1
2  1875      •Setting up of Bombay Cotton Trade Association Ltd.  1883      •A separate association called “The Bombay Cot...
3December 14, 1995    •The NSE sought SEBI’s permission to trade index futures.November 18, 1996    •The LC Gupta Committe...
4
5   Interest rate      • Treasury bills, notes, bonds, debentures,      futures           euro-dollar deposits etc.     Fo...
6Forward contracts were useful, but only up to a point. They didn’teliminate the risk of default among the parties involve...
7
8
9
10
11
12A legally binding, standardized agreement to buy or sell astandardized commodity, specifying quantity and quality at ase...
13Why? They were ―speculating‖ — taking achance that as market conditions changedthey would be able to buy or sell thecont...
14
15           Promise to pay $20,000Buyer                                       Seller        Promise to deliver 5, 000 bus...
16  Promise to pay $20,000                       Promise to pay $20,000Buyer                                              ...
17
18Delivery or cash settlement • Most commodity futures contracts are written for completion of the futures   contract thro...
19Suppose today the price of the futures is $3.95 and nextday, the buyer finds that people are paying $4.15 perbushel for ...
20Day    Price of wheat     Event                                    Amount   Equity in accountIf maintenance margin were ...
21Since B is involved in two wheat contracts, one as aseller and one as a buyer, B is obligated to deliver5000 bushels to ...
22             An Exchange-for-Physicals Transaction                                Before the EFP              Trader A  ...
23Futures game
24The procedures that protect clearinghousefrom potential losses due to non-compliance of the buyer or seller are:• Impose...
25A performance bond is a deposit to cover losses you mayincur on a futures contract as it is marked-to-market.A maintenan...
26In stock trading, margin refers to a partialdeposit you put up with your broker topurchase securities, while borrowing t...
27Futures contracts require an initial performance bond inan amount determined by the exchange itself.This amount is rough...
28At the end of the trading day your position is marked-to-the-market. That is, the clearing house will settle your accoun...
29If your position has lost money and thebalance in the performance bond accounthas fallen below the maintenance level, ap...
30
31
32                  How Trading Affects Open InterestTime               Action                                         Ope...
33
34Spot            Spot Market                    Futures MarketPrice   Gain or Loss   % Return        Gain or Loss      % ...
35
36                          Table 3.2                  Gold Prices and the Basis                           (July 11)Contra...
37
38Prices                  Cash          Basis               Futures                                                   Time...
39
40Basis = current spot price – corresponding future price • Future price here is the purchase price stated in the futures ...
41An Arbitrageur attempts to exploit any discrepancies in price between the futuresand cash markets.An academic arbitrage ...
42                     Price       ExchangeArbitrageur Buys         INFY   (1105) BSEArbitrageur Sells        INFY    1110...
Futures Pricing      43
44Since the futures or forwardsdon’t require front-end fromeither the long or shorttransaction; therefore, thecontract’s i...
45There are three maintheories of future pricing• The expectations hypothesis• Normal backwardation• A full carrying charg...
46Hypothesis: The futures price for a commodity iswhat the marketplace expects the cash price to bewhen the delivery month...
47
48
49
50Normally, the futures price exceeds the spotprice; this market is called contango.If the futures price is less than the ...
A hedger (for example, a farmer) who is selling a futures contract istrying to lock in the price of the commodity in futur...
52
53A full carrying charge market occurs whenfutures prices reflect the cost of storing andfinancing (borrowing) the commodi...
54To the extent that markets adhere to the following equationsmarkets are said to be at ―full carry‖:               F 0, t...
55To determine if a market is at full carry, consider thefollowing example:Suppose that:September Gold                   $...
56Step 1: compute the annualized percentagedifference between two futures contracts.                                12    ...
57                               12                       $417.90 3              AD   (         )                       $4...
58A spread is the difference in price between two futures contractson the same commodity for two different maturity dates:...
We know that there is a relationship between the price of thecommodity in the cash market and price of that commodity in t...
60The common way to value a futures contract is by usingthe Cost-of-Carry Model. The Cost-of-Carry Model saysthat the futu...
Suppose you buy the corn now for the current cash price of S0 per bushel                                      61and store ...
62
63
64The Cost-of-Carry Model can be expressed as:                     F 0, t    S 0(1 C 0, t )S0       =         the current ...
65
66Cash-and-carry arbitrage• When futures are overpricedReverse cash-and-carry arbitrage• When futures are underpriced
67A cash-and-carry arbitrage occurs when a trader borrowsmoney, buys the goods today for cash and carries the goodsto the ...
68The futures price must be greater than orequal to the spot price of the commodityplus the carrying charges necessary to ...
69         Cash-and-Carry Gold Arbitrage Transactions               Prices for the Analysis:       Spot price of gold     ...
