ways derivatives are used to hedge risks to speculate (take a view on the future direction of the...

Ways Derivatives are UsedTo hedge risks

To speculate (take a view on the future direction of the market)

To lock in an arbitrage profit

To change the nature of a liability

To change the nature of an investment without incurring the costs of selling one portfolio and buying another

Options, Futures, and Other Derivatives, 7th International Edition, Copyright © John C. Hull 2008 1

Foreign Exchange Quotes for GBP, July 20, 2007 (See page 4)


Bid Offer

Spot 2.0558 2.0562

1-month forward 2.0547 2.0552



Forward Price

The forward price for a contract is the delivery price that would be applicable to the contract if were negotiated today (i.e., it is the delivery price that would make the contract worth exactly zero)

The forward price may be different for contracts of different maturities


TerminologyThe party that has agreed to buy has what is termed a long position

The party that has agreed to sell has what is termed a short position


Example (page 4)

On July 20, 2007 the treasurer of a corporation enters into a long forward contract to buy £1 million in six months at an exchange rate of 2.0489

This obligates the corporation to pay $2,048,900 for £1 million on January 20, 2008

What are the possible outcomes?


Profit from aLong Forward Position


Profit

Price of Underlying at Maturity, STK

Profit from a Short Forward Position


Profit

Price of Underlying at Maturity, STK

Futures Contracts (page 6)

Agreement to buy or sell an asset for a certain price at a certain time

Similar to forward contract

Whereas a forward contract is traded OTC, a futures contract is traded on an exchange


Exchanges Trading Futures

Chicago Board of Trade

Chicago Mercantile Exchange

LIFFE (London)

Eurex (Europe)

BM&F (Sao Paulo, Brazil)

TIFFE (Tokyo)

and many more (see list at end of book)


Examples of Futures ContractsAgreement to:

Buy 100 oz. of gold @ US$900/oz. in December (NYMEX)

Sell £62,500 @ 2.0500 US$/£ in March (CME)

Sell 1,000 bbl. of oil @ US$120/bbl. in April (NYMEX)


1. Gold: An Arbitrage Opportunity?

Suppose that:The spot price of gold is US$900The 1-year forward price of gold is US$1,020The 1-year US$ interest rate is 5% per

annum

Is there an arbitrage opportunity?


2. Gold: Another Arbitrage Opportunity?

Suppose that:- The spot price of gold is US$900- The 1-year forward price of gold is US$900- The 1-year US$ interest rate is 5% per

annum

Is there an arbitrage opportunity?


The Forward Price of Gold

If the spot price of gold is S and the forward price for a contract deliverable in T years is F, then

F = S (1+r )T

where r is the 1-year (domestic currency) risk-free rate of interest.In our examples, S = 900, T = 1, and r =0.05 so that

F = 900(1+0.05) = 945


Example of a Futures Trade (page

26-28)

An investor takes a long position in 2 December gold futures contracts on June 5

contract size is 100 oz.

futures price is US$600

margin requirement is US$2,000/contract (US$4,000 in total)

maintenance margin is US$1,500/contract (US$3,000 in total)


A Possible Outcome Table 2.1, Page 28


Daily Cumulative Margin

Futures Gain Gain Account Margin

Price (Loss) (Loss) Balance Call

Day (US$) (US$) (US$) (US$) (US$)

600.00 4,000

5-Jun 597.00 (600) (600) 3,400 0. . . . . .. . . . . .. . . . . .

13-Jun 593.30 (420) (1,340) 2,660 1,340 . . . . . .. . . . .. . . . . .

19-Jun 587.00 (1,140) (2,600) 2,740 1,260 . . . . . .. . . . . .. . . . . .

26-Jun 592.30 260 (1,540) 5,060 0

+

= 4,000

3,000

+

= 4,000

<

Convergence of Futures to Spot (Figure 2.1, page 26)


Time Time

(a) (b)

FuturesPrice

FuturesPrice

Spot Price

Spot Price

Forward Contracts vs Futures Contracts


Contract usually closed out

TABLE 2.3 (p. 39)

Private contract between 2 parties Exchange traded

Non-standard contract Standard contract

Usually 1 specified delivery date Range of delivery dates

Settled at end of contract Settled daily

Delivery or final cashsettlement usually occurs prior to maturity

FORWARDS FUTURES

Some credit risk Virtually no credit risk

Hedging Strategies Using Futures

Chapter 3


Long & Short Hedges

A long futures hedge is appropriate when you know you will purchase an asset in the future and want to lock in the price

A short futures hedge is appropriate when you know you will sell an asset in the future and want to lock in the price


Arguments in Favor of Hedging

Companies should focus on the main business they are in and take steps to minimize risks arising from interest rates, exchange rates, and other market variables


Arguments against Hedging

Shareholders are usually well diversified and can make their own hedging decisions

