Risk Management

Topic 5 – Futures Contracts

RM v7 Topic 5 2

Derivatives“financial instruments or

securities that derive their value from the value of some other instrument, commodity or asset”

When the value of underlying asset changes, so will the value of the derivative.

RM v7 Topic 5 3

Forward ContractsForward Contract Definition:

“an agreement to buy (or sell) an agreed quantity of a particular asset or commodity, at a specified future date at a pre-agreed price”

RM v7 Topic 5 4

FuturesFutures Contract Definition:

“a transferable, standardised agreement traded on a regulated exchange, which obliges the seller to deliver, and the purchaser to receive the underlying asset, at a specified time in the future, at an agreed price”

RM v7 Topic 5 5

FuturesDeveloped from trade in Rice NotesCBOT first “modern” exchange,

commenced in 1850’s, primarily in agricultural commodities, later precious metals

Financial Futures emerged in 1970’s, with CBOT Ginnie Mae contract in 1975

RM v7 Topic 5 6

Futures CharacteristicsFutures contracts are standardised wrt:

size (face value), deliverable asset, expiry date settlement terms (cash or delivery)

Only 1-2% of open posns settled by deliveryMost Futures trades “closed out” before

expiry

RM v7 Topic 5 7

Futures Market CharacteristicsExchange TradingShort SellingSettlement

Cash Delivery

Closing outClearing House

Novation Margining

RM v7 Topic 5 8

MarginingInitial Margin

max daily price movementMaintenance MarginMarking to MarketMargin CallVariation Margin

RM v7 Topic 5 9

SFE Sample Contract SpecsContract Contract

Unit Quotes Initial

Margin Min Move

(point move) Point Value

90 Day BAB $A1,000,000 FV BAB

100 - Yield $650 0.01% $24

3 Yr Bond $A100,000 FV 3yr CGS with 6% Coupon

100 - Yield $850 0.01% $28 (varies with i/r

level)

AUD $A100,000 USD per AUD US$2,000 US$ 0.0001 US$10

Share Futures 1000 Shares Cents per share Varies $100 -$1750

1 Cent A$10

ASX/S&P 200 SPI

$A25 x SPI As for All Ords, to one full index point

$2200 1.0 Index Point $A25

Wool Equivalent of 2500 kg clean weight fleece

Cents per kg clean weight.

Varies $650 - $750

1 cent/kg $25

RM v7 Topic 5 10

Futures PricePrice , Long Position GainsCost of Carry

(Net) Cost of ownership of underlying asset for the life of the contract

Basis, Positive and Negative Carry ContangoBackwardation

RM v7 Topic 5 11

Futures Trade Outcomes

Futures Trade AgreementUnder Contract

Futures PriceIncreases

Futures PriceDecreases

Buy a contract Will Buy Asset(will receive

asset atsettlement)

Profit Loss

Sell a contract Will Sell Asset(will deliver asset

at settlement)Loss Profit

RM v7 Topic 5 12

Futures contract timelineConsider a futures contract entered into at time t0, at a forward price f0 and expiring at time T. At a later time in the contract’s term, time t, the market price for a futures contract with the same expiry date (T) is ft

t0

ft

T

f0

t

RM v7 Topic 5 13

Payoff from a Long Futures Contract

f0ft

ft - f0

Profit

Loss

Price

The “payoff” is determined by the relationship between the original futures price (f0) and the new market price of the futures contract (ft)

RM v7 Topic 5 14

Payoff from a Short Futures Contract

f0ft

f0 - ft

Profit

Loss

Price

Again, the payoff is determined by the relationship between the original futures contract price (f0) and the new futures contract price (ft).

RM v7 Topic 5 15

Offset and Payoff – Long Futures

We “close out” the original contract by entering an offsetting contract at the new market forward price.

To “close out” a long (bought) futures position we must sell an equal number of futures contracts with the same expiry date: Payoff (profit) = $ft- $f0

RM v7 Topic 5 16

Offset and Payoff – Short FuturesTo “close out” a short futures position, we

must buy an equal number of futures contracts with the same expiry date: Payoff (profit) = $f0 -$ft

NOTE: For forward contracts, the payoff from offset can

only be realised when the two offsetting contracts expire, and not before. For futures contracts this is not the case. The payoff is realised immediately on closing out your position.