70
71A reverse cash-and-carry arbitrage occurs when a trader sells short aphysical asset. The trader purchases a futures cont...
72The futures price must be equal to or lessthan the spot price of the commodity plusthe carrying charges necessary to car...
73      Reverse Cash-and-Carry Gold Arbitrage Transactions                Prices for the Analysis        Spot price of gol...
74
75           Transactions for Arbitrage StrategiesMarket      Cash-and-Carry                   Reverse Cash-and-CarryDebt ...
Since the futures price must be76 either greater than or equal tothe spot price plus the cost of carrying the commodityfor...
77If prices were not to conform to cost ofcarry rule #3, a cash-and carry arbitrageprofit could be earned.Recall that we h...
78As we have just seen, there must be a relationship between the futures priceand the spot price on the same commodity.Sim...
The distant futures price must be greater than or equal to the nearby futures price plus                                  ...
800                              1                                2                                                 7. Rem...
810                              1                                2                                                 7. Rem...
82              Gold Forward Cash-and-Carry Arbitrage               Prices for the Analysis       Futures price for gold e...
83The nearby futures price plus the cost of carrying the commodity fromthe nearby delivery date to the distant delivery da...
840                                     1                               2    1. Sell futures                             7...
85       Gold Forward Reverse Cash-and-Carry Arbitrage              Prices for the Analysis:       Futures price for gold ...
86Since the distant futures price must be either greater than or equalto the nearby futures price plus the cost of carryin...
87The distant futures price must equal the nearby futures price plus thecost of carrying the commodity from the nearby to ...
88Ease of Short Selling• To the extent that it is easy to short sell a commodity, the market will  become closer to full c...
89Non-Seasonal Production • To the extent that production of a crop is seasonal, temporary imbalances between   supply and...
Hedging with futures         90
91
92          Cash market                       Futures marketMay 10     Anticipate the sale of 20, 000   Sell four contract...
93          Cash market                         Futures marketMay 10    If he had sold today: 1052 x        Sell : 4x5000x...
94
95
96Suppose on June 1, Ms. Deepa realizes she needs to purchase110,000 pieces of wood planks on September 1.Today’s cash pri...
97          Cash market                    Futures marketJune 1     Needs to buy wood planks in   Buys (goes long) one Sep...
98          Cash market                    Futures marketJune 1    $300/MBF X 110 = $33,000       $305/MBF X 110 = $33,550...
99The difference between the cash price and thefutures price is called basis.The basis changes during the life of the futu...
100At any date t, the basis is the spot price minus theforward price for a contract maturing at date T,• Bt,T = St – Ft,T ...
At date 1, B1= S1 – F1                            101At date 2, B2 = S2 – F2For the hedger who takes a short position in f...
102Suppose, an investor wishes in March to hedge a long position of100, 000 pounds of cotton she is planning to sell in Ju...
103
Suppose, cotton prices have declined so that cash price in June are                               104$0.4660 and futures a...
105
106
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derrivatives

  1. 1. 1
  2. 2. 2 1875 •Setting up of Bombay Cotton Trade Association Ltd. 1883 •A separate association called “The Bombay Cotton Exchange Ltd.” was constituted 1900 •Futures trading in oilseeds was started with the setting up of Gujarati Vyapari Mandali 1926 •Seeds Traders’ Association Ltd was set up in Mumbai 1920 •Futures market in bullion began at Mumbai 1952 •Government passed the Forward Contract Regulation Act, which controls all transferable forward contracts and futures. 1960/70 •Central govt suspended trading in several commodities like cotton, jute, edible oilseeds, etc.1966/1980 •Datwala Committee/ Khusro Committee recommended reintroduction of commodities 1993 •The Kabra committee recommended futures trading in many commodities and upgradation of futures market
  3. 3. 3December 14, 1995 •The NSE sought SEBI’s permission to trade index futures.November 18, 1996 •The LC Gupta Committee set up to draft a policy framework for index futures. May 11, 1998 •The LC Gupta Committee submitted a report on the policy framework for index futures. July 7, 1999 •Reserve Bank of India gave permission for OTC forward rate agreements and interest rate swaps. May 25, 2000 •SEBI allowed the NSE and the BSE to trade in index futures. June 9, 2000 •Trading of the BSE Sensex futures commenced on the BSE. June 12, 2000 •Trading of Nifty futures commenced on the NSE.September 25, 2000 •Nifty futures trading commenced July, 2001 •Trading on equity futures commenced at NSE on 31 securities June, 2003 •Trading on interest rate futures commenced at NSE
  4. 4. 4
  5. 5. 5 Interest rate • Treasury bills, notes, bonds, debentures, futures euro-dollar deposits etc. Foreign • USD, Pound Sterling, Yen, etc.currencies futures Stock index • Based on indices of stocks futures Bond index • Indices of bond prices futures Cost of living • Aka inflation futures; CPI, WPI, etc. index futures
  6. 6. 6Forward contracts were useful, but only up to a point. They didn’teliminate the risk of default among the parties involved in the trade.For example, merchants might default on the forward agreements if theyfound the same product cheaper elsewhere, leaving farmers with thegoods and no buyers.Conversely, farmers could also default if prices went up dramaticallybefore the forward contract delivery date, and they could sell to someoneelse at a much higher price.Therefore, a standardized contract was required to address this issue.
