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. 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:
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
They could take the coffee and sell it right away in the market for an immediate profit of $0.70
$2.75/lb
$2.75/lb
Contract payoff
$0.88
-$0.88/lb
$1.87/lb
1.87/lb
The price that the coffee buyer locks-in is the delivery price
$1.87/lb
Just an agreement – no exchange of money

4. Introduction to Forwards & Futures

5. Forward/Future Contract A Primer
Differences between Forwards and Futures
Forward contracts are custom
Futures contracts are standard
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
More exposed to counterparty default risk
Every day the change in the value of the forward contract is added or subtracted from the investors account
Exchange guarantees performance (there is much less counter party default risk)
Almost always delivered
Almost never delivered
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 a 10-year Treasury
Current Market Price of Ford Stock
Current Market Price of Coffee
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 Setup Spot 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.
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.
Spot Prices
Bonds are expensive
Uncertainty
Is JP Morgan exposed to risk?
Setup
Price of 10-year Treasury
Main Point – Spot prices vary through time
Bonds are cheap
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

10. Example: Spot Price Spot 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.
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.
Spot Prices
JP Morgan needs to sell a bond for 900 on March
$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 How? 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.
Spot price S0
Price of the bond
At any point in time I can enter a forward/futures contract at the forward/futures price

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.
Obligated to buy at $938
Delivery Price
$938
Forward/Future Price is a
function of the spot price.
Forward/Future & Spot Prices
$975
$975
$938
Delivery Price !!!
$880
$880
Spot price S0
Price of the bond
We know that we can enter a forward/future at any time at the forward/futures price. This locks-in the future buy price

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
Enter forward contract to buy a T-Note at the delivery price
$890
$10
We have the spot price – that is our source of uncertainty. We are exposed to risk because we have agreed to sell a bond in the future for $900 and we do not know what the price of that bond will be in the future
To hedge the risk we can enter a forward contract – so lets look a the forward price
The current delivery price is $890, which means we can lock-in a price to buy the bond in future for $890
This locks in a small profit of $10 for sure at maturity
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
Forward/Future Price
(March 2012 contract)
If the contract is financial (cash) settled, what does JP Morgan receive at maturity?
$933
Immediately sell in the market at the current spot price (also the forward price)
- $890
Delivery Price
Buy at the delivery price
The way I want you to think about it is like this: we are going to buy the contract at the forward price because that is what we agreed to do. Then we will immediately sell the bond in the market the current market price. The gain or loss on that transaction is the payoff of the forward contract.
Now is this what actually happens? Do you go through these transactions? NO but this is just a way to think about it.
Payoff
$43

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
The way I want you to think about it is like this: we are going to buy the contract at the forward price because that is what we agreed to do. Then we will immediately sell the bond in the market the current market price. The gain or loss on that transaction is the payoff of the forward contract.
Now is this what actually happens? Do you go through these transactions? NO but this is just a way to think about it.
Payoff
$43
$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: Forward Contract
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
Basic Idea
Find the position in the underlying asset
Take the opposite position in the futures
LONG vs. SHORT – underlying
LONG: Better off (happy) when the price goes up
SHORT: Better off (happy) when the price goes down
Investors
T-Bill
Underlying
Investors have some obligation that exposes them to risk (price fluctuations) ie. their position in the underlying asset (Long or Short).
They want to offset this exposure this exposure by taking the opposite position in the forward contract. This locks in a payment in the future

29. 1. Finding the Hedging Position
Current Time (t=0)
Future Time Period
Underlying Position
Investors
Long
Underlying
Forward/Futures Position
T-Bill
Short
Hedged Position
Are you long or short the T-Bill?
Do go long or short the forward?

30. 1. Finding the Hedging Position
Current Time (t=0)
Future Time Period
Underlying Position
Investors
Long
Underlying
Forward/Futures Position
T-Bill
Short
The object of hedging is to eliminate risk – ie. lock in a future value. That value does not have to be the same as the present value!!!!!
Hedged Position

31. 1. Finding the Hedging Position
Current Time (t=0)
Future Time Period
Underlying Position
Investors
Long
Underlying
Forward/Futures Position
T-Bill
Short
Hedged Position
Goldman Sachs wants to hedge $5M of corporate bonds on its balance sheet.

32. 1. Finding the Hedging Position
Current Time (t=0)
Future Time Period
Underlying Position
Investors
Underlying
Long
Forward/Futures Position
T-Bill
Short
Hedged Position
Goldman Sachs agrees to deliver $5M of corporate bonds in six months – payment on delivery?

33. 1. Finding the Hedging Position
Current Time (t=0)
Future Time Period
Underlying Position
Investors
Underlying
Short
Forward/Futures Position
Long
Hedged Position
Exxon will deliver 5M barrels of oil in 6 months for $55/barrel.

34. 1. Finding the Hedging Position
Current Time (t=0)
Future Time Period
Underlying Position
Investors
Underlying
Long
Forward/Futures Position
Short
Hedged Position
A corn farmer will sell 50M bushels of corn at market price in 3 months.

