Hedging with Forward/Futures contracts

Transcript Hedging with Forward/Futures contracts

HEDGING WITH FORWARD/ 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  Payoff of Forward/Future contract    Hedging with Forwards/Futures Micro Hedge Macro Hedge

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

$2.75/lb Contract payoff $0.88

$1.87/lb Just an agreement – no exchange of money 1.87/lb $2.75/lb -$0.88/lb $1.87/lb The price that the coffee buyer locks-in is the

delivery price

Introduction to Forwards & Futures

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 Forwards settled at maturity More exposed to counterparty default risk Almost always delivered 1.

Trade on exchanges Futures are marked-to-market Exchange guarantees performance (there is much less counter party default risk) Almost never delivered Every day the change in the value of

Economic Hedgers Speculators

subtracted from the investors account

Forward/ Future Price, Spot Price & Delivery Price

Prices You Need to Keep Straight



Spot Price (S 0 ):

Price of the underlying asset (coffee)

S 0

 Note: this is for the special case where the

Forward/Futures Price (F t ):

enter a forward contract –

varies over time!

underlying asset does not make payments The current price at which you can not work for coupon bonds dividend paying stocks …

F t



S o

( 1 

) (



)

k F t = future price ; S 0 = underlying spot price k = compounding periods per year; r = risk-free rate; (T-t) = number of years to delivery



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)

Spot Price

Example: Spot 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.

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

Price of 10 year Treasury Is JP Morgan

Setup

On June 20, 2010 JP Morgan agrees to sell a Treasury Bond for $900 on March 23, 2012

Bonds are cheap

On March 23, 2012 JP Morgan needs to deliver a 10-year Treasury Note

Example: Spot 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.

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 23 2012 $900 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

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?

Forward/Future Price

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.

F t



S o

( 1 

) (



)

Spot price S 0 Price of the bond At any point in time I can enter a forward/futures contract at the forward/futures price

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

Delivery Price

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 Price is a function of the spot price.

F t



S o

( 1 

) (



)

Delivery Price

Forward/Future & Spot Prices

$975 $975 $938 Delivery Price !!!

$880 $880 Spot price S 0 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

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

Hedging with a Forward Basic Idea

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.

F t



S o

( 1 

) (



)

Agreed to sell T note for $900 Enter forward contract to buy a T-Note at the

delivery price

$900 -$890 $10 $890 Spot price S 0 Price of the bond

Forward/Futures

Payoff

Payoff of a forward/futures contract



Payoff

– Refers to the cash flow that occurs at maturity for a contract with cash settlement.

Example: Forward/Future Payoff

22 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 Price (March 2012 contract)

F t



S o

( 1 

) (



)

Forward/Future & Spot Prices

If the contract is financial (cash) settled, what does JP Morgan receive at maturity?

Payoff Delivery Price 1.

Buy at the delivery price Immediately sell in the market at the current spot price (also the forward price) $933 - $890 $43

Example: Forward/Future Payoff

23 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)

F t



S o

( 1 

) (



)

Payoff Delivery Price $933 - $890 $43 $43

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 – F D ) - long position Payoff = (F D – 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?

Hedging with Forward/Futures Contracts

Hedging

Find the hedging position long or short forward

Find the number of contracts

Show that the position is hedged

Long & Short Positions

Underlying Asset:



Long:

you

own

the asset Example: Stock → If you are long the stock you own it 

Short:

you

owe

the asset 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

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

)

1. Finding the Hedging Position

Investors Underlying T-Bill

Basic Idea

1. Find the position in the underlying asset 2. Take the opposite position in the futures

3. LONG vs. SHORT – underlying

• LONG: Better off (happy) when the price goes up • SHORT: Better off (happy) when the price goes down • 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

1. Finding the Hedging Position

Current Time (t=0) Future Time Period

Investors

Underlying Position Long

Underlying T-Bill

Forward/Futures Position Short Hedged Position

1. Finding the Hedging Position

Current Time (t=0) Future Time Period

Investors

Underlying Position Long

Underlying T-Bill 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!!!!!

Forward/Futures Position Short Hedged Position

1. Finding the Hedging Position

Current Time (t=0) Future Time Period

Investors

Underlying Position Long

Underlying T-Bill

Forward/Futures Position Short Hedged Position

Goldman Sachs wants to hedge $5M of corporate bonds on its balance sheet.

1. Finding the Hedging Position

Current Time (t=0) Future Time Period

Investors

Underlying Position Long

Underlying T-Bill

Forward/Futures Position Short Hedged Position

Goldman Sachs agrees to deliver $5M of corporate bonds in six months – payment on delivery?

1. Finding the Hedging Position

Current Time (t=0) Future Time Period

Investors

Underlying Position Short

Underlying

Forward/Futures Position Long Hedged Position

Exxon will deliver 5M barrels of oil in 6 months for $55/barrel.

1. Finding the Hedging Position

Current Time (t=0) Future Time Period

Investors

Underlying Position Long

Underlying

Forward/Futures Position Short Hedged Position

A corn farmer will sell 50M bushels of corn at market price in 3 months.