RM v7 Topic 5 17

Realising the Payoff – Held Positions

Futures Contracts are marked to market at the end of every trading day: your position is effectively “closed out” at

the end-of-day settlement price profits or losses are realised at the end of

each day A “new” position is effectively opened at

the start of the next day ie f0 is reset every day

RM v7 Topic 5 18

PV of the Payoff (?)

Unlike Forward Contracts:You do not have to “wait” until your

contracts expire to realise gains/losses

ThereforeIn valuing a futures contract the present

value of the payoff becomes irrelevant

RM v7 Topic 5 19

Valuing a Futures Contract

The value of a long futures contract, ƒ, during the trading day is:

ƒ = (ft-fo)Where f0 is the market opening price and ft is the

observed market price during the trading day Similarly, the value of a short futures contract

during the trading day is: ƒ = (f0-ft)

Immediately after marking to market, the value of a futures contract is zero.

RM v7 Topic 5 20

Futures Price

Futures Price is determined in the same way as forward price:

F = S + (CC – CR)where

CC is the cost of carrying the asset to maturity of the futures contract

CR is the amount of any receipts from holding the asset to maturity of the futures contract

As with forwards, these carry components are expressed differently in different settings.

RM v7 Topic 5 21

Futures Pricing relationshipsExpress Cost of Carry as “Actual” (when

cash dividend is known):F = S + (CC - CR)

or express as a per annum percentage of the spot price:F = S e ( (r + CC - CR) * T)

(or a mix of the above)

RM v7 Topic 5 22

Futures Pricing relationships Assume WMC futures contract for 3 mths

delivery - Assume WMC spot equals $10, dividends per quarter equals $0.40 and interest is paid at 7.00 % p.a. c.c.

PV of dividends is: CR = 0.40 e -

( 0.07 * 0.25 ) = 0.3931The WMC futures is calculated to

equal: F = ( S - CR ) e ( r * T ) F = (10 - 0.39) e ( 0.07 * 0.25 ) F = $ 9.78

RM v7 Topic 5 23

Futures Pricing relationships

Assume BHP futures contract for 45 days to delivery - Assume BHP spot equals $15, dividend yield is 2.50 % pa and interest is paid at 7.00 % p.a. c.c.

The BHP futures is calculated to equal: F = S e ( (r - d) * T ) F = 15 e ( ( 0.07 - 0.025) *( 45 / 365) ) F = $ 15.08

RM v7 Topic 5 24

Futures Pricing relationships Example involving Gold: Spot = $301 Cost of storage = $5 per oz LIBOR = 6 %

Term = 6 monthsPV of storage is: CC = 5.00 e - ( 0.06 *

0.50 ) = 4.8522The Gold futures price is calculated to

equal: F = ( S + CC ) e ( r * T ) F = (301 + 4.85) e ( 0.06 * 0.50 ) F = $ 315.16

RM v7 Topic 5 25

Forward vs Futures Prices

Forward and futures prices are usually assumed to be the same. When interest rates are uncertain they are, in theory, slightly different:

A strong positive correlation between interest rates and the asset price implies the futures price is slightly higher than the forward price

A strong negative correlation implies the reverse

RM v7 Topic 5 26

Interest Rate FuturesLike forwards in other markets, FRAs allow

hedgers to tailor a solution wrt size and maturity

Bid/Offer spreads in FRA market can be wide - FRAs are relatively expensive

Interest Rate Futures Contracts facilitate hedging in a cheaper (but less flexible) way.

RM v7 Topic 5 27

Quoting I/R FuturesQuoted on an “Index Basis”

100 - Yield = Price Implicit yield = 100 - Price $ equivalent is underlying instrument valued

at implicit yieldExample :A 10 year bond futures contract, with a nominal 6% coupon paid semiannually is trading at 93.50Implicit Yield in Futures Price 100 - 93.50 = 6.50Underlying Bond Price per $100 = 96.365

RM v7 Topic 5 28

Hedging with FuturesReduces VolatilityAims to eliminate Risk

i.e. remove uncertainty of outcomeRequires negative correlation

between futures position and spot position Losses on spot offset by gain on futures,

or vice versa

RM v7 Topic 5 29

Short Hedge(protects long spot)

K

Profit

Loss

Price

Long Spot Position

Price Falls

Short Futures Position (hedge)

Loss on spot

Gain on Futures

(long spot loses)

RM v7 Topic 5 30

Long Hedge(protects short spot)

K

Profit

Loss

Price

Long futures Position

Price Rises

Short spot Position

Loss on spot

Gain on Futures

(short spot loses)

