IX: Market Innovations 27: Swap Agreements Credit Arbitrage Swap Currency Swap.
Credit Default Swap Info
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CBOT Credit DefaultSwap Index Futures
RefeRence Guide
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IntroductIon 5
Background 6
contract BenefIts 7
Short Lifespan
Rate Up, Price Up
Buy Futures Buy Protection. Sell Futures Sell Protection.
key BenefIts 9Position Scalability
Administrative Convenience and Low Operational Cost
Transparency
High-Grade Credit Exposure
Capital Efficiency
Off-Exchange Trading
the cdr lIquId 50 Index: composItIon and structure 11
Index Series and Futures Expiries
Selection of Index Components
Maximum Running Spread and Other Index Parameters
the cdr lIquId 50 Index: some sylIzed facts 14
Financials: CDR Liquid 50 versus CDX
synthetIc corporate Bond portfolIos 17
Long Corporates Long IRS Futures + Short CDS Index Futures
Short Corporates Short IRS Futures + Long CDS Index Futures
prIcIng cds Index futures: spot versus forward 23
Spot Forward, Generally
Exceptions Depend on the Hazard Rate
Rolling Down the Curve
appendIx 1 cdS ix ftrs cotrat Spatos 29
appendIx 2 cdS ix ftrs cotrat Rls 30
appendIx 3 cdR Lq 50 nAiG ix costrto a Mata Prors 32
appendIx 4 cMA a cMA dataVso 37
Table of Contents
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IntroductionSince the birth of financial futures, market practitioners have exhorted exchanges to list corporate bond futures.
What they envision, typically, are contracts that would be traded and transparently priced on a regulated
exchange, and that would be guaranteed by a centralized clearing house, and that would (by whatever means)
furnish a generic proxy for the price exposure of investment grade corporate bonds.
Chicago Board of Trade Credit Default Swap (CDS) Index futures meet this need.
CDS Index futures give institutional portfolio managers a simple means of acquiring or laying off
standardized investment grade corporate bond price exposure.
For many users, CDS Index futures should result in lower administrative costs relative to over-the-counter
(OTC) alternatives.
As with all CBOT futures, the guarantee furnished by the Exchanges clearing services provider
consolidates and virtually eliminates counterparty credit risk, permitting contract users to easily adjust their
asset exposures without tying up credit lines.
Used in conjunction with CBOT Interest Rate Swap (IRS) futures, CDS Index futures give market
practitioners a simple, flexible means to create and trade synthetic investment grade corporate
bond portfolios.
This reference guide reviews the key features and benefits of CDS Index futures. It then discusses the structure of
the contracts underlying reference, the CDR Liquid 50TM North America Investment Grade Index (hereafter, CDR
Liquid 50TM) and describes some of the indexs empirical features. It explores in detail how traders and investors
can combine CDS Index futures with CBOT 5-Year IRS futures to achieve an operationally clean and flexible proxy
for generic investment grade corporate bond exposure. It concludes with a discussion of the relationship between
spot values of the CDR Liquid 50 index and the forward values reflected in CDS Index futures prices.
Appendices present a summary of the terms of the CDS Index futures contract, the CBOT Rulebook chapter thatformally defines the contract, the guide to index construction and maintenance procedures for the CDR Liquid 50
index, and an overview of CMA DataVisionTM, the price data source for the CDR Liquid 50 index.
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6
The dramatic growth of credit default swaps marks
one of the great milestones in the saga of financialderivatives. In the short span from year-end 2004 to
year-end 2006, outstanding notional amounts of US
dollar-denominated credit default swaps burgeoned
from around $6.5 trillion to nearly $29 trillion, clocking
growth of 110 percent per annum. The share of this
total that represents index-related (multi-name) credit
default swaps has risen yet faster, from 20 percent in
2004 to nearly 35 percent in 2006. See Exhibit 1.
This achievement has not come without growing
pains. In recent years, regulators have become
increasingly troubled by the inability of dealers
back offices to keep pace with timely capture,confirmation, and booking of credit derivative
transactions. Matters came to a head in September
2005, when the Federal Reserve Bank of New York
convened the first of a series of meetings with major
derivatives market participants and regulators. The
action plan that emerged from these gatherings hasaccomplished much, including marked reduction
in the backlog of outstanding unconfirmed trades,
clarification of procedures for trade assignment and
novation, and widespread acceptance and adoption
of more rigorous protocols for the settlement of credit
derivatives when credit events actually occur. (See,
e.g., Federal Reserve Bank of New York, Statement
Regarding Progress in Credit Derivatives Markets, 27
September 2006, www.frb.ny.org.)
Despite these efforts or perhaps because of them
the operational costs of trading and managing OTC
credit derivative positions have soared in league withthe scale of market activity. This underscores the
need for exchange-listed contracts to assist market
participants in managing their risk exposures. CBOT
CDS Index futures are ideally suited to play this role.
Background
Exhibit 1
Outstanding Notional
Amounts of OTC US Dollar
Credit Default Swaps
Data Source:Bank for International Settlements
0
10
20
30
Dec 04 Jun 05 Dec 05 Jun 06 Dec 06
Total
Multi-Name
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CBOT CDS Index futures expire quarterly, in March,
June, September, and December. The last trading
day for expiring contracts is the so-called IMM
Monday, the Monday before the third Wednesday
of the expiry month.
The underlying reference for CDS Index futures is
the CDR Liquid 50 North America Investment Grade
Index, maintained and published daily by Credit
Derivatives Research LLC (CDR LLC). The CDR Liquid
50 index is simply an arithmetic average of 5-year
credit default swap spreads quoted on each of the 50
most active names in the US investment grade credit
default swap market.
CDS Index futures are quoted as an average credit
spread, directly in terms of the CDR Liquid 50 index,in basis points and hundredths of basis points. Each
basis point of contract price is worth $500. Each
hundredth of a basis point, the contracts minimum
trading increment, is worth $5.
At expiration the CDS Index futures contract settles
to the value of the CDR Liquid 50 index on the
contracts last trading day. Importantly, each futures
expiry references a distinct index series. This means,
for example, that a September CDS Index futures
contract will expire with reference to a CDR Liquid 50
index series that may differ in composition from the
index series that serves as the underlying reference
for the futures contract that expires the following
December. (How this relationship works, and why it is
so, is explained in detail below. See The CDR Liquid
50 Index: Composition and Structure on page 11.)
CDS Index futures expire by cash settlement. There
is no physical delivery. CDR LLC will publish the value
of the pertinent CDR Liquid 50 index series for the
last day of trading, on the next morning. This index
value becomes the expiring contracts final settlement
price. The Exchanges clearing services provider uses
this final settlement price to determine a final mark to
market (versus the futures contracts daily settlement
price on the last day of trading).
Two differences between CDS Index futures and
other CBOT financial futures deserve emphasis:
s li
One is that a CDS Index futures contract has an
unusually abbreviated lifespan, roughly three and a
half months from listing to expiration. A newly listed
contract begins trading on the business day after
the CDR Liquid 50 index series that corresponds to
it has been constituted and announced. The newly
listed contract then coexists with the previously
listed contract for approximately two weeks, until the
previously listed contract expires.
Example:Consider a hypothetical March 2007 CDS
Index futures contract. Its underlying reference
would be the CDR Liquid 50 index series
constituted on the last business day of November
2006 (Thursday, 30 November). The contract wouldbegin trading on the first business day of December
2006 (Friday, 1 December) and would expire on
IMM Monday in March 2007 (Monday, 19 March).
It would trade alongside the (likewise hypothetical)
December 2006 contract from Friday, 1 December,
through Monday, 18 December, the last trading
Contract Features
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8
day in the December 2006 contract. During this
time, strategic open interest holders would be able
to roll their positions from the December 2006
contract to the March 2007 contract. Among the
many considerations they would take into account
when pricing the roll spread are the differences in
composition, if any, between the two CDR Liquid
50 index series 064 and 071, respectively -- thatcorrespond to the December 2006 and March
2007 contracts.
This listing/expiry timetable strikes a judicious balance
between two goals. One is to allow each newly listed
CDS Index futures contract to run in tandem with the
previously listed contract, long enough to let market
participants roll in orderly fashion from one expiry to
the next.
The other is to permit the CDR Liquid 50 index to do
what it is designed to do. The futures contracts short
lifespan enables a comparably short lifespan for the
index series that serves as its underlying reference.
The single-name credit default swaps selected as
index components will have been chosen on the basis
of their trading activity. However, one of the realities of
both the corporate bond and OTC credit derivatives
markets is that liquidity can, and often does, migrate
abruptly from one corporate reference to another. In
view of this, the brief lifespan of the futures contract
and its companion index series is intended to increase
the chances that the 50 names in the index series
might remain active through contract expiration.
r u, pi u
The other distinction is that CDS Index futures are
priced with direct reference to an interest rate spread
to be precise, a forward-starting credit spread.