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 2.

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

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

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

 5 , 000 , 000 100 , 000  50

contracts

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 Underlying position Value an asset Scenario 1 price t = 6 months Scenario 2 price Value an asset Value an asset Forward Payoff Hedged portfolio Payoff on Forward/Futures Sum to get hedged payoff Payoff on Forward/Futures Sum to get hedged payoff Payoff on Forward/Futures Sum to get hedged payoff

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.

a) b) 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

 ( 1 , 000

bonds

)($ 1 , 000 )  $ 1 , 000 , 000

Number of Contracts

 $ 1 , 000 , 000  10

contracts

100 , 000 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

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.

a) b) How many contracts do they need?

months.

$ 99 .

5 $ 100  $ 0 .

995

per dollar of face value

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 Forward Payoff Futures contracts =

$0.00

forward/future cost nothing at inception Sell 1M face value at the forward price $0.995(1,000,000) =

$995,000

Buy a bond in the market:

$905(1,000)

= - $905,000 Forward Payoff $90,000

Sell 1M face value at the forward price $0.995(1,000,000) =

$995,000

Buy a bond in the market:

$1,050(1,000)

= - $1,050,000 Forward Payoff - $55,000

Hedged Portfolio $994,000 $995,000 $995,000

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.

a) b) 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 Bond Price = $905 t = 3m 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 Forward Payoff Futures contracts =

$0.00

forward/future cost nothing at inception Sell 1M face value at the forward price $0.995(1,000,000) =

$995,000

Buy a bond in the market:

$905(1,000)

= - $905,000 Forward Payoff $90,000

Sell 1M face value at the forward price $0.995(1,000,000) =

$995,000

Buy a bond in the market:

$1,050(1,000)

= - $1,050,000 Forward Payoff - $55,000

Hedged $994,000 $995,000 $995,000 Portfolio 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

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.

Types of Hedging Strategies

43 1.

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

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 3 months Forward Contract on a10 year Treasury .5 1 9 9.5 10 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

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 

  

D A



D L k A

1 



will I gain or lose in equity capital

Hedging with Forwards (Macrohedge)



Step #2

Find the total forward position needed to hedge the change in equity  We know that D F = D underlying 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

D underlying



D F

 Set the change in equity equal to the negative change in the value of the forward position and solve for

What

position

(

futures price × total face value

) in the futures contract will offset the gain/loss in equity 



D F

1  

R F R

S&P500 shares, bushels of corn, barrels of oil …

Macrohedge (continued)

Step #3

Find the Number of Contracts: How many contracts do we need to enter (long/short) to get this position

Macrohedge (continued)

48 Step #3

Find the Number of Contracts: 

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)



N F Q F P F

Total position per contract

F P Q F N F F

 total    position Future Size of price (per lb) one Number of in futures futures futures contract contract contracts (37,500 lbs of coffee)

N F



F Q F P F

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 A=$100 mill $100 mill Liabilities L = $90 mill E = $10 mill $100 mill

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

Appendix



Valuing a forward/futures



Forward/Futures Payoff Graphs



Difficulties with Forward/Futures Hedging

 Basis risk

Contract Value

Example: Forward/Future Value

53 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 Price

(March 2012 contract)



S o

( 1 

) (



)

Spot price S 0

Forward/Future & Spot Prices

For example: Oct 8, 2010 Value =

PV(51) =$47.73

Sell $941 Delivery Price Locked–in a sure CF = $51 Because this is sure CF we can discount at the risk free rate Buy -$890 $51

Example: Forward/Future Value

54 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.

Payoff Graphs

Long & Short Positions

Underlying Asset:



Long:

you

own

the asset Example: Stock → If you are long the stock you own it 

Short:

you

owe

the asset 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

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

)

Underlying Asset Long Payoff Graphs

Long One Treasury Bond Payoff For one share

$550 If you sell one Treasury bond the Payoff is $550 Example: suppose the price of a Treasury bond is $550 All possible spot prices for the Treasury Bond Spot Price $550 Spot Price

Underlying Asset Short Payoff Graphs

Short One Treasury Bond Payoff

Spot Price $425 Example: suppose the price of a Treasury bond is $425 - $425 You will have to pay $425 to buy one Treasury bond

Long Forward Payoff Graphs

59 Long Treasury Bond Forward Payoff

If the price of the bond is $280, then you must buy market for $280.

480 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 $900.

payoff = 0 Payoff =500 -620 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 $1,380.

payoff = 1,380-900 = 480 Even if the price of the bond is zero you have still agreed to pay $900 for it

Short Forward Payoff Graphs

Short Treasury Bond Forward Payoff

620 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 900.

payoff = 900-1,380 = -480 -480 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 900.

payoff = 900 - 280 = 620 Payoff = -480

Payoff Graphs

Underlying Asset: Long Short Forward Contract: Long Delivery Price Short

Difficulties Hedging with Futures Contracts

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 http://www.cmegroup.com

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

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

Routine vs. Selective Hedging

65 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

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