2. Forward contract: FORWARD COMTRACT IS A CONTRACT BETWEEN TWO PARTIES TO BUY OR SELL AN UNDERLYING ASSET AT TODAY’S PRE-AGREED PRICE ON A SPECIFIED DATE IN THE FUTURE Basic features Forward contracts are bilateral and hence are exposed to counter party risk. Each contract is customized. One party take long position and the other short. The specified price in a forward contract is referred as the delivery price. Contract has to be settled by the delivery of the goods.

3. Futures contract Futures contracts are traded on commodity exchange or other future exchanges. When a person buys a contract from a stock exchange, he takes long position on an organised future exchange, he in fact assuming the right and obligation of taking the delivery of the specified underlying item on a specific date. When an investor sells a contract to take short position, one assume the right and obligation to make the delivery of underlying asset. There is no risk of non performance involved as clearing corporation is involved. A clearing house guarantees the performance of a future contract. The parties in the contract are required to keep margin with it. It is not necessarily to hold a future contract until maturity and one can easily close out a position.

4. CONTRACT SPECIFICATION FOR THE FUTURES. 1. THE ASSET: 2. PRICE: 3. THE CONTRACT SIZE 4. DELIVERY ARRANGEMENTS 5. DELIVERY MONTHS 6. TICK SIZE 7. LIMITS ON DAILY PRICE MOVEMENTS

5. PARTICIPANTS in the derivatives market

6. Trading participants: Hedgers Speculators Scalpers Arbitrageurs Intermediary participants: Brokers Market markers and jobbers Institutional framework: Exchange Clearing house

7. Futures Versus Forward Contracts Type of Contract Trading Location Clearinghouse Settlement Delivery Collateral Credit risk

8. 1. Use the following data and prepare the margin a/c for investors for both long and short position. Assume that if margin call is made at any time, the investor would deposit the amount called for. contract size = 100 quintals price = Rs. 600/quintal initial margin = Rs. 6000 maintenance margin = Rs. 4500

9. Trading day Futures price Sept 2 598.20 Sept 3 593.60 Sept 4 594 Sept 5 589.50 Sept 6 584.80 Sept 9 582.20 Sept 10 583.70 11577.30 12577.10 13572.40 Trading day Futures price 16570.10 17568.50 18569.80 19573.80 20573.60 23577.30 24576.30 25578.80 26578 27584.2

10. Trading day Futures price Daily gain/loss Cumulative gain/loss Margin a/c balance Margin call Sept 2 598.20 (-1.8 * 100) -180 (180)5820- Sept 3 593.60 (-4.6 * 100) -460 (640)5360- Sept 4 594 (0.4 * 100) 40 (600)5400- Sept 5 589.50-450(1050)4950- Sept 6 584.80-470(1520)44801520 Sept 9 582.20-260(1780)5740- Sept 10 583.70150(1630)5890- 11577.30-640(2270)5250- 12577.10-20(2290)5230- 13572.40-470(2760)4760- Solution : - long position

11. Trading day Futures price Daily gain/loss Cumulati ve gain/loss Margin a/c balance Margin call 16570.10-230(2990)4530- 17568.50-160(3150)43701630 18569.80130(3020)6130- 19573.80410(2610)6540- 20573.60-30(2640)6510- 23577.30370(2270)6880- 24576.30-100(2370)6780- 25578.80250(2120)7030- 26578-80(2200)6950- 27584.2620(1580)7570-

12. Trading day Futures price Daily gain/loss Cumulative gain/loss Margin a/c balance Margin call Sept 2 598.20 (1.8 * 100) 180 1806180- Sept 3 593.60 (4.6 * 100) 460 6406640- Sept 4 594 (-0.4 * 100) -40 6006600- Sept 5 589.5045010507050- Sept 6 584.8047015207520- Sept 9 582.2026017807780- Sept 10 583.70-15016307630- 11577.3064022708270- 12577.102022908290- 13572.4047027608760- Solution : - short position

13. Trading day Futures price Daily gain/loss Cumulativ e gain/loss Margin a/c balance Margin call 16570.1023029908990- 17568.5016031509150- 18569.80-13030209020- 19573.80-41026108610- 20573.603026408640- 23577.30-37022708270- 24576.3010023708370- 25578.80-25021208120- 265788022008200- 27584.2-62015807580-

14. June-July 04 2. Use the following data and prepare the margin a/c for investors for short position. Assume that if margin call is made at any time, the investor would deposit the amt called for. contract size = 500 units price = Rs. 25/unit initial margin = 12% maintenance margin = 3/4 th of initial margin no. of contracts = 10 contract date = 11 th june

15. Trading dayFutures price 225.50 324.30 426.50 525.10 625.75

16. Total contract value 500 * 10 * 25 = Rs. 1,25,000 Initial margin (125000) * 12% = Rs. 15,000 Maintenance margin (15000) * 3/4 = Rs. 11250

