Hedging Interest Rate Risk Treasury/Eurodollar Futures.

Hedging Interest Rate RiskHedging Interest Rate Risk

Treasury/Eurodollar FuturesTreasury/Eurodollar Futures

Derivative SecuritiesDerivative Securities

Stocks and Bonds represent claims to specific Stocks and Bonds represent claims to specific future cash flowsfuture cash flows

Derivative securities on the other hand represent Derivative securities on the other hand represent contracts that designate future transactionscontracts that designate future transactions

Currently, there are approximately 300 million Currently, there are approximately 300 million derivative contracts outstanding with a market derivative contracts outstanding with a market value of around $50 Trillionvalue of around $50 Trillion

While equity trading is centered in New York While equity trading is centered in New York (NYSE, NASDAQ), derivative markets are (NYSE, NASDAQ), derivative markets are centered in Chicago (CME, CBOT, CBOE)centered in Chicago (CME, CBOT, CBOE)

Futures ContractsFutures ContractsA futures contract describes a transaction (Commodity, Price, and Quantity) that will be made in the future.

In “Trading Places” (1983), Eddie Murphy and Dan Ackroyd were trading Orange Juice Futures

Futures ContractsFutures ContractsOrange Juice futures (FCOJ) are traded on the NYBOT (New York Board of Trade)

Exp Open High Low Settle Change Interest

MARMAR 85.7585.75 86.0086.00 84.2084.20 85.2085.20 -1.25-1.25 18,84918,849

MAYMAY 88.2088.20 88.4088.40 86.6086.60 87.7087.70 -1.20-1.20 14,35414,354

JULJUL 88.5088.50 88.5088.50 87.6087.60 88.4588.45 -1.15-1.15 1,8891,889

NOVNOV 91.5091.50 91.5091.50 90.0090.00 89.9589.95 -1.65-1.65 905905

Contract = 15,000 Lbs. ; Price = cents/lb

Every contract must have two participants (Long = Buy, Short = Sell)

Now Mar Apr JuneMay July Aug

Exp Open High Low Settle Change Interest

MARMAR 85.7585.75 86.0086.00 84.2084.20 85.2085.20 -1.25-1.25 18,84918,849

MAYMAY 88.2088.20 88.4088.40 86.6086.60 87.7087.70 -1.20-1.20 14,35414,354

JULJUL 88.5088.50 88.5088.50 87.6087.60 88.4588.45 -1.15-1.15 1,8891,889

NOVNOV 91.5091.50 91.5091.50 90.0090.00 89.9589.95 -1.65-1.65 905905

A long position in MAR FCOJ would require you to purchase FCOJ in March

A short position in JUL FCOJ would require you to deliver FCOJ in March

Dealers pass orders along to the pit traders who create a contract.

Long Short

3 May Contracts (15k * 3 = 45k lbs.) @ 88 cents/lb.

The contracts are then passed along to the exchange who will become the middleman

Short (3 contracts) Long (3 contracts)

Long (3 Contracts) Short (3 Contracts)

Note: the exchange is holding two contracts with a zero net position

Contract Completion (FCOJ)Contract Completion (FCOJ)

May 1 May 8 May 10 May 31May 23

First Notice Date

First Delivery Date

Last Trading Day

Last Notice Date

Last Delivery Date

Contract CompletionContract Completion


Suppose that, on May 3, the short position decides that he wants out of the contract. The current May futures price is .92 per Lb

3 Contracts (Short) @ .88/LB

He could take a long position on 3 May contracts at a price of .92/LB

This would effectively “cancel out” the previous position at a loss of 3 cents/LB

.03*45,000 = $1,350 Loss

Contract CompletionContract Completion


Suppose that, on May 12, the short position opts for delivery of the commodity. The current spot price is .84 per Lb

3 Contracts (Short) @ .88/LB 3 Contracts

(Long) @ .88/LB

The Exchange Pairs up Longs with Shorts

Profit = (.88-.84)*45,000

= $1,800

Loss = (.88-.84)*45,000 = $1,800

Types of FuturesTypes of Futures

Currencies Agriculture Metals & Energy

Financial

British PoundBritish Pound LumberLumber Copper Copper TreasuriesTreasuries

EuroEuro MilkMilk GoldGold LIBORLIBOR

Japanese YenJapanese Yen CocoaCocoa SilverSilver Municipal IndexMunicipal Index

Canadian DollarCanadian Dollar CoffeeCoffee PlatinumPlatinum S&P 500S&P 500

Mexican PesoMexican Peso Sugar Sugar OilOil DJIADJIA

CottonCotton Natural GasNatural Gas NikkeiNikkei

WheatWheat EurodollarEurodollar

CattleCattle

SoybeansSoybeans

Stock Index FuturesStock Index Futures

Stock Index Futures have no underlying Stock Index Futures have no underlying commoditycommodityS&P 500S&P 500NYSE CompositeNYSE Composite Value Line IndexValue Line Index

