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Hedging and Duration Management Hedging and Duration Management with Fixed Income Futureswith Fixed Income Futures

Hedging and Duration Management Hedging and Duration Management with Fixed Income Futureswith Fixed Income Futures

Taipei Interest Rate Futures Conference

November 20, 2003

Nick Ronalds, CFA

Senior Vice President

ABN AMRO Incorporated

Taipei Interest Rate Futures Conference

November 20, 2003

Nick Ronalds, CFA

Senior Vice President

ABN AMRO Incorporated

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““The revolutionary idea that defines The revolutionary idea that defines the boundary between modern times the boundary between modern times and the past is the mastery of risk.”and the past is the mastery of risk.”

““The revolutionary idea that defines The revolutionary idea that defines the boundary between modern times the boundary between modern times and the past is the mastery of risk.”and the past is the mastery of risk.”

Peter Bernstein, Against the Gods.Peter Bernstein, Against the Gods.

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Comments by Tony Latter, Deputy Chief Comments by Tony Latter, Deputy Chief Executive, Hong Kong Monetary AuthorityExecutive, Hong Kong Monetary AuthorityComments by Tony Latter, Deputy Chief Comments by Tony Latter, Deputy Chief Executive, Hong Kong Monetary AuthorityExecutive, Hong Kong Monetary Authority

Derivatives have brought substantial benefits to the commercial community, in facilitating hedging and hence business planning more generally, and have enabled the financial institutions to offer a progressively wider range of services and greater efficiency in the intermediation process, as well as to exploit market imperfections and other trading opportunities for their own gain.

Derivatives have brought substantial benefits to the commercial community, in facilitating hedging and hence business planning more generally, and have enabled the financial institutions to offer a progressively wider range of services and greater efficiency in the intermediation process, as well as to exploit market imperfections and other trading opportunities for their own gain.

November 5, 2001, Hong Kong

See http://www.info.gov.hk/hkma/eng/speeches/speechs/tony/20011106.htm for complete text of his comments.

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““The hardest thing to convey to a The hardest thing to convey to a controller is that if you’re doing controller is that if you’re doing nothing, you’re speculating.”nothing, you’re speculating.”

Christine Snouffer, Treasury Risk Manager, Christine Snouffer, Treasury Risk Manager, Fellowes CorpFellowes Corp..

““The hardest thing to convey to a The hardest thing to convey to a controller is that if you’re doing controller is that if you’re doing nothing, you’re speculating.”nothing, you’re speculating.”

Christine Snouffer, Treasury Risk Manager, Christine Snouffer, Treasury Risk Manager, Fellowes CorpFellowes Corp..

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Advantages of FuturesAdvantages of FuturesAdvantages of FuturesAdvantages of Futures

Low transactions costs– Transaction costs can be as little as 5% of cash

market for comparable exposure.

price transparencyPositions can be offsetSystem financial integrityOff-balance sheet items.“Level playing field” for all participants

Low transactions costs– Transaction costs can be as little as 5% of cash

market for comparable exposure.

price transparencyPositions can be offsetSystem financial integrityOff-balance sheet items.“Level playing field” for all participants

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ABN AMRO FuturesABN AMRO FuturesABN AMRO FuturesABN AMRO Futures

Global Capabilities - Local presence and Expertise

Full product range including: Interest rates, equity indices, energy, metals, grains, softs as well as O-T-C metals and energy products.

Membership on all major futures exchanges around the world

Global Capabilities - Local presence and Expertise

Full product range including: Interest rates, equity indices, energy, metals, grains, softs as well as O-T-C metals and energy products.

Membership on all major futures exchanges around the world

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ABN AMRO FuturesABN AMRO FuturesABN AMRO FuturesABN AMRO Futures

450 Futures professionals in nine offices (Paris, London, New York, Chicago, Singapore, Sydney, Hong Kong, Tokyo and Seoul)

Expect to clear and/or executed 350 Million contracts in 2003.

