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 DetailsCFT Review followed by Immense Details

Ex - Cereal ProductionEx - 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 today’s 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.”

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.

Types of Futures

Commodity Futures

-Sugar -Corn -OJ

-Wheat -Soy beans -Pork bellies

Financial Futures

-Tbills -Yen -GNMA

-Stocks -Eurodollars

Index Futures

-S&P 500 -Value Line Index

-Vanguard Index

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

Ex - Settlement & SpeculateYou 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?

Ex - Settlement & SpeculateYou 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

Since you must settle your account every day, you must give your broker $510.00

50.63

50.80-$510

cents per lbs

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

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 today’s 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.

Ex - Commodity Hedge

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.

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 @ 2.94 = 29,400

Sept: Long 2K @ 2.80 = 28,000 .

Gain on Position------------------------------- 1,400

Total Revenue $ 29,400

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.

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 @ 2.94 = 29,400

Sept: Long 2K @ 3.05 = 30,500 .

Loss on Position------------------------------- ( 1,100 )

Total Revenue $ 29,400

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 @ 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?

Ex - Commodity Speculationreal world

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

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 @ 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?

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.

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 @ 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?

Ex - Commodity Speculationreal world - with margin

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

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 @ 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?

------------ = -------------------- = ------------ = 68% loss

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.”

Example - Hedge

Cash Position Futures Position

Nov Long $1,000 Short 1K @$970

March Sell @ $930 Long 1K @$900

loss $70 gain $ 70

Net position = $ 0

Ex - Financial Futures

Example - Hedge Reality

Cash Position Futures Position

Nov Long $1,000 Short 1K @$970

March Sell @ $930 Long 1K @$920

loss $70 gain $ 50

Net position = $ 20 loss

Ex - Financial Futures

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?

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 $802,812 + (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)

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

# of Ks = ---------------------------------- X Hedge Ratio $ Face Value Cash

$ Face Value of Futures K

HR Goal - Find the # of Ks that will perfectly offset cash position.

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

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.

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.

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

CF Price of bond @ YTM = 8%

100

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

FPCF

Price of bond

?

We will defer a discussion of “?” Handouts have a more detailed description

QPCF QP FP CF[ ]

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

Q: If YTM = 7%, which will you deliver & what is its price?

A:

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

FC Characteristics

Q: If YTM = 9%, which will you deliver & what is its price?

A:

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

FC Characteristics

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

Hedge Ratios

Duration Model

HR =Cash Price

Futures Price

Duration

Duration

1

1+ Er

1

1+ ErUsually tossed out due to poor forecsating

Cash

CTD

Cash

CTD

Cash

CTD

Er

Er

Hedge RatiosDuration Model

• Your cash position is $1,000,000 10% coupon, 26year bonds, with YTM=12.64% and duration of 8.24 years.

• The 8%, 20year, TBill has a duration of 10.14 years, YTM=8.5%

• The FC on this bond is priced at 96.87

Hedge RatiosDuration Model

• Your cash position is $1,000,000 10% coupon, 26year bonds, with YTM=12.64% and duration of 8.24 years.

• The 8%, 20year, TBill has a duration of 10.14 years, YTM=8.5%

• 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

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

Hedge Ratios

Naive Model

• HR = 1.0 (all previous exmaples were naive hedges)

Conversion Factor Model

HR = conversion factor

CF = Price of deliverable bond @ 8% YTM

100

Hedge RatiosConversion 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

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

Hedge RatiosExample - Conversion Factor Model

• CF = PV of 5.1875 @ 4% for 43 periods / 100 = 1.24

• 1.24 x (1mil/100,000) = 12

Cash Futures

Today Own $1mil Short 12 K

@ 100.3125 @ 79.718 (derive)

($1,003,125) + $956,616

6 mths Sell @ 87.50 buy 12 K @ 68.90

+ $875,000 ($826,875)

(128,125) +129,750

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

HRBVC

BVC CFBCASH

CTD CTD

# of Ks

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%.

Hedge Ratiosexample - continued

Cash value @ 9% = 108.737

BVCcash = $107 (PV @ 9% - PV @ 9.01)

BVCctd = $86

B = .6 / .5 = 1.20

CF = .918 (PV of CTD @ 8% / 100)

HR* = ( 107 ) x 1.20 = 1.378

( 86 / .918)

1 mil / 100,000 x 1.378 = 13 or 14 contracts

Hedge Ratiosexample - continued (10%)

Cash Futures

Today $1mil @ 108.737 13K @ 82.44

-$1,087,370 +1,071,720

3 months (YTM = 10%)

$1 mil @ 96.44 13K @ 72.85

+$ 964,427 - $947,050

Net Position $122,943 loss $124,670 gain

net gain of $1,727

Hedge Ratiosexample - continued

Assume YTM = 8% Cash Futures

Today $1mil @ 108.737 13K @ 82.44

-$1,087,370 +1,071,720

3 months (YTM = 8%)

$1 mil @ 117.91 13K @ 90.04

+$ 1,179,100 - $1,170,520

Net Position $91,730 gain $98,800 loss

net loss of $7,070

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

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

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

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

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

Stock Index Futures

Underlying Assets (sample)

• S&P 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

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

Stock Index FuturesExample - arbitrage

The 1 year futures price on S&P500 is 406. the S&P 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

Stock Index FuturesExample - arbitrage (continued)

Index Futures Park

Strategy

Now short @ 400 long @ 406 invest 400 @ 3%

6 mts buy (St + 5) short @ St +406

Cash Flow Net

Now +400 0 -400 0

6 mts -(St + 5) +St +406 +1

+1