This means that when credit spreads widen generally,
the contract price is likely to rise in value. Conversely,
when credit spreads become narrow generally, the
contract is likely to fall.
This is in contrast to other CBOT financial futures,
such as Treasuries, Interest Rate Swaps, or 30-Day
Fed Funds. Because those contracts trade in terms of
notional asset price, rather than notional interest rate
or interest rate spread, their prices tend to fall when
interest rates rise, and vice versa.
Several examples given below will dramatize the
importance of keeping this distinction clear when
constructing and trading spreads between CDS
Index futures and other CBOT financial futures. (SeeSynthetic Corporate Bond Portfolios on page 17.)
B f B pis f s pi
For those familiar with OTC credit default swaps,
a convenient rule of thumb is that owning a long
position in CDS Index futures is similar to owning
protection. Given a general widening of credit
spreads, a CDS Index futures contract price will tend
to rise, and contract longs should benefit. If instead
there is a general narrowing of credit spreads, then
CDS Index futures prices will tend to fall, and contract
longs will have to pay variation margin on the ensuing
marks to market. Obviously the converse holds too:
A seller of CDS Index futures assumes exposure
broadly similar to a protection sellers position in
OTC credit default swaps.
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Users of CBOT CDS Index futures gain several
important benefits from the contract design.
pii sbii CDS Index futures offer
a convenient and standardized means to obtainexposure, long or short, to a generic investment
grade corporate credit spread, without having to
own either an OTC credit default swap or a spread
position between, e.g., corporate bonds and plain-
vanilla interest rate swaps. Unlike OTC credit default
swaps, positions in CDS Index futures can be entered
or liquidated, scaled up or down, without extensive
contractual documentation and without leaving
behind a book of non-nettable or non-offsetting
OTC swap contracts.
aiii ci l
oi c Using CDS Index futures
eliminates the administrative (e.g., accounting,
manpower, record-keeping) costs frequently required
in maintaining a book of OTC credit derivatives.
Moreover, cash settlement means there are no trailing
contractual obligations after contract expiration. The
financial obligations entailed in CDS Index futures
expire with the contract, after the final mark to
market. For this reason, among others, CDS Index
futures make synthetic credit spread exposure readily
available to market participants who cannot be, or
who would prefer not to be, directly involved in OTC
credit derivative transactions.
t By their nature and structure,
futures markets allow participants with differing
information sets and outlooks to discover the
equilibrium price of the moment. By making price
information available for all to see, CDS Index futures
furnish a useful reference point and a daily mark to
market with unmatched transparency.
hi g ci eThe credit
guarantee of the CBOT clearing services provider
makes CDS Index futures comparable to the
strongest counterparty credits in the OTC market.
Among its many benefits, this obviates the needfor entering into potentially cumbersome bilateral
collateralization arrangements to alleviate
counterparty credit exposure.
ci eii Besides virtually eliminating
credit risk, the clearing house guarantee means that
futures position holders need not reserve significant
amounts of capital against the risk of adverse moves
in credit spreads. That is, by using CDS Index
futures portfolio managers and credit spread traders
may substitute (inexpensive) risk management for
(expensive) capital.
o-e ti CDS Index futures are
eligible for a wide variety of bilaterally negotiated
off-exchange transactions. These include:
Wholesale trades in which a buyer and seller
can bilaterally trade a block of CDS Index
futures at a mutually agreeable price, as long
as the scale of the block transaction is large
enough to qualify. The minimum admissible
size for block trades in CDS Index futures
is 100 contracts.
Exchange-for-Physical (EFP) trades inwhich a buyer acquires CDS Index futures
from a seller at a mutually agreeable price.
At the same time, the futures buyer sells (and
the futures seller buys) an equivalent amount
of a credit spread position in cash securities,
for which the credit spread dynamics are
reasonably correlated with the price dynamics
of the CDS Index futures.
Key Benefits
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Example: The buyer of CDS Index futures might
simultaneously sell a comparably scaled Treasury-
Agency spread, by selling 10-year Treasury notes
and buying 10-year Agency debentures. The seller
of the CDS Index futures would take the other side
of the cash transaction as buyer of the 10-year
Treasuries and seller of the 10-year Agencies.
Example:The CDS Index futures buyer might
simultaneously sell a comparably sized exposure
in the Swap-Corporate yield spread, by buying
corporate bonds and taking the fixed-payer side of
an OTC plain-vanilla swap. The seller of the CDS
Index futures would take the other side of the cash
transaction, as the fixed-rate receiver on the plain-
vanilla interest rate swap and as the seller of the
corporate bonds.
Exchange-for-Swap (EFS) trades, which
are similar to EFP trades, except that the
buyer of CDS Index futures enters into a
comparably scaled OTC credit default swap as
the protection seller. Conversely, the seller of
the CDS Index futures position takes the other
side of the OTC credit default swap, as the
protection buyer.Exchange-for-Risk (EFR) trades, which are
similar to EFS trades, except that the buyer of
CDS Index futures enters into an OTC option
position with a delta that is negatively related to
the level of credit default swap spreads. That is,
he is either the purchaser of a put on protection
or the seller of a call on protection. Conversely,
the seller of the CDS Index futures takes the
other side of the OTC option transaction: She
is either the buyer of a call on protection or the
seller of a put on protection. The DV01 of the
CDS Index futures position is approximately
the same size as the delta of the OTC
option position.
The Chicago Board of Trade Rules and Regulations
are the authoritative source regarding permissible
off-exchange transactions. Regulation 331.05
covers wholesale trades. Regulation 331.08 governs
EFP, EFR, and EFS transactions. The Rules and
Regulations are found on the CBOT website at
www.cbot.com.
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As noted earlier, the underlying reference for CBOTCDS Index futures is the CDR Liquid 50 North America
Investment Grade Index, maintained and published by
Credit Derivatives Research LLC.
In broad overview, the index mechanism is delightfully
simple: an arithmetic average of standard 5-year
single-name credit default swap spreads, quoted on
each of the 50 corporate names represented in the
index. Index components are selected on the basis of
their credit quality -- all must be issuers of investment
grade debt and on the basis of trading activity in the
single-name credit default swaps that reference them.
I si f eii
The CDR Liquid 50 index is reconstituted quarterly,
such that each index series corresponds to an
individual futures contract expiry. (For details, see
Sections 2 and 3 of Appendix 3.)
Example: Consider a hypothetical December 2008
CDS Index futures contract. Its underlying reference
would be the 084 series of the CDR Liquid 50
index (where 084 refers to the fourth, or December,
quarter of 2008). Index components of the 084
series would be chosen and published after close ofbusiness on the last business day of August (Friday,
29 August 2008). The next business day (Tuesday,
2 September) would be both the index roll date and
the first day of trading in December 2008 futures.
This pairing December 2008 futures and the084 index series -- would briefly coexist with the
(hypothetical) September 2008 futures and the
corresponding 083 index series. Since the last
trading day in September 2008 futures would be
Monday, 15 September, the overlap would be just
under two weeks.
The composition of the two index series, 083 and
084, may differ, but this would have no direct
bearing upon the expiry value of the September
2008 futures. The underlying reference for that
contract would be the 083 index series, and no
other. Similarly, the expiry value of December 2008
futures would rely solely upon the 084 index series,
and no other.
si I c
For each new CDR Liquid 50 index series, the
50 components are selected from the universe
of standard credit default swap spreads, where
standard means any on-the-run credit default swap
with 5 years to maturity, denominated in US dollars,
referencing taxable bonds that are rated BBB/Baa2
or higher and that are issued by a North American
corporation. (For details, see Sections 1, 4, and5 of Appendix 3.)
The CDR Liquid 50 Index:Composition and Structure
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Sidenote: The rating standard requirement
Standard & Poors BBB and Moodys Baa2 -- is
more stringent than the requirements that apply
to many other investment grade credit default
swap indexes. For example, to be considered
for admission to the well-known CDX.NA.IG
(the CDX North America investment grade
credit default swap index) a credit default swapmay reference securities rated anywhere within
the investment grade spectrum. (See Index
Methodology for the CDX Indices, 22 May 2007,
www.markit.com.) This means that a debt issuer
rated as low as BBB-/Baa3 might be eligible
to become a component of the CDX.NA.IG
index, whereas the same debt issuer would be
automatically ruled out for inclusion in the CDR
Liquid 50 index. The index managers at CDR
LLC have incorporated this tighter definition of
investment grade into their index design in
order to lend stability to the indexs composition
i.e., to reduce the rate of turnover among indexcomponents -- from one index series to another.