  7. 7. 7
  8. 8. 8
  9. 9. 9
  10. 10. 10
  11. 11. 11
  12. 12. 12A legally binding, standardized agreement to buy or sell astandardized commodity, specifying quantity and quality at aset price on a future date.A great advantage of standardized contracts was that they wereeasy to trade.As a result, the contracts usually changed hands many timesbefore their specified delivery dates.Many people who never intended to make or take delivery of acommodity began to actively engage in buying and sellingfutures contracts.
  13. 13. 13Why? They were ―speculating‖ — taking achance that as market conditions changedthey would be able to buy or sell thecontracts at a profit.The ability to eliminate a ―position‖ on acontract by buying or selling it before thedelivery date — called ―offsetting‖ — is akey feature of futures trading.
  14. 14. 14
  15. 15. 15 Promise to pay $20,000Buyer Seller Promise to deliver 5, 000 bushels
  16. 16. 16 Promise to pay $20,000 Promise to pay $20,000Buyer Seller Clearinghouse Promise to deliver 5, 000 bushelsPromise to deliver 5, 000 bushels
  17. 17. 17
  18. 18. 18Delivery or cash settlement • Most commodity futures contracts are written for completion of the futures contract through the physical delivery of a particular good. • Most financial futures contracts allow completion through cash settlement. In cash settlement, traders make payments at the expiration of the contract to settle any gains or losses, instead of making physical delivery.Offset or reversing trade • If you previously sold a futures contract, you can close out your position by purchasing an identical futures contract. The exchange will cancel out your two positions.Exchange-for-physicals (EFP) or ex-pit transaction • Two traders agree to a simultaneous exchange of a cash commodity and futures contracts based on that cash commodity.
  19. 19. 19Suppose today the price of the futures is $3.95 and nextday, the buyer finds that people are paying $4.15 perbushel for wheat. If B believes that the price of wheatwill not go any higher, then B might sell a wheatfutures contract for $4.15 to someone else.In this situation, B has made a reversing trade.
  20. 20. 20Day Price of wheat Event Amount Equity in accountIf maintenance margin were not required1 4 Deposit initial margin 1000 10002 4.10 Mark to market 500 15003 3.95 Mark to market -750 7504 4.15 Mark to market 1000 1750With required maintenance margin1 4 Deposit initial margin 1000 10002 4.10 Mark to market 500 1500 Buyer withdraws cash -500 10003 3.95 Mark to market -750 250 Buyer deposits cash 750 10004 4.15 Mark to market 1000 2000 Reversing trade and withdrawal of cash -2000 0
  21. 21. 21Since B is involved in two wheat contracts, one as aseller and one as a buyer, B is obligated to deliver5000 bushels to clearing house and clearing housein turn is required to deliver it back to B.The moment B offsets his positions, clearing housewill immediately cancel both of them, and B will beable to withdraw $2000 from his account.
  22. 22. 22 An Exchange-for-Physicals Transaction Before the EFP Trader A Trader BLong 1 wheat futures Short 1 wheat futuresWants to acquire actual wheat Owns wheat and wishes to sell EFP Transaction Trader A Trader BAgrees with Trader B to purchase Agrees with Trader A to sell wheat andwheat and cancel futures cancel futuresReceives wheat; pays Trader B Delivers wheat; receives payment from Trader AReports EFP to exchange; exchange a- Reports EFP to exchange; exchangedjusts books to show that Trader A is adjusts books to show that Trader B isout of the market out of the market
  23. 23. 23Futures game
  24. 24. 24The procedures that protect clearinghousefrom potential losses due to non-compliance of the buyer or seller are:• Impose initial margin requirements on both buyers and sellers• Mark to market the accounts of buyers and sellers every day• Impose daily maintenance margin requirements on both buyers and sellers.
  25. 25. 25A performance bond is a deposit to cover losses you mayincur on a futures contract as it is marked-to-market.A maintenance performance bond is a minimum amountof money (a lesser amount than the initial performance bond)that must be maintained on deposit in your account.A performance bond call is a demand for an additionaldeposit to bring your account up to the initial performancebond level.
