Credit Derivatives

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Credit Derivatives

• 2003 Notional value 2.31 trillion
• Investment grade bonds - 3.1 trillion

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Purposes

• Transfer and repackaging of credit risk
• Default baskets and synthetic loss tranches
• New exposure to credit risk to leverage credit
  risk

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Credit Derivatives Market

• 2.306 trillion notional value in 2003 was a 50
  increase from 2002
• Credit default swaps - 73
• Correlation products Synthetic loss tranches
  and default baskets 22
• U.S companies 43.8
• European 40.1
• U.S. has a much larger cash market

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• Banks 50
• Hedging and diversification
• Insurance companies 14
• Hedge funds 13

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Credit Default Swaps

• Bilateral contract to transfer credit risk of a
  reference entity from one party (protection
  buyer) to another party (protection seller)
• Protection buyer shorting credit risk
• Protection buyer makes regular payments (usually
  quarterly) know as the premium leg until credit
  event or maturity

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Default swap mechanics

• If a default occurs, there is a cash settlement
  or physical settlement

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Pari Passu

• From Wikipedia, the free encyclopedia
• pari passu is a Latin phrase that means "at the
  same pace", and by extension also "fairly",
  "without partiality".
• In finance this term refers to two or more loans,
  bonds or series of preferred stock having equal
  rights of payment, i.e., have the same level of
  seniority. In asset management firms, the term
  denotes an equal allotment of trades to
  strategically identical funds or managed
  accounts.
• This term is also often used in bankruptcy
  proceedings where creditors are said to be paid
  'pari passu', or each creditor is paid pro rata
  in accordance with the amount of his claim. Here
  its meaning is 'equally and without preference'.

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• Physical settlement most common
• Requires protection buyer deliver notional amount
  to the seller for notional amount paid in cash.
  Generally, the deliverable instrument is a basket
  with restrictions on maturity and pari passu. The
  buyer is long a cheapest-to-deliver option.

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• Cash settlement not generally used in CDS, but
  is common in default baskets and synthetic CDOs

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CDS Maturity

• Maturity tends to be one of 4 roll dates
• 20th of March, June, September, and December
• New contract 5-year contract on April 12th 2004
  will mature June 20th 2009
• Assume contract has a spread of 160 bp
• Convention is Actual/360
• Default occurs on August 18, 2005

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• 10 million notional value
• Assume contract has a spread of 160 bp
• Convention is Actual/360
• Default occurs on August 18, 2005
• Cash price of deliverable asset 34

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CDS Cash Flow
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Uses of CDS

• Easy to short credit risk. Allows hedging of
  credit risk or for those with a bearish credit
  view.
• CDS are unfunded so leverage is possible.
• CDS are customizable in terms of maturity,
  seniority, and currency. Deviation from market
  standard may incur a liquidity cost.

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• CDS can be used to take a spread view on credit.
  A CDS can be unwound to realize gains (or losses)
  owing to changes in credit spread,
• Liquidity can be better than the cash market.
  Most liquid is 5-year. 3-year, 7-year, and
  10-year are less liquid.

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• International Swaps and Derivatives Association
  (ISDA) has a master agreement.
• Reduces legal risk, speeds up confirmation, and
  therefore enhances liquidity.
• However, CDS market is not standardized. U.S,
  European, and Asian markets are segmented.

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ISDA Credit Events

• Bankruptcy corporation becomes insolvent.
• Failure to pay reference entity does not make
  due payments, taking into account a grace period
  to avoid administrative error.
• Restructuring changes in the debt obligations
  of the reference creditor but excluding those
  that are not associated with credit
  deterioration, such as the renegotiation of more
  favorable crdit terms.

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• Obligation acceleration/obligation default
  Obligations become due and payable earlier than
  they would have been due to default or similar
  condition.
• Repudiation/Moratorium A reference entity or
  government rejects or challenges the validity of
  the obligations.

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Restructuring Clause

• Following bankruptcy, pari passu assets should
  have the same recovery value.
• After a restructuring
• Short term may have higher value than long-term
• High coupon bonds may be more valuable than low
  coupon bonds
• Loans are more valuable than bonds due to
  covenants

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• This makes a CDS valuable
• Consider a protection buyer with a hedge on
  short-term debt trading at 80 while long-term
  debt trades at 65.
• Buy the CDS, buy the long-term bond, and make
  delivery. An immediate 15 profit (at the expense
  of the protection seller).
• 2000 Restructuring of Conseco

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Old restructuring

• Original standard for which delivery is a bond
  with a maximum maturity of 30 years

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Modified Restructuring (Mod-re)

• Current standard in U.S. Roughly speaking, it
  limits the maturity of the deliverable to the
  maturity of the CDS contract plus 30 months.

