TOPIC 4A: Credit Risk – Estimating Default Probabilities

Overview

* Theory of credit risk less developed than VaR based models of market risk. * Much less amenable to precise measurement than market risk – default probabilities are much more difficult to measure than dispersion of market movements. * Measurement on individual loans is important to FI for pricing and setting limits on credit risk exposure.

Default Risk Models

1. Qualitative Models

* Assembling relevant information from private and external sources to make a judgement on the probability of default. * Borrower specific factors (idiosyncratic or specific to individual borrower) include: reputation, leverage, volatility of earnings, covenants and collateral. * Market-specific factors (systematic factors that impact all borrowers include): business cycle and interest rate levels. * FI manager weighs these factors to come to an overall credit decision. * Subjective

2. Credit Scoring Models

* Quantitative models that use data on observed borrower characteristics to calculate a score that represents borrower’s probability of default or sort borrowers into different default risk categories.

Linear Probability Models (LPMs)

* Econometric model to explain repayment experience on past/old loans. * Regression model with a “dummy” dependent variable Z; Z = 1 default and Z=0 no default. * Weakness: no guarantee that the estimated default probabilities will always lie between 0 and 1 (theoretical flaw)

Logit and Probit Models

* Developed to overcome weakness of LPM.

* Explicitly restrict the estimated range of default probabilities to lie between 0 and 1. * Logit: assumes probability of default to be logistically distributed. * Probit: assumes probability of default has a cumulative normal distribution function.

Linear Discriminant Analysis

* Derived from statistical technique called multivariate analysis. * Divides borrowers into high or low default risk classes. * Altman’s LDM = most famous model developed in the late 1960s. Z < 1.8 (critical value), there is a high chance of default. * Weaknesses

* Only considers two extreme cases (default/no default). * Weights need not be stationary over time.

3. New Credit Risk Evaluation Models

* Newer models have been developed – use financial theory and financial market data to make inferences about default probabilities. * Most relevant for evaluating loans to larger corporate borrowers. * Area of very active continuing research by FIs.

Credit Ratings

* Ratings change relatively infrequently – objective of ratings stability. * Only chance when there is reason to believe that a long-term change in the company’s creditworthiness has taken place. * S&P: AAA, AA, A, BBB, BB, B and CCC

* Moody’s: Aaa, Aa, A, Baa, Ba, B and Caa

* Bonds with ratings of BBB and above are considered to be “investment grade”

Estimating Default Probabilities

1. Historical Data

* Provided by rating agencies e.g. cumulative average default rates * If a company starts with a:

* Good credit rating, default probabilities tend to increase with time. * Poor credit rating, default probabilities tend to decrease with time. * Default Intensity vs Unconditional Default Probability

* Default intensity or hazard rate is the probability of default conditional on no earlier default. * Unconditional default probability is the probability of default as seen at time zero. * Default intensities and unconditional default probabilities for a Caa rated company in the third year * Unconditional default probability = Caa defaulting during the 3rd year = 39.709 – 30.204 = 9.505% * Probability that Caa will survive until the end of year 2 = 100 – 30.204 = 69.796%. * Probability that Caa will default in 3rd year conditional on no earlier...