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# Derivatives lecture3 & 4- futures

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### Derivatives lecture3 & 4- futures

1. 1. OPTIONS FUTURES AND DERIVATIVES Lecture 3,4 Futures SANJAY MEHROTRA
2. 2. Futures
3. 3. Reading a Futures Quote Expiry month Opening price Highest price that day Lowest price that day Closing price Daily Change Highest and lowest prices over the lifetime of the contract. Number of open contracts
4. 4. <ul><li>Settlement price: average of the prices at which the contract is traded before the close. Used for calculating daily gains and losses and margins requirements. </li></ul><ul><li>Change in settlement price= change in settlement price from previous day. </li></ul><ul><li>Open interest: Number of contracts outstanding at any time </li></ul>
5. 5. Futures Contracts A futures contract calls for delivery of an asset at a specified delivery or maturity date, for an agreed-upon price, called the futures price , to be paid on contract maturity. The trader taking the long position commits to purchasing the asset on delivery date. The trader taking the short position commits to delivering the asset at contract maturity.
6. 6. Futures Contracts The trader in the long position is said to “buy” a contract; the short-side trader “sells” a contract. At maturity: Profit to long = Spot price at maturity – Original futures price Profit to short = Original futures price - Spot price at maturity The spot price is the actual market price of the asset at the time of the delivery.
7. 7. Payoffs From Futures Contracts Asset price at maturity Payoff 0 K K: Delivery price LONG POSITION
8. 8. Payoffs From Futures Contracts Asset price at maturity Payoff 0 K K: Delivery price SHORT POSITION
9. 9. Futures Contracts The futures contract is a zero-sum game. The losses and gains to all positions netting out to zero. Every long position is offset by a short position. The aggregate profits to futures trading, summing over all investors, also must be zero, as is the net exposure to changes in the asset prices.
10. 10. Futures Contracts <ul><li>Buyers and sellers in the futures market primarily enter into futures contracts to hedge risk or speculate rather than exchange assets (which is the primary activity of the cash / spot market ). </li></ul>
11. 11. Futures Contracts <ul><li>Available on a wide range of underlying assets </li></ul><ul><li>Exchange traded </li></ul><ul><li>Specifications need to be defined: </li></ul><ul><ul><li>What can be delivered, </li></ul></ul><ul><ul><li>Where it can be delivered, </li></ul></ul><ul><ul><li>When it can be delivered </li></ul></ul><ul><li>Settled daily </li></ul>
12. 12. Specifications of the Future Contract <ul><li>Asset: </li></ul><ul><ul><li>Commodity: There may be quite a variation in the quality of what is available in the marketplace. </li></ul></ul><ul><ul><li>Financial Assets in futures contracts are generally well defined and unambiguous. </li></ul></ul>
13. 13. Contract size & Lot Size: <ul><li>Contract size: The contract size specifies the amount of asset that has to be delivered under one contract. </li></ul><ul><ul><li>Too large: Many investors who wish to hedge relatively small exposures would not be able to do so. </li></ul></ul><ul><ul><li>Too small: Trading may be expensive as there is a cost associated with each contract. </li></ul></ul><ul><li>Lot size refers to number of underlying securities in one contract. The lot size is determined keeping in mind the minimum contract size requirement at the time of introduction of derivative contracts on a particular underlying. </li></ul>
14. 14. Delivery Arrangement <ul><li>The place where the delivery will be made must be specified by the exchange. </li></ul><ul><li>- specially important for commodities that involve significant transportation costs. </li></ul>
15. 15. Delivery months <ul><li>A future contract is referred to by its delivery month. The exchange must specify the precise period during the month when delivery can be made. </li></ul><ul><li>- For many future contracts the delivery period is the whole month. </li></ul>
16. 16. Types of Futures Contracts <ul><li>Physical commodities </li></ul><ul><ul><li>Agricultural (e.g., corn, livestock) </li></ul></ul><ul><ul><li>Non-agricultural (e.g., lumber, oil) </li></ul></ul><ul><li>Financial futures </li></ul><ul><ul><li>Currency futures </li></ul></ul><ul><ul><li>Stock index / Stock futures </li></ul></ul><ul><ul><li>Interest rate futures </li></ul></ul>
