Lecture 14 Credit Default Risk Measuring default risk

Lecture 14 Credit Default Risk

Measuring default risk • Default risk is the primary component of credit 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

• Actuarial measures of default probabilities are provided by credit rating agencies , which classify borrowers by credit ratings that are supposed to quantify default risk • Such ratings are external to the firm. • Similar techniques can be used to develop internal ratings

Default rates and credit ratings • A credit rating is an “evaluation of creditworthiness” issued by a rating agency

• These ratings represent objective (or actuarial) probabilities of default • the agencies have published studies that track the frequency of bond default in the United States, classified by initial ratings for different horizons. • These frequencies can be used to convert ratings to default probabilities.

• The agencies use a number of criteria to decide on the credit rating, among other accounting ratios • Table on the next slide presents median value for selected accounting ratios for industrial corporations

S&P’s Financial Ratios Across Ratings

Historical Default Rates • The following table displays display historical default rates as reported by Moody’s. • These default rates describe the proportion of firms that defaulted • For example, borrowers with an initial Moody’s rating of Baa experienced an average 0. 34% default rate over the next year, and 7. 99% over the following ten years

Moody’s Cumulative Default Rates (Percent), 1920 – 2002

Recovery Rates • Credit risk also depends on the loss given default (LGD) • This can be measured as one minus the recovery rate , or fraction recovered after default. • Bankruptcy process creates a pecking order for a company’s creditors. • This specifies the order in which creditors are paid, thereby creating differences in the recovery rate across creditors. • Within each class, however, creditors should be treated equally.

Estimates of Recovery Rates • Credit rating agencies measure recovery rates using the value of the debt right after default • This is viewed as the market’s best estimate of the future recovery and takes into account the value of the firm’s assets, the estimated cost of the bankruptcy process, and various means of payment (e. g. , using equity to pay bondholders), discounted into the present.

• The recovery rate depend on a number of factors • The status or seniority of the debtor • The state of the economy • Table on next slide shows recovery rates for corporate debt. • Moody’s, for instance, estimates the average recovery rate for senior unsecured debt at f=49%

Moody’s Recovery Rates for U. S. Corporate Debt

Measuring Default Risk from Market Prices • Credit risk can also be assessed from market prices of securities whose values are affected by default. • This includes corporate bonds, equities, and credit derivatives • Since financial markets have access to large amount of information, securities should theoretically provide up-to-date and accurate measure of credit risk

Calculating PD from Bond Prices • Assume for simplicity that a bond makes only one 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 y over the same period

• The payoffs on the bond can be described by a simplified default process, which is illustrated in Figure • At maturity, the bond can be in default or not Its value is $100 if there is no default

• But if the bond defaults, its value will be 100*recovery rate (f). • If π 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

• After rearranging terms • which implies a default probability of

• The equation further simplifies into • what does this equation tell?

Multiple periods • For multiple periods, the probability of default is given by • Which can be rewritten as • or

An example of calculating default prob • We wish to compare a 10 -year Treasury bond a 10 -year zero issued by OGDC which is rated A by PACRA. The respective yields are 6% and 7%, using semiannual compounding. Assuming that the recovery rate is 45% of the face value, what does the credit spread imply for the probability of default?

Example cont. . • Using equation • Therefore, the cumulative probability of defaulting during next ten years is 16. 8%.

Credit Derivatives • Credit derivatives are the latest tool in the management of portfolio credit risk • Credit derivatives are contracts that pass credit risk from one counterparty to another. • Why credit derivatives? • Though banks are there because of diversification advantage, banks still tend to be too concentrated in geographic or industrial sectors

Why credit derivatives? cont. . • This is because their comparative advantage is “relationship banking, ” which is usually limited to a clientele banks know best • it has been difficult to lay off this credit exposure, as there is only a limited market for secondary loans • In addition, borrowers may not like to see their bank selling their loans to another party, even for diversification reasons

Types of CD by instruments • Table in the next slide provides a breakdown of the credit derivatives market by instruments, • The largest share of the market consists of plain-vanilla, credit default swaps, typically with 5 -year maturities • The next segment consists of synthetic securitization, or collateralized debt obligations (CDOs)

Credit Derivatives by Type Percentage of Total Notionals

Credit Default Swaps • In a credit default swap contract, a protection buyer (say A) pays a premium to the protection seller (say B), in exchange for payment if a credit event occurs • The premium payment can be a lump sum or periodic • The contingent payment is triggered by a credit event (like default of rating downgrades) on the underlying credit

Credit Default Swap

An example • The protection buyer, call it A, enters a 1 -year credit default swap on a notional of $100 million worth of 10 -year bonds issued by XYZ. The swap entails an annual payment of 50 bp. 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 counterparty then has to pay $60 million to A. If A holds this bond in its portfolio, the credit default swap provides protection against credit loss due to default.

Credit Default Swap • It is important to realize that entering a credit swap does not eliminate credit risk entirely. • Instead, the protection buyer decreases exposure to the reference credit but assumes new credit exposure to seller • To be effective, there has to be a low correlation between the default risk of the underlying credit and of the counterparty.