The Role of Fixed Income Benchmarks

May 2007

Lev Dynkin, Managing Director

Global Head of Quantitative Portfolio Strategies

2

Why use a benchmark?

� Is the portfolio manager adding value vs a naive (“zero skill”) investment

strategy given the opportunity set and constraints?

� What is the long term risk appetite?

� Long-term strategic asset allocation

� Most asset management mandates come with a specified benchmark and

constraints on deviation from it

� Most mutual funds have a stated benchmark to let buyers know the nature of

major allocations

� Reasons for benchmark customization:

− Liability-based benchmarks

− Reflect constraints

3

Common and Distinct Features of Bond Indices

� Bond indices are market weighted average returns of individual securities

� Most fixed income securities trade OTC and are priced by the index provider

or a third party service

� Lehman bond indices have index statistics (risk sensitivities to yield curve

and spread changes, avg. yield, avg. coupon) in addition to returns

� Standard Lehman bond indices include securities that meet pre-specified rules

� Customized indices may follow a different set of rules for inclusion of

securities

� Indices may be produced for strategies (long corporate bonds, short duration-

matched Treasury bonds) or derivatives (swap indices)

4

Customized Indices

� Lehman publishes daily on its website about 2,000 standard indices covering

a broad range of asset classes in 30 currencies and over 5,000 customized

indices for specific investors

� Customized indices reflect constraints of specific investors

− Constraints on realized gains or losses � book yield indices

− Liability-matching constraints

− Changes to index inclusion criteria (e.g. only bonds rated A and above)

− Target specific asset class weights (e.g. 50% govt, 50% corporates)

− Issuer caps (e.g. no more that 2% of portfolio in any issuer)

5

Main Dilemma of Indices

�Investable vs representative indices:

− baskets of securities

− broad-based reflection of the opportunity set

�Under-sampling vs over-sampling

�Pricing a broad universe of securities

�Systematic risk vs idiosyncratic risk

Lehman’s Bond Market Indices are broad-based representations of the

investment opportunity set

6

What defines a good benchmark?

A good benchmark should include the following properties]− Universe is well defined, with transparent rules

− Securities are investable; benchmark is replicable

− Daily performance data is available

− Current characteristics are available (e.g., price, coupon, duration, etc.)

− Historical information is available

− Investment style is clearly defined

− Risk profile is well defined

− Benchmark is specified in advance

− Turnover is low

The Lehman Global Family of Indices meets these criteria.

− All indices are rules-based, meaning that inclusion in a Lehman Brothers index depends on

satisfying clearly pre-specified criteria.

− Comprehensive statistics about each index are readily available to investors, and

performance results are available daily for most indices.

[1]

