Hedge by Financial Derivative

Option, Forward, Futures and SWAP

• Define the risk

• Measure the risk

• Manage the risk – Establish the amount of economic capital to

be held against such risks– Hedge: reduce the risks

Interest Rate SWAP

Why Use Interest Rate SWAP

• Reduce interest rate risk– RSA (rate-sensitive asset) not equal to RSL

(rate-sensitive liability)– If RSA >RSL, then increase RSA (from fixed-

rate to floating-rate) or/and decrease RSL (from floating-rate to fixed-rate)

• Reduce borrowing cost

An Interest Rate Swap Between Two Corporations

• Borrowing costs – Big Boy:

• T-bill+2% for debt with floating rate and 7% for debt with fixed rate

• Would like to borrow the money with floating rate

– Little Guy: • T-bill+2.5% for debt with floating rate and 9% for debt with

fixed rate• Would like to borrow the money with fixed rate

• The borrowing costs of Big Boy are smaller than Little guy regardless of fixed or floating rate

• No need to SWAP?

• Comparative advantage versus Absolute advantage

• For Big Boy– if he borrows the debt with fixed rate, then he

can add a benefit of 2%– if he borrows the debt with floating rate, then

he can add a benefit of 0.5% only

• For Little Guy, – if he borrows the debt with fixed rate, then he

can add a benefit of -2%– if he borrows the debt with floating rate, then

he can add a benefit of -0.5% only

• If Big Boy borrows the debt with fixed rate and Little Guy borrows the debt with floating rate, then the benefit for the whole system is?

• How to allocate the benefit?

• How to decide the swap contract?

International Funding Management

Forward and Money Market

• Forward Contract– an agreement between a bank and a custome

r to deliver a specified amount of currency against another currency at a specified future date and at a fixed exchange rate

• Futures contract– contracts written requiring a standard quantity

of an available currency at a fixed exchange rate at a set delivery date

• Option– A contract from a writer ( the seller) that gives

the right not the obligation to the holder (the buyer) to buy or sell a standard amount of an available currency at a fixed exchange rate for a fixed time period.

Two Dimensions SystemA manager who holds US$ now wants € in the future.

time dimension

curr

ency

dim

ensi

on

Jan 1 Jul 1

US$

€ D

B A

Buy €forward

at F

Path 1

Invest US$ at i$

Path 2

C

Buy €spot at S

Invest € at i€

Investors would take the lower cost path

• American Airlines is trying to decide how to go about hedging SFr70 million in ticket sales receivable in 180 days. Suppose it faces the following exchange and interest rates.

Spot rate:$0.6433-42/SFr

Forward rate (180 days): $0.6578-99/SFrSFr 180-day interest rate (annualized):

4.01%-3.97%U.S. dollar 180-day interest rate (annualized):

8.01%-7.98%

a.What is the hedged value of American's ticket sales using a forward market hedge?

• Answer. By selling the ticket receipts forward, American Airlines can lock in a dollar value of 70,000,000 x 0.6578 = $46,046,000.

b.What is the hedged value of American's ticket sales using a money market hedge? Assume the first interest rate is the rate at which money can be borrowed and the second one the rate at which it can be lent.

• Answer. American can also hedge it euro receivable by borrowing the present value of SFr 70 million at a 180-day interest rate of 2.005% (4.01%/2), sell the proceeds in the spot market at a rate of $0.6433/SFr, and invest the dollar proceeds at a 180-day interest rate of 3.99% (7.98%/2). Using this money market hedge, American can lock in a value for its SFr 70 million receivable of $45,907,296 (70,000,000/1.02005 x 0.6433 x 1.0399).

c.Which hedge is less expensive?

• Answer. The forward market hedge yields a higher dollar value for the ticket receivables, so it is preferable.

d. Is there an arbitrage opportunity here?

• Answer. Yes. By borrowing dollars at a semiannual rate of 4.005% (8.01%/2), converting them to SFr at the ask rate of $0.6442, and simultaneously investing the SFr at a semiannual rate of 1.985% (3.97%/2) and selling the loan proceeds forward at a bid rate of $0.6578, you can lock in an arbitrage spread of 0.133% semiannually.

e.Suppose the expected spot rate in 180 days is $0.67/SFr with a most likely range of $0.64-$0.70/SFr. Should American hedge? What factors should enter into its decision?

• Answer. • Based on the expected 180-day spot rate

and its expected range, it would appear that American would be better off waiting to convert its ticket sales at the future spot rate.

• However, American must ask itself where its comparative advantage lies?

• Does it lie in running an innovative airline or does it reside in trying to outguess apparently sophisticated financial markets?

• If the former, the company should hedge its position

International Funding Management

Option

• Apex Corporation must pay its Japanese supplier ¥125 million in three months. It is thinking of buying 20 yen call options (contract size is ¥6.25 million) at a strike price of $0.00800 in order to protect against the risk of a rising yen. The premium is 0.015 cents per yen.

• Alternatively, Apex could buy 10 three‑month yen futures contracts (contract size is ¥12.5 million) at a price of $0.007940 per yen. The current spot rate is ¥1 = $0.007823. Suppose Apex's treasurer believes that the most likely value for the yen in 90 days is $0.007900, but the yen could go as high as $0.008400 or as low as $0.007500.

• a. Diagram Apex's gains and losses on the call option position and the futures position within its range of expected prices. Ignore transaction costs and margins.

PROFIT (LOSS) ON APEX CORPORATION'S FUTURES AND OPTIONS POSITIONS

($60,000)

($40,000)

($20,000)

$0

$20,000

$40,000

$60,000

75 76 77 78 79 80 81 82 83 84

Pro

fit

(lo

ss)

Yen price ($0.0000 omitted)

Profit (loss) on futures position

Profit (loss) on call option position

79.4

$31,250

$57,500

81.5

($18,750)

• b. Calculate what Apex would gain or lose on the option and futures positions if the yen settled at its most likely value.

• Answer. If the yen settles at its most likely price of $0.007900, Apex will not exercise its call option and will lose the call premium of $18,750. If Apex hedges with futures, it will have to buy yen at a price of $0.007940 when the spot rate is $0.0079. This will cost Apex $0.000040/¥, for a total futures contract cost of 0.000040 x 125,000,000 = $5,000.

• c. What is Apex's break‑even future spot price on the option contract? On the futures contract?

• Answer. On the option contract, the spot rate will have to rise to the exercise price plus the call premium for Apex to break even on the contract, or $0.008000 + $0.000150 = $0.008150. In the case of the futures contract, break-even occurs when the spot rate equals the futures rate, or $0.007940.

• d. Calculate and diagram the corresponding profit and loss and break‑even positions on the futures and options contracts for the sellers of these contracts.

• Answer. • The sellers' profit and loss and break-even

positions on the futures and options contracts will be the mirror image of Apex's position on these contracts.

• For example, the sellers of the futures contract will breakeven at a future spot price of ¥1 = $0.007940, while the options sellers will breakeven at a future spot rate of ¥1 = $0.008150.

• Similarly, if the yen settles at its minimum value, the options sellers will earn the call premium of $18,750 and the futures sellers will earn $55,000. But if the yen settles at its maximum value of $0.008400, the options sellers will lose $31,250 and the futures sellers will lose $57,500.