Hedging

1
Hedging Futures

• Today
• Business has risk
• Business Risk - variable costs
• Financial Risk - Interest rate changes
• Goal - Eliminate risk
• HOW?
• Hedging Futures Contracts
• CFT Review followed by Immense Details

2
Ex - Cereal Production

• Ex - Kellogg produces cereal. A major component
  and cost factor is sugar.
• Forecasted income sales volume is set by using
  a fixed selling price.
• Changes in cost can impact these forecasts.
• To fix your sugar costs, you would ideally like
  to purchase all your sugar today, since you like
  todays price, and made your forecasts based on
  it. But, you can not.
• You can, however, sign a contract to purchase
  sugar at various points in the future for a price
  negotiated today.
• This contract is called a Forward Contract.
• This technique of managing your sugar costs is
  called Hedging.

3
Type of Contracts

• 1- Spot Contract - A K for immediate sale
  delivery of an asset.
• 2- Forward Contract - A K between two people for
  the delivery of an asset at a negotiated price on
  a set date in the future.
• 3- Futures Contract - A K similar to a forward
  contract, except there is an intermediary that
  creates a standardized contract. Thus, the two
  parties do not have to negotiate the terms of
  the contract.
• The intermediary is the Commodity Clearing Corp
  (CCC). The CCC guarantees all trades provides
  a secondary market for the speculation of
  Futures.

4
Types of Futures

• Commodity Futures
• -Sugar -Corn -OJ
• -Wheat -Soy beans -Pork bellies
• Financial Futures
• -Tbills -Yen -GNMA
• -Stocks -Eurodollars
• Index Futures
• -SP 500 -Value Line Index
• -Vanguard Index

5
Futures Contract Concepts

• Not an actual sale
• Always a winner a loser (unlike stocks)
• K are settled every day. (Marked to Market)
• Hedge - K used to eliminate risk by locking in
  prices
• Speculation - K used to gamble
• Margin - not a sale - post partial amount
• Hog K 30,000 lbs
• Tbill K 1.0 mil
• Value line Index K index x 500

6
Ex - Settlement Speculate

• You are speculating in Hog Futures. You think
  that the Spot Price of hogs will rise in the
  future. Thus, you go Long on 10 Hog Futures. If
  the price drops .17 cents per pound (.0017)
  what is total change in your position?

7
Ex - Settlement Speculate

• You are speculating in Hog Futures. You think
  that the Spot Price of hogs will rise in the
  future. Thus, you go Long on 10 Hog Futures. If
  the price drops .17 cents per pound (.0017)
  what is total change in your position?

30,000 lbs x .0017 loss x 10 Ks
510.00 loss
50.63
cents per lbs
50.80
-510
Since you must settle your account every day, you
must give your broker 510.00
8
Ex - Commodity Hedge

• You are an Illinois farmer. You planted 100
  acres of winter wheat this week, and plan on
  harvesting 5,000 bushels in March. If todays
  wheat price is 1.56 per bushel, and you would
  like to lock in that price, what would you do?

9
Ex - Commodity Hedge

• You are an Illinois farmer. You planted 100
  acres of winter wheat this week, and plan on
  harvesting 5,000 bushels in March. If todays
  wheat price is 1.56 per bushel, and you would
  like to lock in that price, what would you do?
• Since you are long in Wheat, you will need to go
  short on March wheat. Since 1 K 5,000 bushels,
  you should short one contract and close your
  position in March.

10
Ex - Commodity Hedgereal world

• In June, farmer John Smith expects to harvest
  10,000 bushels of corn during the month of
  August. In June, the September corn futures are
  selling for 2.94 per bushel (1K 5,000
  bushels). Farmer Smith wishes to lock in this
  price.
• Show the transactions if the Sept spot price
  drops to 2.80.

11
Ex - Commodity Hedgereal world

• In June, farmer John Smith expects to harvest
  10,000 bushels of corn during the month of
  August. In June, the September corn futures are
  selling for 2.94 per bushel (1K 5,000
  bushels). Farmer Smith wishes to lock in this
  price.
• Show the transactions if the Sept spot price
  drops to 2.80.