7

Assets under Management Benchmarked vs. Major Lehman Brothers Indices

December 2006 Total: $6.11trn

$1.10trnCustom / Other

$82bnU.S. High-Yield

$483bnEuro Aggregate

$105bnPan-Euro Aggregate

$613bnU.S. Government / Credit

$1.10trnGlobal Aggregate

$194bnU.S. Universal

$2.40trnU.S. Aggregate

AUM (Estimated)Lehman Brothers Index

8

Lehman Brothers Global Family of Indices: May 2007

U.S. HY

Pan Euro

HY

CMBS HY

EM HY

Sterling

Aggregate

Euro Securitized

Gilt

Non-Gilt

Euro

Aggregate

Euro

Treasury

Euro Corporate

Euro Gov-

Related

Non-

EMU

Danish

Aggregate

Swedish Aggregate

Norwegian

Aggregate

Eastern

Europe

Treasury

Danish

MBS

Global Asset Class IndicesGlobal Aggregate Global High-Yield

Euroyen

CanadianAggregate

Investment-Grade EM

ZAR, CHP, MXN

Treasury

Eurodollar Ex Agg

Asia-Pacific

Treasury

Asia-Pacific

Gov-Related

Asia-Pacific

Corporate

Asia-Pacific

Securitized

USD

EUR

GBP

MBS

CMBS

ABS

Covered

Global Inv-Grade Corp

144-A’s

Eurodolla

r

Global

HY Corp

G-7

Majors

Others

U.S. TIPS

UK Gilt

Eurozone

Global

CreditGlobal

Securitized

Global Emerging Markets

JGB FRN

U.S. ABS FRN

Pan Euro ABS FRN

U.S. Corp. FRN

Pan Euro Corp FRN

U.S. HY FRN

U.S. HY Loan

Other Global AggComponents

Multiverse

U.S. Universal

Dollar, Euro, Sterling, & Yen

Swap Indices

Zero-Coupon Nominal & Inflation

Swaps Indices

Global Capital Securities

High-Yield Issuer Capped / VLIs

U.S. Convertibles Index

U.S., Euro, Yen CDS/ CDX iTraxx

TR

Indian Government

Chinese Aggregate Index

U.S. Municipals

CMBS High-Yield

Mexican Government Bond

Index

Swiss Franc Aggregate

Short U.S. Gov/Credit

CMBS IO

ABS

ERISA

CMBS

U.S. HY

Corp

Euro

dollar

144A

Non-

ERISA

CMBS

U.S. EM

Non-U.S.

Aggregate

Non-Debt Indices

Commodity Index (LBCI)

Global Hedge Fund Indices

FX Indices

Global Inflation-Linked

Global

Treasury

U.S. Gov-Related

U.S. Corporate

U.S. Treasury

Floating-Rate IndicesOther Debt and Swaps Indices

96 Indices; 7 Flagship IndicesGlobal Aggregate, U.S. Aggregate, U.S. Universal, Pan-European Aggregate,

Euro-Aggregate, Asian-Pacific Aggregate, Multiverse

U.S.

AggregateAsian-Pacific

Aggregate

Pan-European

Aggregate

Japan

Agg

Non-

Japan

Fixed Rate

Passthroughs

Hybrid ARM (U.S. Agg Only)

MBS

U.S. Securitized

Emerged

GHLC RMBS(Japan Agg Only)

144A Ex Agg

JGB

Canada

Index Rules & Construction

10

Basic Principles of Lehman Indices

� Rules-Based

� Monthly Reset

� Market Value Weighted

� Total Return Calculations

11

Monthly Index Dynamics: Building a Rules-Based Index

� Static universe set at

beginning of month

– Avoids “hitting a

moving target”

� Includes bonds that

during the month

have been –

– Called

– Downgraded below

investment grade

– Sunk below $250MM

� Used to report index

performance (returns)

Returns Universe Statistics Universe

Returns

Universe

Statistics Universe

Forward

Backward

� Dynamic universe

changes daily

– Used for rebalancing

purposes

� Includes bonds that during

the month have been –

– Newly issued

– Upgraded to investment

grade

� Used to forecast next

month’s returns universe

12

Global Aggregate Index: Factsheet / Rules

Sector Breakdown as of 12/31/2006 Access to the IndexQuality Breakdown as of 12/31/2006

The Global Aggregate Index provides a broad-based measure of the global investment-grade fixed-rate debt markets.

The Global Aggregate Index contains three major components: the U.S. Aggregate Index (USD 300 million), the Pan-

European Aggregate Index (EUR 300 million), and the Asian-Pacific Aggregate Index (JPY 35 billion). In addition to

securities from these three benchmarks (94.4% of the overall Global Aggregate market value), the Global Aggregate

Index includes Global Treasury, Eurodollar (USD 300 million), Euro-Yen (JPY 35 billion), Canadian (CAD 300

million), and Investment-Grade 144A (USD 300 million) index-eligible securities not already in the three regional

aggregate indices. The Global Aggregate Index family includes a wide range of standard and customized subindices by

liquidity constraint, sector, quality, and maturity.

LehmanLive Website

www.lehmanlive.com

• Daily index returns and statistics

• Historical time series downloadable into Excel

• Standardized market structure reports

• Fully customizable views

• Index primers and shelf reference documents

• Latest index and portfolio strategies research

publications

Treasury

48.7%

Government-

Related

15.0%

Corporate

16.0%

Securitized

20.4%

Aaa

55.5%Aa

28.2%

A

11.1%

Baa

5.2%

Index Overview

13

Global Aggregate Index: Factsheet / Rules

Rules for Inclusion

Currencies eligible for inclusion must be freely tradable and hedgeable; local currencies’ sovereign bonds (both local and foreign) must have an investment-grade sovereign rating using the middle rating. The list of eligible currencies is reviewed once a year. Thai baht debt was removed from the index on March 1, 2007.� U.S. and Canadian Aggregate Index securities: USD, CAD. � Pan-European Aggregate Index securities: EUR, GBP, CZK, DKK, HUF, NOK, PLN, SKK, SEK.� Asian-Pacific Aggregate Index securities: JPY, AUD, HKD, KRW, NZD, SGD, TWD, MYR.� Additional eligible currencies: CLP, MXN, ZAR.