The CDR index managers then rank all elements of
the universe by trading activity, measured in terms of
frequency of actionable bid-offer quotes, during the
three months preceding the index roll date. The more
quoting activity, the higher the rank. The quote data
that CDR LLC employs in determining this ranking are
furnished by CMA through its DataVision service. (For
a description of CMA DataVision and an overview of
its framework for data collection and preparation, see
Appendix 4.) Broadly speaking, the 50 highest-rankedelements of the universe become the components of
the new index series.
mi ri s
o I p
To assemble these components into a new index
series, the CDR index managers begin by computing
index component DV01s. Each index component
DV01 is the dollar value of a 1 basis point change in
one of the single-name credit default swap spreads
serving as an index component, with the notional
amount of the credit default swap assumed to be
$1. The key inputs in computing this collection of
parameters are the levels of credit default swap
spreads for each of the 50 index components, and thelevel of the 5-year plain-vanilla swap rate, at the time
the index series is constituted.
Using these 50 index component DV01s, CDR
LLC will then compute and publish various
index parameters:
the index DV01, the arithmetic average of the
50 index component DV01s. Like the index
component DV01s, the index DV01 presumes
a $1 notional amount.
the
notional size of the credit default swapexposure embodied in the corresponding CDS
Index futures contract. This is equal to the
futures contract DV01, always $500 per basis
point, divided by the index DV01.
the standard recoveryrate that the index
managers will employ in all subsequent index
calculations. The standard recovery rate may
vary from one CDR Liquid 50 index series to
another, depending upon what is deemed to be
market convention at the time the index series
is constituted. (The recovery rate that market
participants regard as customary has varied in
recent years between 0.3 and 0.4, i.e., 30 to
40 percent of notional.) Setting the standard
recovery rate is left to the sole discretion of
CDR LLC. Once the standard recovery rate
for an index series has been set, however, it
remains fixed for the life of that index series.
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Perhaps most important is the maximum
running spread, which functions as an upper
bound on the values that index components
may take. The maximum running spread is
computed as1
Maximum Running Spread =
(1 Standard Recovery Rate) / Index DV01.
For definitions and detailed explanations, see Section
6 of Appendix 3.
Imposing the maximum running spread as an upper
bound on index inputs might appear to be arbitrary.
In fact, it is not. It plays a natural role in ensuring the
stability, continuity, and responsiveness of the CDR
Liquid 50 index
Stability. Suppose a credit event overtakes, or
threatens to overtake, one of the 50 corporate entities
in the index. Market quotes on credit default swap
spreads referencing that entity are apt to widen,
possibly to extreme levels, relative to credit default
swap spreads for other index components. Cappingthe index inputs at the maximum running spread
permits the distressed outlier to enter the index, while
simultaneously preventing it from exerting undue
outlier influence upon the index average.
Continuity. Whenever a corporate entity becomes
distressed, or threatens to become distressed, liquidity
commonly gets patchy in single-name credit default
swaps referencing that entity. Conversely, whenever
market quote activity dries up in single-name credit
default swaps for a given corporate debt issuer, the
likeliest explanation is market apprehension that the
issuer is under imminent threat of a credit event.
Against this backdrop, the maximum running spread
serves as a reasonable place-holder, enabling the
index managers to assign plausible values to all
index components, and thus to publish a valid and
methodologically consistent index value each day,
irrespective of discontinuities in market quote traffic.
Responsiveness. Imposing a structural limit upon
admissible values of index components enables the
index to rely solely upon market rates as inputs.
Importantly, this means index evaluation requires noarbitrary or ad hoc decisions, or speculation, on the
part of the index managers as to whether a credit
event may have occurred or might be imminent.
Thus, paradoxically, the maximum running spread
mechanism makes the CDR Liquid 50 index more
directly responsive to market rates, prices, and
expectations.
1 To appreciate the conceptual role of the maximum running spread, readers familiar with credit derivatives will want to recall the iron triangle of
credit default swap valuation:
Hazard Rate = Credit Default Swap Spread / ( 1 Recovery Rate )
In this framework, the maximum running spread identifies the threshold at which the implied credit event hazard rate equals the basis point value
of a $1 change in the value of the index portfolio.
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14
Exhibit 2 shows daily readings of CDR Liquid 50
index series from late March 2006 through early June
2007. It juxtaposes them with daily values for the three
coeval series of the CDX.NA.IG, widely acknowledged
to be the benchmark in the US credit derivatives
index arena.
The two time series plots obviously mimic each
others broad trends and low frequency swings. Just
as clearly, however, they are far from identical. The
correlation between their daily changes is a modest
0.67. Given the differences in their index composition
procedures rule-based selection on the basis of
trading activity in the case of CDR Liquid 50, versus
an elaborate dealer polling procedure in the case
of CDX.NA.IG such behavioral differences are
unsurprising.
Exhibits 3 and 4 demonstrate these compositional
differences via comparison of on-the-run index series
as of June 2007 specifically the CDR Liquid 50
series 072, and the CDX.NA.IG Series 8 Version
1. At least three features of the comparison are
worth pointing out. First, the CDR Liquid 50 index
places notably more weight upon the Financial and
Communications & Technology sectors. Second, its
emphasis upon the liquidity of its index constituents
leads it, in this example at least, to concentrate nearly
The CDR Liquid 50 Index:Some Stylized Facts
Exhibit 2
CDR Liquid 50 and CDX,
Daily, 21 March 2006 to
11 June 2007
Data Sources: CDR LLC, CMA,
Markit Group Ltd.
Notes: CDX.NA.IG index components
are as given by Markit Group Ltd.
CDX.NA.IG index values are
computed with single-name credit
default swap spread data furnished
by CMA.25
35
45
CDR 062 CDR 063 CDR 064 CDR 071 CDR 072
CDX 6 CDX 7 CDX 8
IndexCreditSpr
ead(Bps)
21-M
ar-06
2-Ma
y-06
13-Jun-06
25-Jul-0
6
5-Se
p-06
17-O
ct-06
28-N
ov-06
9-Jan-07
20-Apr-
07
3-Ap
r-07
15-M
ay-07
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all of its sectoral exposure in just four sectors: Consumer Cyclicals and Noncyclicals, in addition to Financials and
Communication & Technology. Third, for the same reason, the CDR Liquid 50 index accords relatively little or no
weight to Industrials, Materials, Energy, Utilities, and Government (i.e., Fannie Mae and Freddie Mac).
Exhibit 3
Sector Composition as
Percent of Index Weight:
CDR Liquid 50 versus CDX
(CDR Liquid 50 Series 072
and CDX.NA.IG Series 8Version 1, Maturing 20
June 2012)
Data Sources: CDR LLC, Markit
Group Ltd
Among sectors that dominate the CDR Liquid 50 index make-up, the degree of overlap with corresponding
sectors in the CDX.NA.IG is generally high. For example, as Exhibit 4 shows, of 14 corporate names from the
Consumer Cyclicals sector that serve as CDR Liquid 50 index components, 11 also stand as CDX.NA.IG index
components. As a general rule, approximately three quarters of each sectors weight in the CDR Liquid 50 index
signifies overlap with the CDX.NA.IG. The one glaring exception is the Financials sector.
Exhibit 4
Index Overlap Between
CDR Liquid 50 and
CDX: Numbers of Index
Components
(CDR Liquid 50 Series 072
and CDX.NA.IG Series 8
Version 1, Maturing 20June 2012)
Data Sources: CDR LLC, Markit
Group Ltd
18
22
14
1211
9
6
5
2 2
30
28
24
14
2 2
Financial Cons
Cyclical
Comm +
Tech
Cons
Noncyclical
Industrial Materials Utilities Energy Govt Other
CDX
CDR Liquid 50
4
119
5
CDR Liquid 50 NAIG Index, Series 072:
30 of 50 index components also appear in
CDX.NA.IG expiring 20 June 2012
CDR Liquid 50 NAIG
Sector Totals
Overlap with C DX .NA.I G
CDX.NA.IG
Sector Totals
27
23
17
15
14
11
8
6
2 2
1 1
7
12
1415
Financial
ConsCynical
Comm+Tech
ConsNoncyclical
Industrial
Materials
Utilities
Energy
Govt
Other
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fii: cdr lii 50 cdx
The sharp divergence between the two indexes in their
emphasis on Financials arises directly from the CDX.
NA.IG index constitution procedures. The composition
of the CDX indexes is decided collectively by the
consortium of 16 credit derivative dealers who support
the CDX family. This roster includes ABN AMRO,
Bank of America, Barclays Capital, Bear Stearns,BNP Paribas, Citigroup, Credit Suisse First Boston,
Deutsche Bank, Goldman Sachs, HSBC, JPMorgan,
Lehman Brothers, Merrill Lynch, Morgan Stanley, UBS,
and Wachovia. (Source: Markit Ltd.)
Not only do these dealers decide CDX index
composition, they also serve as the main price-makers
and liquidity-providers for the vast OTC derivatives
market that has grown up around the CDX indexes.
Potential conflict of interest considerations dictate that
no consortium member should be eligible for inclusion
as a CDX index component. Because the consortiummembership encompasses most of the leading issuers
of investment grade US financial corporate debt, this
means the CDX.NA.IG index is thus structurally tilted
toward under-representation of Financials.