Backed by the resources of ABN AMRO Bank. (Group capital of 31.1 euros)

450 Futures professionals in nine offices (Paris, London, New York, Chicago, Singapore, Sydney, Hong Kong, Tokyo and Seoul)

Expect to clear and/or executed 350 Million contracts in 2003.

Backed by the resources of ABN AMRO Bank. (Group capital of 31.1 euros)

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Key Areas of Futures ExpertiseKey Areas of Futures ExpertiseKey Areas of Futures ExpertiseKey Areas of Futures Expertise

Open Outcry Execution in Fixed Income Derivatives including: Eurodollar, Treasury Bond & Note futures.

Open outcry and electronic execution of all major U.S. and non-U.S. equity index and fixed income futures.

Client-focused access to global futures markets, including our 24-hour desk, access to our local specialists around the world, and electronic execution where available.

Options Strategies Electronic Delivery of Client Trade and Clearing Data

Open Outcry Execution in Fixed Income Derivatives including: Eurodollar, Treasury Bond & Note futures.

Open outcry and electronic execution of all major U.S. and non-U.S. equity index and fixed income futures.

Client-focused access to global futures markets, including our 24-hour desk, access to our local specialists around the world, and electronic execution where available.

Options Strategies Electronic Delivery of Client Trade and Clearing Data

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ABN AMRO Futures - HighlightsABN AMRO Futures - HighlightsABN AMRO Futures - HighlightsABN AMRO Futures - HighlightsA range of electronic Order Entry Solutions suited to

client needs.Global Capabilities - Local presence and expertiseNumber one in Execution Volume for CME

Eurodollar Futures & OptionsNo. 2 overall in CME execution volume in 2002,

including interest rates and equity futures.Top Five in Execution Volume in CBOT Treasury

Futures& options

A range of electronic Order Entry Solutions suited to client needs.

Global Capabilities - Local presence and expertiseNumber one in Execution Volume for CME

Eurodollar Futures & OptionsNo. 2 overall in CME execution volume in 2002,

including interest rates and equity futures.Top Five in Execution Volume in CBOT Treasury

Futures& options

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World Futures VolumeWorld Futures VolumeWorld Futures VolumeWorld Futures Volume

2001 2002 % Change

Interest Rate 1,034,117,052 1,153,992,720 11.6%

Equity Indexes 331,803,291 527,282,311 58.9%

Futures on Individual Equities 14,738,302 32,525,250 120.7%

Ag Commodities 121,547,657 127,261,926 4.7%

Energy Products 151,108,996 185,299,608 22.6%

Foreign Currency/Index 44,822,428 43,395,379 -3.2%

Precious Metals 36,466,402 48,463,665 32.9%

NonPrecious Metals 66,908,376 73,226,592 9.4%

Other 723,233 779,160 7.7%- -

TOTAL 1,802,235,737 2,192,226,611 21.6%

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World Options on FuturesWorld Options on FuturesWorld Options on FuturesWorld Options on Futures

2001 2002 % Change

Interest Rate 199,401,871 240,232,920 20.5%

Equity Indexes 1,086,793,263 2,162,146,685 98.9%

(Minus Options on Cash Ind.) (914,576,667) (2,038,690,388) 122.9%

Net Options on Index Futures 172,216,596 123,456,297 -28.3%

Ag Commodities 17,856,874 19,696,268 10.3%

Energy Products 15,786,522 24,075,360 52.5%

Foreign Currency/Index 10,002,110 16,699,883 67.0%

Precious Metals 2,674,987 2,795,885 4.5%

NonPrecious Metals 3,239,581 2,367,540 -26.9%

Other 29,986 17,270 -42.4%

TOTAL 421,208,527 429,341,423 1.9%

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Total World Futures Total World Futures + Options on Futures+ Options on FuturesTotal World Futures Total World Futures + Options on Futures+ Options on Futures