  26. 26. 26In stock trading, margin refers to a partialdeposit you put up with your broker topurchase securities, while borrowing theremaining amount (typically half) from thebroker (expecting to pay interest).In futures, this ―down payment‖ is actually agood faith deposit you pay to indicate thatyou will be able to ensure fulfillment of thecontract.
  27. 27. 27Futures contracts require an initial performance bond inan amount determined by the exchange itself.This amount is roughly 5% to 15% of the total purchase priceof the futures contract. This margin covers only a part of theprotection against the total loss in the case of default.Therefore, the use of marking to market coupled with amaintenance margin requirement provides the requisiteamount of additional protection.
  28. 28. 28At the end of the trading day your position is marked-to-the-market. That is, the clearing house will settle your account on acash basis.Money will be added to your performance bond balance if yourposition has made a profit that day.If you’ve sustained a loss that day, money is deducted from yourperformance bond account.This rebalancing occurs each day after the close of trading.
  29. 29. 29If your position has lost money and thebalance in the performance bond accounthas fallen below the maintenance level, aperformance bond call will be issued.That means you have to put in more moneyto bring the account up to the initialperformance bond level.
  30. 30. 30
  31. 31. 31
  32. 32. 32 How Trading Affects Open InterestTime Action Open Interestt=0 Trading opens for the popular widget contract. 0t=1 Trader A buys and Trader B sells 1 widget contract. 1t=2 Trader C buys and Trader D sells 3 widget contracts. 4t=3 Trader A sells and Trader D buys 1 widget contract. 3 (Trader A has offset 1 contract and is out of the mar- ket. Trader D has offset 1 contract and is now short 2 contracts.)t=4 Trader C sells and Trader E buys 1 widget contract. 3Ending Trader Long Position Short PositionPosi- B 1tions C 2 D 2 E 1 All Traders 3 3
  33. 33. 33
  34. 34. 34Spot Spot Market Futures MarketPrice Gain or Loss % Return Gain or Loss % Return$420 $2,000 5% $2,000 100%$410 $1,000 2.5% $1,000 50%$400 0 0% 0 0%$390 -$1,000 -2.5% -$1,000 -50%$380 -$2,000 -5% -$2,000 -100%
  35. 35. 35
  36. 36. 36 Table 3.2 Gold Prices and the Basis (July 11)Contract Prices The BasisCASH 353.70JUL (this year) 354.10 -.40AUG 355.60 -1.90OCT 359.80 -6.10DEC 364.20 -10.50FEB (next year) 368.70 -15.00APR 373.00 -19.30JUN 377.50 -23.80AUG 381.90 -28.20OCT 386.70 -33.00DEC 391.50 -37.80
  37. 37. 37
  38. 38. 38Prices Cash Basis Futures TimePresent Maturity
  39. 39. 39
  40. 40. 40Basis = current spot price – corresponding future price • Future price here is the purchase price stated in the futures contract. • Spot price is the price of a good for immediate delivery. • Open interest is the number of futures contracts for which delivery is currently obligated.Repo Rate • The repo rate is the finance charges faced by traders. The repo rate is the interest rate on repurchase agreements. • ―Repo‖ is the name commonly used to refer to a repurchase agreement. Under a repurchase agreement, one party to the transaction, referred to as the repo side, borrows money by posting government securities as collateral. The counterparty, referred to as the reverse repo side, lends money secured by the collateral. The reverse repo party has use of the collateral for the term of the repo while the repo party retains claim to any coupon payments or price appreciation. (Ref. Randall Dodd Director, Financial Policy Forum, March 20, 2006)A Repurchase Agreement • An agreement where a person sells securities at one point in time with the understanding that he/she will repurchase the security at a certain price at a later time.
  41. 41. 41An Arbitrageur attempts to exploit any discrepancies in price between the futuresand cash markets.An academic arbitrage is a risk-free transaction consisting of purchasing an assetat one price and simultaneously selling it that same asset at a higher price,generating a profit on the difference.Example: riskless arbitrage scenario for INFOSYS stock trading on the NSE andBSE.Assumptions: • Perfect futures market • No taxes • No transactions costs • Commodity can be sold short
  42. 42. 42 Price ExchangeArbitrageur Buys INFY (1105) BSEArbitrageur Sells INFY 1110 NSERiskless Profit 5
  43. 43. Futures Pricing 43
  44. 44. 44Since the futures or forwardsdon’t require front-end fromeither the long or shorttransaction; therefore, thecontract’s initial marketvalue is usually zero.