17. Trading day Futures price Daily gain/lossCumulative gain/loss Margin a/c balance Margin call 225.50(-0.5 * 500 * 10) -2500 (2500)12500- 324.30 (1.2 * 500 * 10) 6000 350018500- 426.50 (-2.2 * 500 * 10) -11000 (7500)7500 525.107000(500)22000- 625.75-3250(3750)18750-

18. Dec 06 3. The settlement prices of sensex futures contract on a particular day was Rs. 4600. Initial margin is set at Rs. 10000 while maintenance margin is Rs. 8000. multiplier of each contract is 50. the settlement prices of the next few days are as follows : Trading day Price 14700 24500 34650 44750 54700

19. Prepare a marginal a/c : On an investor who has gone long at Rs.4600 On an investor who has gone short at Rs.4600 Calculate net profit or loss on each day of the account.

20. Tradin g day Price Daily gain/loss Cumulative gain/loss Margin a/c bal Margin call 14700 -5000(5000)5000 24500 10000500020000- 34650 -7500(2500)12500- 44750 -5000(7500)75002500 54700 2500(5000)12500- Position : short Net loss Rs 5000

21. Position : long Trading day Price Daily gain/loss Cumulative gain/loss Margin a/c bal Margin call 14700 5000 15000 - 24500 -10000(5000)5000 34650 7500250017500- 44750 5000750022500- 54700 -2500500020000- Net profit Rs 5000

22. 4. A futures contract is available for petrol at $28/barrel. Each contract is for 100000 barrels. You have contracted for 8 long barrels. Contract is on 15/06/09 and expires on 30/06/09. Initial margin is 10% of contract value and maintenance margin is 75% of initial margin. Prepare a statement of marking to market.

23. Trading dayFutures price 1528 1628.50 1731.50 1833.00 1929.00 2028.25 2127.55 2226.50 Trading dayFutures price 2326.45 2426.10 2526.70 2625.95 2725.45 2825.15 2925.75 3024.90

24. Total contract value 28 * 100000 * 8 = $22400000 Initial margin (22400000) * 10% = $2240000 Maintenance margin (2240000) * 75% = $1680000

25. Trading day Futures price Daily gain/loss Cumulative gain/loss Margin a/c balance Margin call 1528--22.4- 1628.504426.4- 1731.50242850.4- 1833.00124038.4- 1929.00-3286.416 2028.25-6216.46 2127.55-5.6(3.6)16.8- 2226.50-8.4(12)8.414

26. Trading day Futures price Daily gain/loss Cumulative gain/loss Margin a/c balance Margin call 2326.45-0.4(12.4)22- 2426.10-2.8(15.2)19.2- 2526.704.8(10.4)24- 2625.95-6(16.4)18- 2725.45-4(20.4)148.4 2825.15-2.4(22.8)20- 2925.754.8(18)24.8- 3024.90-6.8(24.8)18-

27. Continuous compounding Normal compounding FV = P(1+r) n Multiple compounding FV = P(1+r/m) m*n Continuous compounding F = P e r*t or F = S 0 e r*t r1 be the rate of interest when m compounding are done and r2 be the equivalent rate when continuous compounding is done then r2 =m ln (1+r1/m) And r1 = m ( e r2/m - 1)

28. Problems 1. A company offers an interest rate of 15% p.a. compounded half yearly. Obtain the equivalent rate with an annual compounding rate and continuous compounding.

29. Given: r1=15%, m=2 For continuous compounding r2 =m ln (1+r1/m) =2 ln (1+0.15/2) = 14.46% For annual compounding R= (1+r/m) m – 1 =(1+0.15/2) 2 – 1 = 15.56%

30. Pricing of forward contracts Case I : Securities providing no income F=S 0 e rt F=S 0 e rt So= spot price of the asset underlying the contract r= risk free rate of interest per annum with continuous compounding t= time of maturity.

31. Problem: On a non dividend paying share a 4 month forward contract is entered into.when it is selling at Rs 72. If risk free rate of interest with continuous compounding is 12%. What could be the forward price?

32. F = S 0 e r*t = 72* e 0.12 * 4/12 = Rs 74.93 per share

33. 5. A forward contract on a share that is selling at Rs 92 is entered into a price of Rs 96.50. Contract has maturity of 3 months. Determine continuously compounding risk free rate of interest implied.

34. F= S 0 * e r * t 96.50 = 92 * e r * 3/12 e r/4 = 96.50/92 e r/4 = 1.048 e 0.25 r = 1.048 taking natural log on both sides, we get 0.25 r ln e = ln 1.048 0.25 r = 0.0468 r = 18.75 %

35. Case II Securities providing known cash income F=(S 0 -I)e rt I=Ye (-rt) F=(S 0 -I)e rt I=Ye (-rt) Y= the present value of income receivables.

36. Problem Calculate the price of 100 forward contract using the following information. Price of share Rs 75. Time to expiration 9months. Dividend expected Rs 2.20per share. Time to dividend 4 months. Continuously compounded risk free rate of interest is 12%.

