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Hedging with F orward/ Futures contracts

Hedging with F orward/ Futures contracts. Chap 22 & Chap 24. Lecture Outline. Purpose: Introduce Forwards & Futures contracts and show how they can be used to hedge. Introduction to Forwards and Futures Three types of prices: Forward/Future, Spot & Delivery

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Hedging with F orward/ Futures contracts

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  1. Hedging with Forward/ Futures contracts Chap 22 & Chap 24

  2. Lecture Outline Purpose: Introduce Forwards & Futures contracts and show how they can be used to hedge. • Introduction to Forwards and Futures • Three types of prices: • Forward/Future, Spot & Delivery • Payoff of Forward/Future contract • Hedging with Forwards/Futures • Micro Hedge • Macro Hedge

  3. Introduction to Forwards & Futures

  4. Forward/Future Contract a Primer Forward & future contracts: are agreements, made at t=0, obligating parties to exchange some pre-specified amount of an asset at a pre-specified price some time in the future. Example: http://www.cmegroup.com • If your company is a large coffee buyer (Starbucks) you may want to hedge against movements in the price of coffee – lock in a price today for the purchase of coffee in 1.5 years Coffee Forward Prices The price that the coffee buyer can lock in at any time is the forward price The price that the coffee buyer locks-in is the delivery price Just an agreement – no exchange of money $2.75/lb -$0.88/lb $1.87/lb Contract payoff $0.88 $2.75/lb 1.87/lb $1.87/lb

  5. Forward/Future Contract A Primer Differences between Forwards and Futures Futures contracts are standard Forward contracts are custom Who Trades in each market Speculators or Hedgers? • Trade on OTC dealer markets • Trade on exchanges • Forwards settled at maturity • Futures are marked-to-market • Exchange guarantees performance (there is much less counter party default risk) • More exposed to counterparty default risk • Almost always delivered • Almost never delivered Every day the change in the value of the forward contract is added or subtracted from the investors account Economic Hedgers Speculators

  6. Forward/ Future Price, Spot Price & Delivery Price

  7. Prices You Need to Keep Straight • Spot Price (S0): Price of the underlying asset (coffee) • Forward/Futures Price (Ft): The current price at which you can enter a forward contract – varies over time! • Delivery Price: The transaction price specified in the contract. • Equal to the forward/futures price when the contract is entered • Remains constant over the life of the contract. (Locked-in) S0 = Current Market Price of Coffee Current Market Price of Ford Stock Current Market Price of a 10-year Treasury Note: this is for the special case where the underlying asset does not make payments for the life of the contract. That is, it does not work for coupon bonds dividend paying stocks … Ft = future price ; S0 = underlying spot price k = compounding periods per year; r = risk-free rate; (T-t) = number of years to delivery

  8. Spot Price

  9. Example: Spot Price Problem: Assuming JP Morgan will buy the 10-year Treasury Note on March 2012 to satisfy the contract, they don’t know how much they will pay for it. So, they are exposed to interest rate risk. On June 20, 2010 JP Morgan enters into an agreement to sell a10-year Treasury note with $1000 face value. They agree to a delivery price is $900 for the March 2012 contract. Spot Prices Bonds are expensive Is JP Morgan exposed to risk? Setup Price of 10-year Treasury Uncertainty On June 20, 2010 JP Morgan agrees to sell a Treasury Bond for $900 on March 23, 2012 On March 23, 2012 JP Morgan needs to deliver a 10-year Treasury Note Bonds are cheap

  10. Example: Spot Price Problem: Assuming JP Morgan will buy the 10-year Treasury Note on March 2012 to satisfy the contract, they don’t know how much they will pay for it. So, they are exposed to interest rate risk. On June 20, 2010 JP Morgan enters into an agreement to sell a10-year Treasury Note with $1000 face value. They agree to a delivery price is $900 for the March 2012 contract. Spot Prices JP Morgan needs to sell a bond for 900 on March 23 2012 $900 Can JP Morgan hedge using a forward contract? Yes JP Morgan can enter a forward contract to buy the 10 year Treasury. That would lock-in a price to buy the 10-Treasury on March 23, 2012 Can JP Morgan hedge using a forward contract?

  11. Example: Spot Price Main Point: • Spot prices vary through time which exposes banks/investors to risk (interest rate risk, price risk, FX risk … ) • Forward/Futures contracts can be used to hedge that risk How?