2001 2002 % Change

Interest Rate 1,233,518,923 1,394,225,640 13.0%

Equity Indexes 504,019,887 650,738,608 29.1%

Futures on Individual Equities 14,738,302 32,525,250 120.7%

Ag Commodities 139,404,531 146,958,194 5.4%

Energy Products 166,895,518 209,374,968 25.5%

Foreign Currency/Index 54,824,538 60,095,262 9.6%

Precious Metals 39,141,389 51,259,550 31.0%

NonPrecious Metals 70,147,957 75,594,132 7.8%

Other 753,219 796,430 5.7%

TOTAL 2,223,444,264 2,621,568,034 17.9%

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Global Futures & Options Global Futures & Options by Subgroupby SubgroupGlobal Futures & Options Global Futures & Options by Subgroupby Subgroup

2001 2002

Interest Rate 55.5% 53.2%

Equity Indexes 22.7% 24.8%

Futures on Individual Equities 0.7% 1.2%

Ag Commodities 6.3% 5.6%

Energy Products 7.5% 8.0%

Foreign Currency/Index 2.5% 2.3%

Precious Metals 1.8% 2.0%

NonPrecious Metals 3.2% 2.9%

Other 0.0% 0.0%

TOTAL 100.0% 100.0%

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Part 1Part 1

A Conceptual IntroductionA Conceptual Introduction

Part 1Part 1

A Conceptual IntroductionA Conceptual Introduction

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A Conceptual Introduction To Treasury A Conceptual Introduction To Treasury Futures:Futures:A Conceptual Introduction To Treasury A Conceptual Introduction To Treasury Futures:Futures:

They are highly liquid contracts with low transactions costs.

Treasuries are traded on the Chicago Board of Trade (CBOT). There are March, June, September and December contracts.

They are priced off of a basket of cash Treasury notes or bonds (CBOT).

The Treasuries in the basket can be delivered at expiration of

the futures contract , assuring a strong correlation to the Treasury market.

They are highly liquid contracts with low transactions costs.

Treasuries are traded on the Chicago Board of Trade (CBOT). There are March, June, September and December contracts.

They are priced off of a basket of cash Treasury notes or bonds (CBOT).

The Treasuries in the basket can be delivered at expiration of

the futures contract , assuring a strong correlation to the Treasury market.

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Other Bond FuturesOther Bond FuturesOther Bond FuturesOther Bond Futures

Other sovereign debt futures such as the German Bund contract, for the most part are structured similarly to the U.S. Treasury Futures contracts.

Other sovereign debt futures such as the German Bund contract, for the most part are structured similarly to the U.S. Treasury Futures contracts.

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Treasury Futures Are Used To:Treasury Futures Are Used To:Treasury Futures Are Used To:Treasury Futures Are Used To:

Hedge fixed income securities - Sovereign debt, Treasuries, Corporates, MBS, Agencies, etc.

Create synthetic money market vehicles that can be traded as part of an arbitrage strategy in conjunction with other real or synthetic money market instruments.

Achieve portfolio allocation strategies that unbundled the decision of market exposure from relative value decisions.

Extend or shorten duration. Speculate on the direction of interest rates.

– Remember: doing nothing = speculation

Hedge fixed income securities - Sovereign debt, Treasuries, Corporates, MBS, Agencies, etc.

Create synthetic money market vehicles that can be traded as part of an arbitrage strategy in conjunction with other real or synthetic money market instruments.

Achieve portfolio allocation strategies that unbundled the decision of market exposure from relative value decisions.

Extend or shorten duration. Speculate on the direction of interest rates.

– Remember: doing nothing = speculation

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The Users of Treasury Futures:The Users of Treasury Futures:The Users of Treasury Futures:The Users of Treasury Futures:

Broker/dealers who hedge their fixed income inventories or opt to express interest rate views with futures.

Portfolio managers who may opt to hedge, manage duration, or make preemptive allocation decisions based upon the pattern of funds coming in or leaving the fund. These managers may work for a mutual fund, pension fund, insurance company, bank, or the treasurers department of a corporation.

CTAs and hedge funds who may hedge or speculate on the direction of interest rates.

Broker/dealers who hedge their fixed income inventories or opt to express interest rate views with futures.

Portfolio managers who may opt to hedge, manage duration, or make preemptive allocation decisions based upon the pattern of funds coming in or leaving the fund. These managers may work for a mutual fund, pension fund, insurance company, bank, or the treasurers department of a corporation.