Revenue from Crop 10,000 x 2.80 28,000 June
Short 2K _at_ 2.94 29,400 Sept Long 2K _at_ 2.80
28,000 . Gain on
Position-------------------------------
1,400 Total Revenue
29,400
12
Ex - Commodity Hedgereal world

• In June, farmer John Smith expects to harvest
  10,000 bushels of corn during the month of
  August. In June, the September corn futures are
  selling for 2.94 per bushel (1K 5,000
  bushels). Farmer Smith wishes to lock in this
  price.
• Show the transactions if the Sept spot price
  rises to 3.05.

13
Ex - Commodity Hedgereal world

• In June, farmer John Smith expects to harvest
  10,000 bushels of corn during the month of
  August. In June, the September corn futures are
  selling for 2.94 per bushel (1K 5,000
  bushels). Farmer Smith wishes to lock in this
  price.
• Show the transactions if the Sept spot price
  rises to 3.05.

Revenue from Crop 10,000 x 3.05 30,500 June
Short 2K _at_ 2.94 29,400 Sept Long 2K _at_ 3.05
30,500 . Loss on
Position------------------------------- ( 1,100
) Total Revenue
29,400
14
Ex - Commodity Speculationreal world

You have lived in NYC your whole life and are
independently wealthy. You think you know
everything there is to know abot pork bellies
(uncurred bacon) because your butler fixes it for
you every morning. Because you have decided to
go on a diet, you think the price will drop over
the next few months. On the CME, each PB K is
38,000 lbs. Today, you decide to short three May
Ks _at_ 44.00 cents per lbs. In Feb, the price
rises to 48.5 cents and you decide to close your
position. What is your gain/loss?
15
Ex - Commodity Speculationreal world

You have lived in NYC your whole life and are
independently wealthy. You think you know
everything there is to know abot pork bellies
(uncurred bacon) because your butler fixes it for
you every morning. Because you have decided to
go on a diet, you think the price will drop over
the next few months. On the CME, each PB K is
38,000 lbs. Today, you decide to short three May
Ks _at_ 44.00 cents per lbs. In Feb, the price
rises to 48.5 cents and you decide to close your
position. What is your gain/loss?
Nov Short 3 May K (.4400 x 38,000 x 3 )
50,160 Feb Long 3 May K (.4850 x 38,000 x 3 )
- 55,290 Loss of 10.23 -
5,130
16
Margin

• The amount (percentage) of a Futures Contract
  Value that must be on deposit with a broker.
• Since a Futures Contract is not an actual sale,
  you need only pay a fraction of the asset value
  to open a position margin.
• CME margin requirements are 15
• Thus, you can control 100,000 of assets with
  only 15,000.

17
Ex - Commodity Speculationreal world - with
margin

You have lived in NYC your whole life and are
independently wealthy. You think you know
everything there is to know abot pork bellies
(uncurred bacon) because your butler fixes it for
you every morning. Because you have decided to
go on a diet, you think the price will drop over
the next few months. On the CME, each PB K is
38,000 lbs. Today, you decide to short three May
Ks _at_ 44.00 cents per lbs. In Feb, the price
rises to 48.5 cents and you decide to close your
position. What is your gain/loss?
18
Ex - Commodity Speculationreal world - with
margin

You have lived in NYC your whole life and are
independently wealthy. You think you know
everything there is to know abot pork bellies
(uncurred bacon) because your butler fixes it for
you every morning. Because you have decided to
go on a diet, you think the price will drop over
the next few months. On the CME, each PB K is
38,000 lbs. Today, you decide to short three May
Ks _at_ 44.00 cents per lbs. In Feb, the price
rises to 48.5 cents and you decide to close your
position. What is your gain/loss?
Nov Short 3 May K (.4400 x 38,000 x 3 )
50,160 Feb Long 3 May K (.4850 x 38,000 x 3 )
- 55,290 Loss -
5,130 Loss 5130 5130 Margin 50160
x.15 7524
------------ --------------------
------------ 68 loss
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Financial Futures

• Goal (Hedge) - To create an exactly opposite
  reaction in price changes, from your cash
  position.
• Commodities - Simple because assets types are
  standard.
• Financials - Difficult because assets types are
  infinte.
• - You must attempt to approximate your position
  with futures via Hedge Ratios.

