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 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.”

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 -S&P 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 Since you must settle your account every day, you must give your broker $510.00 50.63 50.80 -$510 cents per lbs

8. 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

9. 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

10. 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 (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 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 (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 2.8028,000 June: Short 2K @ 2.94 = 29,400 Sept: Long 2K @ 2.80 = 28,000. Gain on Position------------------------------- 1,400 Total Revenue $ 29,400

12. 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 (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 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 (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 3.0530,500 June: Short 2K @ 2.94 = 29,400 Sept: Long 2K @ 3.05 = 30,500. Loss on Position------------------------------- ( 1,100 ) Total Revenue $ 29,400

14. 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?

15. Ex - Commodity Speculation real 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?

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 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?

18. Ex - Commodity Speculation real 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

19. 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.”

20. Example - Hedge Cash PositionFutures Position NovLong $1,000 Short 1K @$970 MarchSell @ $930Long 1K @$900 loss $70 gain $ 70 Net position = $ 0 Ex - Financial Futures

21. Example - Hedge Reality Cash PositionFutures Position NovLong $1,000 Short 1K @$970 MarchSell @ $930Long 1K @$920 loss $70 gain $ 50 Net position = $ 20 loss Ex - Financial Futures

22. 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? CashFuturesBasis 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)

24. 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.

25. 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

26. 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.

28. 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

29. 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

30. 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

31. Q: If YTM = 7%, which will you deliver & what is its price? A: FC Characteristics

32. Q: If YTM = 7%, which will you deliver * what is its price? A:CFBond PriceFC Spot Price 9.875Nov231.20134.39111.99 7.25May24.918103.00112.20 Deliver 9 7/8 Nov23 FC Characteristics

33. Q: If YTM = 9%, which will you deliver & what is its price? A: FC Characteristics

34. Q: If YTM = 9%, which will you deliver & what is its price? A:CFBond PriceFC Spot Price 9.875Nov231.20108.7690.63 7.25May24.91882.3689.72 Deliver 7 1/4 May24 FC Characteristics

35. Q: If YTM = 7% and the lisyted futures price is 110.50, which bond is CTD? A: 9 7/8Nov23CTD = 134.39 - (110.5 x 1.20) = 1.79 7 1/4May24CTD = 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 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

38. 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

39. 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 @ 8% YTM 100

41. 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 @ 4% for 43 periods / 100 = 1.24 1.24 x (1mil/100,000) = 12 CashFutures TodayOwn $1mil Short 12 K @ 100.3125@ 79.718 (derive) ($1,003,125)+ $956,616 6 mthsSell @ 87.50buy 12 K @ 68.90 + $875,000($826,875) (128,125)+129,750

44. Hedge Ratios Basis Point Model BVC cash = $ change in value per basis point of cash position B = Relative yield volatility of cash to CTD = (V cash / V ctd ) BVC ctd = $ change in value per basis point of CTD CF ctd =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 @ 9% = 108.737 BVC cash = $107 (PV @ 9% - PV @ 9.01) BVC ctd = $86 B =.6 /.5 = 1.20 CF =.918 (PV of CTD @ 8% / 100) HR* = ( 107 ) x1.20 = 1.378 ( 86 /.918) 1 mil / 100,000 x 1.378 = 13 or 14 contracts

47. Hedge Ratios example - continued (10%) CashFutures Today $1mil @ 108.73713K @ 82.44 -$1,087,370+1,071,720 3 months (YTM = 10%) $1 mil @ 96.4413K @ 72.85 +$ 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% CashFutures Today $1mil @ 108.73713K @ 82.44 -$1,087,370+1,071,720 3 months (YTM = 8%) $1 mil @ 117.9113K @ 90.04 +$ 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 CVYTM FCCVFCCVdiffFCdiffHR 12.6511.25101.7275.063.772.561.48 12.8511.40100.1474.142.201.641.34 13.5512.0594.9970.37-2.95-2.131.36 13.7512.2093.6269.54-4.33-2.961.47

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) 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

55. Stock index Futures Price relationship also called “cost of carry” or “cash & carry” F 0 = F t = S 0 (1 + r f - d)t t = % of year F t2 = F t1 (1 + r f - d) (t2-t1) Profit = S t - F 0

56. Stock Index Futures Example - 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 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

57. Stock Index Futures Example - arbitrage (continued) IndexFuturesPark Strategy Nowshort @ 400long @ 406invest 400 @ 3% 6 mtsbuy (St + 5)short @ St+406 Cash FlowNet Now+4000-4000 6 mts-(St + 5)+St+406+1 +1