CTAs and hedge funds who may hedge or speculate on the direction of interest rates.

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Treasury Note and Bond Futures Cover 4 Treasury Note and Bond Futures Cover 4 Points on the US Yield Curve. Points on the US Yield Curve. Treasury Note and Bond Futures Cover 4 Treasury Note and Bond Futures Cover 4 Points on the US Yield Curve. Points on the US Yield Curve.

T-BONDS 10-Yr NOTES 5-Yr NOTES 2-Yr NOTES

FACE AMOUNT $ 100,000 $ 100,000 $ 100,000 $ 200,000

MATURITY 15 years + 6-1/2 yearsto 10 years

4-1/6 yearsto 5-1/4 years

1-3/4 yearsto 2 years

PRICING BASIS 6.0 % Coupon 6.0 % Coupon 6.0 % Coupon 6.0 % Coupon

PRICEINCREMENTS

32nds 32nds and1/2 of 32nds

32nds and1/2 of 32nds

32nds and1/4 of 32nds

VALUE OF 1/32nd $ 31.25 $ 31.25 $ 31.25 $ 62.50

Contract Details Include the Following:

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Cash and Futures MarketsCash and Futures MarketsCash and Futures MarketsCash and Futures Markets

Price Notations :The fractional part of the price is denoted in 32nds

i.e. 107-25 = 107 25/32 = 107.78125 in Decimal

and 107-25 107.25 decimal.

Cash market price progression : 107-25, 107-25+, 107-26 …

T-Bond futures price progression : 102-25, 102-26, 102-27 …

10-Year / 5-Year T-Note futures price progression :

104-25, 104-255, 104-26…

2-Year T-Note price progression :103-2500, 103-2525, 103-2550 ...

Price Notations :The fractional part of the price is denoted in 32nds

i.e. 107-25 = 107 25/32 = 107.78125 in Decimal

and 107-25 107.25 decimal.

Cash market price progression : 107-25, 107-25+, 107-26 …

T-Bond futures price progression : 102-25, 102-26, 102-27 …

10-Year / 5-Year T-Note futures price progression :

104-25, 104-255, 104-26…

2-Year T-Note price progression :103-2500, 103-2525, 103-2550 ...

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Review of DurationReview of DurationReview of DurationReview of Duration

Duration tells you by what percentage a bond or bond portfolio will change in price with a 100 bp change in yield.

Duration tells you by what percentage a bond or bond portfolio will change in price with a 100 bp change in yield.

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Treasuries 2-yr Note - 3 5-yr Note - 5 10-yr Note - 9 Bond - 28

Treasuries 2-yr Note - 3 5-yr Note - 5 10-yr Note - 9 Bond - 28

The Number of Different Treasuries The Number of Different Treasuries that May be Delivered into the that May be Delivered into the December 2003 Contracts?December 2003 Contracts?

The Number of Different Treasuries The Number of Different Treasuries that May be Delivered into the that May be Delivered into the December 2003 Contracts?December 2003 Contracts?

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Part 2Part 2

Conversion Factors, etc.Conversion Factors, etc.

Part 2Part 2

Conversion Factors, etc.Conversion Factors, etc.

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Conversion Factors Conversion Factors Conversion Factors Conversion Factors Conversion factors adjust the price of a deliverable bond or note, with

different coupon, maturity and yield characteristics, to the equivalent price of an 6.00 % coupon.

To calculate invoice price of treasury issue, to be delivered into the futures contract.

Securities with coupons > 6.00 % will have conversion factors > 1.0000 to reflect a premium.

Securities with coupons < 6.00 % will have conversion factors < 1.0000 to reflect a discount

Conversion factors adjust the price of a deliverable bond or note, with different coupon, maturity and yield characteristics, to the equivalent price of an 6.00 % coupon.

To calculate invoice price of treasury issue, to be delivered into the futures contract.

Securities with coupons > 6.00 % will have conversion factors > 1.0000 to reflect a premium.