Currency

Must be rated investment grade (Baa3/BBB-/BBB- or above) using the middle rating of Moody’s, S&P, and Fitch, respectively.

� When all three agencies rate an issue, a median or “two out of three” rating is used to determine index eligibility by dropping the highest and lowest rating.

� When a rating from only two agencies is available, the lower (“most conservative”) of the two is used.� When a rating from only one agency is available, that rating is used to determine index eligibility.� Unrated securities are included provided that an issuer rating is applicable.� Domestic local currency sovereign debt will be use the most observed bond level rating for all outstanding bonds.

Quality

� At least 1-year until final maturity, regardless of optionality. For securities with coupon that converts from fixed to floating rate, at least 1-year until the conversion date.

� MBS must have a weighted average life of at least 1-year; ABS must have a remaining average life of at least 1 year; CMBS must have an expected maturity of at least 1-year.

� Perpetual securities are included in the index provided they are callable or their coupons switch from fixed to variable rate. These are included until one year before their first call date, providing they meet all other index criteria.

Maturity

The minimum liquidity criterion is based on eligible currencies, as follows:� For U.S. Aggregate, Canadian, Eurodollar, and Investment-Grade 144A Index securities, USD 300 million (or

equivalent) minimum par amount outstanding. CMBS and ABS securities must belong to a deal with a minimum aggregate transaction size of USD 500 million.

� For Pan-European Aggregate Index securities, EUR 300 million currency equivalent minimum par amount.� For Asian-Pacific Aggregate and Euro-Yen Index securities, JPY 35 billion minimum par amount outstanding. � For GBP denominated securities, GBP 200 million currency equivalent minimum par amount outstanding.� For securities in other eligible currencies, minimum amount outstanding is pegged to one of the four major

currencies above, using an exchange rate that is reset once a year on the last business day of November. WM/Reuters exchange rates are used.

Amount Outstanding

14

Global Aggregate Index: Factsheet / Rules

Rebalancing

Pricing & Related Issues

Interest and principal payments earned by the returns universe are held in the index without a reinvestment return until month-end

when it is removed from the index.

Reinvestment of

Cash flows

The composition of the Returns Universe is rebalanced monthly, at each month end and represents the set of bonds that returns are

calculated on. The Statistics Universe changes daily to reflect issues dropping out and entering the index, but is not used for return

calculation. On the last business day of the month, the composition of the latest Statistics Universe becomes the Returns Universe for

the following month.

Frequency

During the month, indicative changes to securities (maturity, credit rating change, sector reclassification, amount outstanding) are

reflected in both the statistics and returns universe of the index on a daily basis.

Index Changes

Qualifying securities issued, but not necessarily settled, on or before the month-end rebalancing date qualify for inclusion in the

following month’s returns universe.

New Issues

Bonds can be quoted in a variety of ways including nominal spreads over benchmark securities/treasuries, spreads over swap curves, or

direct price quotes as a percentage of par. In most instances the quote type used is a spread measure that results in daily security price

changes from the movement of the underlying curve (swap or treasury) and/or changes in the quoted spread.

Pricing Quotes

Bonds in the index are priced on the bid side. The initial price for new corporate issues entering the index is the offer side; after that,

the bid side price is used.

Bid or Offer

Side

Unless noted otherwise, index bonds are priced by Lehman Brothers traders at mid-month and month-end. On a daily basis, a subset of

the index continues to be trader priced, with the remaining bonds model/ matrix priced using actively traded benchmark securities to

generate issuer pricing curves and populate a spread matrix algorithm or sourced from third parties.

�U.S. Aggregate Index, Eurodollar Index, 144A Index: Treasuries are trader priced daily; up to 1,000 benchmark Corporates are

trader priced daily; some Agency debentures are trader priced daily; MBS bonds are priced by traders on a daily basis, with generic

prices derived from these marks; ABS spreads are marked weekly to generate daily prices using changes in the Treasury and swap

curves; CMBS spreads are marked daily.

�Pan-European Aggregate Index: Lehman Brothers traders price more than 75% of the market value of the index; the remainder is

priced by third party sources or by a spread matrix algorithm. Traditional Pfandbriefe are curve-based, Jumbo Pfandbriefe and Danish

MBS are vendor priced.

