Risk Management 3 2

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International risk management, Kirsten Ralf 1

3. Futures




Content of the chapter

• Mechanics of futures markets.

• Hedging strategies using futures.

• Determination of forward andfutures prices.

• Interest rates futures.

• Foreign exchange futures.




Mechanics of futuresmarkets

• Futures contracts are available on awide range of underlying assets.

• They are exchange traded.• Specifications need to be defined:

– What can be delivered,

– Where it can be delivered, – When it can be delivered.

• They are settled daily.




Futures contracts

• Agreement to buy or sell an asset fora certain price at a certain time.

• Similar to forward contract.

• Whereas a forward contract is tradedOTC, a futures contract is traded on

an exchange.




Other key points aboutfutures

• Closing out a futuresposition involves enteringinto an offsetting trade.

• Most contracts are closedout before maturity.




Forward contracts

• Forward contracts are similar to futuresexcept that they trade in the over-the-counter market.

• Forward contracts are particularly popularon currencies and interest rates.

• Advantage: Forward contracts are moreflexible than futures contracts.

• Disadvantage: The transactions costs forforward contracts are usually higher thanfor futures contracts.




Forward contracts

• The forward price for a contract isthe delivery price that would be

applicable to the contract if werenegotiated today (i.e., it is thedelivery price that would make the

contract worth exactly zero).• The forward price may be different

for contracts of different maturities.




Margins

• A margin is cash or marketablesecurities deposited by an investor

with his or her broker.• The balance in the margin account is

adjusted to reflect daily settlement.

• Margins minimize the possibility of aloss through a default on a contract.




Example of a futurestrade (page 27-28)

• An investor takes a long positionin 2 December gold futures

contracts on June 5 – contract size is 100 oz.

– futures price is US$400

– 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 outcomeTable 2.1, Page 28

Daily Cumulative Margin

Futures Gain Gain Account Margin

Price (Loss) (Loss) Balance Call

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

400.00 4,000

5-Jun 397.00 (600) (600) 3,400 0. . . . . .. . . . . .. . . . . .

13-Jun 393.30 (420) (1,340) 2,660 1,340. . . . . .

. . . . .. . . . . .

19-Jun 387.00 (1,140) (2,600) 2,740 1,260. . . . . .. . . . . .. . . . . .

26-Jun 392.30 260 (1,540) 5,060 0

+

= 4,000

3,000

+

= 4,000

<




Collateralization in OTCmarkets

• It is becoming increasingly commonfor contracts to be collateralized in

OTC markets.• They are then similar to futures

contracts in that they are settled

regularly (e.g. every day or everyweek).




Futures prices for Gold on Feb 4,

2004: Prices increase with maturity (Figure 2.2, page 35)

(a) Gold

398

399400

401402403404405

406407408

Feb-04 Apr-04 Jun-04 Aug-04 Oct-04 Dec-04

Contract Maturity Month

F u t u r e s

P r i c e

( $

p e r o z )



Gold futures

• http://www.cmegroup.com/trading/metals/precious/gold.html


http://www.cmegroup.com/trading/metals/precious/gold.html







Futures prices for oil on February4, 2004: Prices decrease with

maturity (Figure 2.2, page 35)

(b) Brent Crude Oil

24

25

26

27

28

29

30

Mar-04 May-04 Jul-04 Sep-04 Nov-04 Jan-05

Contract Maturity Month

F u t u

r e s

P r i c e

( $

p e r b a r r e l )



Brent crude oil futures

• http://www.cmegroup.com/trading/energy/crude-oil/brent-crude-oil-last-

day_quotes_globex.html


http://www.cmegroup.com/trading/energy/crude-oil/brent-crude-oil-last-day_quotes_globex.html


















Convergence of futures tospot (Figure 2.1, page 26)

Time Time

(a) (b)

FuturesPrice

FuturesPriceSpot Price

Spot Price




Delivery

• If a futures contract is not closed out beforematurity, it is usually settled by deliveringthe assets underlying the contract. When

there are alternatives about what isdelivered, where it is delivered, and when itis delivered, the party with the short positionchooses.

• A few contracts (for example, those onstock indices and Eurodollars) are settled incash.




Some terminology

• Open interest: the total number ofcontracts outstanding

– equal to number of long positions ornumber of short positions.

• Settlement price: the price just beforethe final bell each day

– used for the daily settlement process.• Volume of trading: the number of

trades in 1 day.




