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University of Colorado at Boulder – Leeds School of Business – FNCE4040 Derivatives

FNCE4040 – Derivatives Chapter 3

Hedging Strategies Using Futures

University of Colorado at Boulder – Leeds School of Business – FNCE4040 Derivatives

Hedging and Risk Management

• Hedging is used as a form of risk

management:

– You can use futures to minimize the uncertainty

• n the future cash flows resulting from an existing

portfolio of assets (physical or financial)

• Risk management does not end when you

put the hedge on: you still need to manage

– Market risk – Counterparty risk – Funding risk

University of Colorado at Boulder – Leeds School of Business – FNCE4040 Derivatives

To Hedge or Not To Hedge?

PROs

• Companies should

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

• ther market variables

CONs

• Shareholders can make

their own hedging decisions

• It may increase risk to

hedge (e.g. Ashanti 1999)

• Explaining to

shareholders a loss on the hedge when there is a gain on the underlying can be difficult

University of Colorado at Boulder – Leeds School of Business – FNCE4040 Derivatives

Hedging considerations

When you put on a hedge you need to ask yourself:

• Am I hedging the exact thing I want to

hedge?

– If not, you still have some residual market risk that you need to manage, and it can be large

• Do I need to worry about my counterpart?

– If yes, then you need to manage that risk

• Do I need additional cash flows?

– Often yes and you need to manage that risk

University of Colorado at Boulder – Leeds School of Business – FNCE4040 Derivatives

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

University of Colorado at Boulder – Leeds School of Business – FNCE4040 Derivatives

Basis Risk

• Basis is usually* defined as the spot price

minus the futures price

• Basis risk arises because of the uncertainty

about the basis when the hedge is closed out

(*) in some commodity markets the market jargon “basis” or “spread” refers to the price difference between grades or locations, and the difference between contract months is called “calendar spread”.

University of Colorado at Boulder – Leeds School of Business – FNCE4040 Derivatives

Long Hedge for Purchase of an Asset

• Define

F1 : Futures price at time hedge is set up F2 : Futures price at time asset is purchased S2 : Asset price at time of purchase b2 : Basis at time of purchase Cost of asset S2 Gain on Futures F2 −F1 Net amount paid S2 − (F2 −F1) =F1 + b2

University of Colorado at Boulder – Leeds School of Business – FNCE4040 Derivatives

Short Hedge for Sale of an Asset

Define F1 : Futures price at time hedge is set up F2 : Futures price at time asset is sold S2 : Asset price at time of sale b2 : Basis at time of sale Price of asset S2 Gain on Futures F1 −F2 Net amount received S2 + (F1 −F2) =F1 + b2

University of Colorado at Boulder – Leeds School of Business – FNCE4040 Derivatives

Choice of Contract Month

• Especially for physical commodities, 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- (or proxy-) hedging.

University of Colorado at Boulder – Leeds School of Business – FNCE4040 Derivatives

HEDGING OIL

University of Colorado at Boulder – Leeds School of Business – FNCE4040 Derivatives

Risk Management example: oil

• You own an oil field

– You have fixed and variable costs – Your revenues will depend on the oil price at the moment of sale

• How can you lock you revenues?

– You can enter a long term sales contract with a corporation that buys oil – You can enter a forward contract with a bank – You can sell oil futures – What are the pro’s and con’s of each strategy?

University of Colorado at Boulder – Leeds School of Business – FNCE4040 Derivatives

Example – hedge oil production

• You own an oil field and hedge revenues
• You produce WTI-like oil near Cushing, OK
• You know you will produce 1mm bbl in March
• You sell 1000 March WTI contracts (NYMEX)

– initialmarginrequirement=$4,950/contract – So you deposit $4,950,000 – Maintenance margin is $4,500/contract. So for your position it is ___________

University of Colorado at Boulder – Leeds School of Business – FNCE4040 Derivatives

Example – hedge oil production (cont)

Day Settle Price Profit (Loss)

aka P/L

Margin Account Balance Margin Call

1 $48.75 $0 $4,950,000 $0 2 $49.00 ($250,000) $4,700,000 $0 3 $50.75 ($1,750,000) $2,950,000 $2,000,000 4 $52.00 ($1,250,000) $3,700,000 $1,250,000 5 $49.00 $3,000,000 $7,950,000 $0

…

You short 1,000 contracts at 48.75

University of Colorado at Boulder – Leeds School of Business – FNCE4040 Derivatives

Example – hedge oil production (cont)

• You continue to manage your short futures

position until last trade day (20-Feb-2013)

• Given your physical business location and the

type of oil you produce, you let the futures contract expire and go into delivery

• On 22-Feb-2013 you receive a delivery notice
• You deliver 1mm bbl of WTI-like grade into

Cushing and receive the futures price as of the last trade day

University of Colorado at Boulder – Leeds School of Business – FNCE4040 Derivatives

Example – hedge oil production (cont)

• This hedge removes the revenue risk

associated with the price of oil

• However, you are now left with a cash flow

needs from having to meet margin calls

• Just in a few days, you need approx. $8mm
• How much cash do you anticipate needing to

meet margin calls during the hedge life?