Securities with coupons < 6.00 % will have conversion factors < 1.0000 to reflect a discount

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Ex: Nov 6, 2003. Five Year Note issues deliverable Ex: Nov 6, 2003. Five Year Note issues deliverable against the Dec-03 Five Year Futures Contract against the Dec-03 Five Year Futures Contract (Last Delivery Date Dec 31, 2003)(Last Delivery Date Dec 31, 2003)

Ex: Nov 6, 2003. Five Year Note issues deliverable Ex: Nov 6, 2003. Five Year Note issues deliverable against the Dec-03 Five Year Futures Contract against the Dec-03 Five Year Futures Contract (Last Delivery Date Dec 31, 2003)(Last Delivery Date Dec 31, 2003)

Issue Maturity Price Yield C. Factor2 5/8 5/15/08 97-12+ 3.258 0.87073 2/15/08 99-14 3.149 0.89083 1/8 9/15/08 98-29+ 3.374 0.88263 1/8 10/15/08 98-28 3/4 3.393 0.88093 1/4 8/15/08 99-18 3.356 0.8894

These would be the prices if yields were 6%

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Conversion FactorsConversion FactorsConversion FactorsConversion Factors

In effect, as you can see, what conversion factors are doing is establishing the relative values of the various deliverable issues.

In effect, as you can see, what conversion factors are doing is establishing the relative values of the various deliverable issues.

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Conversion FactorsConversion FactorsConversion FactorsConversion Factors

Conversion Factors (CF) are used to determine futures invoice price :

FIP = (FP x CF) + AI where:

FIP = Futures Invoice Price

FP = Futures Price

CF = Conversion Factor

AI = Accrued Interest

Conversion Factors (CF) are used to determine futures invoice price :

FIP = (FP x CF) + AI where:

FIP = Futures Invoice Price

FP = Futures Price

CF = Conversion Factor

AI = Accrued Interest

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Conversion factorsConversion factorsConversion factorsConversion factors

There’s one little problem with the conversion factors.

They don’t do a perfect job of establishing relative prices of the deliverable bonds!

As a result, some bonds are slightly “cheaper” than others, and one will be the “cheapest to deliver,” or CTD.

There’s one little problem with the conversion factors.

They don’t do a perfect job of establishing relative prices of the deliverable bonds!

As a result, some bonds are slightly “cheaper” than others, and one will be the “cheapest to deliver,” or CTD.

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Pricing--Pricing--“Cost of Carry Model”“Cost of Carry Model”Pricing--Pricing--“Cost of Carry Model”“Cost of Carry Model”

Futures = S(1 + rf + c - y)tFutures = S(1 + rf + c - y)t

The price of a futures should be:

Price of CTD

Repo rate

Costs of storage & insurance, as a % of spot = 0

The “coupon”

In this case, the repo or financing cost is higher than the coupon, so futures are above spot.

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Basis and ConvergenceBasis and ConvergenceBasis and ConvergenceBasis and Convergence Price

Delivery Month

Futures xConversion Factor

Convergence at expiration

Basis

{CTD

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Part 6Part 6

Constructing a Basic HedgeConstructing a Basic Hedge

Part 6Part 6

Constructing a Basic HedgeConstructing a Basic Hedge

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Hedge objectiveHedge objectiveHedge objectiveHedge objective

What is the objective of a hedge?

To establish a position with a hedge instrument such that changes in the value of the hedge instrument exactly offset changes in the value of the instrument being hedged.

What is the objective of a hedge?

To establish a position with a hedge instrument such that changes in the value of the hedge instrument exactly offset changes in the value of the instrument being hedged.

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Dollar Value of a Basis Point (BPV Dollar Value of a Basis Point (BPV or DV01)or DV01)Dollar Value of a Basis Point (BPV Dollar Value of a Basis Point (BPV or DV01)or DV01)

With Treasury futures, we equate the the values of the instrument being hedged and the hedge instrument using the value of a basis point.

With Treasury futures, we equate the the values of the instrument being hedged and the hedge instrument using the value of a basis point.