Regulation of futures

• Institution: Commodity FuturesTrading Commission (CFTC).

• Regulation is designed to protect thepublic interest.

• Regulators try to prevent

questionable trading practices byeither individuals on the floor of theexchange or outside groups.




Accounting and tax

• Ideally hedging profits (losses) should berecognized at the same time as the losses(profits) on the item being hedged.

• Ideally profits and losses from speculationshould be recognized on a mark-to-marketbasis.

• Roughly speaking, this is what the

accounting and tax treatment of futures inthe U.S.and many other countries attemptsto achieve.




Forward contracts vsfutures contracts

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

Contract usually closed outprior to maturity

FORWARDS FUTURES

Hull, TABLE 2.3 (p. 41)

Some credit risk Virtually no credit risk




Hedging strategies usingfutures

• A long futures hedge is appropriatewhen you know you will purchase an

asset in the future and want to lockin the price.

• A short futures hedge is appropriate

when you know you will sell an assetin the future and want to lock in theprice.




Arguments in favor ofhedging

Companies should focus on themain business they are in and take

steps to minimize risks arisingfrom interest rates, exchangerates, and other market variables.




Arguments againsthedging

• Shareholders are usually welldiversified and can make their own

hedging decisions.• It may increase risk to hedge when

competitors do not.

• Explaining a situation where there isa loss on the hedge and a gain onthe underlying can be difficult.




Basis risk

• Basis is the difference betweenspot price of the asset to be

hedged and futures price ofcontract used.

• Basis risk arises because of the

uncertainty about the basis whenthe hedge is closed out.




Long hedge

• Suppose that

F 1 : Initial Futures Price

F 2 : Final Futures PriceS 2 : Final Asset Price

• You hedge the future purchase of anasset by entering into a long futures

contract• Cost of Asset=S 2 – ( F 2 – F 1) = F 1 + Basis




Short hedge

• Suppose that

F 1 : Initial Futures Price

F 2 : Final Futures PriceS 2 : Final Asset Price

• You hedge the future sale of an asset by

entering into a short futures contract.• Price Realized=S 2+ ( F 1 – F 2) = F 1 + Basis.




Choice of contract

• Choose a delivery month that is asclose 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 mosthighly correlated with the asset price.This is known as cross hedging.




Optimal hedge ratio

Proportion of the exposure that should optimallybe hedged is

wheresS is the standard deviation of DS , the change inthe spot price during the hedging period,s F is the standard deviation of D F , the change in

the futures price during the hedging periodr is the coefficient of correlation between DS andD F .

F

S

s

s r

Hedging using index




Hedging using indexfutures

(Hull, Page 63)

To hedge the risk in a portfolio thenumber of contracts that should be

shorted is

where P is the value of the portfolio,

b is its beta, and A is the value ofthe assets underlying one futurescontract.

b P A




Reasons for hedging anequity portfolio

• Desire to be out of the market for ashort period of time. (Hedging may

be cheaper than selling the portfolioand buying it back.)

• Desire to hedge systematic risk

(Appropriate when you feel that youhave picked stocks that willoutperform the market.)



Index futures

• http://www.bloomberg.com/markets/stocks/futures/


http://www.bloomberg.com/markets/stocks/futures/







Example

Value of S&P 500 is 1,000Value of Portfolio is $5 millionBeta of portfolio is 1.5One futures contract with 4 monthsmaturity is $250 times the index at a priceof 1,010

What position in futures contracts on theS&P 500 is necessary to hedge theportfolio over the next 3 months?




Changing beta

• What position is necessary to reducethe beta of the portfolio to 0.75?

• What position is necessary toincrease the beta of the portfolio to2.0?




Hedging price of anindividual stock

• Similar to hedging a portfolio.

• Does not work as well because only

the systematic risk is hedged.• The unsystematic risk that is unique

to the stock is not hedged.




Rolling the hedge forward(Hull, page 67-68)

• We can use a series of futurescontracts to increase the life of ahedge.

• Each time we switch from 1futures contract to another weincur a type of basis risk.




Determination of forwardand futures prices

• Types of assets – Investment assets are assets held by

significant numbers of people purely for

investment purposes (Examples: bonds, gold,silver).

– Consumption assets are assets held primarilyfor consumption (Examples: copper, oil).

• Types of activities – Long hedge.