• Let’s take a look at oil price history

– You are holding your position for roughly 1m – Total cash needed ≅ sum of daily moves – So look at monthly cumulative price changes

University of Colorado at Boulder – Leeds School of Business – FNCE4040 Derivatives

WTI prices – 1st nearby

($/bbl)

20 40 60 80 100 120 140 160 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015

University of Colorado at Boulder – Leeds School of Business – FNCE4040 Derivatives

WTI price daily differences

($/bbl)

• 20
• 15
• 10
• 5

5 10 15 20

2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014

Average = 0.01 Min = -14.3 Max = 16.4 StDev = 1.12

University of Colorado at Boulder – Leeds School of Business – FNCE4040 Derivatives

Example – hedge oil production (cont)

• Daily changes do not tell you how much cash

collateral you may need

• Need to look at the cumulative daily changes
• ver the hedge holding period
• In our example, we hold the hedge for ~1m:

– Average = 0.06 ($/bbl) – StDev = 4.9 – Min =-54.2 – Max = 21.0

• You may need as much as $21 or 54mm !!!

University of Colorado at Boulder – Leeds School of Business – FNCE4040 Derivatives

Example – hedge oil – variation A

• Assume your oil is WTI grade but not at

Cushing

• You plan to sell the oil in the open physical

market in Cushing

• It costs $8/bbl to transport oil to Cushing
• How does your hedging strategy change,

assuming you can only hedge with WTI?

– How many contracts will you short? – Will you let your futures position go into delivery?

University of Colorado at Boulder – Leeds School of Business – FNCE4040 Derivatives

Example – hedge oil – variation B

• Assume now that

– Your oil is still WTI grade but not at Cushing – It still costs $8/bbl to transport oil to Cushing – You have a contract with a local refinery which will take your oil at the WTI price, minus $4/bbl

• How does your hedging strategy change,

assuming you can only hedge with WTI?

– How many contracts will you short? – Will you let your futures position go into delivery?

University of Colorado at Boulder – Leeds School of Business – FNCE4040 Derivatives

Example – hedge oil – variation C

• Assume now that

– Your oil is less than WTI grade and not at

• Cushing. Your oil is worth roughly 95% of WTI

– It still costs $8/bbl to transport oil to Cushing – You have a contract with a local refinery which will take your oil at (𝑋𝑈𝐽 × 0.95 − 4) ($/bbl)

• How does your hedging strategy change,

assuming you can only hedge with WTI?

– How many contracts will you short? – Will you let your futures position go into delivery?

University of Colorado at Boulder – Leeds School of Business – FNCE4040 Derivatives

HEDGING EQUITY

University of Colorado at Boulder – Leeds School of Business – FNCE4040 Derivatives

Hedging equity returns

• May want to be out of the market for a while.

Hedging avoids the costs of selling and repurchasing the portfolio

• Suppose stocks in your portfolio have an

average beta of 1.0, but you feel they have been chosen well and will outperform the market in both good and bad times. Hedging ensures that the return you earn is the risk- free return plus the excess return of your portfolio over the market.

University of Colorado at Boulder – Leeds School of Business – FNCE4040 Derivatives

S&P 500 Futures contract specs

Feature Specs Contract Unit 250 x S&P 500 futures price 1 index point = $250 Tick size = 0.10 index points (=$25) Contract Months March, June, September and December Settlement Price The Final Settlement Price shall be a special quotation of the S&P 500 Index based on the

• pening prices of the component stocks in the

index, determined on the third Friday of the contract month. Margin Initial = $25,300 –– Maintenance = $23,000

University of Colorado at Boulder – Leeds School of Business – FNCE4040 Derivatives

Hedging a well-diversified portfolio

• Assume you own a portfolio of well diversified

stocks

– We will take well diversified to mean that your portfolio mirrors the S&P 500

• Assume that your portfolio has a value of

$1mm

• How many contracts do you need to reduce

your exposure to the market to zero?