  45. 45. 45There are three maintheories of future pricing• The expectations hypothesis• Normal backwardation• A full carrying charge market
  46. 46. 46Hypothesis: The futures price for a commodity iswhat the marketplace expects the cash price to bewhen the delivery month arrives.The expectation hypothesis is a good predictorbecause it provides an important source ofinformation about what the future price is likelyto be. It works like a price discovery mechanism.
  47. 47. 47
  48. 48. 48
  49. 49. 49
  50. 50. 50Normally, the futures price exceeds the spotprice; this market is called contango.If the futures price is less than the spot price,this is called backwardation, or aninverted market.As the gap between the futures price and spotnarrows, we say that the basis is strengthened.
  51. 51. A hedger (for example, a farmer) who is selling a futures contract istrying to lock in the price of the commodity in future. i.e. the hedger istrying to reduce the risk, but this risk has to be borne by somebody i.e.speculators.Now question is if the future price equals the spot price + storage costs +other costs exactly, what the speculator will earn by bearing the risk?Therefore, the speculator will agree to that future price where he expectsthat the spot price on the delivery date will be higher than futures price.This is called normal backwardation.
  52. 52. 52
  53. 53. 53A full carrying charge market occurs whenfutures prices reflect the cost of storing andfinancing (borrowing) the commodity untilthe delivery month.In the world of certainty, the futures priceis equal to the current spot price plus thecarrying charges until the delivery month.
  54. 54. 54To the extent that markets adhere to the following equationsmarkets are said to be at ―full carry‖: F 0, t S 0(1 C 0, t ) F 0, d F 0, n(1 Cn, d )If the futures price is higher than that specified by aboveequations, the market is said to be above full carry.If the futures price is below that specified by the aboveequations, the market is said to be below full carry.
  55. 55. 55To determine if a market is at full carry, consider thefollowing example:Suppose that:September Gold $410.20December Gold $417.90Bankers Rate 7.8%
  56. 56. 56Step 1: compute the annualized percentagedifference between two futures contracts. 12 AD (F ) F 0, d 0. N M 1Where• AD = Annualized percentage difference• M = Number of months between the maturity of the futures contracts.
  57. 57. 57 12 $417.90 3 AD ( ) $410.20 1 AD 0.0772Step 2: compare the annualized difference to theinterest rate in the market.The gold market is almost always at full carry. Othermarkets can diverge substantially from full carry.
  58. 58. 58A spread is the difference in price between two futures contractson the same commodity for two different maturity dates: Spread F 0, t k F 0, tF0,t = The current futures price for delivery of the product at time t. • This might be the price of a futures contract on wheat for delivery in 3 months.F0,t+k = The current futures price for delivery of the product at timet +k. • This might be the price of a futures contract for wheat for delivery in 6 months.Spread relationships are important to speculators.
  59. 59. We know that there is a relationship between the price of thecommodity in the cash market and price of that commodity in thefutures market. 59The futures market price should reflect the storage cost ofthat commodity unto that future date plus the cash price of thatcommodity today and any other costs.If futures price is more than this price (= cash price + storage cost+ other costs) then there is a possibility of arbitrage.One will purchase the commodity today, store it and at the sametime short a futures contract to deliver it on the futures date.Since there is a difference in prices, there is a scope for arbitrage.
  60. 60. 60The common way to value a futures contract is by usingthe Cost-of-Carry Model. The Cost-of-Carry Model saysthat the futures price should depend upon two things:• The current spot price.• The cost of carrying or storing the underlying good from now until the futures contract matures.Assumptions:• There are no transaction costs or margin requirements.• There are no restrictions on short selling.• Investors can borrow and lend at the same rate of interest.