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Dollar Value of a Basis Point (Dollar Value of a Basis Point (BPV or DV01BPV or DV01))Dollar Value of a Basis Point (Dollar Value of a Basis Point (BPV or DV01BPV or DV01))

Definition : It is the dollar change in the price of cash instrument due to a basis point (0.01) change in the yield.

Since it represents the sensitivity to a given change in yield, it is useful, among other things, when constructing precise hedges.

Definition : It is the dollar change in the price of cash instrument due to a basis point (0.01) change in the yield.

Since it represents the sensitivity to a given change in yield, it is useful, among other things, when constructing precise hedges.

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Using “BPV” to Hedge a Fixed Income Using “BPV” to Hedge a Fixed Income Position With Treasury FuturesPosition With Treasury FuturesUsing “BPV” to Hedge a Fixed Income Using “BPV” to Hedge a Fixed Income Position With Treasury FuturesPosition With Treasury Futures

Number of contracts required = BPV cash issue

BPV futures

Where:

BPV futures = BPV cheapest-to-deliver

CTD conversion factor

Number of contracts required = BPV cash issue

BPV futures

Where:

BPV futures = BPV cheapest-to-deliver

CTD conversion factor

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Using “BPV” to Hedge a Fixed Income PositionUsing “BPV” to Hedge a Fixed Income PositionUsing “BPV” to Hedge a Fixed Income PositionUsing “BPV” to Hedge a Fixed Income PositionOn Nov 6, a trader wants to hedge a $10 M long position in a 30yr

bond treasury, the 5 3/8 of 02/15/31. The treasury issue has a BPV of $146.10 per $100,000, i.e.

The BPV of the portfolio is $14,610 per $10 Million.The trader wants to hedge this position using the Dec-03 bond

futures contract. On Nov 6, the CTD issue for the Dec-03 bond futures contract was

the 6 7/8 of 08/15/25. This issue had a conversion factor of 1.1049 and a BPV of $145.10 per $100,000.

On Nov 6, a trader wants to hedge a $10 M long position in a 30yr bond treasury, the 5 3/8 of 02/15/31. The treasury issue has a BPV of $146.10 per $100,000, i.e.

The BPV of the portfolio is $14,610 per $10 Million.The trader wants to hedge this position using the Dec-03 bond

futures contract. On Nov 6, the CTD issue for the Dec-03 bond futures contract was

the 6 7/8 of 08/15/25. This issue had a conversion factor of 1.1049 and a BPV of $145.10 per $100,000.

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BPV of FuturesBPV of FuturesBPV of FuturesBPV of Futures

Remember, the invoice price of a treasury delivered into a futures contract is – Price x Conversion Factor +AI

Since we multiply the futures price by the conversion factor to get the invoice price, which should be very close to the market value of the bond…

Remember, the invoice price of a treasury delivered into a futures contract is – Price x Conversion Factor +AI

Since we multiply the futures price by the conversion factor to get the invoice price, which should be very close to the market value of the bond…

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BPV of FuturesBPV of FuturesBPV of FuturesBPV of Futures

To get the basis point value of the futures, we need to divide the BPV of the bond by the conversion Factor:– BPV (Futures) = Price (CTD)/CF

To get the basis point value of the futures, we need to divide the BPV of the bond by the conversion Factor:– BPV (Futures) = Price (CTD)/CF

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Using “BPV” to Hedge a Fixed Income PositionUsing “BPV” to Hedge a Fixed Income PositionUsing “BPV” to Hedge a Fixed Income PositionUsing “BPV” to Hedge a Fixed Income Position

BPV of Future = BPV CTD / Conversion Factor of CTD

= $145.10 / 1.1049

= $131.32 per $ 100,000.

Hedge Ratio = BPV of portfolio / BPV of future

= $14,610 / $131.32 = 111

The trader should sell 124 of the Dec-03 bond futures contracts.

BPV of Future = BPV CTD / Conversion Factor of CTD

= $145.10 / 1.1049

= $131.32 per $ 100,000.

Hedge Ratio = BPV of portfolio / BPV of future

= $14,610 / $131.32 = 111

The trader should sell 124 of the Dec-03 bond futures contracts.