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Ex - Financial Futures

• Example - Hedge
• Cash Position Futures Position
• Nov Long 1,000 Short 1K _at_970
• March Sell _at_ 930 Long 1K _at_900
• loss 70 gain 70
• Net position 0

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Ex - Financial Futures

• Example - Hedge Reality
• Cash Position Futures Position
• Nov Long 1,000 Short 1K _at_970
• March Sell _at_ 930 Long 1K _at_920
• loss 70 gain 50
• Net position 20
  loss

22
Ex - Financial Futures
You are long in 1mil of bonds (15 yr 8.3125
bonds) The current YTM is 10.45 and the current
price is 82-17. You want to cash out now, but
your accountant wants to defer the taxes until
next year. The March Bond K is selling for 80-09.
Since each K is 100,000, you need to short 10
March Ks. In March you cash out with the Bond
price 70-26 and the K price 66-29. What is
the gain/loss?
23
Ex - Financial Futures
You are long in 1mil of bonds (15 yr 8.3125
bonds) The current YTM is 10.45 and the current
price is 82-17. You want to cash out now, but
your accountant wants to defer the taxes until
next year. The March Bond K is selling for 80-09.
Since each K is 100,000, you need to short 10
March Ks. In March you cash out with the Bond
price 70-26 and the K price 66-29. What is
the gain/loss?
Cash Futures Basis Nov 825,312 802,81
2 (2-8) March 708,125 669,062
(3-29) Gain/Loss (117,187) 133,750 (1-21)

Net Gain 16,563 ( 1-21 x 1mil)
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Financial Futures
The art in Financial futures is finding the exact
number of contracts to make the net gain/loss
0. This is called the Hedge Ratio
Face Value Cash Face Value of Futures K
of Ks ---------------------------------- X
Hedge Ratio
HR Goal - Find the of Ks that will perfectly
offset cash position.
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Hedge Ratio Determination

• 1 - The Duration Model
• 2 - Naive Hedging Model
• 3 - Conversion Factor Model
• 4 - Basis Point Model
• 5 - Regression Model
• 6 - Yield Forecast Model

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Futures Project

• Goal - To use futures contract to maximize the
  return on two mutual fund investments.
• ASAP Send me Via Email your choices for
• Select a bond Mutual Fund
• Select an equity Mutual Fund
• select simple funds (nothing exotic) it will make
  your project easier.

27
Futures Project

• Due DEC 9
• You manage two mutual funds
• Fund 1 - Bond fund
• Fund 2 - Equity fund
• Assume that interest rates will rise over the
  next few weeks. Hedge your entire fund against a
  rise in rates.
• Assume that the stock market will increase in
  value over the next few weeks. Assume 5 of your
  fund is held in cash.
• Create a futures strategy for each fund that will
  maximize your return on each.
• Equity Fund - fully invested strategy
• Bond Fund - Hedge Interest rate risk strategy
• Over next 2 weeks project will come into focus.

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Cheapest To Deliver

• How To Calculate Delivery Cost (steps)
• 1 - Look up the price - FP
• 2 - Compute Conversin Factor (CF)
• 3 - CF x FP x (contract size) (accrued
  interest)
• Delivery cost

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Cheapest To Deliver

• Theoretical Futures Price (FP)?
• 3 Ways to Derive CTD (select lowest )
• 1 - Calculate delivery costs compare
• 2 - Calculate Futures Delivery Spot Price
• 3 - Cost of Delivery

We will defer a discussion of ? Handouts have a
more detailed description
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FC Characteristics

• Example
• Two bonds are eligable for delivery on the June
  1997 T Bond Futures K
• 1 - 9.875Nov23 deilveries on 15th of maturity
  month
• 2 - 7.25May24
• On June 12, you announce to deliver a bond

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FC Characteristics

• Q If YTM 7, which will you deliver what is
  its price?
• A

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FC Characteristics

• Q If YTM 7, which will you deliver what is
  its price?
• A CF Bond Price FC Spot Price
• 9.875Nov23 1.20 134.39 111.99
• 7.25May24 .918 103.00 112.20
• Deliver 9 7/8 Nov23

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FC Characteristics

• Q If YTM 9, which will you deliver what is
  its price?
• A

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FC Characteristics

• Q If YTM 9, which will you deliver what is
  its price?
• A CF Bond Price FC Spot Price
• 9.875Nov23 1.20 108.76 90.63
• 7.25May24 .918 82.36 89.72
• Deliver 7 1/4 May24

