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Table 12.2: Average One-Year Rating Transition Rates, 1970-2010

Table 12.2: Average One-Year Rating Transition Rates, 1970-2010

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Credit Quality Dynamics



59



• Table 12.2 shows a matrix of one-year transition rates

between Moody’s ratings

• The number in each cell corresponds to the probability that

a company will transition from the row rating to the

column rating in a year

• For example, the probability of a Baa rated firm getting

downgraded to Ba is 4.112%

• The transition probabilities are estimated from the actual

ratings changes during each year in the 1970–2010 period

• The Ca_C category combines the companies rated Ca and

C

Elements of Financial Risk Management Second Edition â 2012 by Peter Christoffersen



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60



The second-to-last column, which is labeled WR, denotes

companies for which rating was withdrawn

• More interestingly, the right-most column shows the

probability of a firm with a particular row rating defaulting

within a year

• Notice that the default rates are monotonically increasing as

the credit ratings worsen

• The probability of an Aaa rated firm defaulting is virtually

zero whereas the probability of a Ca or C rated firm

defaulting within a year is 35.451%

Elements of Financial Risk Management Second Edition â 2012 by Peter Christoffersen



Credit Quality Dynamics



61



Note also that for all the rating categories, the highest

probability is to remain within the same category within the

year

• Ratings are thus persistent over time

• The lowest rated firms have the least persistent rating

• Many of them default or their ratings are withdrawn

• The rating transition matrices can be used in Monte Carlo

simulations to generate a distribution of ratings outcomes

for a credit risk portfolio

Elements of Financial Risk Management Second Edition © 2012 by Peter Christoffersen



Credit Quality Dynamics



62



• This can in turn be used along with ratings-based bond

prices to compute the credit VaR of the portfolio

• JP Morgan’s CreditMetrics system for credit risk

management is based on such an approach

• The credit risk portfolio model developed in Section 4 can

also be extended to allow for debt value declines due to a

deterioration of credit quality



Elements of Financial Risk Management Second Edition © 2012 by Peter Christoffersen



Credit Default Swaps



63



• As discussed earlier, the price of corporate debt such as

bonds is highly affected by the probability of default of the

corporation issuing the debt

• However, corporate bond prices are also affected by the

prevailing risk-free interest rate as the Merton model

showed us

• Furthermore, in reality, corporate bonds are often relatively

illiquid and so command a premium for illiquidity and

illiquidity risk

• Observed corporate bond prices therefore do not give a

clean view of default risk

Elements of Financial Risk Management Second Edition â 2012 by Peter Christoffersen



Credit Default Swaps



64



Fortunately, derivative contracts known as credit default

swaps (CDS) that allow investors to trade default risk

directly have appeared

• CDS contracts give a pure market-based view of the default

probability and its market price

• In a CDS contract the default protection buyer pays fixed

quarterly cash payments (usually quoted in basis points per

year) to the default protection seller

• In return, in the event that the underlying corporation

defaults, the protection seller will pay the protection buyer

an amount equal to the par value of the underlying corporate

bond minus the recovered value

Elements of Financial Risk Management Second Edition © 2012 by Peter Christoffersen



Credit Default Swaps



65



• CDS contracts are typically quoted in spreads or premiums

• A premium or spread of 200 basis points means that the

protection buyer has to pay the protection seller 2% of the

underlying face value of debt each year if a new CDS

contract is entered into

• Although the payments are made quarterly, the spreads are

quoted in annual terms

• CDS contracts have become very popular because they

allow the protection buyer to hedge default risk



Elements of Financial Risk Management Second Edition â 2012 by Peter Christoffersen



66



Credit Default Swaps

They of course also allow investors to take speculative views

on default risk as well as to arbitrage relative mispricings

between corporate equity and bond prices

• Paralleling the developments in equity markets, CDS index

contracts have developed as well

• They allow investors to trade a basket of default risks using

one liquid index contract rather than many illiquid firmspecific contracts

• Figure 12.11 shows the time series of CDS premia for two of

the most prominent indices, namely the CDX NA (North

American) and iTraxx EU (Europe)

Elements of Financial Risk Management Second Edition © 2012 by Peter Christoffersen



Figure 12.11: CDS Index Premia. CDX North

America and iTraxx Europe



Elements of Financial Risk Management Second Edition © 2012 by Peter Christoffersen



67



Credit Default Swaps

• The CDX NA and iTraxx EU indexes each contain 125

underlying firms

• The data in Figure 12.11 are for five-year CDS contracts

and the spreads are observed daily from March 20, 2007

through September 30, 2010

• The financial crisis is painfully evident in Figure 12.11

• Perhaps remarkably, unlike CDOs, trading in CDSs

remained strong throughout the crisis and CDS contracts

have become an important tool for managing credit risk

exposures

Elements of Financial Risk Management Second Edition â 2012 by Peter Christoffersen



68



Summary



69



Credit risk is of fundamental interest to lenders but it is

also of interest to investors who face counterparty default

risk or investors who hold portfolios with corporate bonds

or distressed equities.

• This chapter has provided some important stylized facts on

corporate default and recovery rates

• Merton’s seminal model

• Vasicek’s factor model structure

• Credit Default Swaps

Elements of Financial Risk Management Second Edition © 2012 by Peter Christoffersen



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Table 12.2: Average One-Year Rating Transition Rates, 1970-2010

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