17. 17. Requirements for Viable Markets <ul><li>Assets must have: </li></ul><ul><li>The ability to be standardized </li></ul><ul><li>Active demand </li></ul><ul><li>The ability to be stored for a period of time </li></ul><ul><li>Relatively high value in proportion to bulk </li></ul><ul><li>Relatively high value in proportion to storage and other carrying costs </li></ul>
18. 18. Closing out positions <ul><li>Vast majority of futures contracts do not lead to delivery. </li></ul><ul><li>Most traders close out their positions prior to delivery period specified in the contract. </li></ul><ul><li>Closing out a position involves entering into the opposite type of trade from the original one. </li></ul>
19. 19. Mechanics of Futures Markets <ul><li>Trading styles </li></ul><ul><li>Scalpers attempt to profit from small changes in contract prices, hold positions for just a few minutes </li></ul><ul><li>Day traders also look for short-term movements, do not hold positions overnight </li></ul><ul><li>Position traders hold positions for longer periods of time looking for long-term movements </li></ul>
20. 20. Mechanics of Futures Markets <ul><li>Settlement price </li></ul><ul><ul><li>Price established at the end of each trading day </li></ul></ul><ul><li>Marked to market </li></ul><ul><ul><li>Adjusting each margin account by changes in the settlement price each day </li></ul></ul><ul><li>Limit up/down </li></ul><ul><ul><li>The maximum amounts by which futures prices can change during a trading day </li></ul></ul>
21. 21. Margins <ul><li>A margin is cash or marketable securities deposited by an investor with his or her broker </li></ul><ul><li>The balance in the margin account is adjusted to reflect daily settlement </li></ul><ul><li>Margins minimize the possibility of a loss through a default on a contract </li></ul>
22. 22. Margins… <ul><li>Initial margin : Amount that is deposited at the time of contract </li></ul><ul><li>At the end of each trading day the margin account is adjusted to reflect the investor’s gain or loss - marking to market the account. </li></ul><ul><li>Maintenance margin : To ensure that the balance never becomes negative ( if balance falls below this level margin call – investor required to top up the margin account to the initial margin level) </li></ul>
23. 23. Example of a Futures Trade <ul><li>An investor takes a long position in 2 December gold futures contracts on June 5 </li></ul><ul><ul><li>contract size is 100 oz. </li></ul></ul><ul><ul><li>futures price is US\$400/oz </li></ul></ul><ul><ul><li>margin requirement is US\$2,000/contract (US\$4,000 in total) </li></ul></ul><ul><ul><li>maintenance margin is US\$1,500/contract (US\$3,000 in total) </li></ul></ul>
24. 24. Example of a Futures Trade <ul><li>Total margin requirement </li></ul><ul><li>= 2 x 2000 = \$ 4000 </li></ul><ul><li>Maintenance margin requirement </li></ul><ul><li>= 2 x 1000 = \$ 3000 </li></ul><ul><li>Suppose the price goes down to 397 the next day </li></ul><ul><li>Loss = (397-400) x 2 x 100 = (600) </li></ul>
25. 26. Convergence of Futures Price to Spot Price <ul><li>As the delivery month of futures contract is approached , the future price converges to the spot price of the underlying asset. </li></ul><ul><li>When the delivery period is reached , the future price equals – or is very close to - the spot price. </li></ul>
26. 27. Convergence of Prices Time Prices Futures Price Spot Price
27. 28. Convergence of Futures Price to Spot Price… <ul><li>Assume that the spot price is higher than the future price during the delivery month. </li></ul><ul><li>Arbitrage opportunity: </li></ul><ul><li>Long a futures contract </li></ul><ul><li>Get delivery </li></ul><ul><li>Sell the asset </li></ul><ul><li>Since spot price is greater than the future price the investor makes a profit </li></ul>
28. 29. Convergence of Futures Price to Spot Price… <ul><li>Conversely assume that the future price is higher than the spot price during the delivery month. </li></ul><ul><li>Arbitrage opportunity: </li></ul><ul><li>Short a futures contract </li></ul><ul><li>Buy the asset </li></ul><ul><li>Make delivery </li></ul><ul><li>Since future price is greater than the spot price the investor makes a profit </li></ul>
29. 30. Hedging Strategies Using Futures
30. 31. Long & Short Hedges <ul><li>A long futures hedge is appropriate when you know you will purchase an asset in the future and want to lock in the price </li></ul><ul><li>A short futures hedge is appropriate when you know you will sell an asset in the future & want to lock in the price </li></ul>