– Short selling.




Short selling

• Short selling involves selling securitiesyou do not own.

• Your broker borrows the securities from

another client and sells them in themarket in the usual way.

• At some stage you must buy thesecurities back so they can be replaced in

the account of the client.• You must pay dividends and otherbenefits the owner of the securitiesreceives.




Notation for valuing futuresand forward contracts

S 0: Spot price today

F 0: Futures or forward price today

T : Time until delivery date

r : Risk-free interest rate for

maturity T

1 G ld A bi




1. Gold: An arbitrageopportunity?

• Suppose that:

– The spot price of gold is US$ 390.

– The quoted 1-year forward price ofgold is US$ 425.

– The 1-year US$ interest rate is 5% perannum.

– No income or storage costs for gold.• Is there an arbitrage opportunity?

2 G ld A th bit




2. Gold: Another arbitrageopportunity?

• Suppose that:

– The spot price of gold is US$ 390.

– The quoted 1-year forward price ofgold is US$ 390.

– The 1-year US$ interest rate is 5%per annum.

– No income or storage costs for gold.

• Is there an arbitrage opportunity?




The forward price of gold

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

F = S (1+r )T ,where r is the 1-year (domestic currency)risk-free rate of interest.

In our examples, S =390, T =1, and r =0.05, sothat

F = 390(1+0.05) = 409.50.




When interest rates aremeasured with continuous

compounding

F 0 = S 0erT

This equation relates the forwardprice and the spot price for any

investment asset that provides noincome and has no storage costs.

When an investment asset




When an investment assetprovides a known dollar

income (Hull, page 105, equation 5.2)

F 0 = (S 0 –

I )erT

where I is the present value of theincome during life of forward

contract.




When an investment asset

provides a known yield(Hull, Page 107, equation 5.3)

F 0

= S 0

e(r – q )T

where q is the average yield duringthe life of the contract (expressed withcontinuous compounding).

Valuing a forward




Valuing a forwardcontract

Page 108

• Suppose that

K is delivery price in a forward contract and

F 0 is forward price that would apply to thecontract today

• The value of a long forward contract, ƒ, isƒ = ( F 0 – K )e – rT

• Similarly, the value of a short forward contract is

f = ( K –

F 0 )e – rT




Forward vs futures prices

• Forward and futures prices are usuallyassumed to be the same. When interest rates

are uncertain they are, in theory, slightlydifferent:

• A strong positive correlation between interestrates and the asset price implies the futures

price is slightly higher than the forward price.• A strong negative correlation implies the

reverse.




Stock index (Page 110-112)

• A stock index can be viewed as aninvestment asset paying a dividend yield.

• The futures price and spot pricerelationship is therefore

F 0 = S 0 e(r – q )T

where q is the average dividend yield onthe portfolio represented by the indexduring life of contract.




Stock index(continued)

• For the formula to be true it is importantthat the index represent an investmentasset.

• In other words, changes in the indexmust correspond to changes in thevalue of a tradable portfolio.

• The Nikkei index viewed as a dollarnumber does not represent aninvestment asset




Index arbitrage

• When F 0 > S 0e(r-q)T an arbitrageur

buys the stocks underlying the index

and sells futures.• When F 0 < S 0e

(r-q)T an arbitrageurbuys futures and shorts or sells the

stocks underlying the index.




• A Eurodollar is a dollar deposited in abank outside the United States.

• Eurodollar futures are futures on the 3-

month Eurodollar deposit rate (same as 3-month LIBOR rate).• One contract is on the rate earned on $1

million.

• A change of one basis point or 0.01 in aEurodollar futures quote corresponds to acontract price change of $25.

Eurodollar futures (Hull, Page

137-142)

E rodollar f t res




Eurodollar futurescontinued

• A Eurodollar futures contract issettled in cash.

• When it expires (on the thirdWednesday of the delivery month)the final settlement price is 100

minus the actual three month depositrate.



International risk management Kirsten Ralf 53

Foreign exchange futures

• A foreign currency futures contract is analternative to a forward contract that calls forfuture delivery of a standard amount of foreign

exchange at a fixed time, place and price.• It is similar to futures contracts that exist for

commodities such as cattle, lumber, interest-bearing deposits, gold, etc.

• In the US, the most important market for foreigncurrency futures is the International MonetaryMarket (IMM), a division of the ChicagoMercantile Exchange.

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