35. 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

36. 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

37. 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

38. 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
Value an asset
Payoff on Forward/Futures
Forward Payoff
Hedged portfolio
Sum to get hedged payoff

39. Example: Hedging with Forwards/Futures
A hedge fund currently holds 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.
Total face value held by the hedge fund
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?
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

40. Example: Hedging with Forwards/Futures
A hedge fund currently holds 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 = $905
Bond Price = $1,050
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
Why cant the hedge fund just walk away from the forward when the price of the bon goes up to $1,050
Forward Payoff
Buy a bond in the market:
-$905(1,000) = - $905,000
Buy a bond in the market:
-$1,050(1,000) = - $1,050,000
Forward Payoff $90,000
Forward Payoff $55,000
Hedged Portfolio
$994,000
$995,000
$995,000

41. Example: Hedging with Forwards/Futures
A hedge fund currently holds 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 = $905
Bond Price = $1,050
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
Why cant the hedge fund just walk away from the forward when the price of the bon goes up to $1,050
Forward Payoff
Buy a bond in the market:
-$905(1,000) = - $905,000
Buy a bond in the market:
-$1,050(1,000) = - $1,050,000
Forward Payoff $90,000
Forward Payoff $55,000
Hedged Portfolio
$994,000
$995,000
$995,000
These are the transactions you would have to execute if the contract was physically settled – For financially, settled you just think through these transactions to get to the payoff

42. 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.

43. 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

44. 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
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

45. 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
If interest rates change – how much will I gain or lose in equity capital

46. 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
What position (futures price × total face value) in the futures contract will offset the gain/loss in equity
S&P500 shares, bushels of corn, barrels of oil …

47. Macrohedge (continued)
Step #3 Find the Number of Contracts:
How many contracts do we need to enter (long/short) to get this position

48. 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 position in futures contracts
(futures price × total face value)
Total position per contract

49. 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
Assets
Liabilities
A=$100 mill
L = $90 mill
E = $10 mill
$100 mill

50. 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

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

52. Contract Value

53. 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
Because this is sure CF we can discount at the risk free rate
Value = PV(51)
=$47.73
Spot price S0

54. 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.

55. Payoff Graphs

56. Long & Short Positions Underlying Asset: Forward Contract
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

57. Underlying Asset Long Payoff Graphs
Long One Treasury Bond Payoff
For one share
If you sell one Treasury bond the Payoff is $550
Payoff
$550
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

58. 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

59. Long Forward Payoff Graphs
Long Treasury Bond Forward Payoff
If the price of the bond is $280, then you must buy it using the forward for $900 and sell it in the market for $ payoff = = -620
If the price of the bond is $900, then you can buy it using the forward for $900 and sell it in the market for $ payoff = 0
480
Payoff =500
If the price of the bond is $1,380, then you can buy it using the forward for $900 and sell it in the market for $1, payoff = 1, = 480
-620
Even if the price of the bond is zero you have still agreed to pay $900 for it

60. Short Forward Payoff Graphs
Short Treasury Bond Forward Payoff
If the price of the bond is $1,380, then you can buy it in the market for $1,380 and sell it at the delivery price of payoff = 900-1,380 = -480
620
If the price of the bond is $280, then you can buy it in the market for $280 and sell it using the forward for payoff = = 620
Payoff = -480
-480

61. Payoff Graphs Underlying Asset: Forward Contract: Short Long Long
Delivery Price

62. Difficulties Hedging with Futures Contracts

63. Difficulties with Futures Hedge
Basis Risk: the risk that the gains/losses on the forward position do not exactly match the gains/losses on the underlying economic position over time
Example:
Suppose you are a farmer in the heartland of America
Your crop of choice is white corn (you think it makes you stand out)
You routinely use forward contracts to hedge against unexpected price movements.
You will have 5,000 bushels of corn to sell in September
Forward contract
You have entered into the September contract to sell 5000 bushels of yellow corn for $6.78/bushel. (6.78 x 5000 = $33,900)
The fact that the contract is on yellow corn dose not concern you because the prices have always been very similar

64. Difficulties with hedging
In September there is a large shock to the demand for white corn in the global market. International producers divert excess supply to the US driving the price of white corn down to $5/bushel
Surprisingly, the price of yellow corn is unaffected and still sells for $6.50 / bushel
Calculate the unexpected gain or loss on your position
With the forward contract you would have expected to be able to sell white corn for $6.78/bushel but the actual sale price was $5
loss = $5.00(5,000)-$6.78(5,000) = -$8,900
But you have the futures contract:
Buy 5000 bushels of yellow corn in the market = ($6.50/bushel)(5000) = - 32,500
Sell 5000 bushels of yellow corn using the forward = + ($6.78/bushel)(5000) = +33,900
The gains from the forward position do not cover the economic losses
+1,400

65. Routine vs. Selective Hedging
Question: why would a manager choose to perform a selective hedge instead of a routine hedge?
Answer: In finance, there is always a risk vs. return tradeoff!
As managers reduce the FI’s risk by hedging positions, they also decrease the expected return on their investments.
This also reduces the expected return to shareholders
Therefore, routine hedging usually occurs when interest rates are extremely unpredictable

66. Lecture Summary
We talked about how banks can hedge some or all of their interest rate risk exposure using Forward/Futures contracts
Forwards/Futures
Introduction
Prices: Forward/Future, Spot, and Delivery
Payoffs vs Value
Payoff Graphs
Microhedge with Forward/Future contracts
Macrohedge with Forward/Futures contracts
Basis Risk – difficulties with Forward/Future hedge