RM v7 Topic 5 31

SFE Interest Rate FuturesContract Contract

Unit Quotes Initial

Margin Min Move

(point move)

90 Day BAB

$A1,000,000 FV 90day

BAB

100 - Yield $650 0.01%

3 Yr Bond $A100,000 FV 3yr CGS

with 6% Coupon

100 - Yield $850 0.01%

10 Yr Bond $A100,000 FV 10yr

CGS with 6% Coupon

100 - Yield $2000 0.005%

RM v7 Topic 5 32

Hedging with Bank Bill FuturesHedge Protocol:

Long Asset Short Hedge Short Asset Long Hedge

An Intending Borrower will undertake a Short Hedge in Bill Futures

An Intending Investor will undertake a Long Hedge in Bill Futures

RM v7 Topic 5 33

Short (Borrower’s) HedgeIn December, XYZ Co. knows it will require $10 million (short term) in March of the following year. XYZ Co. decides to sell bank bill futures to protect against an interest rate rise.Cash/ Physical Market Futures Market

December:Do Nothing Sell 10 March BAB Futures @93.05

(6.95% I.Y)Value: $9,831,517

March:Issue $10mio 90 Day BABs @ 8.10%Proceeds: 9,804,185

Close Short Position by buying 10 MarchBAB Futures @ 91.88 (8.12% I.Y)Value: $9,803,711

Interest Cost: $195,815 Futures Profit: $27,806

$168,009 365$9,804,185 x 90 x 100 = 6.95% = Effective Cost

RM v7 Topic 5 34

Long HedgeIn December, XYZ Co. knows it will have $10m surplus funds to invest in March of the following year. XYZ Co. decides to buy bank bill futures to protect against an interest rate fall.Cash/ Physical Market Futures Market

December:Do Nothing Buy 10 March BAB Futures @ 91.88

(8.12% I.Y)Value: $9,803,711

March:Buy $10mio 90 Day BABs @ 6.95%Purchase price: $9,831,517

Close Long Position by selling 10 MarchBAB Futures @ 93.05 (6.95% I.Y)Value: $9,831,517

Interest Earnings: $168,483 Futures Profit: $27,806

$196,289 365$9,831,517 x 90 x 100 = 8.10% = Effective Return

RM v7 Topic 5 35

Hedging with Bond FuturesWe want to establish a hedge position in

futures, which matches the sensitivity of our physical bonds

Interest-sensitivity of Bonds means we must modify the naive hedge ratio to hedge more accurately, using: Duration-modified hedge ratio Volatility-modified hedge ratio

RM v7 Topic 5 36

Mod.D Hedging

futures of Mod.Dx price Futuressecurity of Mod.Dx security of Price

Dhmod

EXAMPLE:At 1st of April, 1998:

Price D*(approx)CGS 10% 15.10.04 107.001 4.982June 98 10Y Futures 112.749 8.95

How many contracts would a lender need to sell in order to hedge $10,000,000 of the Oct 04?

RM v7 Topic 5 37

ModD Hedging

528.095.8749.11298.4001.107

ModDh

Therefore we sell:

contracts538.52000,100

000,000,10528.0

(Note: we could substitute DVBP or convexity for Duration using this approach.)

RM v7 Topic 5 38

Hedging Wool with FuturesA garment mfr requires 20,000 kg of

superfine wool (16-17 micron fibre, currently 760 cents per kg) for their winter range. They are locked into fixed-price supply

contracts, so cannot afford a price increase on the wool they buy.

The SFE offers a 2,500 kg 21 micron wool futures contract (trading at 650 cents per kg).

RM v7 Topic 5 39

Wool Buyer’s HedgeCash/ Physical Market Futures Market

August: Do Nothing Superfine Wool Price 760c per kg (20,000kg $152,000)

Buy 8 Nov Greasy Wool Futures @ 650c per kg Value: 8 x 2500 x 650c = $130,000

Nov: Buy 20,000 kg Superfine (16 Micron) wool @ 950c Purchase price: $190,000

Close Long Position by selling 8 Nov Greasy wool futures @ 750c Value: $150,000

Increased Cost: $38,000 Futures Profit: $20,000

The manufacturer is unable to hedge its exposure to 16 micron wool with a futures contract written on that grade of wool - it must hedge with a contract written on a different grade of wool - this gives rise to a problem of Commodity Basis Risk

RM v7 Topic 5 40

Commodity Basis RiskWhen commodity basis risk is a factor, the

hedger must consider the commodity to be hedged, and how it relates to the “nearest possible” available futures contract.