31. 32. <ul><li>Speculation - </li></ul><ul><ul><li>short - believe price will fall </li></ul></ul><ul><ul><li>long - believe price will rise </li></ul></ul><ul><li>Hedging - </li></ul><ul><ul><li>long hedge - protecting against a rise in price </li></ul></ul><ul><ul><li>short hedge - protecting against a fall in price </li></ul></ul>Trading Strategies
32. 33. Basis Risk <ul><li>Basis is the difference between spot & futures </li></ul><ul><li>Basis = Spot price of the asset to be hedged- Future price of the contract used </li></ul>
33. 34. Convergence of Futures to Spot Time Time (a) (b) Futures Price Futures Price Spot Price Spot Price
34. 35. Basis risk <ul><li>Basis risk arises because of the uncertainty about the basis when the hedge is closed out: </li></ul><ul><li>Asset whose price is to be hedged may not be the same as the asset underlying the futures contract </li></ul><ul><li>Hedger may be uncertain as to the exact date when asset is bought or sold </li></ul><ul><li>Hedge may require the futures contract to be closed out well before its expiration date. </li></ul>
35. 36. Long Hedge <ul><li>Suppose that </li></ul><ul><ul><ul><li>F 1 : Initial Futures Price </li></ul></ul></ul><ul><ul><ul><li>F 2 : Final Futures Price </li></ul></ul></ul><ul><ul><ul><li>S 2 : Final Asset Price </li></ul></ul></ul><ul><li>You hedge the future purchase of an asset by entering into a long futures contract </li></ul><ul><li>Cost of Asset= S 2 –( F 2 – F 1 ) = F 1 + (S 2 -F2) = F 1 + Basis (b 2 ) </li></ul>
36. 37. Short Hedge <ul><li>Suppose that </li></ul><ul><ul><ul><li>F 1 : Initial Futures Price </li></ul></ul></ul><ul><ul><ul><li>F 2 : Final Futures Price </li></ul></ul></ul><ul><ul><ul><li>S 2 : Final Asset Price </li></ul></ul></ul><ul><li>You hedge the future sale of an asset by entering into a short futures contract </li></ul><ul><li>Price Realized= S 2 + ( F 1 –F 2 ) = F 1 + (S 2 -F2) = F 1 + Basis (b 2 ) </li></ul>
37. 38. <ul><li>When the spot price increases by more than the future price, the basis increases-strengthening of basis. </li></ul><ul><li>When the future price increases by more than the spot price, the basis declines-weakening of basis. </li></ul><ul><li>If the basis increases unexpectedly, the short hedger’s position improves, if the basis declines unexpectedly, the hedger’s position worsens. For a long hedge the reverse is true. </li></ul>
38. 39. Short hedge <ul><li>Today is March 1. A US company expects to get 50 million Japanese yen at the end of July. </li></ul><ul><li>Contract size= 12.5 million yen </li></ul><ul><li>Future price (September ) on March 1= 0.7800 cents/yen </li></ul><ul><li>Company enters September Future. </li></ul><ul><li>In July when the Yen is received the spot and futures price are 0.7200 and 0.7250 cents/Yen respectively. </li></ul><ul><li>Payoff? </li></ul>
39. 40. <ul><li>Short 4 contracts </li></ul><ul><li>In the spot market sell Yen @ 0.7200 cents /yen </li></ul><ul><li>Gain from futures contract= 0.7800-0.7250 cents/Yen=0.0550 cents/ Yen </li></ul><ul><li>Therefore effective price obtained per yen = 0.7200 + 0.0550 = 0.7750 cents/Yen </li></ul><ul><li>_____________________________ </li></ul><ul><li>Alternatively. </li></ul><ul><li>Basis when the contract is closed out = 0.7200-0.7250= -0.0050 </li></ul><ul><li>F 1 + b 2 = 0.7800-0.0050= 0.7750 cents/Yen </li></ul>
40. 41. Long hedge <ul><li>Its June 8. A company needs to purchase 20,000 barrels of crude in Oct/Nov. Contract size is 1000 barrels </li></ul><ul><li>On June 8, December contract future price is \$18.00 per barrel. Company buys 20 contracts (long) </li></ul><ul><li>On Nov 10 company decides to purchase the crude oil. The spot and futures price are \$20.00 and \$19.10 per barrel respectively. </li></ul><ul><li>payoff </li></ul>
41. 42. <ul><li>In the spot market buy crude @ \$20.00 per barrel </li></ul><ul><li>Gain from futures contract= \$19.10-\$18.00\$ per barrel = \$1.10 per barrel </li></ul><ul><li>Therefore effective price paid per barrel = \$20.00 - \$1.10= \$ 18.90 per barrel </li></ul><ul><li>_____________________________ </li></ul><ul><li>Alternatively. </li></ul><ul><li>Basis when the contract is closed out = \$20.00-\$19.10= \$0.90 </li></ul><ul><li>F 1 + b 2 = \$18 + \$0.90 = \$ 18.90 per barrel </li></ul>
42. 43. Choice of Contract <ul><li>Choose a delivery month that is as close as possible to, but later than, the end of the life of the hedge </li></ul><ul><li>When there is no futures contract on the asset being hedged, choose the contract whose futures price is most highly correlated with the asset price. </li></ul>