These contracts are settled on a cash basis:

Short Position Profits = (F – S)*500

Long Position Profits = (S – F)*500

F = Futures Price, S = Current Spot Price

Regardless, futures positions are making Regardless, futures positions are making “bets” on the price of the underlying “bets” on the price of the underlying commodity. commodity.

Long Position

Short Position

Profits from price increases

Profits from price decreases

Treasury FuturesTreasury Futures

Treasury futures first began trading on the CME in 1976. The underlying commodity is a Treasury Bill, Note, or Bond. Remember, when interest rates rise, Treasury prices fall!

Long Position

Short Position

Profits from price increases


Profits from decreasing interest rates

Profits from increasing interest rates

T-Bill FuturesT-Bill Futures

With T-Bill Futures, the commodity is a $1M Treasury Bill with 3 months left until maturity

Contracts exist for February, March, April, June, September, and December delivery

Nov 16, 2004 Feb 14 Feb 18

First Trading Day

Last Trading Day (T-Bill Auction)

Delivery Day

T-Bill Yields T-Bill Yields We have already calculated the Yield to Maturity for 90 Day Treasury Bills

YTM = Face Value - Price

Price365 t

Annualized

Often, the yield referred to for Treasury Bills is the discount yield

DY = Face Value - Price

Face Value

360 t

Interest As a percentage of Face Value rather than Price

Annualized with a 360 day year

Days left until maturity

*100

*100

Pricing T-Bill FuturesPricing T-Bill Futures

T-Bill futures are listed using the IMM (International Monetary Market) Index

IMM = 100 – Discount Yield

For example, if the Price of a $100, 90 Day Treasury were $98.

DY = $100 - $98

$10036090

IMM = 100 – 8 = 92

*100 = 8%

Every .005 increase in the IMM raises the value of a long T-Bill position by $12.50 ($25 per basis point).

EurodollarEurodollar

The term The term Eurodollar refers to deposits refers to deposits denominated in a currency other than the denominated in a currency other than the bank’s home currency bank’s home currency European banks offer Eurodollar time European banks offer Eurodollar time

deposits (terms can range from overnight to deposits (terms can range from overnight to several years)several years)

European banks will lend dollar reserves to European banks will lend dollar reserves to each other at the LIBOR rate (London Inter-each other at the LIBOR rate (London Inter-bank Offering Rate)bank Offering Rate)

Eurodollar Futures (1981)Eurodollar Futures (1981)

The underlying commodity is a $1M 3 month Eurodollar The underlying commodity is a $1M 3 month Eurodollar time deposit. However, these deposits are not time deposit. However, these deposits are not marketable. Therefore, Eurodollar futures are settled on marketable. Therefore, Eurodollar futures are settled on a cash basisa cash basis

Eurodollar futures can be treated like a T-Bill FutureEurodollar futures can be treated like a T-Bill Future

IMM = 100 – LIBOR

Every .005 increase in the IMM raises the value of the long position by $12.50. ($25 per basis point)

Eurodollar Futures vs. T-Bill Eurodollar Futures vs. T-Bill FuturesFutures

T-Bill FuturesT-Bill Futures Eurodollar Eurodollar FuturesFutures

Volume (2001)Volume (2001) 123123

($123M)($123M)

730,000730,000

($730B)($730B)

•As the Eurodollar market grew, it became more liquid relative to the T-Bill market

•LIBOR is a “risky” rate. Therefore, it correlates better with other risks

Pricing T-Bill/Eurodollar FuturesPricing T-Bill/Eurodollar Futures

Suppose that a march Eurodollar future (expires in 47 days) was currently selling for 94.555

Term Yield

1 Month1 Month 5.18%5.18%

3 Months3 Months 5.31255.3125

6 Months 6 Months 5.64385.6438

1 Year1 Year 5.81635.8163

We also have the current money rates (LIBOR)