The CDR Liquid 50 index is not so encumbered,
because its composition, maintenance, and data
sourcing are performed by neutral parties (namely
CDR LLC and CMA). Insofar as its representation of
the Financials sector is unconstrained, the CDR Liquid
50 makes a potentially closer match for the sector
mix held by many corporate bond portfolio managers.
Exhibit 5 suggests as much, via comparison of theCDR Liquid 50 and CDX.NA.IG indexes with the
Lehman Brothers US Corporate Index.
Sidenote:A popular proverb in market folklore
holds that, for any index of credit default swap
spreads, the more weight the index accords
to Financials, the less volatile the index should
be. The time series data portrayed in Exhibit 2,
however, reveal just the opposite: The median
of absolute values of daily changes in the CDR
Liquid 50 index is 0.44 basis points versus 0.38
basis points for the CDX.NA.IG index.
Exhibit 5
Sector Composition as
Percent of Index Weight:
Lehman Brothers US
Corp, CDR Liquid 50,
and CDX
(Lehman Brothers US
Corporate Index, 31 Dec
2006, CDR Liquid 50 Series
072, and CDX.NA.IG Series
8 Version 1)
Data Sources: CDR LLC, Lehman
Brothers Inc, Markit Group Ltd
47
70
30
74
18
62
43
10
Industrials Financial Utilities Govt
Lehman US Corporate CDR Liquid 50 CDX
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By combining appropriate numbers of CBOT CDS Index futures with CBOT 5-Year IRS futures, an investor or
trader can assemble a futures position that mimics the price exposure of a generic portfolio of liquid investmentgrade US corporate bonds. This synthetic portfolio is both simple and flexible in terms of the mechanics of futures
position management and pricing. The two component contracts cease trading on the same day and at the same
time. Both contracts expire by cash settlement. At contract expiry, the underlying references for both contracts
signify maturity exposure of 5 years.
Moreover, toggling back and forth between contract price exposure and implied yield exposure is unusually
straightforward. The 5-Year IRS futures contract is designed so that there is a one-to-one mapping from its price
to the implied forward-starting plain-vanilla swap rate2. CDS Index futures are priced with direct reference to a
forward-starting market-average 5-year credit default swap spread, quoted as a yield spread versus the 5-year
plain-vanilla swap rate. Thus, the implied forward-starting yield for the synthetic portfolio is the sum of (a) the
implied yield for 5-Year IRS futures and (b) the CDS Index futures price. Exhibit 6 shows the resultant implied
corporate bond portfolio yields, daily from late March 2006 to early June 2007, and how they compare with theMoodys Aaa Industrial/Utility average and the Moodys Baa average.
Synthetic CorporateBond Portfolios
Exhibit 6
CBOT Synthetic Corporate
Bond Yields vs Moodys
Aaa Industrial/Utility and
Baa Averages
(CBOT synthetic corporate
bond yield equals (a) the
forward-starting swap
rate implied by the nearby
5-Year IRS futures priceplus (b) the average credit
spread reflected in the CDR
Liquid 50 index.)
Data Sources: Board of Governors of
the Federal Reserve System, CBOT,
CDR LLC
5
6
7
CBOT Synthetic Corporate M oody's Aaa Ind&Utility M oody's Baa
Yield(Percent)
21-Mar-06
2-May06
13-Jun-06
25-Jul-06
5-Sep-06
17-Oct-06
28-Nov-06
9-Jan-07
20-Feb-07
3-Apr-07
15-May-07
2 Translation from price to yield in CBOT IRS futures is facilitated by lookup tables furnished by the Exchange at www.cbot.com/swaps.
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As the scatter plots in Exhibit 7 suggest, daily changes in the CBOT synthetic corporate bond yield are reasonably
well correlated with these market averages: 0.87 for the Moodys Aaa Industrial/Utility, 0.89 for the Moodys
Baa. By no means is either a perfect fit. But given the absence of any other exchange-listed contract or contract
spread that might be remotely suitable for hedging or replicating corporate bond exposure, the CBOT synthetic
portfolio makes an attractive and useful addition to any credit product traders risk-management toolkit.
Exhibit 7
Daily Yield Changes:
CBOT Synthetic Corporate
Bond Portfolio, Moodys
Aaa Industrial/Utility,
and Moodys Baa
(21 March 2006 to
11 June 2007)
Data Sources: Board of Governors of
the Federal Reserve System, CBOT,
CDR LLC
-20
-15
-10
-5
0
5
10
15
20
-20 -15 -10 -5 0 5 10 15 20
Daily Changes in CBOT Synthetic Bond Yield (Bps)
Baa Corr = 0.89
Aaa Corr = 0.87
DailyChan
gesinMoodysBondYields(Bps)
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l c l Irs f + s cds I f
A few examples should make this concrete. To begin, consider a portfolio manager who anticipates buying
$1 billion of 5-year Aaa corporate bonds. Between now and when she actually acquires the bonds, she faces
two primary sources of yield risk:
changes in the 5-year benchmark yield (here, the 5-year plain-vanilla swap rate) and
changes in the corporate credit spread, the spread between the 5-year benchmark yield and 5-year corporate
bond yields.
To manage this exposure, she creates a synthetic place-holder portfolio by combining CBOT CDS Index futuresand 5-Year IRS futures. Properly structured, this should serve adequately both as an anticipatory hedge and as
a means of avoiding cash drag on the portfolios returns. If market conditions are as shown in Exhibit 8, then the
appropriate DV01-weighted hedge should consist of two components:
Long 9,798 5-Year IRS futures = $430,897/($43.98 per contract)
Short 862 CDS Index futures = $430,897/($500 per contract)
Exhibit 8
Market Conditions on Day 1
pi yi dv01
5-Year Aaa Corporate Bonds $1 billion (par) 5.60 $430,897
CBOT 5-Year IRS Futures 102-19/32nds 5.401 $43.98/contract
CBOT CDS Index Futures 36.00 bps 0.36 $500/contract
Note that the long position in the synthetic portfolio comprises along position in IRS futures (which references a
notional asset price) and ashort position in CDS Index futures (which references a notional interest rate spread).
Now suppose market interest rates fall 50 bps, with credit spreads holding steady. Exhibit 9 summarizes the
change in market conditions.
Exhibit 9Change in Market Conditions from Day 1 to Day 2
Day 1 Day 2
pi yi pi yi prie change ($)
5-Year Aaa Corporates $1 billion (par) 5.60 $1,021,823,737 5.10 21,823,737
Long 9,798 5-Year IRS Futures 102-19/32nds 5.401 104-26.5/32nds 4.901 21,892,406
Short 862 CDS Index Futures 36.00 bps 0.36 36.00 bps 0.36 Zero
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Bonds that would have cost $1 billion to purchase at par previously are now $21.8 million more expensive. The
anticipatory hedge has generated sufficient proceeds, however, for the portfolio manager to keep up with market
valuations. Specifically, the 50 bps drop in yields translates into a jump of 2 points and 7.5/32nds in the price of
5-Year IRS futures. The corresponding mark to market on that portion of the hedge structure is:
$21,892,406.25 = 71.5/32nds x $31.25 per 32nd per contract x 9,798 contracts
Now, suppose instead that benchmark market rates hold steady, but that investment grade corporate creditspreads narrow by 5 bps. Exhibit 10 details the change in market conditions.
Exhibit 10
Change in Market Conditions from Day 1 to Day 2
Day 1 Day 2
pi yi pi yi prie change ($)
5-Year Aaa Corporates $1 billion (par) 5.60 $1,002,157,249 5.55 2,157,249
Long 9,798 5-Year IRS Futures 102-19/32nds 5.40 102-19/32nds 5.40 Zero
Short 862 CDS Index Futures 36.00 bps 0.36 36.00 bps 0.31 2,155,000
As before, the rise in bond prices might compel the portfolio manager to chase after the market. Without the
protection afforded by her anticipatory hedge structure, she would find herself paying nearly $2.2 million more
for the same bonds today than she would have paid previously. However, the protection seller exposure to
corporate credit spreads that she established by selling CDS Index futures keeps her overall portfolio in synch
with market conditions. The mark to market on the CDS Index futures component of her hedge structure comes
reasonably close to matching the move in bond prices:
$2,155,000 = -5 bps x $500 per bp per contract x -862 contracts
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s c s Irs f + l cds I f
The same strategy applies to more elaborate hedge structures. Thus, consider another portfolio manager who
intends to sell $1 billion of 8-year Baa corporate bonds. Rather than exiting the position abruptly, he decides to
hedge his exposure by selling a synthetic corporate bond portfolio consisting of CBOT futures.
