example 1:

The Forward Contact is settled by the margin of C $ 0.2 million is remitted from the seller to the buyer.

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5. Forward Market for Hedging

Hedging is covering yourself from Risk of Uncertainty of Changes between Now and the Future.

Hedging is the same as ‘Buying Insurance’.

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1) How does it work?

• Suppose that a Canadian exporter to U.S., but he receive US$ 1 million, not now(say, t) , but in 12 months(say, t+1) ; that is his ‘receivable’

• What he really needs is Canadian dollars to pay to his workers and suppliers in Canada; these wages and costs are ‘payables’.

• There is no guarantee of how much he would get in C $. He will suffer loss if St+1 goes up above St or the U.S. $ depreciates in

a year – This is his original risk from FOREX volatility.• He can cover himself from the FOREX risk by going into a forward

FOREX contract. That is ‘Hedging’ by Forward.• He can only sell what he will get: He should sell U.S. $ forward or be

short on U.S. $ forward to his partner at the agreed rate F. • Whether he is successful or not depends on what St+1 turns out to be in

the settlement period.

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2) General Cases of Forward Hedging

First, Assess your original FOREX market risk by drawing the net profit/loss curve with all the possible values of the future spot FOREX rate St+1 on the horizontal axis.

That net profit/loss curve passes through ‘zero’ profit when St+1 is the same as the given value of the current spot rate St.

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Step 1: Draw the Net Payoff curve of your Initial FOREX risk:

St+1-

+ +

-

As St+1 goes up, you get profits, or loss. Your initial FOREX risk for your business would be either one of the two:

Case 1. You are to receive FOREX in the future

Case 2.You are to pay/need FOREX in the future

or

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Step 2. Offset the above FOREX risk by taking Forward Hedging, which has the opposite shape of the initial net payoff curve:

This forward hedging is “Long” position (selling foreign currency forward) :

You gain when St+1 rises above F.

St+1

If you are initially exposed to FOREX risk as in Case 2, then your forward hedging should have the payoff curve like

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* 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.

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Alternatively, for the initial FOREX risk exposure of Case 1, you should choose ‘Hedging by Selling FOREX Forward’, which has the down-ward sloping Pay-off line:

“Short” position with FOREX: You win when St+1 falls below F.

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1.Initial FOREX Risk before Hedging

2. Forward Hedging: “Short Position” (with FOREX)

Step 3: combining the above two graphs, we get the ‘zero’ net:

Zero profit line

Whether the future spot FOREX rate or E1falls 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).

+

-

+

-

3. Net profit/loss= 0 at all times

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3) Specific Numerical Example of Forward Hedging

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Suppose that you are an Canadian exporter to U.S.

Asset: you have a receivable of US $1 million coming from U.S. in 1 year.

Liabilities: you have payables of Canadian $1 million for wages, salaries, and expenses in Canada. You need Canadian dollars.

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(1) Initial FX Risk of Original Business

Think about ‘Unexpected Gains or Loss’ of your ASSET(RECEIVALBE IN THIS CASE) you might have due to fluctuations of spot FOREX rates

St+1

Possibility 1: St+1 = 1.10

‘Windfall’ Gains

from FOREX: C$ 0.10 m

Suppose Now (St=) 1.0

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Possiblity 2: St+1 = 0.90

‘Unexpected’ Loss

from FOREX: - C $ 0.10 m

Zero profit line

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Your T-Account of Business Account exposed to Initial FOREX risk

• There will be gains if St+1 goes above St

• There will be loss in net worth if St+1 falls below

At t+1 Assets Liabilities

US $1 mil C $ 1 mil

Present value in C $

C$ 1 mil x St C $ 1 mil

RevisedValue in C $

C$ 1mil x St+1

C $ 1 mil

Net Profit/Loss: St+1 - S

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(2) Forward Hedging

You as a Canadian exporter 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)?

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* The General principle of hedging is, “In insurance, you bet on your (possible) loss”.

You as a Canadian exporter hate ‘the depreciation of the U.S. dollar’ or falling St+1 in business.

Thus in forward hedging(=buying insurance), he should bet on the falling U.S. dollar or a lower St+1.

Thus, if the U.S. dollar depreciates, you may lose in business but you may win in the 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.

