Credit Risk

Credit risk

• Risk of financial loss owing to counterparty failure to perform its contractual obligations.

• For financial institutions credit risk is far more important than market risk.

Sources of risk

• 1. Default risk: risk of default by the counterparty.

• Measured by the probability of default• 2. Credit exposure risk: risk of fluctuations in

the market value of the claim on the counterparty.

• At default, known as exposure at default.

Sources of risk

• 3. Recovery risk. Uncertainty in the fraction of the claim recovered after default.

• This is 1 minus the loss given at default.

Credit risk vs. Market risk

• 1. Credit risk deals with the combined effect of market risk, default and recovery risk.

• Market risk appears through movements in credit exposures

• 2. Credit risk applies to each counterparty• Market risk applies to levels of the trading

organization such as business units, trading desks or portfolios

Credit risk vs. Market risk

• 3. Time horizon is shorter for market risk while longer for credit risk.

• 4. Legal issues are important for evaluating credit risk (like bankruptcy law) while not applicable to market risk.

Credit risk as short option

• Creates an asymmetric risk profile.• When the bond or loan is fully paid, the

upside is small.• At worst, default wipes the asset, downside is

large.

Credit risk as short option

• When the exposure is stochastic, credit risk is complex.

• 1. Credit exposure: There should be a net claim against counterparty

• 2. Counterparty must default

Credit risk as short option

• Credit risk when applied to only bonds and loans, exposure is the face value of the investment.

• Derivatives can have either a positive value ( a net asset to the solvent party) or negative value (a liability of the solvent party)

• Credit exposure exists only when the contract is in the money

Credit risk as short option

• Consider a credit risk of a forward contract on a foreign currency.

• Credit exposure is the positive value of the contract, depends on the exchange rate movements.

Credit risk as short option

• Losst = max (V0,0)

• V0 = is the current or the replacement value of the asset to the solvent party

• No recovery in case of default

Credit risk as short option

• Asymmetric treatment stems from the fact that if the counterparty defaults while the contract has negative value, the solvent party is not free to ‘walk away’

• In contrast, a loss may occur if the defaulting party goes bankrupt, payment will be only a fraction of the funds owed.

Portfolio effects

• Traditionally viewed transaction by transaction• For example, consider a long yen forward and

a short yen forward• Loss in long contract, when yen appreciates• Loss in short contract, when yen depreciates

Portfolio effects

• In traditional approach, potential default losses in two positions added up

• But, events are mutually exclusive• Portfolio approach:• Takes into account interactions between

market movements• Assuming equal probability, it is only half of

previous measure

Components of credit risk

Default and Recovery risk

• Default risk:• Risk that counterparty will default on its

obligation, bi

• bi = 1, in case of default

• bi = 0, no default• Expectation of the variable is the probability

of default.

Default probabilities

• Actuarial models• Credit ratings

Actuarial models

• Forecast objective default probabilities by analysing factors associated with historical default rates

• Example z-score by Altman

Credit ratings

• Adopted by credit rating agencies• Classify issuers by credit ratings

Survival rate

Recovery risk

• Loss given default• Represents the fraction of the exposure lost

on default• 1 minus the fractional recovery rate

Recovery risk

• Depends on• 1. priority of debt• As the seniority decreases, the recovery rate

decreases• 2. industry with tangibles or intangible assets• 3. Legal environment

Market based models

• Credit risk can also be assessed from the price of traded assets whose value is affected by default

• Like bonds, credit default swaps and equities• Prices incorporate expectations of traders

about potential losses owing to default

Market based models

• Payoff on a credit sensitive bond depends on the state of default

• y* is yield on credit risky bond• y is yield on identical risk-free bond• π is the cumulative default rate from now to

maturity T• f is the probability density function of recovery

rate

Market based models

• is approximately equal to • y+π(1-f) assuming T=1• Credit spread y*-y measures the cumulative

probability of default π times the loss given default (1-f)

Market based models

• This is a risk neutral probability• Risk premium to be included in case of• 1. Credit sensitive debt carries some

systematic risk, if economy is bad?• 2. Liquidity effects• 3. Tax effects

Structural models

• Value of the firm = value of debt + value of equity

• Debt has to be repaid at a fixed price in future• If the firm has insufficient funds to repay, firm

is in default• Stock price becomes zero

Structural models

• Merton (1974) • Equity is a call option on the assets of the firm• Exercise price is the face value of debt• Current stock price embodies a forecast of

default probability in the same way that an option embodies a forecast of being exercised

Default comovements

• We cannot observe occurrences of historical defaults on existing companies (that are not bankrupt)

• For investment-grade firms, defaults are scarce

Causative models

• Take observable financial variables as input data and generate default probabilities and correlations

• Models start with a latent, or unobserved, variable, which is the market value V of the company’s assets and modeled via simulations

• Default process is modeled by choosing a cut-off point below which the company goes into default

Causative models

• Mapping this variable on a set of common factors then creates co-movements in asset values, which generates co-movements in defaults.

Credit exposure

• Replacement value of the asset, if positive, on the target date

• Derived from exposure profile• Credit exposuret = max (V0+ΔVt,0)

• V0 = Current replacement value

• ΔVt = increase in value to time t• This market price and hence random variable

Bonds versus Derivatives

• In case of risky debt, credit exposure at expiration is the principal

• Before expiration, exposure varies if the market value fluctuates, but generally close to principal

Bonds versus Derivatives

• Exposure represents positive value of contract, which is much less than the notional amount

• Consider a fixed to floating interest rate swap• No exchange of principal at initiation or

expiration• Payments are netted and represent a small

proportion of principal

Bonds versus Derivatives

• Exposure is the difference between the fixed rate and the prevailing market rates

• At maturity, this risk is zero as there are no coupons to be paid

• In case of currency swap:• Exposure increases steadily with the passage

of time

Bonds versus Derivatives

• Exchange rate risk applies to coupons and the principal

Expected and worst exposure

• Expected credit exposure (ECE) is the expected value of the asset replacement value x, if positive, on a target date

• f(x) is the distribution function of x

Expected credit exposure

• For a bond or a loan, changes in the market value are small relative to the principal, that is

• ECE=0

Netting arrangements

• Offsetting obligations under the same agreement, resulting in one single net claim against the counterparty

• Gross loss = • Net loss = max (V,0) = max [• Larger the N and the lower is the correlation,

the greater is the benefit from netting.

Measuring credit risk

Pricing credit risk

• For pricing purposes, the distribution of expected credit losses over the entire life of the asset has to be computed

Portfolio credit risk

• Once information on exposures, default probabilities, and recovery rates for all the assets in the portfolio, the distribution of losses owing to credit risk at the selected horizon can be computed.

Managing credit risk

• Portfolio management trades off expected profit against risk

• 1. Measure the expected net profit on each position, taking into account the pricing of the instrument and expected credit losses

• 2. Compare these expected net profits with the marginal or incremental contribution to risk

• Choose the best risk-return profile