37. Total value of dividend = 100 * 2.20 = Rs 220 PV of 220 is calculated as follows I = e – r t = 220 * e – 0.12 * 4/12 = Rs 211.37 e rt F = ( S 0 - I ) e rt = ( 75 * 100 – 211.37 ) e 0.12 * 9/12 = Rs 7973.76 for 100 contracts

38. Problem Consider a forward contract on a non dividend paying share which is available at Rs 80,to mature in 3 months time. If risk free rate of interest is 7% p.a. compounded continuously. What is price of a forward contract ?

39. F = S 0 * e r * t = 80 * e 0.07 * 3/12 = Rs 81.4123/ share

40. Problem Using the following data obtain the value of future contract to an index. Spot value Rs 1216, risk free rate of interest is 7% p.a. time to expiration 146 days. Contract multiplier is 200.

41. r1 = 7% r2 = m ln ( 1 + r1/m ) = 1 ln ( 1 + 1+ 0.07 ) = 6.76% F = S 0 e r * t = 1216 * e 0.076 * 146 / 365 * 200 = Rs 2,49,865.84

42. Securities paying known yield F=S 0 e (r-y)t F=S 0 e (r-y)t y= dividend yield in percentage y= dividend yield in percentage

43. Problem;The stock index is currently selling at Rs 820 continuously compounded risk free rate of interest is 9%. Dividend yield is 3% p.a. what should be the future prices for a contract with 3months expiration ?

44. F = S 0 * e ( r – y ) t = 820 * e ( 0.09 – 0.03 ) 3/12 = Rs 839

45. Consider a 3month future contract for NSE 50. assume that spot value is 1100 continuously compounded risk free rate of interest is 10% and continuously compound yield on share underlying NSE 50 is 3% p.a. assuming multiplier to be 50. Find value of contract.

46. F = S 0 e ( r - y ) t = 1100 * e ( 0.10 - 0.03 ) 3/12 * 50 = Rs 55,970.9711

47. . On April 5, 2002. BXXMAY 2002 ( future contract on BSE sensex expiring on may 30, 2002) were selling at Rs 3540.10 while index value was 3500.57. using the values obtain the annualized risk free interest implied in future.

48. F = S 0 e r * t 3540.1 = 3500.57 e r * 55 / 365 e r * 55 / 365 = 1.0012 0.1056 ln e = ln 1.0012 r2 = 7.45% r1 = m ( e r / m - 1 ) = 1 ( e 0.0745 /1 - 1) =7.73 %

49. Futures on commodities a) carry type commodities F=(S 0 +S)e rt F=(S 0 +S)e rt Where “s” is the storage cost in percentage Where “s” is the storage cost in percentage

50. Non carrying commodities. a) F=(s 0 +s)e (r-c)t Where “c” is the convenience return, which the return that an investor realises for carrying inventory of the commodities over his/her immediate short term need. Financial assets have no convenience return while the agricultural commodities frequently have high return(which is different for different investors) Where “c” is the convenience return, which the return that an investor realises for carrying inventory of the commodities over his/her immediate short term need. Financial assets have no convenience return while the agricultural commodities frequently have high return(which is different for different investors) And if the storage cost per unit as a constant proportion And if the storage cost per unit as a constant proportion F=S 0 e (r+p-c)t F=S 0 e (r+p-c)t

51. Case 1 When the securities included in index are not expected to pay any dividends during the life of the contract. F=S 0 e rt F=S 0 e rt So= spot price of the asset underlying the contract r= risk free rate of return per annum with continuous compounding t= time of maturity.

52. Case-2 When dividend is expected to be paid by one or more of the securities include in the index during the life of the contract F=(S 0 -I)e rt F=F=(S 0 -I)e rt I = is the discounted value if the dividends I=Ye (-rt)

53. Case 3 Case 3 When dividend on the security included on the index is assumed to be paid continuously during th life of the contract. When dividend on the security included on the index is assumed to be paid continuously during th life of the contract. F=S 0 e (r-y)t F=S 0 e (r-y)t

54. Long & Short Hedges A long futures hedge is appropriate when you know you will purchase an asset in the future and want to lock in the price A short futures hedge is appropriate when you know you will sell an asset in the future & want to lock in the price

55. Trading Strategies Hedging: taking opposite positions to reduce risk exposure on one of positions Speculating: the act of committing funds in anticipation of specific price movement Spreading: creating a combination trade, such as both long and short position in the futures market

56. Hedging Person must take position in commodity for business reason Example: a farmer is long the crop in his field While crop is growing, farmer is exposed to price risk—risk spot market price of crop will fall If farmer sells a futures contract, he replaces price risk with basis risk

57. Basis Risk Basis = cash market price – futures market price In perfect hedge, basis does not change Basis risk = risk that basis will change Hedger substituting basis risk for price risk Hedge successful as long as basis risk is less than price risk

58. Thank you