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.

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Forward Hedging: Suppse now he can get one-year ‘Forward’ ‘Sell U.S. dollars’ at F =1.00. What will be his pay-off one year later?

St+1

Possibility 1: St+1 turns out to be below F

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

F

Zero profit line

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Forward Hedging (continued): Suppse now he can get one-year ‘Forward’ ‘Sell U.S. dollars’ at F =1.00. What will be his pay-off one year later?

St+1

Possibility 2: St+1 turns out to be above F

For instance, St+1 = 1.10

Hedging: As you have to buy U.S. dollar at St+1 (1.10) at the spot and deliver it at F (0.9) And the forward contact will bring you - C $0.10 million of profits.

Profit from Hedging: - C $0.10 m

F

Zero profit line

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Forward Hedging of Selling U.S. dollar creates the following additional/separate T account for forward contract:

Assets

(receiving payment)

Liabilities

(having to sell)

C $1 mil U.S. $1 mil

This can be modified as in the following page.

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Modified T Account for the Seller of U.S. dollar Forward:

Assets

(receiving payment at F)

Liabilities

(having to sell)

Net Profit/ Loss

C ( $1 mil x F ) U.S. $1 mil

In C$ C $1 mil x F C $ St+1 mil F – St+1

Net Profit from this forward operation = F- St+1

*Why conversion by St+1?

(3) Net Result

• The loss from the initial FOREX risk exposure will be offset by the gains from the Forward Hedging.

• The net will be

(St+1 - St ) - (St+1 – F) = F – St, which is constant(fixed) at all times.

• The offset could be ‘complete’ or ‘partial’ depending on the relative value of St and F.

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*Specific Point on St+1 :

Suppose that St+1 turns out to be equal to 0.9,

the loss from the initial FOREX risk will be offset by the gains from Forward Hedging.

This is only one specific point on the line of St+1.

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Illustration

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0.9

(b)

(a)

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(a) Changes in the initial business assets and liabilities with St =1 andSt+1 =0.9:

Assets Liabilities

US $1.0 mil C $1 mil

US $1.0 mil at St C $1.0 mil

C $ 0.9 mil at St+1 C $ 1.0 milC $ 1.0 mil

Loss = C $ 0.1 m - (a)

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(b) Changes in the forward hedging assets and liabilities with F=1 and St+1 =0.9:

Hedging itself creates the following in the T accounts

Assets(F) Liabilities

C $1.0 mil x 1 US $1 mil

In C$ value

C $ 1.0 mil x 1 C $ 0.9 million*C $ 0.9 million*

Profits = C $ 0.1 m –(b)

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As for the settlement in the Forward Contract, you may recall that

• On the settlement date, compare the current spot market rate( in fact St+1) and the agreed rate(F).

• When St+1 >F, the seller has won; the buyer has lost.

• By the amount of St+1 - F, the payment goes from the buyer’s account to the seller’s.

6. Equilibrium Forward Rate

• So far we have assumed that F is given.

• A ‘fair’ or ‘equilibrium’ F is determined in line with the Covered Interest Parity Theorem,

i = if + (F – St)/ St (at equilibrium),

and Efficient Market Theory.

F = St+1 + e .

• In the short run, the actual forward rate F could be different from the equilibrium F.

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*Question 1:

• You are a Canadian

• Spot exchange rate = 1.20 Cd $/ 1 U.S. $

• Canadian (one year) interest rate: 5%

• U.S. (one year) interest rate: 6%

• What should be the ‘fair 12-month Forward Rate’ which comes with no unilateral capital flows from one country to the other?

*Question 2

• Canadian annual interest rate =5%

• U.S. annual interest rate = 4%

• St = 1.00 in Canada ( SC$/US$ )

• What will be a ‘fair’ 3 month Forward Rate in Canada?

Hint: use ¼ of the annual interest rate for the UCIPT equation.

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7. Limitation of Forward Hedging

-This is not the best ideal Hedging: The hedging has eliminated the upside potential along with the downside risk.

-OTC may have liquidity problems with no standardized products, possibility of no partners, and cumbersome personal contacts.

-OTC has no immediately effective binding power against breach of contract – ‘Credit Risk’