  61. 61. Suppose you buy the corn now for the current cash price of S0 per bushel 61and store it until you have to deliver it at date T, the forward price youwould be willing to commit would have to be high enough to cover • The present cost of the corn and • The cost of storing the corn until contract maturityThese storage costs involve • Commission paid to the warehouse for storing • Cost of financing the initial purchase • LESS cash flows received by owing the asset.F0,T = S0 + SC0,T= S0 + (PC0, T + i 0, T – D0, T)
  62. 62. 62
  63. 63. 63
  64. 64. 64The Cost-of-Carry Model can be expressed as: F 0, t S 0(1 C 0, t )S0 = the current spot priceF0,t = the current futures price for delivery of the product at time t.C0,t = the percentage cost required to store (or carry) thecommodity from today until time t.The cost of carrying or storing includes: • Storage costs • Insurance costs • Transportation costs • Financing costs
  65. 65. 65
  66. 66. 66Cash-and-carry arbitrage• When futures are overpricedReverse cash-and-carry arbitrage• When futures are underpriced
  67. 67. 67A cash-and-carry arbitrage occurs when a trader borrowsmoney, buys the goods today for cash and carries the goodsto the expiration of the futures contract. Then, delivers thecommodity against a futures contract and pays off the loan.Any profit from this strategy would be an arbitrage profit. 0 1 1. Borrow money 4. Deliver the commodity 2. Sell futures contract against the futures contract 3. Buy commodity 5. Recover money & payoff loan
  68. 68. 68The futures price must be greater than orequal to the spot price of the commodityplus the carrying charges necessary to carrythe spot commodity forward to delivery. F 0, t S 0(1 C 0, t ) 0 1 1. Borrow $400 4. Deliver gold against 2. Buy 1 oz gold futures contract 3. Sell futures contract 5. Repay loan
  69. 69. 69 Cash-and-Carry Gold Arbitrage Transactions Prices for the Analysis: Spot price of gold $400 Future price of gold (for delivery in one year) $450 Interest rate 10%Transaction Cash Flowt=0 Borrow $400 for one year at 10%. +$400 Buy 1 ounce of gold in the spot market for $400. - 400 Sell a futures contract for $450 for delivery of 0 one ounce in one year. Total Cash Flow $0t=1 Remove the gold from storage. $0 Deliver the ounce of gold against the futures +450 contract. Repay loan, including interest. -440 Total Cash Flow +$10
  70. 70. 70
  71. 71. 71A reverse cash-and-carry arbitrage occurs when a trader sells short aphysical asset. The trader purchases a futures contract, which will beused to honor the short sale commitment. Then the trader lends theproceeds at an established rate of interest. In the future, the traderaccepts delivery against the futures contract and uses the commodityreceived to cover the short position. Any profit from this strategy wouldbe an arbitrage profit. 0 1 1. Sell short the commodity 4. Accept delivery from futures 2. Lend money received contract from short sale 5. Use commodity received 3. Buy futures contract to cover the short sale
  72. 72. 72The futures price must be equal to or lessthan the spot price of the commodity plusthe carrying charges necessary to carrythe spot commodity forward to delivery. 0 F 0, t S 0(1 C 0, t ) 1 1. Sell short 1 oz. gold 4. Collect proceeds 2. Lend $420 at 10% from loan interest 5. Accept delivery on 3. Buy a futures contract futures contract 6. Use gold from futures contract to repay the short sale
  73. 73. 73 Reverse Cash-and-Carry Gold Arbitrage Transactions Prices for the Analysis Spot price of gold $420 Future price of gold (for delivery in one year) $450 Interest rate 10%Transaction Cash Flowt=0 Sell 1 ounce of gold short. +$420 Lend the $420 for one year at 10%. - 420 Buy 1 ounce of gold futures for delivery in 1 0 year. Total Cash Flow $0t=1 Collect proceeds from the loan ($420 x 1.1). +$462 Accept delivery on the futures contract. -450 Use gold from futures delivery to repay short 0 sale. Total Cash Flow +$12
  74. 74. 74
  75. 75. 75 Transactions for Arbitrage StrategiesMarket Cash-and-Carry Reverse Cash-and-CarryDebt Borrow funds Lend short sale proceedsPhysical Buy asset and store; deliver Sell asset short; secure against futures proceeds from short saleFutures Sell futures Buy futures; accept delivery; return physical asset to honor short sale commitment
  76. 76. Since the futures price must be76 either greater than or equal tothe spot price plus the cost of carrying the commodityforward by rule #1.And the futures price must be less than or equal to the spotprice plus the cost of carrying the commodity forward by rule#2.The only way that these two rules can reconciled so there isno arbitrage opportunity is by the cost of carry rule #3.Rule #3: the futures price must be equal to the spot price plusthe cost of carrying the commodity forward to the deliverydate of the futures contract. F 0, t S 0(1 C 0, t )
  77. 77. 77If prices were not to conform to cost ofcarry rule #3, a cash-and carry arbitrageprofit could be earned.Recall that we have assumed awaytransaction costs, margin requirements,and restrictions against short selling.
  78. 78. 78As we have just seen, there must be a relationship between the futures priceand the spot price on the same commodity.Similarly, there must be a relationship between the futures prices on the samecommodity with differing times to maturity.The following rules address these relationships:Cost-of-Carry Rule 4Cost-of-Carry Rule 5Cost-of-Carry Rule 6
  79. 79. The distant futures price must be greater than or equal to the nearby futures price plus 79the cost of carrying the commodity from the nearby delivery date to the distantdelivery date. F 0, d F 0, n(1 Cn, d )F0,d = the futures price at t=0 for the distant delivery contract maturing at t=d.Fo,n = the futures price at t=0 for the nearby delivery contract maturing at t=n.Cn,d = the percentage cost of carrying the good from t=n to t=d.If prices were not to conform to cost of carry rule # 4, a cash-and-carry arbitrage profitcould be earned.