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Modified-Modified-Restructuring (mod-mod-re)

• Current European standard. it limits the maturity
  of the deliverable to the maturity of the CDS
  contract plus 60 months. It also allows the
  delivery of conditionally transferable
  obligations rather than only fully transferable
  obligations.

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No restructuring

• Eliminates restructuring as a credit event.

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Restructuring and Spread

• Contracts may be available with all four
  restructuring options.
• No-re will have tightest spread.
• Mod-re spread.
• Mod-mod-re more valuable than mod-re and will
  have next widest spread.
• Old-re should have widest spread

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CDS Formats

• Swap format (unfunded format)
• No initial payment
• Counterparty risk
• Credit-linked note (funded format)
• Buyer has to buy fund the purchase of a high
  credit quality bond
• At maturity, the bond is returned to the buyer

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Determining the CDS Spread

• Before credit event

Protection seller
Default swap spread (D)
Pay
Hedged Investor (protection buyer)
Asset
Libor F
LIBOR B
Borrows 100
Funding
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Before credit event

• On the annual payment dates, hedged investor
  receives
• F D B
• At maturity, buyer receives par from asset and
  repays borrowed amount

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Determining the CDS Spread

• After credit event

Protection seller
100
Defaulted asset
Defaulted asset
Hedged Investor (protection buyer)
Repay 100
Funding
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After credit event

• Buyer delivers the defaulted asst to seller in
  return for par and repays the funding loan with
  this principal (assume at par)
• Strategy has no initial cost and is flat
  following credit event, so CF before event have
  to equal zero

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No arbitrage condition

• D F B
• Par floater LIBOR 25bp
• Funding LIBOR 5bp
• F 25bp
• B 5bp
• D 25bp 5bp 20bp

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• Not exact
• Ignores accrued interest and coupon recovery
• Also lacks adjustments for availability of cash,
  liquidity, supply and demand, and counterparty
  risk
• Good starting point, and if incorrect by a lot,
  arbitrage may exist

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Default Swap Basis

• CDS unfunded proxy for cash bond
• Divergence between CDS and cash bonds is default
  swap basis
• Default swap basis CDS spread cash LIBOR
  spread
• Positive basis cash bond spread inside CDS
  spread
• Negative basis CDS spread inside cash LIBOR
  spread

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• Divergence between cash and CDS spread
• Fundamental factors
• Market factors

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Fundamental Factors

• 1) Funding
• If buyer borrows cash to purchase a bond, and
  their credit quality is high, they may be able to
  issue below LIBOR. This means it may be better to
  buy bond than sell protection in CDS. If funding
  cost is above LIBOR, the reverse may be true.

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• 2) The delivery option
• The cheapest to deliver option may be valuable,
  so long position in CDS is more valuable than
  short position. Widens CDS spread and increases
  basis.

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• 3) CDS protects par
• Bonds can trade above or below par because of
  interest rates. Bonds with high (low) coupons
  exposes the to a greater (lower) credit risk.
  Bonds below par value should pay a lower spread
  than the CDS, bonds above par should pay a higher
  spread than default swaps.

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• 4) Counterparty risk
• Protection buyers will pay a lower spread because
  of counterparty risk. Posting collateral can
  reduce this risk.

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Market Factors

• 1) Technical short
• Hedging of synthetic loss tranches requires a
  significant amount of dealer hedging, reducing
  the basis.

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• 2) Convertible issuance
• Convertible equity funds use CDS to hedge credit
  risk in convertibles. This drives default swap
  spreads higher since there are few outstanding
  convertible bonds. Widening is usually not
  sustained and reverts to normalized levels.

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• 3) Demand for protection
• Negative view on credit can be traded in two ways
  - Bond can be sold short or CDS can be purchased.
  This can widen both cash and default swap spread.
  However, it is easier to do a CDS, so the
  widening of the spread is first observed in the
  CDS market.

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• On October 22, 2001, Enrons stock price dropped
  20 to 20.65 per share, and five-year credit
  default swap (CDS) spreads jumped 20 to 48 basis
  points, after the Securities Exchange
  Commission announced it was looking into the
  firms accounting practices. When Enron announced
  it had overstated profits by nearly 600m over
  five years on November 8, the stock was at 8.41
  and CDS spreads were at 133bp. By the time
  Moodys and SP finally downgraded Enron to junk
  status on November 28, its stock was worth little
  more than a dollar per share. Bankruptcy was
  filed on December 2, 2001.