�Asian-Pacific Aggregate Index, Euro-Yen Index, and Other Currencies: Daily prices provided by outside sources if trader marks

are unavailable.

�Canadian Index: Daily pricing is provided by Scotia Capital.

Sources &

Frequency

15

Global Aggregate Index Returns (Hedged and Unhedged in ILS)

Monthly Global Aggregate Index Returns Since 2001 (in Israeli Shekel)

-4.00

-2.00

0.00

2.00

4.00

6.00

8.00

Jan-0

1

Apr-

01

Jul-01

Oct-

01

Jan-0

2

Apr-

02

Jul-02

Oct-

02

Jan-0

3

Apr-

03

Jul-03

Oct-

03

Jan-0

4

Apr-

04

Jul-04

Oct-

04

Jan-0

5

Apr-

05

Jul-05

Oct-

05

Jan-0

6

Apr-

06

Jul-06

Oct-

06

Jan-0

7

Apr-

07

Unhedged Hedged

16

Global Aggregate Index Returns (Hedged and Unhedged in ILS)

Cumulative Global Aggregate Index Returns Since 2001 (in Israeli Shekel)

0

10

20

30

40

50

60

70

Jan-0

1

Apr-

01

Jul-01

Oct-

01

Jan-0

2

Apr-

02

Jul-02

Oct-

02

Jan-0

3

Apr-

03

Jul-03

Oct-

03

Jan-0

4

Apr-

04

Jul-04

Oct-

04

Jan-0

5

Apr-

05

Jul-05

Oct-

05

Jan-0

6

Apr-

06

Jul-06

Oct-

06

Jan-0

7

Apr-

07

Cu

mu

lati

ve R

etu

rn (

%)

Unhedged Hedged

17

Non-traditional benchmarks

� Traditional indices represent the investment opportunity set in proportions to

market capitalization

� Benchmark may represent a “no view” investment portfolio

� Any investment process can be benchmarked:

Corporation Z generates its revenue in US$ and Euro, but reports earnings

in US$. The Treasurer can hedge expected Euro revenue into US$ 1 year

out and take the risk of revenue fluctuation or hedge monthly and take

the currency risk. How should the Treasurer be evaluated at the end of

the year?

Managing a Portfolio

Relative to a Benchmark

19

� Standard and custom indices

� Justification of asset class selection in the benchmark

� Setting a benchmark duration target

� Justification of investment style

� Profiling of the portfolio vs. benchmark to examine intentional and

unintentional exposures (Market Structure)

� Measuring portfolio risk relative to benchmark (Risk Model)

� Comparing projected scenario returns (Scenario Analysis)

� Attribution of achieved return advantage to manager decisions

(Performance Attribution)

Basic Steps in Quantitative Portfolio Management vs. an Index

“Market structure” example:

Profiling the portfolio relative to the Benchmark

80/20 Composite vs. Govt/Corp Index80/20 Composite vs. Govt/Corp Index

Govt Corp Total

Portfolio (%)Benchmark (%)Difference (%)

80.00%69.66%10.34%

20.00%30.34%

–10.34%

100.00%100.00%

0.00%

Portfolio Dur.Bmk. Dur.Difference

5.415.410.00

6.086.080.00

5.545.61

–0.07

Portfolio Cnt. Dur.Bmk. Cnt. Dur.Difference

4.333.770.56

1.221.84

–0.62

5.545.61

–0.07

Scenario Analysis

80/20 Composite vs. Govt/Corp Index80/20 Composite vs. Govt/Corp Index

Scenario(1-month horizon)

PositionReturn %

BenchmarkReturn %

Difference%

Up 50 bps –2.25 –2.28 0.03

2–30s Steepen 20 bps 0.42 0.43 –0.01

No Change 0.41 0.42 –0.01

2–30s Flatten 20 bps 0.40 0.41 –0.01

Down 50 bps 3.23 3.28 –0.05

Spreads widen 20% 0.13 0.02 0.11

22

Quantify the market risk embedded in a portfolio

� In absolute terms: expected volatility of the portfolio total returns

� In relative terms: tracking error volatility

Attributes ex-ante risk to major decisions implemented by fund managers

� Currency allocation

� Interest rate management: duration and yield curve exposure

� Swap spreads

� Interest rate volatility

� Credit allocation

� Name and security selection

Can be used in

� Monitoring active risk

� Portfolio optimization

� Risk budgeting

� Scenario analysis

Why do we need a Risk Model?

