individual loan credit risk

BUS FINANCE 826

Overview

• The analysis and measurement of credit risk on individual loans. This is important for purposes of:– Pricing loans and bonds– Setting limits on credit risk exposure

Credit Quality Problems• Problems with junk bonds, LDC loans,

residential and farm mortgage loans.

• More recently, credit card loans and auto loans.

• Crises in Asian countries such as Korea, Indonesia, Thailand, and Malaysia.

Web Resources

• For further information on credit ratings visit:

Moody’s www.moodys.com

Standard & Poors www.standardandpoors.com

Web Surf

Credit Quality Problems

• Over the 90s, improvements in NPLs for large banks and overall credit quality.

• Recent exposure to borrowers such as Enron.

• New types of credit risk related to loan guarantees and off-balance-sheet activities.

• Increased emphasis on credit risk evaluation.

Types of Loans:

• C&I loans: secured and unsecured– Spot loans, Loan commitments– Decline in C&I loans originated by commercial

banks and growth in commercial paper market.

• RE loans: primarily mortgages– Fixed-rate, ARM– Mortgages can be subject to default risk when

loan-to-value declines.

Consumer loans

• Individual (consumer) loans: personal, auto, credit card.– Nonrevolving loans

• Automobile, mobile home, personal loans

– Growth in credit card debt• Visa, MasterCard • Proprietary cards such as Sears, AT&T

– Risks affected by competitive conditions and usury ceilings

Other loans

• Other loans include:– Farm loans– Other banks– Nonbank FIs– Broker margin loans– Foreign banks and sovereign governments– State and local governments

Return on a Loan:

• Factors: interest payments, fees, credit risk premium, collateral, other requirements such as compensating balances and reserve requirements.

• Return = inflow/outflow

k = (f + (L + M ))/(1-[b(1-R)])

• Expected return: E(r) = p(1+k)

Lending Rates and Rationing

• At retail: Usually a simple accept/reject decision rather than adjustments to the rate.– Credit rationing.– If accepted, customers sorted by loan

quantity.

• At wholesale: – Use both quantity and pricing adjustments.

Measuring Credit Risk

• Qualitative models: borrower specific factors are considered as well as market or systematic factors.

• Specific factors include: reputation, leverage, volatility of earnings, covenants and collateral.

• Market specific factors include: business cycle and interest rate levels.

Credit Scoring Models

• Linear probability models:

Zi =

– Statistically unsound since the Z’s obtained are not probabilities at all.

– *Since superior statistical techniques are readily available, little justification for employing linear probability models.

n

jjijX

1, error

Other Credit Scoring Models

• Logit models: overcome weakness of the linear probability models using a transformation (logistic function) that restricts the probabilities to the zero-one interval.

• Other alternatives include Probit and other variants with nonlinear indicator functions.

Altman’s Linear Discriminant Model:

• Z=1.2X1+ 1.4X2 +3.3X3 + 0.6X4 + 1.0X5

Critical value of Z = 1.81.

– X1 = Working capital/total assets.

– X2 = Retained earnings/total assets.

– X3 = EBIT/total assets.

– X4 = Market value equity/ book value LT debt.

– X5 = Sales/total assets.

Linear Discriminant Model

• Problems:– Only considers two extreme cases (default/no

default). – Weights need not be stationary over time.– Ignores hard to quantify factors including

business cycle effects. – Database of defaulted loans is not available to

benchmark the model.

Term Structure Based Methods

– If we know the risk premium we can infer the probability of default. Expected return equals risk free rate after accounting for probability of default.

p (1+ k) = 1+ i– May be generalized to loans with any maturity

or to adjust for varying default recovery rates.– The loan can be assessed using the inferred

probabilities from comparable quality bonds.

Mortality Rate Models

– Similar to the process employed by insurance companies to price policies. The probability of default is estimated from past data on defaults.

– Marginal Mortality Rates:

MMR1 = (Value Grade B default in year 1) (Value Grade B outstanding yr.1)

MMR2 = (Value Grade B default in year 2) (Value Grade B outstanding yr.2)

RAROC Models

– Risk adjusted return on capital. This is one of the more widely used models.

– Incorporates duration approach to estimate worst case loss in value of the loan:

– L = -DL x L x (R/(1+R)) where R is an estimate of the worst change in credit risk premiums for the loan class over the past year.

– RAROC = one-year income on loan/L

Option Models:

– Employ option pricing methods to evaluate the option to default.

– Used by many of the largest banks to monitor credit risk.

– KMV Corporation markets this model quite widely.

Applying Option Valuation Model

• Merton showed value of a risky loan

F() = Be-i[(1/d)N(h1) +N(h2)]

• Written as a yield spread

k() - i = (-1/)ln[N(h2) +(1/d)N(h1)]

where k() = Required yield on risky debt

ln = Natural logarithm

i = Risk-free rate on debt of equivalent maturity.

*CreditMetrics

• “If next year is a bad year, how much will I lose on my loans and loan portfolio?”

VAR = P × 1.65 ×

• Neither P, nor observed.

Calculated using:– (i)Data on borrower’s credit rating; (ii) Rating

transition matrix; (iii) Recovery rates on defaulted loans; (iv) Yield spreads.

* Credit Risk+

• Developed by Credit Suisse Financial Products.– Based on insurance literature:

• Losses reflect frequency of event and severity of loss.

– Loan default is random.– Loan default probabilities are independent.

• Appropriate for large portfolios of small loans.

• Modeled by a Poisson distribution.

Pertinent Websites

• For more information visit:

Federal Reserve Bank www.federalreserve.gov

OCC www.occ.treas.gov KMV www.kmv.com

Card Source One www.cardsourceone.com

FDIC www.fdic.gov

Credit Metrics www.creditmetrics.com

Robert Morris Assoc. www.rmahq.orgWeb Surf

Pertinent Websites

The Economist www.economist.com

Fed. Reserve Bank St. Louis www.stls.frb.gov

Federal Housing Finance Board www.fhfb.gov

Moody’s www.moodys.com

Standard & Poors www.standardandpoors.com

Web Surf