15 Credit Risk

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Lecture 14

Credit Default Risk


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Measuring default risk

Default risk is the primary component ofcredit risk.

It represents the probability of default (PD),

as well as the loss given default (LGD)

Default risk can be measured using two

approaches: Actuarial methods

Market-price methods


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Actuarial measures of default probabilities areprovided by credit rating agencies, which classifyborrowers by credit ratings that are supposed to

quantify default risk

Such ratings are external to the firm.

Similar techniques can be used to developinternal ratings


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Default rates and credit ratings

A credit ratingis an evaluation ofcreditworthiness issued by a rating agency


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These ratings represent objective (oractuarial) probabilities of default

the agencies have published studies that

track the frequency of bond default in theUnited States, classified by initial ratings fordifferent horizons.

These frequencies can be used to convertratings to default probabilities.


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The agencies use a number of criteria todecide on the credit rating, among otheraccounting ratios

Table on the next slide presents medianvalue for selected accounting ratios for

industrial corporations


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S&Ps Financial Ratios Across Ratings


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Historical Default Rates

The following table displays display historicaldefault rates as reported by Moodys.

These default rates describe the proportion of

firms that defaulted

For example, borrowers with an initial Moodys

rating of Baa experienced an average 0.34%default rate over the next year, and 7.99% over the

following ten years


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Moodys Cumulative Default Rates (Percent),

19202002


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Recovery Rates

Credit risk also depends on the loss given default(LGD)

This can be measured as one minus the recoveryrate , or fraction recovered after default.

Bankruptcy process creates a pecking order for acompanys creditors.

This specifies the order in which creditors are paid,

thereby creating differences in the recovery rateacross creditors.

Within each class, however, creditors should betreated equally.


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Estimates of Recovery Rates

Credit rating agencies measure recoveryrates using the value of the debt right afterdefault

This is viewed as the markets best estimateof the future recovery and takes into accountthe value of the firms assets, the estimated

cost of the bankruptcy process, and variousmeans of payment (e.g., using equity to paybondholders), discounted into the present.


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The recovery rate depend on a number offactors

The status or seniority of the debtor

The state of the economy Table on next slide shows recovery rates for

corporate debt.

Moodys, for instance, estimates the averagerecovery rate for senior unsecured debt atf=49%


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Moodys Recovery Rates for U.S. Corporate

Debt


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Measuring Default Riskfrom Market Prices

Credit risk can also be assessed from marketprices of securities whose values are affected by

default.

This includes corporate bonds, equities, and creditderivatives

Since financial markets have access to large

amount of information, securities shouldtheoretically provide up-to-date and accurate

measure of credit risk


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Calculating PD from Bond Prices

Assume for simplicity that a bond makes onlyone payment of $100 in one period.

We can compute a market-determined yield y*

from the price p* as

This can be compared with the risk-free yield yover the same period

*)1(

100.*

y

Rsp


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The payoffs on the bond can be described bya simplified default process, which isillustrated in Figure

At maturity, the bond

can be in default or not

Its value is $100

if there is no default


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But if the bond defaults, its value will be100*recovery rate (f).

If is the probability of default, how can we

value this bond now? The current price must be the mathematical

expectation of the values in the two states,

discounting the payoffs at the risk-free rate


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After rearranging terms

which implies a default probability of


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Multiple periods

For multiple periods,the probability ofdefault is given by

Which can be re-written as

or

T

T

y

yf

)1(

*)1(1)1(


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An example of calculating default prob

We wish to compare a 10-year Treasury bondand a 10-year zero issued by OGDC which israted A by PACRA. The respective yields are6% and 7%, using semiannual compounding.Assuming that the recovery rate is 45% of theface value, what does the credit spread implyfor the probability of default?


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Example cont..

Using equation

Therefore, thecumulative

probability ofdefaulting duringnext ten years is16.8%.

T

T

y

yf

*)1(

)1(1)1(

20

20

)035.1(

)03.1(1)45.1(

1678.0

55./09231.0


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Credit Derivatives

Credit derivatives are the latest tool in themanagement of portfolio credit risk

Credit derivativesare contracts that pass

credit risk from one counterparty to another.

Why credit derivatives?

Though banks are there because ofdiversification advantage, banks still tend tobe too concentrated in geographic orindustrial sectors


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Types of CD by instruments

Table in the next slide provides a breakdownof the credit derivatives market byinstruments,

The largest share of the market consists ofplain-vanilla, credit default swaps, typically

with 5-year maturities.


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Credit Derivatives by Type Percentage of TotalNotionals


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Credit Default Swaps

In a credit default swapcontract, a protectionbuyer (say A) pays a premium to theprotection seller (say B), in exchange forpayment if a credit event occurs

The premium payment can be a lump sum orperiodic

The contingent payment is triggered by acredit event (like default of ratingdowngrades) on the underlying credit


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Credit Default Swap


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An example

The protection buyer, call it A, enters a 1-year creditdefault swap on a notional of $100 million worth of10-year bonds issued by XYZ. The swap entails anannual payment of 50bp. The bond is called the

reference credit asset At the beginning of the year, A pays $500,000 to the

protection seller. Say that at the end of the year,Company XYZ defaults on this bond, which now

trades at 40 cents on the dollar. The counterpartythen has to pay $60 million to A. If A holds this bondin its portfolio, the credit default swap providesprotection against credit loss due to default.


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It is important to realize that entering a creditswap does not eliminate credit risk entirely.

Instead, the protection buyer decreases

exposure to the reference credit but assumesnew credit exposure to seller

To be effective, there has to be a lowcorrelation between the default risk of theunderlying credit and of the counterparty.

Credit Default Swap

15 Credit Risk

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