  12. Forward/Future Price

  13. Example: Forward/Futures Prices On June 20, 2010 JP Morgan enters into an agreement to sell a10-year Treasury Note with $1000 face value. They agree to a delivery price is $900 for the March 2012 contract. Forward/Future & Spot Prices Forward/Future Price is a function of the spot price. At any point in time I can enter a forward/futures contract at the forward/futures price Spot price S0 Price of the bond

  14. Example: Forward/Futures Price Main Point: • The Forward/Futures price is a function of the spot price and varies through time. • At any point in time you can enter a forward/futures at the current forward/futures price

  15. Delivery Price

  16. Example: Delivery Price On June 20, 2010 JP Morgan enters into an agreement to sell a10-year Treasury Note with $1000 face value. They agree to a delivery price is $900 for the March 2012 contract. Forward/Future & Spot Prices Obligated to buy at $938 Delivery Price $938 $880 $975 $938 Forward/Future Price is a function of the spot price. Delivery Price !!! $880 $975 We know that we can enter a forward/future at any time at the forward/futures price. This locks-in the future buy price Spot price S0 Price of the bond

  17. Example: Delivery Price Main Point: • The delivery price is specified in the contract. Once you enter the contract the delivery price does not change. • This is the price you agree to buy or sell at in the future

  18. Hedging with a Forward Basic Idea

  19. Example: Bring it all together On June 20, 2010 JP Morgan enters into an agreement to sell a 10-year Treasury note with $1000 face value. They agree to a delivery price is $900 for the March 23, 2012 contract. Forward/Future & Spot Prices Forward/Future Price is a function of the spot price. Agreed to sell T-note for $900 $900 $890 -$890 Enter forward contract to buy a T-Note at the delivery price $10 Spot price S0 Price of the bond

  20. Forward/Futures Payoff

  21. Payoff of a forward/futures contract • Payoff – Refers to the cash flow that occurs at maturity for a contract with cash settlement.

  22. Example: Forward/Future Payoff ONLY CONSIDER THE FORWARD TO BUY AT $890: JP Morgan entered a forward contract to buy a Treasury Note on March 23, 2012 with a delivery price of $890. They have locked-in a buy price. The question is: what happens at maturity? Forward/Future & Spot Prices If the contract is financial (cash) settled, what does JP Morgan receive at maturity? Forward/Future Price (March 2012 contract) $933 Delivery Price - $890 $43 • Buy at the delivery price Payoff • Immediately sell in the market at the current spot price (also the forward price

  23. Example: Forward/Future Payoff ONLY CONSIDER THE FORWARD TO BUY AT $890: JP Morgan entered a forward contract to buy a Treasury Note on March 23, 2012 with a delivery price of $890. They have locked-in a buy price. The question is: what happens at maturity? Forward/Future & Spot Prices Forward/Future Price (March 2012 contract) $933 Delivery Price - $890 $43 Payoff $43

  24. Example: Forward/Future Payoff • Take Away • The payoff of the forward/futures contract is difference between the price of the underlying asset (bond) at maturity and the delivery price that was locked in the on the contract • Payoff = (S – FD) - long position • Payoff = (FD – S) - short position Question: Will the Forward/Future contract payoff always be positive? Question: Can you calculate the payoff on a forward/future prior to maturity?

  25. Hedging with Forward/Futures Contracts

  26. Hedging • Find the hedging position long or short forward • Find the number of contracts • Show that the position is hedged

  27. Long & Short Positions Underlying Asset: • Long: you own the asset • Short: you owe the asset Forward Contract • Long:you have agreed to buy the asset in the future at a pre- specified price (locked-in a price to buy) • Short: you have agreed to sell the asset in the future at a pre- specified price (locked-in a price to sell) Example: Stock → If you are long the stock you own it Example: Stock → If you are short the stock you have borrowed # shares from a dealer and sold them. So, you owe # shares back to the dealer

  28. 1. Finding the Hedging Position These 3 questions can help determine the hedging position: • Does the hedging party own or owe the underlying asset? • Answer: own. Then they are long the underlying and need to take a short position in the forward contract to hedge • Answer: owe. Then they are short the underlying and need to take a long position in the forward contract to hedge • Does the hedging party want to lock in a price to buy or sell in the future? • Answer: lock-in a price to buy. Then they need to go long the forward • Answer: lock-in a price to sell. Then they need to go short the forward

  29. 1. Finding the Hedging Position These 3 questions can help determine the hedging position: • Is the hedging party happy if the price of the underlying asset increases or decreases? • Answer: Increases. Then the hedging party is long the underlying asset and needs to take a short position in the forward contract • Answer: Decreases. Then the hedging party is short the underlying and needs to take a long position in the forward contract