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• The moral of the story, dont ignore the
  market, was a hard lesson for the rating
  agencies to learn. Five years on, one agency,
  Moodys, has something to show for it.
• Moodys, the oldest rating agency, and alongside
  Standard Poors one of the two largest agencies
  by market share, has developed a set of ratings
  indicators derived from market signals. These may
  be used as a counterpart to Moodys normal
  ratings, which are based on analysts views of an
  issuers creditworthiness.
• The indicators, dubbed market implied ratings
  (MIR), highlight discrepancies between an
  issuers credit rating in essence, the rating
  agencys assessment of a companys financial
  situation and future outlook and the markets
  view of that issuer which is in effect the sum
  total of the expression of all bond, credit
  derivatives and equity investors views on that
  company.

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It might seem like something of a no-brainer that
securities the market takes a dim view of are
more likely to default but what is surprising is
the degree to which it is true. Using a
data set of 2,900 issuers, with 180,000
observations gathered between January 1, 1999 and
February 28, 2006, the one-year default rate for
B2 rated issuers trading two notches below their
Moodys rating was a massive 17.82. That
compares with a default rate of 3.61 for issuers
trading flat to their Moodys rating or 0.59
for those trading two notches rich. In other
words, if you held a portfolio of bonds that were
trading two notches cheaper than the Moodys
rating, you should expect nearly a fifth of them
to default within a year. Market implied
ratings (MIR) can also be used to predict
potential ratings changes. An issuer trading
three notches below its Moodys rating is looking
at about a 25 chance of downgrade over a
one-year horizon, according to MIR data from the
same data set.
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Valuing a CDS

• Value at inception is zero no cost to enter
• Value will change over time
• At inception
• E(PV) protection leg E(PV) premium leg
• Mark-to-market (MTM) value is the value the
  market would pay us to unwind the position

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• Suppose a 5-year CDS was issued at a 250bp
  spread. In one year, the spread on the reference
  entity falls to 100bp.
• MTM E(PV) of premium leg of 250bp
• - E(PV) of 4-year protection leg
• New 4-year CDS
• E(PV) of premium leg of 250bp
• - E(PV) of 4-year protection leg

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• Substituting
• MTM E(PV) of premium leg of 250bp
• - E(PV) of 4-year premium pmts 100 bp
• MTM E(PV) of premium leg of 150bp

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• Discount PV of 150bp payments. However, payments
  are made only until credit event, so
• MTM 150bp RPV01
• RPV01 risky PV01 of a 1bp paid on the premium
  leg. Calculating the RPV01 requires a model that
  uses market spreads to determine probability of
  default.
• Bloomberg CDWS function

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Basket Default Swaps(or default baskets)

• Synthetic correlation products that redistribute
  the risk of a portfolio of 5 to 200 CDS.
• Similar to a CDS, except that the nth credit
  event is the trigger. The first-to-default (FTD)
  basket takes the first defaults. Protection
  seller receives a spread based on the notional
  value until the nth credit event or maturity.

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• A basket default swap exposes the protection
  seller to the tendency of the assets to default
  together, or default correlation.

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Why?

• Consider a reference portfolio with CDS spreads
  of 30bp, 30bp, 27bp, 29bp, and 30bp. The FTD
  basket may pay 120bp. A more risk averse investor
  could take the second-to-default (STD) basket or
  lower.

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Valuing a Default Basket

• Value of n A FTD is riskier than a STD and
  commands a higher spread.
• Number of credits The more credits in the
  basket, the greater the likelihood of one or more
  credit events, so the higher the spread.
• Credit quality The lower the credit quality of
  the credits, the higher the spread,

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• Maturity The effect of maturity depends on the
  shape the individual credit curves and the
  correlation of the term structure.
• Default correlation The greater the default
  correlation, the greater the spread.

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Use of Default Baskets

• Investors can leverage credit exposure and get a
  higher yield without increasing notional at risk.
• Reference credits are typically investment grade
  and require little extra analysis.
• Basket can be customized for the investors exact
  view regarding notional value, maturity, number
  of credits, credit selection, and the order of
  protection (FTD, STD, etc.)

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• Default baskets can be more cheaply used to hedge
  a portfolio of credits than hedging individually.
• Can be used to express a view on default
  correlation.

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Synthetic CDOs

• Similar to default basket
• Example
• 100 CDS pool, 10 million notional value each. 3
  tranches
• 50 million equity tranche, 100 million
  mezzanine tranche, 850 million senior tranche

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• Spreads
• Equity tranche 1500bp
• Mezzanine tranche 200p
• Senior tranche 15bp
• A default in 1 of the 100 with a 30 recovery
  rate (7 million loss).

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• Equity tranche loses 7 million of value.
• Equity tranche notional value is now 43 million.
  The spread is now paid on this new value of 43
  million.
• The process is repeated until 50 million losses
  are incurred. At that point the equity tranche is
  depleted and losses now accrue to the mezzanine
  tranche.

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CDOs and beyond

• A CDS is a derivative.
• CDOs are a double derivative.
• There are triple derivatives. A CDO made up of
  CDOs.