– What is the difference between the futures contract and the position in the index

University of Colorado at Boulder – Leeds School of Business – FNCE4040 Derivatives

Dividends

• The current S&P 500 index is at 2022 (close
• f business Jan 20th 2015)
• The March 2015 S&P futures contract is at

2010.

• Ignoring interest rates the difference between

the futures price and the index price will be the expected dividends paid until the futures expiry or $12

University of Colorado at Boulder – Leeds School of Business – FNCE4040 Derivatives

Market Moves

• What happens if we allow the market to move

in the previous example:

– Starting levels

• Index Price is 2022
• Futures Price is 2010
• Expected dividend is 12

– Market drops by 10

• New index price is 2012
• New futures price is 2000
• Expected dividend is 12

– Need to have same number of futures contracts as “index contracts”

University of Colorado at Boulder – Leeds School of Business – FNCE4040 Derivatives

Sizing the Hedge

• Assume you can have fractional contracts.
• If you have $1m invested then you have

1mm/2022=494.55 units of the SP500.

• That is 495.55/ 250 = 1.978 contracts.
• You should have 1.978 futures contracts or

1.978 × 2010 × 250 = $993,945 worth of futures contracts.

• If the index falls 10 then you lose $4,945.60
• Your short futures position will thus make $4,945.60

and you are hedged.

University of Colorado at Boulder – Leeds School of Business – FNCE4040 Derivatives

Dividend Expectations

• Dividend Expectations are priced into the futures

contract

• If these are wrong then your PL will be different than

expected

• In the previous example

– If the dividend paid is equal to the expected dividend then the hedge works – If the dividend paid is less than the expected dividend then you lose money – If the dividend paid is more than the expected dividend then you make money.

University of Colorado at Boulder – Leeds School of Business – FNCE4040 Derivatives

Margin

• Your futures position will require you to

maintain a margin account

– What the expected margin account size?

• For one S&P 500 index contract you must post $25,300
• If we have 1.987 futures contracts then we will post

$50,271 in margin

University of Colorado at Boulder – Leeds School of Business – FNCE4040 Derivatives

Margin

• Over the past 10 years if you were running a

“hedged” position of $1mm long S&P 500 index tracking and short $1mm of futures. What would have been your largest 1-month draw-down of margin?

University of Colorado at Boulder – Leeds School of Business – FNCE4040 Derivatives

Monthly Moves of S&P 500

• 15%
• 10%
• 5%

0% 5% 10% 15% 20% 25% Jan-05 May-05 Sep-05 Jan-06 May-06 Sep-06 Jan-07 May-07 Sep-07 Jan-08 May-08 Sep-08 Jan-09 May-09 Sep-09 Jan-10 May-10 Sep-10 Jan-11 May-11 Sep-11 Jan-12 May-12 Sep-12 Jan-13 May-13 Sep-13 Jan-14 May-14 Sep-14

University of Colorado at Boulder – Leeds School of Business – FNCE4040 Derivatives

Margin

• The largest monthly up move in the S&P 500

was approximately 20%

– This approximately 400 index points today – A 400 point move in the futures contract will lose 1.987 × 250 × 400 = 198,700

University of Colorado at Boulder – Leeds School of Business – FNCE4040 Derivatives

STACK AND ROLL

University of Colorado at Boulder – Leeds School of Business – FNCE4040 Derivatives

Stack and Roll

• We can roll futures contracts forward to

hedge future exposures

• Initially we enter into futures contracts to

hedge exposures up to a time horizon

• Just before maturity we close them out an

replace them with new contract reflect the new exposure

• etc.

University of Colorado at Boulder – Leeds School of Business – FNCE4040 Derivatives

Liquidity Issues

• When hedging there is a danger that losses

will be realized immediately on the hedge, while gains on the underlying are unrealized

• This can create liquidity problems
• One example is Metallgesellschaft which sold

long term fixed-price contracts on heating oil and gasoline and hedged using stack and roll

• Oversized hedge (market knew), basis risk,
• il went from backwardation to contango…

University of Colorado at Boulder – Leeds School of Business – FNCE4040 Derivatives

Liquidity Issues - Ashanti

• Ashanti is a Gold mine in Ghana
• In 1999, Ashanti had hedges for about ~60% of

each of the next 10 years worth of production

• Absent the need to post margin, this was a

conservative hedge

• 30-Sep-1999 gold price spiked up after European

Central Banks decided to hold off selling gold (from 260 to 320 in 1-2 days)

• The resulting margin call from Banks to Ashanti was

massive (100’s of $mm)