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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
( )
( ) ( )
( )∑ ∑
∑ ∑
∑
∑
∑
+−=
−+−=
−+−=−
=
=
i i
B
i
P
i
P
i
i i
B
i
B
i
P
i
B
i
P
i
P
i
i
B
i
B
i
B
i
P
i
B
i
P
i
P
i
P
iBP
i
P
i
P
iP
i
B
i
B
iB
rrw
rwwrrw
rwrwrwrwRR
rwR
rwR
Security selectionSecurity selectionAllocationAllocation
( )B
i
P
i ww − ( )B
B
i Rr −
sector i overweight × sector i outperf vs. index
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 ([email protected]; 212-526-3173) or clients may go to.
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