Exhibit 11
Market Conditions on Day 1
pi yi dv01
8-Year Aaa Corporate Bonds $1 billion (par) 6.50 $616,218CBOT 5-Year IRS Futures 102-19/32nds 5.401 $43.98/contract
CBOT 10-Year IRS Futures 103-24.5/32nds 5.505 $77.88/contract
CBOT CDS Index Futures 36.00 bps 0.36 $500/contract
Assume market conditions are as in Exhibit 11. Because the portfolio manager is concerned about adverse
portfolio impacts from both increases in the outright level of benchmark yields and changes in the slope of
the yield curve, he decides to combine a short position in an IRS futures barbell with a long protection buyer
position in CDS Index futures. Using conventional DV01 weights to set the wings of his IRS futures barbell3, he
determines that the benchmark yield component of his hedge structure should consist of 48 percent 5-Year IRS
futures and 52 percent 10-Year IRS futures. Thus his hedge structure is:
Short 6,720 5-Year IRS futures
Short 4,118 10-Year IRS futures
Long 1,232 CDS Index futures = $616,218/($500 per contract)
As before, note the mix of long and short contract positions: The short synthetic portfolio comprises a
shortposition in the IRS futures barbell and along position in CDS Index futures.
Now, suppose a sudden burst of buoyant economic conditions pushes the yield curve into inversion, with rising
short- and intermediate-term yields pivoting around unchanged long-term yields: 5-year swap rates increase 40
bps, 8-year swap rates gain 16 bps, and 10-year swap rates hold steady. Suppose moreover that corporate
credit spreads across the curve narrow by 5 basis points. The combined impact is an 11 bps rise in 8-year
corporate yields (16 bps increase in benchmark 8-year yields, minus 5 bps decline in credit spreads).
Exhibit 12 summarizes.
3 Let D10, D5, and D, respectively, represent DV01s for a 10-Year IRS futures contract, a 5-Year IRS futures contract, and $100,000 face
value of the cash 8-year corporate bonds, and note that a $1 billion par position in corporate bonds contains 10,000 units of $100,000 par value.
Then the 5-Year IRS futures wing of the butterfly is computed as
10,000 x (D/D5) x (D10 D)/(D10 D5)
The (D10 D)/(D10 D5) term, which plays the principal role in shaping the wing, takes the value of 0.48 in the example above.
Similarly, the 10-Year IRS futures wing of the butterfly is equal to
10,000 x (D/D10) x (D D5)/(D10 D5)
The (D D5)/(D10 D5) term, which shapes this wing, equals 0.52 in the example above.
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Exhibit 12
Change in Market Conditions from Day 1 to Day 2
Day 1 Day 2
pi yi pi yi prie change ($)
8-Year Baa Corporates $1 billion (par) 6.50 $993,249,765 6.61 -6,750,235
Short 6,720 5-Year IRS Futures 102-19/32nds 5.401 100-27.5/32nds 5.801 11,655,000Short 4,118 10-Year IRS Futures 103-24.5/32nds 5.505 103-24.5/32nds 5.505 Zero
Long 1,232 CDS Index Futures 36.00 bps 0.36 31.00 bps 0.31 -3,080,000
Hedge Total 8,575,000
The updraft in short- and intermediate-term yields
hands the portfolio manager a $6.8 million loss on his
core bond position. Fortunately, the hedge affords
more than enough protection, generating proceeds of
nearly $8.6 million, for a net gain of $1.8 million.
Three remarks warrant mention. The first is simply tonote the relative accuracy that the portfolio manager
achieves by using an IRS futures barbell to hedge
his benchmark interest rate exposure. If instead he
had used a DV01-equivalent number of 10-Year IRS
futures alone (7,912 contracts in this case), he would
have found himself underhedged and consequently
nursing a $9.8 million net loss (comprising the $6.75
million loss on the core bond position and the $3.1
million margin payout on the CDS Index futures
position).
Had he used a DV01-equivalent number of 5-YearIRS futures alone (here, 14,011 contracts), he would
have been lavishly overhedged. Gains on his hedge
position would have exceeded triple the loss on his
core bond position ($21.2 million, comprising $24.3
million margin collects on 5-Year IRS futures, less
$3.08 million in margin pays on CDS Index futures).
Thats a gratifying outcome, at least in this case, but
any market practitioner who takes risk management
seriously would warn that such an imbalanced hedge
(in essence, the yield curve exposure between 5-year
and 8-year swap rates) might just as easily hurt you as
help you.
Second, the CDS Index futures hedge ratios in
the examples above are set on the rudimentaryassumption that the credit spread exposure in the
hedge target and the CDS Index futures price move
in lockstep, basis point for basis point. Generally,
this presumption would be unrealistic. A more
refined approach might incorporate the credit spread
analogue to stock index betas. That is, in setting the
credit spread component of the hedge structure,
the portfolio manager might take explicit account of
systematic differences in volatility between the CDS
Index futures contract price and the hedge targets
credit spread.
Third, at first blush, the sizes of the futures
transactions in the examples above may appear
imprudently large. In fact, given that both IRS futures
and CDS Index futures are eligible for a wide array of
bilaterally negotiated off-exchange trades, including
block trades, such magnitudes are neither unrealistic
nor infeasible. (See Off-Exchange Trading on pages
9 and 10.)
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Each day CDR LLC publishes the spot value of the
CDR Liquid 50 index. As noted earlier, this is theaverage of on-the-run 5-year single-name credit
default swap spreads quoted that day, for spot
settlement, for each of the 50 index components. In
contrast, the index value reflected in the price of the
companion CBOT CDS Index contract is a forward
value, the market expectation of the pertinent CDR
Liquid 50 index series on the contracts last day of
trading.
s f, g
As with any other pair of spot and forward market
rates or prices, these two will seldom be identical,except when the futures contract expires. In practice,
however, the difference between spot and forward
typically will be negligible. To make this clear, consider
the three primary linkages in the pricing of a credit
default swap:
The recovery rate, the percentage of face
value that a bond holder would expect to
recover from the bond issuer in the event
that the issuer defaults, enters bankruptcy, or
suffers some other credit event that impairs
timely payments to his debt holders.
The hazard rate (or, when cumulated,
the survival function) which determines the
probability per unit of time that the bond issuer
will suffer a credit event.
The credit default spread essentially the
price of the credit default swap itself -- whichdictates the amount, measured in basis points
per annum, that the protection buyer pays to
the protection seller to guarantee coverage of
the portion of asset exposure not covered by
the recovery rate.
In a world where the yield curve is flat and the hazard
rate is constant, these three elements form the well-
known iron triangle of credit default swap pricing:
Credit Default Spread =
(1 Recovery Rate) x Hazard Rate
Example:Assume the representative average
member of the CDR Liquid 50 index features a
credit default swap spread of 39 basis points.
Assume as well a standard recovery rate of 40
percent and a hazard rate of 0.65 percent per year.
Then the iron triangle takes shape as: 39 bps =
0.0039 percent = ( 1 - 0.40 ) x 0.0065
Given the assumptions underpinning the iron triangle
flat yield curve and flat survival function -- spot and
forward-starting credit default swap spreads should be
identical. More generally, even though yield curves are
seldom flat, and the hazard rate is seldom constant,
spot and forward-starting credit spread values will
tend to be quite close, if not indistinguishable.
Pricing CDS Index Futures:Spot versus Forward
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ei d h r
On those occasions when spot and forward do deviate significantly, the most likely cause is apt to be a non-
constant hazard rate. To see this, consider the pricing of 5-year protection on the CDR Liquid 50 index portfolio,
and assume the following hypothetical market conditions
Arbitrarily, today is 18 June 2003.
Spot rates quoted today are for T+2 settlement on 20 June 2003. (In fact, this signifies standard
settlement for interest rate swaps, but skip day settlement for credit default swaps.)
The LIBOR/plain-vanilla interest rate swap curve is flat at 5 percent
The assumed standard recovery rate is 40 percent.
For spot settlement, market participants value protection on the CDR Liquid 50 index portfolio at 100 bps
per annum.
If the hazard rate were constant, then given these market conditions, the iron triangle would imply a hazard rate of
1.666 percent for the representative average member of the index portfolio:
100 bps = 0.01 percent = ( 1 - 0.40 ) x 0.01666
Assume instead that market participants believe (a) that the average hazard rate will be zero over the coming year
-- reflecting perhaps the very strong presumption of a benign credit environment -- and (b) that the hazard rate
will run thereafter at a constant 2.156 percent per annum. The two far left-hand columns of Exhibit 13 summarize
this set-up.
The two main panels Exhibit 13 il lustrate, on the left, the valuation of a hypothetical 5-year credit default swap for
spot settlement on 20 June 2003 and, on the right, the valuation of forward-starting 5-year credit default swap
that is constructed to mimic a hypothetical September 2003 CDS Index futures contract. The settlement date for
this hypothetical forward-starting swap is IMM Wednesday, 17 September 2003.
