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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
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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.