35
FC Characteristics

• Q If YTM 7 and the lisyted futures price is
  110.50, which bond is CTD?
• A
• 9 7/8Nov23 CTD 134.39 - (110.5 x 1.20) 1.79
• 7 1/4May24 CTD 103.00 - (110.5 x .918) 1.56
• Implied Repo Rate
• Cost of Carry

36
Hedge Ratios

• Duration Model

37
Hedge Ratios

• Duration Model
• Your cash position is 1,000,000 10 coupon,
  26year bonds, with YTM12.64 and duration of
  8.24 years.
• The 8, 20year, TBill has a duration of 10.14
  years, YTM8.5
• The FC on this bond is priced at 96.87

38
Hedge Ratios

• Duration Model
• Your cash position is 1,000,000 10 coupon,
  26year bonds, with YTM12.64 and duration of
  8.24 years.
• The 8, 20year, TBill has a duration of 10.14
  years, YTM8.5
• The FC on this bond is priced at 96.87
• HR 82x8.24 675.68 .688
• 96.87x10.14 982.26
• (1,000,000 / 100,000) x .688 6.88 or 7
  contracts

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Hedge Ratios

• Duration Example
• In 3 months, you will receive 3.3 mil in cash
  and must invest it for 6 months. The current 6
  month rate is 11.20. You like that rate, and
  wish to lock it in.
• 6 month tbills have a .50 duration, while 3 month
  bills have a .25 duration.
• If the 3 month futures price is 97.36, what
  number of Ks are required to lock in the rate?
• HR 100 x .5 2.05 x (3.3 / .1)
  67.8 kks
• 97.36 x .25

40
Hedge Ratios

• Naive Model
• HR 1.0 (all previous exmaples were naive
  hedges)
• Conversion Factor Model
• HR conversion factor
• CF Price of deliverable bond _at_ 8 YTM
• 100

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Hedge Ratios

• Conversion Factor Model
• Example
• You own a 1mil portfolio you wish to hedge.
  Your are considering a 3 month futures K. The
  bond that could be delivered against the contract
  is a 12.54(semiannual) bond with a 30year
  maturity. The bond is callable in 15 years.
• How many Ks hsould you use to hedge the position?
• CF 141.07/100 1.41 x (1mil/.1) 14 Ks

42
Hedge Ratios

• Example - Conversion Factor Model
• You have a 1mil portfolio, containing 21.5 year
  10 3/8 bonds. Price 100.3125 (YTM 10 5/16)
• CTD 20year, 8 bond has YTM 10.43
• Create the hedge.
• Assume that in 6 months YTM on your portfolio
  rises to 12 and YTm on CTD rises to 12.217
• Create a table showing your position/profit/loss

43
Hedge Ratios

• Example - Conversion Factor Model
• CF PV of 5.1875 _at_ 4 for 43 periods / 100
  1.24
• 1.24 x (1mil/100,000) 12
• Cash Futures
• Today Own 1mil Short 12 K
• _at_ 100.3125 _at_ 79.718 (derive)
• (1,003,125) 956,616
• 6 mths Sell _at_ 87.50 buy 12 K _at_ 68.90
• 875,000 (826,875)
• (128,125) 129,750

44
Hedge Ratios

• Basis Point Model
• BVCcash change in value per basis point of
• cash position
• B Relative yield volatility of cash to CTD
• (Vcash / Vctd)
• BVCctd change in value per basis point of
• CTD
• CFctd conversion factor of CTD

45
Hedge Ratios

• Example
• YTM 9 on semi-annual bonds
• Your cash portfolio consists 1mil of 26 year 9
  7/8 bonds, that have a yield volatility of .60
• Futures CTD is a 7.25 26.5 year note with a
  yield volatility of .50 (assume futures price
  bonds price)
• Use the basis point model model to create a hedge
  and show the position table for a 3month time
  period and a change in YTM to 10.