Valuation is elementary and, to market practitioners active in credit derivatives, quite familiar. The present value
of the swaps premium leg (the stream of fixed protection payments weighted by the cumulative probability
that there is no credit event) must equal the present value of the swaps recovery leg (the probability that the
protection seller will be obliged to pay the protection buyer if a credit event occurs):
pi l r l
Spread x [ai x zi x (1-pi)] = (1 Recovery) x [zi x (pi -pi-1)]
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Spread is the credit default swap spread, in interest rate percentage points per annum
Recovery is the recovery rate, assumed to be 40 percent, or 0.40
ai are daycount terms. Any ai represents the interval from payment date i-1 to payment date i, measured in
actual/360 terms, and it determines exactly how the credit default swap spread is apportioned to quarterly
protection payments.
zi are present value discount factors, bootstrapped from the plain-vanilla interest rate swap curve. Note that in
the left-hand panel of the table, these are spot discount factors, denoting present value as of the spot settlement
date (20 June 2003) of one dollar on date i. In the right-hand panel, they are forward discount factors, giving thearbitrage-free present value as of the forward settlement date (17 September 2003) of one dollar on date i.
pi represent the survival function. Each pi signifies the probability that a credit event occurs prior to date i.
Exhibit 13
Spot versus Futures-Equivalent Forward Settlement: How the Hazard Function Matters
s s 20 J 2003 f s 17 s 2003
pi l pi l pi l pi l
Spot Spread Recovery Rate Spot Spread Recovery Rate
100 bps 0.4 107 bps 0.4
Spot Spot Forward ForwardDate p a z a *z*(1-pi) (1-0.4)*z*(pi - pi-1) a z a *z*(1-pi) (1-0.4)*z*(pi - pi-1)
20-Jun-0317-Sep-03 0.9878
22-Sep-03 0.0000 0.26 0.9871 0.2577 0.0000 0.01 0.9993 0.0139 0.000022-Dec-03 0.0000 0.25 0.9749 0.2464 0.0000 0.25 0.9870 0.2495 0.000022-Mar-04 0.0000 0.25 0.9631 0.2434 0.0000 0.25 0.9750 0.2465 0.0000
21-Jun-04 0.0000 0.25 0.9517 0.2406 0.0000 0.25 0.9635 0.2435 0.000020-Sep-04 0.0054 0.25 0.9401 0.2363 0.0031 0.25 0.9517 0.2393 0.003120-Dec-04 0.0108 0.25 0.9286 0.2322 0.0030 0.25 0.9401 0.2351 0.0030
21-Mar-05 0.0162 0.25 0.9172 0.2281 0.0030 0.25 0.9286 0.2309 0.003020-Jun-05 0.0216 0.25 0.9060 0.2241 0.0029 0.25 0.9172 0.2268 0.002920-Sep-05 0.0269 0.26 0.8948 0.2225 0.0029 0.26 0.9058 0.2253 0.0029
20-Dec-05 0.0322 0.25 0.8839 0.2162 0.0028 0.25 0.8948 0.2189 0.002820-Mar-06 0.0374 0.25 0.8731 0.2101 0.0027 0.25 0.8839 0.2127 0.0028
20-Jun-06 0.0427 0.26 0.8623 0.2110 0.0027 0.26 0.8730 0.2136 0.002820-Sep-06 0.0480 0.26 0.8517 0.2072 0.0027 0.26 0.8622 0.2098 0.002720-Dec-06 0.0531 0.25 0.8413 0.2014 0.0026 0.25 0.8517 0.2038 0.002620-Mar-07 0.0582 0.25 0.8311 0.1957 0.0025 0.25 0.8413 0.1981 0.0026
20-Jun-07 0.0634 0.26 0.8208 0.1964 0.0025 0.26 0.8309 0.1989 0.002620-Sep-07 0.0686 0.26 0.8106 0.1930 0.0025 0.26 0.8206 0.1953 0.002520-Dec-07 0.0736 0.25 0.8007 0.1875 0.0024 0.25 0.8106 0.1898 0.0025
20-Mar-08 0.0786 0.25 0.7910 0.1842 0.0024 0.25 0.8007 0.1865 0.002420-Jun-08 0.0837 0.26 0.7812 0.1829 0.0024 0.26 0.7909 0.1852 0.002422-Sep-08 0.0888 0.26 0.7809 0.1858 0.0024
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If one knew everything about the market landscape
except the credit default spread itself, one could then
use the framework above to solve for it4:
Spread = { (1 Recovery) x [zi x (pi -pi-1)] }
[ai x zi x (1-pi)]
Exhibit 13 does precisely this. That is, to get the credit
default swap spread for spot settlement, in the left-
hand panel of table one would divide the sum of the
Protection Leg column by the sum of the Premium
Leg column. Similarly, to obtain the forward-starting
credit default swap spread, in the right-hand panel
one would divide the sum of the Protection Leg
column by the sum of the Premium Leg column.
Unlike the spot spread, which is fairly valued at 100
bps, the forward-starting spread is fairly valued at 107
bps. Intuitively, this is because the level of credit event
insurance furnished by the forward-starting swap isgreater than the coverage provided by the spot swap:
Given the survival functions shape, the 5-year
interval spanned by the spot credit default
swap comprises relatively more moments when
the probability of a credit event is presumed to
be zero.
Conversely, the 5-year interval spanned by the
forward-starting credit default swap comprises
relatively more moments when credit events
might occur.
In short, the shape of the hazard rate function in this
example dictates that the spread for the forward-
starting credit default swap should have higher fair
value than for the spot swap. With the passage
of time, the two must converge, so that on 15
September 2003 they will be identical. That is, given
our maintained assumption of a T+2 timetable for
spot settlement, both the forward-starting swap and
a spot swap quoted on Monday, 15 September,
would be intended for settlement on Wednesday,17 September5. Moreover, if the other assumptions
above regarding market conditions were to remain
static, then convergence would be achieved through
a gradual increase in the spot spread, until it reaches
107 bps on Monday, 15 September.
ri d c
On occasion, market practitioners may observe
discontinuities in the time series plots of spot values
for individual CDR Liquid 50 index series. Such
discontinuities, when they occur, are apt to coincide
with the standard quarterly payment dates in the OTCsingle-name credit default swap market (i.e., on or
just after the 20th of March, June, September, and
December).
Example: Consider the hypothetical credit default
swap sketched in the main left-hand panel of Exhibit
13. It corresponds to the hypothetical 032 series
of the CDR Liquid 50 index, which would have
been constituted on Friday, 28 February 2003. (The
equally hypothetical companion CDS Index futures
would have been the June 2003 contract, listed for
trading on Monday, 3 March 2003.)
Between 3 March and 18 March, the on-the-run
credit default swap spreads that CDR LLC uses
4 Students of the credit derivatives market will recognize that this computation incorporates not merely the assumption of a flat hazard rate
function, but also the assumption of a stationary copula scheme governing the manner in which credit events occurring among the 50 index
components might, or might not, occur in bunches.
5 This clarifies precisely how the forward-starting swap corresponds to the hypothetical September 2003 CDS Index futures contract: Monday,
15 September, would also be the last day of trading in futures.
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to evaluate the index would be quoted for spot
settlement, with 5-year term to maturity extending
to 20 March 2008. That is, the indexs inputs would
be swap spreads with terms to maturity that are
actually close to 5 years.
By contrast, from 19 March through 16 June 2003
(the last day of trading in the June 2003 futures),
CDR LLC would evaluate the index components
with quotes for on-the-run spot-settled credit default
swaps that mature on 20 June 2008. Note that, atthe outset of this interval, the indexs inputs abruptly
become swap spreads with terms to maturity of
approximately 5.25 years.
Now suppose the hazard rate function is not
constant. That is, suppose the survival function is
either upward sloping or downward sloping. The
switch in data for index evaluation that occurs on
19 March -- from on-the-run quotes with 5 years
to maturity, to on-the-run quotes with 5.25 year to
maturity may produce a corresponding break in
the time series of spot index values. Whether the
break is up or down, large or small, will depend
upon the slope and pitch of the term structure of
the survival function.
Users of CDS Index futures may note with relief that
there should be no such valuation notch in the daily
progression of futures prices, because fair valuation of
the futures contract is independent of the mechanics
of spot index valuation.
Thus, in the example above, market participants
would assess fair value in June 2003 CDS Index
futures on the presumption that, at contract expiry, theunderlying CDR Liquid 50 index would be evaluated
with market quote data for credit default swaps that
mature in June 2008. Moreover, they would knowingly
entertain this presumption throughout the entire
interval from first day of trading in June 2003 futures
until contract expiration.
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Underlying The corresponding series of the CDR Liquid 50TM North American InvestmentGrade Index
Index Methodology Average of the five-year single-name credit default swap spreads of the 50 mostactively traded corporate names in the North American investment grade creditdefault swap market. Initially all index components are equally weighted(i.e., 2 percent index weight per component).
Contract Multiplier $500 per one basis point
Contract Value The index value in basis points multiplied by the contract multiplier
Price Quotation The index value in basis points and hundredths (1/100) of basis points. For example,a futures price quotation of 38.10 implies an index value of 38.10 basis points.
