Hedging & FuturesToday Business has risk
Business Risk - variable costsFinancial 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 Contracts1- 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 lbsTbill K = $1.0 milValue 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
PositionNov 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 PositionNov 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 FuturesYou 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 FuturesThe 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 Model2 - Naive Hedging Model3 - Conversion Factor Model4 - Basis Point Model5 - Regression Model6 - 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 ProjectDue 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 - FP2 - Compute “Conversin Factor” (CF)
3 - CF x FP x (contract size) + (accrued interest)= Delivery cost
CF Price of bond @ YTM = 8%
100
Cheapest To DeliverTheoretical Futures Price (FP)?
3 Ways to Derive CTD (select lowest )1 - Calculate delivery costs & compare2 - Calculate Futures Delivery Spot Price3 - Cost of Delivery
FPCF
Price of bond ?
We will defer a discussion of “?” Handouts have a more detailed description
QPCF QP FP CF[ ]
FC CharacteristicsExampleTwo 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 Price9.875Nov23 1.20 134.39 111.997.25May24 .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 Price9.875Nov23 1.20 108.76 90.637.25May24 .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) =
1.797 1/4May24 CTD = 103.00 - (110.5 x .918) =
1.56
Implied Repo Rate
Cost of Carry
Hedge Ratios
Duration Model
HR = Cash PriceFutures Price
DurationDuration
11+ Er
11+ Er
Usually 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 RatiosDuration 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 FuturesToday 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 RatiosBasis 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
HR BVCBVC CF
BCASH
CTD CTD
# of Ks
Hedge Ratios
ExampleYTM = 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 - continuedCash value @ 9% = 108.737BVCcash = $107 (PV @ 9% - PV @ 9.01)BVCctd = $86B = .6 / .5 = 1.20CF = .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 RatiosRegression 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 RatiosYield Forecast Model• Given various yield forecasts, the HR changes• Term Structure can forecast yieldsHR = CVdiff / FCV diff
ExampleCash Value = 97.94 & Futures = 72.50 Forecasted YTMYTM CV YTM FC CV FC CVdiff FCdiff HR12.65 11.25 101.72 75.06 3.77 2.56 1.4812.85 11.40 100.14 74.14 2.20 1.64 1.3413.55 12.05 94.99 70.37 -2.95 -2.13 1.3613.75 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
ExampleOn 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 $/YDec Futures = 139.18 (Y/$) or .00719 $/YEach K is Y12,5000,000
How can we hedge this position
Currency Futuresexample continued100,000 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 Futuresexample continued
• if $/Y drops to .00650 ($/Y) or 153.846Y/$Cost = $ cost - futures profitcost = 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 profitcost = 20235 (.008) - (1619)(12.50)(.0080- .007190)cost = 161.88 - 16.39 = $ 145.49 mil
Stock Index FuturesUnderlying Assets (sample)• S&P 500• NYSE Composite Index• Major Market Index (MMI) (CBOE)• Value Line Index
Why Are They Traded?1 - Change position quickly2 - Create synthetic fund3 - 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 $1.00We should dhort the index and long the futures
Stock Index FuturesExample - arbitrage (continued)
Index Futures ParkStrategyNow short @ 400 long @ 406 invest 400 @ 3%6 mts buy (St + 5) short @ St +406
Cash Flow NetNow +400 0 -400 06 mts -(St + 5) +St +406 +1 +1