23

Example Risk Model Report

What are the sources of risk?

� Tracking error volatility

(TEV) is the primary

measure of portfolio risk

vs. the benchmark

� TEV is the projected

standard deviation of the

return difference between

the portfolio and the

benchmark

� It is calculated based on

differences between

portfolio and benchmark

exposures to risk factors

from several categories

24

Example Risk Report: Factor Exposures

What is the portfolio’s sensitivity to risk factors?

� For each market risk factor, there is a

contribution to tracking error:

TE impact of risk factor =

Net exposure x Factor volatility

� The overall TEV of the portfolio

considers correlations among factors as

well as their volatilities

� Modeling can be very specific: for

example, yield curve exposures are

modeled by key rate durations along the

curve, not just a single duration

25

Performance Attribution

� Explain portfolio outperformance relative to the benchmark in terms of

manager decisions:

– Positioning along the yield curve (duration, etc.)

– Sector allocation

– Security selection

� Answers two types of questions:

– Assume portfolio earns benchmark returns in each risk sub-category.

What outperformance results from weight differences alone?

– Portfolio return differs from benchmark return within the most

narrowly defined cell. What outperformance results from this

difference in security selection?

26

Basics of Performance Attribution

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27

� A portfolio of 50 corporate bonds can replicate a corporate index of 3,000+

securities with a TEV (Tracking Error Volatility) of 15 bp/month

� A portfolio of 12-14 TBA securities can replicate the MBS index of 360+

securities with a tracking error of 4 bp/month

� RBISM (Replicating Bond Index) baskets of liquid derivatives (Treasury

futures, interest rate swaps, CDX/iTraxx & FX forwards)

can replicate the Global Aggregate Index of 11,000+ securities with a TEV of

5 bp/month

RBI is a service mark of Lehman Brothers, patent pending

Index Replication

28

� Benchmarks provide an objective way to measure portfolio performance

� Benchmarks can be customized to fit almost any mandate

� Benchmark selection shifts the strategic asset allocation decision from the

portfolio manager to the plan sponsor

� Benchmarking changes the framework for measuring risk:

– Active risk instead of absolute risk

– Measured by tracking error volatility (TEV)

– Keep track of net exposures vs. the benchmark

� Index replication techniques can help build “portable alpha” strategies

designed to outperform a desired benchmark

Conclusion

29

Analyst CertificationThe views expressed in this report accurately reflect the personal views of Lev Dynkin, the primary analysts responsible for this report, about the subject securities or issuers referred to herein, and no part of such analyst's compensation was, is or will be directly or indirectly related to the specific recommendations or views expressed herein.

Important DisclosuresLehman Brothers Inc. and/or an affiliate thereof (the "firm") regularly trades, generally deals as principal and generally provides liquidity (as market maker or otherwise) in the debt securities that are the subject of this research report (and related derivatives thereof). The firm's proprietary trading accounts may have either a long and / or short position in such securities and / or derivative instruments, which may pose a conflict with the interests of investing customers.Wherepermitted and subject to appropriate information barrier restrictions, the firm's fixed income research analysts regularly interact with its trading desk personnel to determine current prices of fixed income securities.The firm's fixed income research analyst(s) receive compensation based on various factors including, but not limited to, the quality of their work, the overall performance of the firm (including the profitability of the investment banking department), the profitability and revenues of the Fixed Income Division and the outstanding principal amount and trading value of, the profitability of, and the potential interest of the firms investing clients in research with respect to, the asset class covered by the analyst. Lehman Brothers generally does and seeks to do investment banking and other business with the companies discussed in its research reports. As a result, investors should be aware that the firm may have a conflict of interest.To the extent that any historical pricing information was obtained from Lehman Brothers' trading desks, the firm makes no representation that it is accurate or complete. All levels, prices and spreads are historical and do not represent current market levels, prices or spreads, some or all of which may have changed since the publication of this document.Lehman Brothers' global policy for managing conflicts of interest in connection with investment research is available at www.lehman.com/researchconflictspolicy.To obtain copies of fixed income research reports published by Lehman Brothers please contact Valerie Monchi (vmonchi@lehman.com; 212-526-3173) or clients may go to.

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