Minimum Trading
1 tick = 0.01 basis points = $5Increment
Expiration Months Generally, the nearest month in the March-June-September-December quarterly cycle
Last Trading Day The IMM Monday of the contract expiration month (i.e., the second Londonbusiness day preceding the third Wednesday of the contract expiration month)
Final Settlement Day The business day following the last trading day.
Final Settlement The index value, measured in basis points and hundredths (1/100) of basis points,Price evaluated with single-name credit default swap spread quotes, as of close of
business on the last trading day, as furnished by CMA through CMA DataVisionTM
Settlement Cash settlement based on the final settlement price
Trading Hours 6:02 pm to 4 pm Chicago time, Sunday through Friday
Wholesale Trading Minimum wholesale transaction is 100 contracts. Permissible hours for wholesaletransactions are 7 am to 4 pm Chicago time, Monday through Friday. Consultwww.cbot.com for wholesale trading procedures.
Ticker Symbol CX
Appendix 1CDS Index Futures Contract Specifications
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For the current and authoritative version of the CBOT
Rulebook, visit the CBOT website at www.cbot.com
c 61
Credit Default Swap Index Futures
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6101.01 Authority- Trading in Credit Default Swap
Index futures may be conducted under such terms
and conditions as may be prescribed by regulation.
6102.01 Application of Regulations - Credit Default
Swap Index futures shall be referenced hereafter as
CDS Index futures. Transactions in CDS Index futures
shall be subject to the general rules of the Exchange
as far as applicable and shall also be subject to
the regulations contained in this chapter, which
are exclusively applicable to trading in CDS Index
futures. CDS Index futures are listed for trading by the
Exchange pursuant to Commodity Futures Trading
Commission exchange certification procedures.
6104.01 Unit of Trading - The unit of trading shall be
the Contract Reference Index. The Contract Reference
Index shall be referenced hereafter as CRI. CRI shall
be constituted and maintained by the Exchanges
designated index provider.
The designated index provider shall constitute and
maintain a distinct CRI for each distinct CDS Index
futures contract month.
CRI shall be an arithmetic average of interest rate
credit default spreads, as reflected in prices of over-
the-counter credit default swap contracts with five (5)
years to expiry as of the CDS Index futures contracts
last day of trading. Each interest rate credit default
swap spread that serves as a CRI component shall
reference senior, unsecured, taxable, investment
grade debt securities that are denominated in US
dollars and that are issued by a firm domiciled inthe US.
6105.01 Months Traded In - Trading in CDS
Index futures may be scheduled in such months as
determined by the Exchange.
6106.01 Price Basis - The price of CDS Index futures
contracts shall be quoted in interest rate basis points
and hundredths (1/100) of basis points. One basis
point shall equal $500. The minimum price fluctuation
shall be one one-hundredth (1/100) of one basis point
($5 per contract). Contracts shall not be made on any
other price basis.
Appendix 2CDS Index Futures Rules
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6107.01 Hours of Trading - The hours of trading
in CDS Index futures shall be determined by the
Exchange. Trading in an expiring CDS Index futures
contract shall cease at 4:00 pm Chicago time on the
last day of trading in said futures contract.
6109.01 Last Day of Trading - The last day of
trading day in a CDS Index futures contract shall be
the second London business day before the third
Wednesday of the contracts delivery month.
6109.02 Liquidation During the Delivery Month
- After trading has ceased in expiring contracts (in
accordance with Regulation 6109.01 of this chapter),
outstanding contracts shall be liquidated by cash
settlement as prescribed in Regulation 6142.01.
6110.01 Margin Requirements - (See Regulation
431.03.)
6112.01 Position Limits and Reportable Positions
- (See Regulation 425.01 and Appendix 4C.)
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6136.01 Standards - The contract grade shall be the
final settlement value of the Unit of Trading (as defined
in Regulation 6104.01) for the Last Day of Trading
(as defined in Regulation 6109.01), as determined
and furnished to the Exchange by the Exchanges
designated index provider. The value of the CRI
shall be represented in interest rate basis points and
hundredths (1/100) of basis points.
If the Exchanges designated index provider fails to
report a value for the CRI for the Last Day of Trading,
then the contract final settlement price shall be based
upon the value of the CRI for the first preceding US
business day for which a value has been reported by
the Exchanges designated index provider.
6142.01 Delivery on Futures Contracts - Delivery
against expiring CDS Index futures shall be made
by cash settlement through the Clearing Services
Provider following normal variation margin procedures.
The final settlement price shall be $500 times the
final settlement value of the CRI for the Last Day of
Trading, as furnished by the Exchanges designated
index provider.
The final settlement price for an expiring CDS Indexfutures contract shall be determined on the business
day following the Last Day of Trading. For exceptions
to this schedule, see Regulation 6136.01.
6147.01 Payment - (See Regulation 1049.04.)
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The CDR Liquid 50 North America Investment Grade
Index (the Index) is an arithmetic average of 5-year
credit default swap (CDS) spreads for the 50 most
actively traded names in the North American CDS
market.
1 I cIndex components are based upon CDSspreads with the following characteristics --
1.1 CDS reference securities: Taxable bond issuesof North American corporations
1.2 Priority of CDS reference securities: Senior,unsecured
1.3 Maturity of CDS contracts: Five years
1.4 Type of restructuring of CDS contracts:Modified restructuring
1.5 Currency denomination of CDS contracts: USdollar
2 I r dFirst business day of March, June, September,
or December
3 I r pThe Index will be reconstituted each quarter.The components of each new constitutionof the Index, as well as various Indexcharacteristics (6.1), will be publicly announcedfollowing close of business on the businessday preceding the Roll Date (i.e., on the lastbusiness day of the month preceding themonth of the Roll Date).
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4.1 Eligibility Evaluation Period: The three-monthinterval immediately preceding the Roll Date.
4.2 Data Universe: Actionable bid-offers on five-year CDS spreads delivered by dealers directlyto their customers or to inter-dealer brokersduring the Eligibility Evaluation Period.
4.3 Credit Rating Filter: Reference securitiesmust be rated BBB/Baa2 or higher by two ofthe three primary US Nationally RecognizedStatistical Rating Organizations throughout theEligibility Evaluation Period.
5 si I cThe following procedure will govern theselection of Index Components for anyreconstitution of the Index.
5.1 Names that satisfy the Eligibility Criteria forIndex Components, given in Section 4, will formthe pool of eligible names (the eligible pool).
5.2 For each business day during the EligibilityEvaluation Period (4.1), for each eligible name,compute the number of actionable bid-offerquotes (4.2).
5.3 For each business day during the EligibilityEvaluation Period (4.1), rank all eligible namesin descending order according to each namesnumber of actionable bid-offer quotes (5.2).
Appendix 3PROPRIETARY INFORMATION OF CREDIT DERIVATIVES RESEARCH LLC. REPRODUCTION WITHOUT EXPRESSWRITTEN CONSENT OF CREDIT DERIVATIVES RESEARCH LLC IS PROHIBITED.
CDR Liquid 50
TM
NAIG Index Construction andMaintenance Procedures
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5.4 Compute the top-50 count for each eligiblename. For any eligible name, the top-50 countis defined as the number of days during theEligibility Evaluation Period (4.1) on which thatname appears among the 50 highest-rankedeligible names, as determined in 5.3.
5.5 Rank all eligible names in descending orderaccording to their top-50 counts (5.4).
5.6 Eligible names that share a parent corporateentity (sibling names) are filtered from the
ranking determined in 5.5 as follows:5.6.1 If an eligible name serves as an Index
Component in the previous Index constitution,it will remain in the eligible pool for the newIndex constitution, and all of its other siblingnames will be eliminated from the eligible pool.
5.6.2 If, within a group of sibling names, noneappears as an Index Component in theprevious Index constitution, then the siblingname with the highest top-50 count within saidgroup of sibling names will remain in the eligiblepool for the new Index constitution, and all ofthe other sibling names in said group will be
eliminated from the eligible pool.5.6.3 If, within a group of sibling names, more
than one appears as an Index Componentin the previous Index constitution, then theComponent sibling name with the highesttop-50 count among said Component siblingnames will remain in the eligible pool for thenew Index constitution, and all of the otherComponent sibling names will be eliminatedfrom the eligible pool.
5.7 If the resultant eligible pool has fewer than60 names, then proceed directly to 5.8. If theresultant eligible pool has 60 or more eligible
names, then reduce it to those 60 names withthe highest top-50 counts, as determined in5.5 and 5.6.
5.8 Of the remaining names in the eligible pool, the40 names with the highest top-50 counts shallbe automatically selected for inclusion as IndexComponents in the new Index constitution.
5.9 Of the remaining names in the eligible pool,those names that appear as members in theprevious Index constitution shall be admittedas Index Components in the new Indexconstitution, in descending order of their top-50 counts. If and when 50 Index Componentshave been identified, then the new Indexconstitution is complete. Proceed to Section 6.
If fewer than 50 Index Components have beenidentified, then proceed to 5.10.