It may increase risk to hedge when competitors do not

Explaining a situation where there is a loss on the hedge and a gain on the underlying can be difficult


Convergence of Futures to Spot(Hedge initiated at time t1 and closed out at time t2)


Time

Spot Price

FuturesPrice

t1 t2

Basis Risk

Basis is the difference between the spot and futures price

Basis risk arises because of the uncertainty about the basis when the hedge is closed out


Long Hedge

We defineF1 : Initial Futures Price

F2 : Final Futures Price

S2 : Final Asset Price

If you hedge the future purchase of an asset by entering into a long futures contract then

Cost of Asset=S2 – (F2 – F1) = F1 + Basis


Short Hedge

Again we defineF1 : Initial Futures Price

F2 : Final Futures Price

S2 : Final Asset Price

If you hedge the future sale of an asset by entering into a short futures contract then

Price Realized=S2+ (F1 – F2) = F1 + Basis


Choice of Contract

Choose a delivery month that is as close as possible to, but later than, the end of the life of the hedge

When there is no futures contract on the asset being hedged, choose the contract whose futures price is most highly correlated with the asset price. This is known as cross hedging.


Swaps

Chapter 7


Nature of Swaps

A swap is an agreement to exchange cash flows at specified future times according to certain specified rules


An Example of a “Plain Vanilla” Interest Rate Swap

An agreement by Microsoft to receive 6-month LIBOR & pay a fixed rate of 5% per annum every 6 months for 3 years on a notional principal of $100 million

Next slide illustrates cash flows that could occur


Cash Flows to Microsoft(See Table 7.1, page 149)


---------Millions of Dollars---------

LIBOR FLOATING FIXED Net

Date Rate Cash Flow Cash Flow Cash Flow

Mar.5, 2004 4.2%

Sept. 5, 2004 4.8% +2.10 –2.50 –0.40

Mar.5, 2005 5.3% +2.40 –2.50 –0.10

Sept. 5, 2005 5.5% +2.65 –2.50 +0.15

Mar.5, 2006 5.6% +2.75 –2.50 +0.25

Sept. 5, 2006 5.9% +2.80 –2.50 +0.30

Mar.5, 2007 6.4% +2.95 –2.50 +0.45

Typical Uses of anInterest Rate SwapConverting a liability from

fixed rate to floating rate floating rate to fixed rate

Converting an investment from fixed rate to floating ratefloating rate to fixed rate


Intel and Microsoft (MS) Transform a Liability(Figure 7.2, page 150)


Intel MS

LIBOR

5%

LIBOR+0.1%

5.2%

Financial Institution is Involved(Figure 7.4, page 151)


F.I.

LIBOR LIBORLIBOR+0.1

%

4.985% 5.015%

5.2%Intel MS

Financial Institution has two offsetting swaps

Intel and Microsoft (MS) Transform an Asset (Figure 7.3, page 151)


Intel MS

LIBOR

5%

LIBOR-0.2%

4.7%

Financial Institution is Involved(See Figure 7.5, page 152)


Intel F.I. MS

LIBOR LIBOR

4.7%

5.015%4.985%

LIBOR-0.2%

Valuation of an Interest Rate Swap That Is Not New

Interest rate swaps can be valued as the difference between the value of a fixed-rate bond and the value of a floating-rate bond

Alternatively, they can be valued as a portfolio of forward rate agreements (FRAs)


Valuation in Terms of Bonds

The fixed rate bond is valued in the usual way

The floating rate bond is valued by noting that it is worth par immediately after the next payment date


Valuation in Terms of FRAsEach exchange of payments in an interest rate swap is an FRA

The FRAs can be valued on the assumption that today’s forward rates are realized


An Example of a Currency SwapAn agreement to pay 5% on a sterling principal of £10,000,000 & receive 6% on a US$ principal of $18,000,000 every year for 5 years


Exchange of Principal

In an interest rate swap the principal is not exchanged

In a currency swap the principal is usually exchanged at the beginning and the end of the swap’s life


The Cash Flows (Table 7.7, page 164)


Year

Dollars Pounds$

------millions------

2004 –18.00 +10.002005 +1.08 –0.50

2006 +1.08 –0.50 2007 +1.08 –0.50

2008 +1.08 –0.50 2009 +19.08 −10.50

£

Typical Uses of a Currency Swap

Conversion from a liability in one currency to a liability in another currency

Conversion from an investment in one currency to an investment in another currency


Valuation of Currency Swaps

Like interest rate swaps, currency swaps can be valued either as the difference between 2 bonds or as a portfolio of forward contracts


Swaps & Forwards

A swap can be regarded as a convenient way of packaging forward contracts

Although the swap contract is usually worth zero at the outset, each of the underlying forward contracts are not worth zero


ways derivatives are used to hedge risks to speculate (take a view on the future direction of the...

Documents

copyright john

international edition

forward price

profit price

exchange options

futures contracts page

long forward position

short forward position