IMM = 100 - LIBOR

This contract is paying an annualized (yield) of 100 – 94.555 = 5.445%

Now Day 47

Purchase/Sale of Eurodollar Future

Day 137

90 Days

Delivery of a $1M 90Day Eurodollar account

The Eurodollar Future currently has an annual yield of 5.445%

$1M (1.013613) = $1,013,613

5.4454

= 1.3613%

Receipt of $1,013,613

Term Yield




1 Year1 Year 5.81635.8163

Term Yield




1 Year1 Year 5.81635.8163

Term

Yield

1 Month 3 Months

5.18%

5.3125%

47 Days

5.2175%

Use a linear interpolation to get the 47 day spot rate

5.2175%47

360 = .6811%

47 Day Return

Term Yield




1 Year1 Year 5.81635.8163

Term

Yield

3 Months 6 Months

5.3125%

5.6438%

137 Days

5.4855%

Use a linear interpolation to get the 137 day spot rate

5.4855%137360 = 2.0875%

137 Day Return

Term Yield

S(47)S(47) .6811%.6811%

S(137)S(137) 2.0875%2.0875%

Now Day 47 Day 137

The Eurodollar Future currently has an annual yield of 5.445%

5.4454

= 1.3613%

S(47) = .6811%

S(137) = 2.0875%

F(47,90)1.0208751.006811 =1.01397 = 1.3970% =

Now Day 47 Day 137

The Eurodollar Future currently has an annual yield of 5.445% (1.3613%)

IMM = 100 – 5.445 = 94.555

The implied no-arbitrage interest rate between 47 and 137 days is 5.588% (1.3970%)

IMM = 100 – 5.588 = 94.412

The interest rate on the futures contract is to low!!

or, alternatively

The price of the futures contract is too high!!!

Borrow at Futures Rate (Sell a Futures contract)

Lend at the implied forward rate

1.013970 – 1.013613 $1M = $357 Profit =

Now Day 47 Day 137

How do you lend at the implied forward rate?

Lend

Borrow

By lending for the entire 137 day period and borrowing for the first 47 days, your net position is as a lender for the last 90 day period!

Now Day 47 Day 137

Go Short on a the futures contract at a price of 94.555

Lend $992,885 for 137 days at the spot rate of 5.4855% (You will be paid $1,013,613 in 137 days)

Borrow $992,885 for 47 days at the spot rate of 5.2175%

Borrow $1,000,000 at the rate established by the futures contract (5.445%)

Pay back the $992,885 Loan + interest ($999,643)

Receive $1,013,613 from the original 137 day loan

Pay $1,013,613 on the 90 day loan

DateDate Cash InCash In Cash OutCash Out

NowNow $992,855$992,855 $992,855$992,855

47 Days $1,000,000 $999,648

137 Days137 Days $1,013,613$1,013,613 $1,013,613$1,013,613

On the 47th day, you get a net cash flow of $352. This is the present value of $357 dollars to be received in 90 Days (you get the profits on day 47 rather than day 137)

The no arbitrage price of a price of a futures contract will reflect the forward rate implied by the yield curve. But remember, the forward rate is the expected future spot rate

Futures Rate = Expected Future Spot Rate

Treasury Note/Bond FuturesTreasury Note/Bond Futures

Contract Underlying Asset

20 Year T-Bond20 Year T-Bond

(FV = $100,000)(FV = $100,000)

15-20 Year T-Bond with 15-20 Year T-Bond with a 6% coupona 6% coupon

10 Year T-Note10 Year T-Note

(FV = $100,000)(FV = $100,000)

6.5 – 10 Year T-Note 6.5 – 10 Year T-Note with a 6% couponwith a 6% coupon


(FV = $100,000)(FV = $100,000)

4.25 – 5 Year T-Note 4.25 – 5 Year T-Note with 6% couponwith 6% coupon


(FV = $200,000)(FV = $200,000)

1.75 – 2 Year T-Note 1.75 – 2 Year T-Note with 6% couponwith 6% coupon

The commodity for T-Note/Bond futures is a Treasury with a 6% annual coupon. What if there are no 6% bonds available?

Treasury Note/Bond futures are based on cheapest to deliver (CTD) basis.