5.10 Admit remaining names in the eligible poolas Index Components in the new Indexconstitution, in descending order of their top-50counts, until 50 Index Components have beenidentified.
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6.1 At the time a new Index is constituted, thefollowing Index characteristics and parametersshall be published:
6.1.1 Standard Recovery Rate: A parameterwith value between zero and unity thatis set arbitrarily by the Index manager,at his sole discretion, at the time of eachIndex constitution, and shall be used in thecalculation of all other Index characteristicspertaining to the new Index constitution. TheIndex manager, at his sole discretion, maychange the value of the Standard RecoveryRate from one Index reconstitution to the next,in accord with changes in prevailing marketpractice and/or market conditions.
For any given Index constitution, the value ofthe Standard Recovery Rate that the Indexmanager sets shall (a) remain fixed throughoutthe lifespan of that Index constitution and(b) serve as the only value of the Standard
Recovery Rate that the Index manager employsin maintaining that Index constitution.
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6.1.2 Index DV01: The arithmetic average of Index Component DV01s, based on $1 notional. The Index DV01will be computed using the following approximation for Index Component DV01s:
The Index DV01 and all Index Component DV01s shall be rounded to seven decimal places, with halfincrements in the eighth decimal place rounded up.
6.1.2.1 Example: Assume that the 5-year plain-vanilla swap rate is 5 percent, that the on-the-run CDS spreadfor the ith Index Component is 65 basis points, and that the Standard Recovery Rate has been set at 40percent. Then:
6.1.3 Contract Value of a Basis Point: The dollar value of a one basis point change in the price of a CBOT CDSIndex futures contract. Note that this remains constant from one Index Construction date to the next. TheContract Value of a Basis Point should not be confused with the Index DV01.
6.1.4 Implied CDS Notional: The notional underlying value of the CBOT CDS Index futures contract implied jointlyby the Index DV01 and the Contract Value of a Basis Point. The Implied CDS Notional shall be rounded tothe nearest dollar, with half-dollars rounded up to the nearest dollar:
6.1.4.1 Example, contd: Assume the Index DV01 is $0.0004311/bp. By definition the Contract Value of a BasisPoint is $500/bp. Then:
6.1.5 Maximum Running Spread: The maximum admissible value for any Index Component, through the life ofthe Index. The Maximum Running Spread shall be established at the time of Index constitution as:
( )( )
( )0004311.0
010833.005.0
5*010833.005.0exp1
000,10
1DV01ComponentIndex
010833.00.4-1
0.0065
i
=+
+=
==i
( )( )( )
RateRecoveryStandard-1
iComponentIndexforSpreadCDSYear-5Run-the-On
RateSwapVanilla-PlainDollarYear US-5
years5
*exp1
000,10
1DV01ComponentIndex
DV01ComponentIndex50
1DV01Index
i
i
50
1
i
=
=
=
+
+=
= =
r
T
r
Tr
i
i
i
/bp500$01.0
5$
SizeTick
ValueTickPointBasisaofValueContract ===
bp
1$DV01Index
PointBasisaofValueContractNotionalCDSImplied =
824,159,1$1$/bp0004311.$0
$500/bpNotionalCDSImplied ==
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The Maximum Running Spread shall be rounded to the nearest one one-hundredth (1/100) of one basispoint, with half-hundredths rounded up to the nearest hundredth of one basis point.
In any subsequent computation of the Index Value (6.4), any Index Component that exceeds the MaximumRunning Spread shall be replaced by the Maximum Running Spread.
6.1.5.1 Example, contd: Assume as in 6.1.4.1 that the Standard Recovery Rate is 40 percent and that the ImpliedCDS Notional is $1,159,824. Then the Maximum Running Spread will be:
6.2 Index Component Weight: At the time of Index constitution, each Index Component shall be assignedindex weight of one fiftieth (1/50), i.e., a 0.02 share of the Index composition.
6.3 Index Component Spread: The value that the Index manager assigns to each individual Index Componentin computing the Index Value (6.4). The Index Component Spread will depend upon whether single-nameCDS contracts that reference the corresponding Index Component name trade running or trade upfront.
An Index Component shall be identified, at the sole discretion of the Index manager, as to whether ittrades upfront or trades running, according to the conventions by which bid-offer prices are quoted for thecorresponding single-name CDS contracts.
6.3.1 Index Components that trade running: For any Index Component that trades running, the midpoint ofeach bid-offer quote for the corresponding CDS will be used in computing the Index Value, subject to theconstraint that the Index Component Spread must be less than or equal to the Maximum Running Spread(6.1.5).
6.3.2 Index Components that trade upfront: For any Index Component that trades upfront, the sum of therunning spread and the converted upfront percentage will be used in computing the Index Value, subjectto the constraint that the Index Component Spread must be less than or equal to the Maximum RunningSpread (6.1.5). The upfront percentage will be converted to an equivalent spread by multiplying the upfrontpercentage by the Implied CDS Notional and dividing by the Contract Value of a Basis Point.
6.3.2.1 Example, contd: Assume that the Implied CDS Notional is $1,159,824, and that the Maximum RunningSpread is 1,391.79 bps. Assume further that a particular Index Component trades at 18 percent upfront,500 bps running. Then the provisional estimate of the corresponding Index Component is:
Because this provisional estimate is less than the Maximum Running Spread, the Index Component valueshall be set at 917.54 bps.
6.3.3 Index Components that have ceased to trade: For any Index Component that ceases to trade, in the sensethat actionable bid and offer prices cease to be quoted for the corresponding CDS contracts, the IndexComponent Spread shall be set at the Maximum Running Spread.
6.3.4 Each Index Component Spread shall be rounded to the nearest one one-hundredth (1/100) of one basispoint, with half-hundredths rounded up to the nearest hundredth of one basis point.
( )PointBasisaofValueContract
NotionalCDSImplied*RateRecoveryStandard1
SpreadRunningMaximum
=
bps79.1391$500/bps
824,159,1$*)4.01(SpreadRunningMaximum =
=
bps54.917$500/bps
824,159,1$*18.0
500bpsSpreadComponent =+=
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6.4 Index Value: The Index Value is the sum of the products of each Index Component Weight (6.2) and itscorresponding Index Component Spread (6.3):
N is the number of Index Components. At the time of Index constitution, N equals 50, and each IndexComponent Weight is 0.02.
The Index Value, so computed, shall be rounded to the nearest one one-hundredth (1/100) of one basispoint, with half-hundredths rounded up to the nearest hundredth of one basis point.
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7.1 If, subsequent to an Index constitution, the corporate debt issuer referenced by a given Index Componentis superseded by successor corporate entities, then the original Index Component shall be removed fromthe Index, and the successors shall be added as Index Components, regardless of the credit ratings (4.3)that pertain to them. The Index Component Weights assigned to the successors shall sum to the IndexComponent Weight that applied to the original Index Component that the successors shall supersede.
7.2 The Index Component Weight that shall be assigned to each successor shall be set equal to the productof (a) the Index Component Weight that applied to the original Index Component, prior to the successionevent, and (b) the percentage share of the notional amount of the original single-name CDS that isassigned to each successor. The Index Component Weights that shall be assigned to the successors shall
be calculated to six decimal places, with half increments in the seventh decimal place rounded up.7.2.1 Example: Assume Alltel Corp (AT) is an Index Component. On 17 July 2006 Alltel Corp (AT) spins off
Windstream Corp (WIN). Each successor (AT and WIN) is assigned half of the notional value of single-name CDS contracts that referenced the original Index Component (AT). In accommodating thissuccession event, the Index manager makes the following modifications to the Index: the number of IndexComponents rises from 50 to 51; the Index Component Weight that had been assigned to AT is reducedfrom 0.02 to 0.01; and WIN is added as an Index Component with an Index Component Weight of 0.01.
7.3 In the event that the Index Component Weights assigned to the successors, so calculated, fail to sumto the Index weight that applies to the original Index Component, then the successors shall be sortedalphabetically by name, and the weight of the alphabetical first successor shall be adjusted so that thesuccessors Index Component Index weights sum to the Index Component Weight that applied to theoriginal Index Component.
7.3.1 Example: Assume that XYZ Corp is an Index Component, with an Index Component Weight of 0.02.
Assume, moreover, that it has been determined that XYZ Corp will be succeeded by ABC Corp, DEFCorp, and GHI Corp. The Index manager accommodates this succession event by making the followingmodifications to the Index: The number of Index Components rises from 50 to 52; XYZ Corp is removedfrom the Index; ABC Corp is added as an Index Component with Index Component Weight of 0.006666;DEF Corp and GHI Corp are each added as Index Components with Index Component Weights of0.006667 each. Note that the sum of the successor Index Component Weights (0.00666 + 0.006667+0.006667) is identically equal to the Index Component Weight (0.02) that had applied to the originalIndex Component.
=
=N
1i
ii SpreadComponentIndexWeightComponentIndexValueIndex
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