Commodity basis risk is relatively predictable in many markets. There may be an observable relationship between the prices of different grades of the same commodity. When this is the case, a hedge can be adjusted to

take in the additional risk.

RM v7 Topic 5 41

Hedging Equities with FuturesEquity Investors and Fund Managers have

tools available to them in the futures markets, in the form of Index contracts.

The ASX offers the following index futures contracts: ASX SPI 200™ Index Futures S&P/ASX 200 A-REIT Index Futures S&P/ASX 50 Index Futures S&P/ASX 200 Index Futures.

There are also deliverable futures contracts available on blue chip Australian shares, including BHP, NAB, ANZ, FBG, TE and others.

RM v7 Topic 5 42

SPI Futures - Fair Value“Fair Value” of the SPI can be defined

as the theoretical price that the SPI should be trading based on market price and cost-of-carry assumptions: SPI = Current S&P/ASX 200 Market level

+ cost of carry Cost of Carry = S&P/ASX 200 Market

level x (Funding Yield - Dividend Yield) x t

RM v7 Topic 5 43

SPI Fair Value - ExampleMarch SPI expires in 90 days, annual gross

dividend yield on the S&P/ASX 200 is 4.5%, 90-day BBSW 5%, and S&P/ASX 200 is at 2625: SPI Fair Value = 2625 + [2625 x (5%-4.5%) x

90/365]= 2625 + 3.24 = 2628.24SPI Futures determinants:

Dividend yield of the broad market Interest Rates Market level of S&P/ASX 200 Time to expiry

RM v7 Topic 5 44

SPI and Commodity Basis RiskIt is unlikely that any equity portfolio we

wish to hedge will match the S&P/ASX 200 in composition

Hedging with the SPI contract will give rise to CBR - we will be hedging one “asset” with a contract written on a different “asset”

We use the Beta of the Portfolio to adjust our hedge ratio and (hopefully) overcome the CBR problem

RM v7 Topic 5 45

Beta Hedging

n

i

iiip PQ

qp1

pf

pp MV

MVh

The beta of a share portfolio will be the weighted average (by market value) of the individual share betas:

The portfolio beta is used to adjust the market-value naïve hedge ratio:

to determine a hedge position with the same sensitivity to market movements as the physical portfolio.

RM v7 Topic 5 46

Portfolio Beta: ExampleShare Beta Holding Mkt Price Mkt ValueJLH Ltd 0.80 100,000 5.00 500,000SIDS Ltd 0.70 200,000 3.80 760,000UB Ltd 0.72 75,000 11.25 843,750NM NL 1.35 150,000 4.20 630,000

Total 2,733,750

p

0 8500 000

2 733 7500 7

760 0002 733 750

0 72843 750

2 733 750135

630 0002 733 750

0 8742.,

, ,.

,, ,

.,

, ,.

,, ,

.

If (in June) the Market Index is at 2650, and the nearest date SPI contract is at 2665:

hp contracts

$2, ,

$25. .

733 7502665

08742 3587

RM v7 Topic 5 47

Short SPI HedgeIf at expiration (in September) the Market Index is at 2500, and the SPI contract expires at 2525, what would be the outcome of the hedge?. Equity Market Futures Market

June:Portfolio Value $2,733,750 Sell 36 September SPI Futures @ 2665

Value: $2,398,500September:Portfolio value $2,598,476* Close Short Position by buying 36

September SPI Futures @ 2525Value: $2,272,500

Loss on Portfolio: $135,274 Futures Profit: $126,000

8742.0

2650250026501750,733,2*

RM v7 Topic 5 48

Futures vs OTC Forward MarketsIssues:

Regulated exchange Credit Risk & Novation Standardisation vs. Customised Secondary Market & Liquidity Price Visibility Regulation Daily MTM

RM v7 Topic 5 49

Futures RisksBasis RiskCommodity Basis RiskMargin CallsGappingLiquidity out long

RM v7 Topic 5 50

Futures AdvantagesLiquid (due to standardisation)Purpose-built hedge toolLow Transaction costsTransparent PricingRegulatedNegligible credit risk24 Hr Trading

RM v7 Topic 5 51

Futures DisadvantagesStandardisationMaturity, quantity and grade

mismatches commonShort-term hedge onlyMargin Calls

introduce uncertainty of cash flow and potential higher transaction costs

fin.