  80. 80. 800 1 2 7. Remove gold 1. Buy futures 4. Borrow $400 from storage contract w/exp 5. Take delivery on 1 8. Deliver gold in 1 yrs. yr to exp futures against 2 yr. 2. Sell futures contract. futures contract contract w/exp 6. Place the gold in 9. Pay back loan in 2 years storage for one yr. 3. Contract to borrow $400 from yr 1-2
  81. 81. 810 1 2 7. Remove gold 1. Buy futures 4. Borrow $400 from storage contract w/exp 5. Take delivery on 1 8. Deliver gold in 1 yrs. yr to exp futures against 2 yr. 2. Sell futures contract. futures contract contract w/exp 6. Place the gold in 9. Pay back loan in 2 years storage for one yr. 3. Contract to borrow $400 from yr 1-2
  82. 82. 82 Gold Forward Cash-and-Carry Arbitrage Prices for the Analysis Futures price for gold expiring in 1 year $400 Futures price for gold expiring in 2 years $450 Interest rate (to cover from year 1 to year 2) 10%Transaction Cash Flowt=0 Buy the futures expiring in 1 year. +$0 Sell the futures expiring in 2 years. 0 Contract to borrow $400 at 10% for year 1 to 0 year 2. Total Cash Flow $0t=1 Borrow $400 for 1 year at 10% as contracted at +$400 t = 0. Take delivery on the futures contract. - 400 Begin to store gold for one year. 0 Total Cash Flow $0t=2 Deliver gold to honor futures contract. +$450 Repay loan ($400 x 1.1) - 440 Total Cash Flow + $10
  83. 83. 83The nearby futures price plus the cost of carrying the commodity fromthe nearby delivery date to the distant delivery date cannot exceed thedistant futures price.Or alternatively, the distant futures price must be less than or equal tothe nearby futures price plus the cost of carrying the commodity from thenearby futures date to the distant futures date. F0,d F0,n 1 Cn,dIf prices were not to conform to cost of carry rule # 5, a reverse cash-and-carry arbitrage profit could be earned.
  84. 84. 840 1 2 1. Sell futures 7. Accept delivery contract w/exp 4. Borrow 1 oz. gold on exp 2 yr in 1 yrs. 5. Deliver gold on 1 futures contract 2. Buy futures yr to exp futures 8. Repay 1 oz. contract w/exp contract. borrowed gold. in 2 years 6. Invest proceeds 9. Collect $400 3. Contract to from delivery for loan lend $400 one yr. from yr 1-2
  85. 85. 85 Gold Forward Reverse Cash-and-Carry Arbitrage Prices for the Analysis: Futures price for gold expiring in 1 year $440 Futures price for gold expiring in 2 years $450 Interest rate (to cover from year 1 to year 2) 10%Transaction Cash Flowt=0 Sell the futures expiring in one year. +$0 Buy the futures expiring in two years. 0 Contract to lend $440 at 10% from year 1 to 0 year 2. Total Cash Flow $0t=1 Borrow 1 ounce of gold for one year. $0 Deliver gold against the expiring futures. + 440 Invest proceeds from delivery for one year. - 440 Total Cash Flow $0t=2 Accept delivery on expiring futures. - $450 Repay 1 ounce of borrowed gold. 0 Collect on loan of $440 made at t = 1. + 484 Total Cash Flow + $34
  86. 86. 86Since the distant futures price must be either greater than or equalto the nearby futures price plus the cost of carrying thecommodity from the nearby delivery date to the distant deliverydate by rule #4.And the nearby futures price plus the cost of carrying thecommodity from the nearby delivery date to the distant deliverydate can not exceed the distant futures price by rule #5.The only way that rules 4 and 5 can be reconciled so there is noarbitrage opportunity is by cost of carry rule #6.
  87. 87. 87The distant futures price must equal the nearby futures price plus thecost of carrying the commodity from the nearby to the distant deliverydate. F 0, d F 0, n(1 Cn, d )If prices were not to conform to cost of carry rule #6, a cash-and-carryarbitrage profit or reverse cash-and-carry arbitrage profit could beearned.Recall that we have assumed away transaction costs, marginrequirements, and restrictions against short selling.
  88. 88. 88Ease of Short Selling• To the extent that it is easy to short sell a commodity, the market will become closer to full carry.• Difficulties in short selling will move a market away from full carry.• Selling short of physical goods like wheat is more difficult, while selling short of financial assets like Eurodollars is much easier. For this reason, markets for financial assets tend to be closer to full carry than markets for physical assets.Large Supply• If the supply of an asset is large relative to its consumption, the market will tend to be closer to full carry. If the supply of an asset is low relative to its consumption, the market will tend to be further away from full carry.