46
Hedge Ratios

• example - continued
• Cash value _at_ 9 108.737
• BVCcash 107 (PV _at_ 9 - PV _at_ 9.01)
• BVCctd 86
• B .6 / .5 1.20
• CF .918 (PV of CTD _at_ 8 / 100)
• HR ( 107 ) x 1.20 1.378
• ( 86 / .918)
• 1 mil / 100,000 x 1.378 13 or 14 contracts

47
Hedge Ratios

• example - continued (10)
• Cash Futures
• Today 1mil _at_ 108.737 13K _at_ 82.44
• -1,087,370 1,071,720
• 3 months (YTM 10)
• 1 mil _at_ 96.44 13K _at_ 72.85
• 964,427 - 947,050
• Net Position 122,943 loss 124,670 gain
• net gain of 1,727

48
Hedge Ratios

• example - continued
• Assume YTM 8
• Cash Futures
• Today 1mil _at_ 108.737 13K _at_ 82.44
• -1,087,370 1,071,720
• 3 months (YTM 8)
• 1 mil _at_ 117.91 13K _at_ 90.04
• 1,179,100 - 1,170,520
• Net Position 91,730 gain 98,800 loss
• net loss of 7,070

49
Hedge Ratios

• Regression Model
• HR Covariance of Cash Futures
• Variance of futures
• best model
• if HR .90, then we know that a 1 change in
  futures prices correlates to a 0.90 change in
  cash value.
• requires constant monitoring because HR changes
  with duration

50
Hedge Ratios

• Yield Forecast Model
• Given various yield forecasts, the HR changes
• Term Structure can forecast yields
• HR CVdiff / FCV diff
• Example
• Cash Value 97.94 Futures 72.50
• Forecasted YTM
• YTM CV YTM FC CV FC CVdiff FCdiff HR
• 12.65 11.25 101.72 75.06 3.77 2.56 1.48
• 12.85 11.40 100.14 74.14 2.20 1.64 1.34
• 13.55 12.05 94.99 70.37 -2.95 -2.13 1.36
• 13.75 12.20 93.62 69.54 -4.33 -2.96 1.47

51
Currency Futures

• Identical to commodity futures in short term
• Strategy is naive hedge
• Example
• On May 23, a US firm agrees to buy 100,000
  motorcycles from Japan on Dec 20 at Y202,350
  each. The firm fears a decline in value
• Spot price 142.45 (Y/) or .00720 /Y
• Dec Futures 139.18 (Y/) or .00719 /Y
• Each K is Y12,5000,000
• How can we hedge this position

52
Currency Futures

• example continued
• 100,000 x Y202,350 Y 20235 mil
• 20235 mil 1,619 ks
• 12.5 mil
• You should buy 1619 yen futures to hedge the risk

53
Currency Futures

• example continued
• if /Y drops to .00650 (/Y) or 153.846Y/
• Cost cost - futures profit
• cost 20235 (.0065) - (1619)(12.50)(.00065-
  .007190)
• cost 131.53 - (-13.96) 145.49 mil
• if /Y rises to .008 (/Y) or 125 Y/
• Cost cost - futures profit
• cost 20235 (.008) - (1619)(12.50)(.0080-
  .007190)
• cost 161.88 - 16.39 145.49 mil

54
Stock Index Futures

• Underlying Assets (sample)
• SP 500
• NYSE Composite Index
• Major Market Index (MMI) (CBOE)
• Value Line Index
• Why Are They Traded?
• 1 - Change position quickly
• 2 - Create synthetic fund
• 3 - Hedge equity position

55
Stock index Futures

• Price relationship
• also called cost of carry or cash carry
• F0 Ft S0 (1 rf - d)t t of year
• Ft2 Ft1 (1 rf - d) (t2-t1)
• Profit St - F0

56
Stock Index Futures

• Example - arbitrage
• The 1 year futures price on SP500 is 406. the
  SP 500 index is at 400. Rf 3 and the dividend
  rate is 1.25
• Is F0 mispriced and by how much?
• Show a stretegy to take advantage of this.
• F0 400 (1 .03 - .0125) 407
• Index is underpriced by 1.00
• We should dhort the index and long the futures

57
Stock Index Futures

• Example - arbitrage (continued)
• Index Futures Park
• Strategy
• Now short _at_ 400 long _at_ 406 invest 400 _at_ 3
• 6 mts buy (St 5) short _at_ St 406
• Cash Flow Net
• Now 400 0 -400 0
• 6 mts -(St 5) St 406 1
• 1

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