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Hedging with Financial Futures :Hedging with Financial Futures :Hedging with Financial Futures :Hedging with Financial Futures :Choose the futures contract that most closely describes the nature of

the underlying risk in order to minimize yield-curve risk.

Choose the futures expiration month that most closely matches the time period to be addressed while keeping in mind that the “nearby” contract is the most liquid.

The right hedge ratio will equalize the “BPV”s of the hedged issue and the futures position, but some immunization risk (yield-curve risk) may still remain.

Choose the futures contract that most closely describes the nature of the underlying risk in order to minimize yield-curve risk.

Choose the futures expiration month that most closely matches the time period to be addressed while keeping in mind that the “nearby” contract is the most liquid.

The right hedge ratio will equalize the “BPV”s of the hedged issue and the futures position, but some immunization risk (yield-curve risk) may still remain.

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Important Question!Important Question!Important Question!Important Question!

Suppose you have hedged a bond portfolio with a 5.50 % yield.

Now you hedge that portfolio, removing market risk

What will the yield on your portfolio now be?

Suppose you have hedged a bond portfolio with a 5.50 % yield.

Now you hedge that portfolio, removing market risk

What will the yield on your portfolio now be?

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Using Futures to Adjust DurationUsing Futures to Adjust DurationUsing Futures to Adjust DurationUsing Futures to Adjust Duration

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Duration Management Duration Management

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Adjusting Duration of a Bond Portfolio Adjusting Duration of a Bond Portfolio Containing FuturesContaining Futures

Target Bond Bond Portfolio - Portfolio

Hedge = BPV BPVRatio

Futures BPV

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Duration ManagementDuration ManagementDuration ManagementDuration Management

Closing Date : Nov 6, 2003 Settlement Date : Nov 10, 2003

Coupon Maturity # of Quoted Market Price Total Modified EquivalentMM/DD/YY Contracts Price (P+AI) Market Price Duration Duration

(32nds) (Decimal) # * (P+AI)

3.375 04/30/04 400 101-03 1.011494 40,459,760 0.481 0.19

3.500 11/15/06 315 102.21+ 1.043363 32,865,935 2.816 0.89

6.500 02/15/10 125 115-02 1.165285 14,566,063 5.170 0.65

4.875 02/15/12 154 104-16+ 1.056151 16,264,725 6.730 1.04

Weighted Cash Position 994 104,156,482 2.78

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Managing DurationManaging DurationManaging DurationManaging Duration

Your portfolio duration is 2.78Suppose you want a portfolio with the

return and volatility characteristics provided by a duration of 5.0?

Your portfolio duration is 2.78Suppose you want a portfolio with the

return and volatility characteristics provided by a duration of 5.0?

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Basis Point ValuesBasis Point ValuesDuration x Portf Value x .0001Duration x Portf Value x .0001Basis Point ValuesBasis Point ValuesDuration x Portf Value x .0001Duration x Portf Value x .0001

Portfolio BVP:– 2.78 x .0001 x $104,156,482 = $27,799.56

Target BVP:– 5.00 x .0001 x $104,156,482 = $52,078.24

Dec-03 Five Year Treasury Futures BPV:– BPV of CTD: $39.50 per $100,000

– Conversion Factor of CTD: .8908

– BPV of futures: $39.50/.8908 = $44.34

Portfolio BVP:– 2.78 x .0001 x $104,156,482 = $27,799.56

Target BVP:– 5.00 x .0001 x $104,156,482 = $52,078.24

Dec-03 Five Year Treasury Futures BPV:– BPV of CTD: $39.50 per $100,000

– Conversion Factor of CTD: .8908

– BPV of futures: $39.50/.8908 = $44.34

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Adjusting Duration of a Bond Portfolio Adjusting Duration of a Bond Portfolio Containing FuturesContaining Futures

$52,078.24 - $27,799.56

Hedge = Ratio

$44.34

= 547.56, or buy 548 contracts.

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“Today the Chicago Board of Trade closed early to stop and smell the flowers.”

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The EndThe EndThe EndThe End