  89. 89. 89Non-Seasonal Production • To the extent that production of a crop is seasonal, temporary imbalances between supply and demand can occur. In this case, prices can vary widely. • Example: in North America, wheat harvest occurs between May and September.Non-Seasonal Consumption • To the extent that consumption of commodity is seasonal, temporary imbalances between supply and demand can occur. • Example: propane gas during winter Turkeys during thanksgivingHigh Storability • A market moves closer to full carry if its underline commodity can be stored easily. • The Cost-of-Carry Model is not likely to apply to commodities that have poor storage characteristics. • Example: eggs
  90. 90. Hedging with futures 90
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  92. 92. 92 Cash market Futures marketMay 10 Anticipate the sale of 20, 000 Sell four contracts, 5000 ounces ounces in two months and each July futures contract at receive Rs.1052 per ounce Rs.1068 per ounceJuly 5 Cash price of silver is Rs.1071 Buy four contracts at Rs.1087 per ounce; mfg sales 20, 000 ounces at that rateResults Profit of Rs. 19 per ounce However, he loses Rs.19 per ounce when he buys the futures contract.
  93. 93. 93 Cash market Futures marketMay 10 If he had sold today: 1052 x Sell : 4x5000x1068 = 2,13,60,000 20,000 = 2,10,40,000July 5 1071 x 20, 000 = 2,14,20,000 Buy: 4x5000x 1087 = 2,17,40,000Results Profit of Rs. 3, 80, 000 He loses Rs.3, 80, 000 in the futures contract.
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  96. 96. 96Suppose on June 1, Ms. Deepa realizes she needs to purchase110,000 pieces of wood planks on September 1.Today’s cash price for wood planks is $300 per 1000 board feet($300/MBF). She observes that September Lumber futures arecurrently trading at $305/MBF.She also knows that historically the futures price in Septembertends to be about $5/MBF higher than the cash price. So Deepafigures that by buying a September Lumber futures contract inJune at $305, she is locking in a price of about $300.
  97. 97. 97 Cash market Futures marketJune 1 Needs to buy wood planks in Buys (goes long) one September September for $300/MBF Lumber futures contract at to make desired profit. $305/MBF.Sep 1 Cash price rises to $315/MBF. Deepa sells her September Deepa buys lumber for Lumber contract at $320/MBF. $315/MBF.Results Deepa pays $15/MBF more However, she gains $15/MBF when for lumber than she wanted she sells the futures contract. to.
  98. 98. 98 Cash market Futures marketJune 1 $300/MBF X 110 = $33,000 $305/MBF X 110 = $33,550Sep 1 $315/MBF X 110 = $34,650 $320/MBF X 110 = $35,200Results Higher cost in cash market: Net profit in futures market: Spent $1,650 more Gained $1,650
  99. 99. 99The difference between the cash price and thefutures price is called basis.The basis changes during the life of the futurescontract.It tends to narrow as contract maturity approaches.That is, the futures price moves closer to the cashprice during the delivery month.
  100. 100. 100At any date t, the basis is the spot price minus theforward price for a contract maturing at date T,• Bt,T = St – Ft,T (spot price of the asset to be hedged – futures price of contract used)Initial basis at date 0 (B0,T) will always be knownsince both the current spot and forward contractprices can be observed.Consider an investor who hedges her long position ina commodity by taking a short position in a forwardcontract(delivering the commodity at maturity).
  101. 101. At date 1, B1= S1 – F1 101At date 2, B2 = S2 – F2For the hedger who takes a short position in futures attime 1, the price realized for the asset is S2 and theprofit on the futures position is (F1 – F2)Therefore the effective price is = S2 + (F1 – F2) = F1 +(S2 – F2) = F1 + B2
  102. 102. 102Suppose, an investor wishes in March to hedge a long position of100, 000 pounds of cotton she is planning to sell in June.However, each futures contract is requiring only 50, 000 poundsof cotton. Therefore, she decides to short two of the July contracts(intending to liquidate her position before the maturity)Suppose, in the beginning, the spot cotton price was $0.4834 perpound and the July futures contract was $0.5305 per pound.Calculate initial basis. B1= S1 – F1= 0.4834 – 0.5305 = - 0.0471
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  104. 104. Suppose, cotton prices have declined so that cash price in June are 104$0.4660 and futures are trading at $0.4753.Calculate basis for June. B2 = S2 – F2 = 0.4660 – 0.4753 = -0.0093Basis has increased in value or strengthened, which is to the shorthedger’s advantage.Now, she sells cotton in cash market for $0.4660At the same time she also sells the futures for its contract value i.e.$0.5305 whereas the market future price is $0.4753; it means thatshe has made a profit of (0.5305 – 0..4753) = $0.0552
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