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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. Ex - Cereal Production.

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## Hedging & Futures

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**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**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 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 = $index x 500**Ex - Settlement & Speculate**• You are speculating in Hog Futures. You think that the Spot Price of hogs will rise in the future. Thus, you go Long on 10 Hog Futures. If the price drops .17 cents per pound ($.0017) what is total change in your position?**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**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?**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 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**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? 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**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**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? 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**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.”**Ex - Financial Futures**• 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**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 $ 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.**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**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**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**FC Characteristics**• 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**• 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**Hedge Ratios**• Duration 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 Ratios**• Duration 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 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**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 Ratios**• Example - 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**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 Ratios**• example - 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 Ratios**• example - 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 Ratios**• example - 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

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