  30. 1. Finding the Hedging Position Examples: • Goldman Sachs wants to hedge $5M of corporate bonds on its balance sheet. • Citigroup will receive $10M of Treasury bonds in 6 months that were posted as collateral on expired derivative contracts. • JPMorgan has agreed to sell 20,000 Treasury bonds to Carlyle Capital in 3 months for $735/bond. Goldman owns the corporate bonds. So, it is long the underlying and needs to take a short position in the forward to hedge Citigroup is happy if the price of treasuries increases. Therefore, it is long the underlying and must take a short position to hedge. JPMorgan must buy Treasuries in the future. Therefore, it would like to lock-in a price to buy. It can do that by taking a long position in the forward contract

  31. 2. Find the number of contracts • Forward contract: • These are custom contracts. The hedging party can specify the exact notional amount. Therefore, only one contract is needed. • Futures contracts: • These are standard contracts with a standard notional amount. • To find the number of contracts you must divide the total notional by the standard contract notional • Example: Goldman wants to hedge 10-year Treasury bonds with $5M face value with a CME contract. The standard contract size is $100,000

  32. 3. Show that the position is hedged • Show that no matter what the price of the underlying asset is in the future the hedged portfolio has locked-in a payoff t = 0 t = 6 months Scenario 1 price Scenario 2 price Underlying position Forward Payoff Hedged portfolio

  33. Example: Hedging with Forwards/Futures A hedge fund currently holds 1000 20 year treasury notes each note has face value of $1000. The current spot price is $994 per bond. They decide to hedge using a 3-month futures contract on the 20 year treasury bond. The current futures price is $99.5 per $100 of face value and contract size is $100,000. • How many contracts do they need? • Show that the position is hedged if the price of the 20-year Treasury is $905 or $1,050 in three months. Step #1: What contract position do they need to hedge their exposure? • They own the bonds. So, they are long the underlying. • To hedge, they need to take a short position in the forward contract Step #2: How many contracts do they need to short? Total face value held by the hedge fund Once you know the number of contracts to long or short you have enough information to set up the hedge. What we do in the last step is show that the hedge works

  34. Example: Hedging with Forwards/Futures A hedge fund currently holds 1000 20 year treasury notes each note has face value of $1000. The current spot price is $994 per bond. They decide to hedge using a 3-month futures contract on the 20 year treasury bond. The current futures price is $99.5 per $100 of face value and contract size is $100,000. • How many contracts do they need? • Show that the position is hedged if the price of the 20-year Treasury is $905 or $1,050 in three months. t = 0 t = 3m Bond Price = $1,050 Bond Price = $905 Bond Position (1000)(994) = 994,000 They hold 1000 bonds worth $994 a piece (1000)(905) = 905,000 They hold 1000 bonds worth $905 a piece (1000)(1,050) = $1,050,000 They hold 1000 bonds worth $1,050 a piece Sell 1M face value at the forward price $0.995(1,000,000) = $995,000 Sell 1M face value at the forward price $0.995(1,000,000) = $995,000 Futures contracts = $0.00 forward/future cost nothing at inception Forward Payoff Buy a bond in the market: -$1,050(1,000) = - $1,050,000 Buy a bond in the market: -$905(1,000) = - $905,000 Forward Payoff - $55,000 Forward Payoff $90,000 Hedged Portfolio $994,000 $995,000 $995,000

  35. The company you work for is obligated to deliver 5,000 5-year zero coupon bonds in one year. Payment will be maid upon delivery. The current YTM for a 5-year zero is 12%. Each bond has face value of 1,000 Hedge your position using a one-year futures contract. Assume a standard contract size of 250,000 and the current future price is $64 per $100 of face value. Show that you are hedged if the YTM increases to 13% or decreases to 11% in one year.

  36. Types of Hedging Strategies • Microhedge: The FI manager chooses to hedge the risk from a specific asset • Example: An FI manager may believe that American auto manufactures are going to suffer unexpected earnings losses in the near future causing their interest rates (financing cost) to increase. The manager shorts futures contracts on the Ford 5 ¼% 10 year bond which he currently holds • Managers will pick contracts where the underlying asset closely matches assets being hedged • Macrohedge:The FI uses futures contracts to hedge the risk of its entire portfolio (balance sheet). • Example: using futures contracts to reduce the duration gap • Managers hedging strategies must consider the duration of the entire portfolio because durations of individual assets will cancel or multiply (“net out”) • Routine Hedging: The FI uses forward contracts to reduce the interest rate risk on its balance sheet to its lowest level • Selective Hedging: The FI chooses to bear some of the risk on its balance sheet by hedging only certain components of the balance sheet

