Hedging Futures Today Business has risk Business Risk

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 -$510 50. 80 cents per lbs 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 Hedge real 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 (1 K = 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 Hedge real 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 (1 K = 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 2 K @ 2. 94 = 29, 400 Sept: Long 2 K @ 2. 80 = 28, 000 . Gain on Position---------------- 1, 400 Total Revenue $ 29, 400

Ex - Commodity Hedge real 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 (1 K = 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 Hedge real 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 (1 K = 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 2 K @ 2. 94 = 29, 400 Sept: Long 2 K @ 3. 05 = 30, 500 . Loss on Position---------------- ( 1, 100 ) Total Revenue $ 29, 400

Ex - Commodity Speculation real 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 Speculation real 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 Speculation real 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 Speculation real 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 = Loss ------ Margin = 5130 ---------- 50160 x. 15 = 5130 ------ = 7524 - 5, 130 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 Nov Long $1, 000 March Sell @ $930 loss $70 Futures Position Short 1 K @$970 Long 1 K @$900 gain $ 70 Net position = $ 0

Ex - Financial Futures Example - Hedge Reality Nov March Cash Position Long $1, 000 Futures Position Short 1 K @$970 Sell @ $930 loss $70 Long 1 K @$920 gain $ 50 Net position = $ 20 loss

Ex - Financial Futures You are long in $1 mil 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 $1 mil 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 = 7026 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 $1 mil)

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 # of Ks = ----------------- X Hedge Ratio $ 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

Cheapest To Deliver Theoretical Futures Price (FP)? We will defer a discussion of “? ” Handouts have a more detailed description 3 Ways to Derive CTD (select lowest ) 1 - Calculate delivery costs & compare 2 - Calculate Futures Delivery Spot Price 3 - Cost of Delivery

FC Characteristics Example Two bonds are eligable for delivery on the June 1997 T Bond Futures K 1 - 9. 875 Nov 23 2 - 7. 25 May 24 deilveries on 15 th of maturity month 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 9. 875 Nov 23 1. 20 7. 25 May 24. 918 Bond Price FC Spot Price 134. 39 111. 99 103. 00 112. 20 Deliver 9 7/8 Nov 23

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 9. 875 Nov 23 1. 20 7. 25 May 24. 918 Bond Price FC Spot Price 108. 76 90. 63 82. 36 89. 72 Deliver 7 1/4 May 24

FC Characteristics Q: If YTM = 7% and the lisyted futures price is 110. 50, which bond is CTD? A: 9 7/8 Nov 23 CTD = 134. 39 - (110. 5 x 1. 20) = 1. 79 7 1/4 May 24 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 10% coupon, 26 year bonds, with YTM=12. 64% and duration of 8. 24 years. • The 8%, 20 year, 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 10% coupon, 26 year bonds, with YTM=12. 64% and duration of 8. 24 years. • The 8%, 20 year, TBill has a duration of 10. 14 years, YTM=8. 5% • The FC on this bond is priced at 96. 87 HR = 82 x 8. 24 = 675. 68 =. 688 96. 87 x 10. 14 982. 26 (1, 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 $1 mil 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 30 year 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 (1 mil/. 1) = 14 Ks

Hedge Ratios Example - Conversion Factor Model • You have a $1 mil portfolio, containing 21. 5 year 10 3/8 bonds. Price = 100. 3125 (YTM = 10 5/16) • CTD 20 year, 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 (1 mil/100, 000) = 12 Today 6 mths Cash Own $1 mil @ 100. 3125 ($1, 003, 125) Futures Short 12 K @ 79. 718 (derive) + $956, 616 Sell @ 87. 50 + $875, 000 (128, 125) buy 12 K @ 68. 90 ($826, 875) +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 $1 mil 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 to create a hedge and show the position table for a 3 month 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 ( 86 /. 918) 1. 20 = 1. 378 1 mil / 100, 000 x 1. 378 = 13 or 14 contracts

Hedge Ratios example - continued (10%) Today Cash Futures $1 mil @ 108. 737 -$1, 087, 370 13 K @ 82. 44 +1, 071, 720 3 months (YTM = 10%) $1 mil @ 96. 44 +$ 964, 427 13 K @ 72. 85 - $947, 050 Net Position $124, 670 gain $122, 943 loss net gain of $1, 727

Hedge Ratios example - continued Assume YTM = 8% Cash Futures $1 mil @ 108. 737 -$1, 087, 370 13 K @ 82. 44 +1, 071, 720 3 months (YTM = 8%) $1 mil @ 117. 91 +$ 1, 179, 100 13 K @ 90. 04 - $1, 170, 520 Net Position $98, 800 loss Today $91, 730 gain 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 CV YTM FC CV 12. 65 11. 25 101. 72 12. 85 11. 40 100. 14 13. 55 12. 05 94. 99 13. 75 12. 20 93. 62 FC 75. 06 74. 14 70. 37 69. 54 CVdiff 3. 77 2. 20 -2. 95 -4. 33 FCdiff 2. 56 1. 64 -2. 13 -2. 96 HR 1. 48 1. 34 1. 36 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 Y 202, 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 Y 12, 5000, 000 How can we hedge this position

Currency Futures example continued 100, 000 x Y 202, 350 = Y 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. 846 Y/$ 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” F 0 = Ft = S 0 (1 + rf - d)t Ft 2 = Ft 1 (1 + rf - d) (t 2 -t 1) Profit = St - F 0 t = % of year

Stock Index Futures Example - arbitrage The 1 year futures price on S&P 500 is 406. the S&P 500 index is at 400. Rf= 3% and the dividend rate is 1. 25% Is F 0 mispriced and by how much? Show a stretegy to take advantage of this. F 0 = 400 (1 +. 03 -. 0125) = 407 Index is underpriced by $1. 00 We should dhort the index and long the futures

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