Requirements for Delivery

1. The Face value of the delivered notes must sum to $100,000 (per contract)

2. All the notes must have the same characteristics (term, coupon)

It’s the short position’s option to deliver whatever has the lowest cost

Conversion FactorsConversion Factors

Suppose that you have a short position on a a Treasury bond future that expires this month (any bond with an expiration date between 2020 and 2030 would be acceptable for delivery:

Maturity Coupon Bid Price

May 2020May 2020 8.75%8.75% 149:16149:16

August 2023August 2023 7.25%7.25% 134:21134:21

August 2025 6.875% 132:21

The cheapest to deliver bond will always be the lowest coupon, longest maturity bond

Conversion FactorsConversion Factors

The conversion factors are meant to make all deliverable bonds “equally attractive”

Maturity Coupon Conversion Factor

May 2020May 2020 8.75%8.75% 1.26951.2695

August 2023August 2023 7.25%7.25% 1.13311.1331

August 2025 6.875% 1.1017

Invoice Amount

=Contract Size

Futures Price

Conversion Factor

Accrued Interest

Requirements for Delivery

1. The Face value of the delivered notes must sum to $100,000 (per contract)

2. All the notes must have the same characteristics (term, coupon)

It’s the short position’s option to deliver whatever has the lowest cost

To Find the cheapest to deliver bond/note

-Spot Price

Current Futures Price

Conversion FactorMaximize

Note: This will always be negative

Pricing T-Note/Bond FuturesPricing T-Note/Bond Futures

Now March March 2025

20 Year Treasury Delivered

20 Year Treasury Expires

The Logic behind pricing treasury note/bond futures is the same as with T-Bill futures. The price should reflect expectation of future spot rates. However, note that expectations of future spot rates are already incorporated in bond prices!

Futures Price =

Expected Future Treasury Price

+ (Carry Costs – Carry Return)

Arbitrage Costs

HedgingHedging

$25,000= ++++

(1.05) (1.05) (1.05) (1.05) (1.05)2 3 4 5P = $500,000

Lets return to the 5 year Treasury Note example. Interest rates are currently 5% and are expected to stay at 5% (the yield curve is flat). A 5 year treasury note with $500,000 of face value and a 5% annual coupon.

$25,000 $25,000 $25,000 $525,000

We already calculated the Modified Duration for this bond

MD = 4.3

That is, a 100 basis point increase in the interest rate lowers this bond’s price by (.043)($500,000) = $21,500

Hedging with T-Bill FuturesHedging with T-Bill Futures

Short Position (Futures)



If you are long in bonds, you are worried about rising interest rates (rising interest rates lower the value of your bond). Therefore, you could hedge this risk by holding short positions in T-Bill futures (Short positions make money when interest rates drop)


Short Position (Futures)



A perfect hedge eliminates all your interest rate risk

Change in value of Value of Futures position

= # of Futures Contracts

Change in value of each contract

=

Change in value of bond position

$21,500$2,500

$21,500/$2,500 = 8.6 Contracts





=


$21,500$2,500

$21,500/$2,500 = 8.6 Contracts

Hedge Ratio =

Dollar Duration of Bonds

Dollar Duration of Futures

MD(B)MD(F)=

FV(B)FV(F)

4.3.25

$500K$1M

=

45.35

86.38

123.41

156.71

39.18

0

20

40

60

80

100

120

140

160

1Yr 2Yr 3Yr 4Yr 5Yr

Here we have the 5 year Treasury key durations. Note that this bond’s price is most sensitive to the 5 Year spot rate. The future’s value is based on the 90 day treasury rate

X 100

One Problem…..




=


$21,500$2,500

$21,500/$2,500 = 8.6 Contracts

We assumed that the 90 Day T-Bill rate and the 5 Year Rate were perfectly correlated. Suppose, instead, that we have

Change in 5 Year Rate = (.5)

Change in 90 Day Treasury Rate

The hedge ratio drops to 4.3!

Hedging with T-Note/Bond FuturesHedging with T-Note/Bond Futures

The strategy would be the same. If you are The strategy would be the same. If you are worried about increasing interest rates, take a worried about increasing interest rates, take a short position in futures contracts. The hedge short position in futures contracts. The hedge ratio for T-Note/Bond futures depends onratio for T-Note/Bond futures depends on Size of bond position relative to the size of a futures Size of bond position relative to the size of a futures

contractcontract Duration of your bond position relative to the duration Duration of your bond position relative to the duration

of the underlying asset in the futures contractof the underlying asset in the futures contract Correlation between the interest rate affecting your Correlation between the interest rate affecting your

bond portfolio and the interest rate influencing the bond portfolio and the interest rate influencing the futures pricefutures price

Impact of interest rate on CTD bondImpact of interest rate on CTD bond

Hedging Interest Rate Risk Treasury/Eurodollar Futures.

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Transcript of Hedging Interest Rate Risk Treasury/Eurodollar Futures.