  37. Duration of a Forward Contract • Suppose you enter into a forward contract to purchase a 10 year treasury bond in 3 months. The duration of the treasury is currently 7.5 years. What is the duration of the forward contract? • Draw the cash flows of each investment assuming there are no payments made on the underlying during the life of the forward contract 10 year Treasury 0.5 1 9 9.5 10 .5 1 9 9.5 10 Forward Contract on a10 year Treasury 3 months The string of cash flows from the forward contract and the 10 year note are the same. Therefore, the duration of the futures contract is the same as the duration of the underlying asset

  38. Hedging with Forwards (Macrohedge) • Object: immunize the balance sheet against changes in interest rates • Basic Idea: Construct a portfolio of futures contracts such that any gains/losses in equity capital on the balance sheet will be offset by gains/losses on the portfolio of futures (held off balance sheet) • Step #1 Calculate the potential gain or loss in equity capital

  39. Hedging with Forwards (Macrohedge) • Step #2 Find the total forward position needed to hedge the change in equity • We know that DF = Dunderlying we can use this to find the total forward position Note: we can use a forward on any asset as long as we know its duration • Set the change in equity equal to the negative change in the value of the forward position and solve for F Duration of a asset X Duration of the forward/futures contract on the asset X

  40. Macrohedge (continued) Step #3 Find the Number of Contracts: • F is the total position in the futures contracts but how many contracts do we need to buy to cover the position? Total payment you have locked-in in the future

  41. Example: Suppose a FI has assets and liabilities on its balance sheet with total values shown below. The duration of its assets and liabilities is 5 years and 3 years respectively. Management at the FI expects interest rates to increase from 10% to 11%. They hire you as a consultant to recommend a macrohedge. Futures contract: A futures contract on a 20 year Treasury bond with 8% coupon and 100,000 face value is available. The current futures price is $97 / $100 face value. Analysts have computed the duration of the bond to be 9.5 years

  42. Lecture Summary • What are Forward and Future contracts • Three types of prices: • Spot • Forward/Future • Delivery • Payoffs of Forwards/Futures • Hedging with Forwards/Futures • Micro Hedge • Macro Hedge

  43. Appendix • Valuing a forward/futures • Forward/Futures Payoff Graphs • Difficulties with Forward/Futures Hedging • Basis risk

  44. Contract Value

  45. Example: Forward/Future Value ONLY CONSIDER THE FORWARD/FUTURE CONTRACT: On June 20, 2010, JP Morgan entered the forward contract to buy a 10-year Treasury with $1000 face value for $890 on March 23, 2012. Forward/Future & Spot Prices For example: Oct 8, 2010 Forward/Future Price (March 2012 contract) $941 Sell -$890 Delivery Price Buy $51 Locked–in a sure CF = $51 Spot price S0 Value = PV(51) =$47.73 Because this is sure CF we can discount at the risk free rate

  46. Example: Forward/Future Value ONLY CONSIDER THE FORWARD/FUTURE CONTRACT: On June 20, 2010, JP Morgan entered the forward contract to buy a 10-year Treasury with $1000 face value for $890 on March 23, 2012. Take Away: • The forward price will continue to change after you enter the forward contract. This will cause the value of your contract to change over time. • At any point in time the value of the forward/futures contract is the present value of the difference between the delivery price and the price that you can close out your contract for.

  47. Payoff Graphs

  48. Long & Short Positions Underlying Asset: • Long: you own the asset • Short: you owe the asset Forward Contract • Long:you have agreed to buy the asset in the future at a pre- specified price (locked-in a price to buy) • Short: you have agreed to sell the asset in the future at a pre- specified price (locked-in a price to sell) Example: Stock → If you are long the stock you own it Example: Stock → If you are short the stock you have borrowed # shares from a dealer and sold them. So, you owe # shares back to the dealer

  49. Underlying Asset Long Payoff Graphs Long One Treasury Bond Payoff For one share If you sell one Treasury bond the Payoff is $550 $550 Payoff This gives us all the possible payoffs for one Treasury Bond Example: suppose the price of a Treasury bond is $550 All possible spot prices for the Treasury Bond Spot Price $550 Spot Price

  50. Underlying Asset Short Payoff Graphs Short One Treasury Bond Payoff Spot Price $425 Example: suppose the price of a Treasury bond is $425 Payoff - $425 You will have to pay $425 to buy one Treasury bond

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