23. Analysing credit risk

Question 1

Define credit risk

Answer 1

• Risk of loss due to contractual obligations not being met (in terms of quantity, quality or timing) either in part/in full whether due to inability or by decision

Question 2

What are the two components

Answer 2

• Default risk
• Credit spread risk

Question 3

Which give examples of credit risk events?

Answer 3

 Missed payment
 Financial ratio falling below some level
 Legal proceedings starting against credit issuer
 Present value of A falls below L because of economic factors

Question 4

What are the two components of default risk

Answer 4

 Probability of default
 Loss on default

Question 5

What are the 3 things that must be assessed when assessing default risk

Answer 5

 Probability of default
 Loss on default
 Level and nature of interactions between credit exposures and other risks in a portfolio

Question 6

Identify sources of information for credit risk

Answer 6

• Credit rating agencies
• Counterparty
• Publicly available data
• Proprietary databases

Question 7

Outline the items that qualitative assessments of credit risk can be based on

Answer 7

o Nature of contract e.g. seniority of a loan
o Level and nature of security e.g. parental guarantees, collateral
o Nature of borrower e.g. industry sector / employment status
o Economic indicators
o Financial ratios
o Face to face meetings with credit issuer and/or counterparty

Question 8

Outline the merits of qualitative risk assessments

Answer 8

Advantages:
o Range of (subjective) factors can be incorporated into assessment

Disadvantages:
o Excessive subjectivity
o Inconsistency between ratings
o Meaning of subjective ratings could change over eco cycle and/or due to changes in eco environment
o Ratings might fail to respond to changing eco cycles or circumstances of counterparty- often reluctance to change rating

Question 9

List examples of quantitative credit models

Answer 9

• Credit scoring
• Structural models
• Reduced form models
• Credit portfolio models
• Credit exposure models

Question 10

Describe credit scoring models

Answer 10

• Use fundamental info to get likelihood of default
• E.g.
  o Empirical models
  o Expert models

Question 11

Outline structural models

Answer 11

• AKA Firm value
• Use share price and volatility
• E.g., KMV and Merton

Question 12

Explain how the Merton model works

Answer 12

o Uses Black-Scholes option pricing theory along with equity share price volatility to get info on value of total A and value of D
o Considers total A = total E + total D
o D is zero-coupon bond redeemable at some future t
o Total A assumed to follow geometric Brownian motion (continuous-time lognormal random walk)
o Shareholders can be thought of as call option holders of total A
o If A > nominal value of D by t then D repaid and sh get residual A
o Nominal value of D is strike price of call
o If A < nominal value of D by t then sh get nothing aka call not exercised
o Equity shares are like call options and can be valued using option-pricing theory and B-S
o D valued as diff between A and E
o Equivalentlt, by Put-call parity, value of D = value of risk free bond – value of put on company’s total A
o Idea: if A increase in value, bh get same amount at maturity as holder of risk free bond
o If A<nominal value of D, equity sh default and bh lose diff between total A at redemption and nominal value of D

Question 13

Outline the pros of the Merton model

Answer 13

 Mathematically tractable using B-S option pricing results
 Intuitive results, eco explanation for P(default) as based on capital structure of co and changes in co value
 Can estimate appropriate credit spread for bond if unquoted or unrated

Question 14

Outline the cons of the Merton model

Answer 14

1. Assumptions of:
    Frictionless markets (no transaction costs) with continuous trading
    Risk free rate deterministic and constant for borrowers and lenders
    X_t follows lognormal random walk with fixed growth rate and volatility independent of firm financial structure which is unrealistic assumption
    Bond is zero-coupon with one defalt opportunity
    Default = liquidation- can mean diff things in real life
2. Can only be solved when X_t and sigma are observable- impossible
3. Accurate sigma estimate needed&raquo_space; more appropriate for larger cos with frequently traded stocks
4. Results sensitive to market sentiments in absence of real changes

Question 15

Outline how the KMV model works

Answer 15

o Uses Merton’s concept: company will default first instance X_t falls below (or some B^ based on term structure of liabilities, usually 1 year L)
o Distance to Default(DD): # of std deviations company’s A must fall in value before breaching B
DD(t)=[X(t)-B]/[X(t)*σ(x)]
o Use empircal data on co defaults and how linked to DD to get P(Default)

Question 16

Outline how the KMV model is better than the Merton model

Answer 16

 Coupon-paying bonds can be modelled
 More complex L structures can be accommodated as system uses average and overall gearing level (rather than having to assume sing zero-coupon bond)
 X(t) not assumed to be observable and derived from co’s equity shares.

Question 17

Outline what reduced-form models are

Answer 17

• Model default as statistical process dependent on eco variables
• E.g., Credit migration models

Question 18

Outline how credit migration models work

Answer 18

o For longer term exposures
o E.g. 2 state model and Jarrow-Lando-Turnbull
o Estimate probability:
 Historical data use to determine probability that co moves to lower rating at end of year and probs recorded in transition probability matrices
 Matrices applied to counterparty’s current rating to estimate likelihood of each possible rating in each future year
 Use prob of default for company of given rating to estimate chance of default in each year

Question 19

Outline the merits of credit migration models

Answer 19

Pros:
 Volatile equity markets shouldn’t overly affect results – makes sense as empirically, this is usually the case

Cons- assumptions:
 Likelihood of default determined just by credit rating
 Credit rating reflect average company’s default likeligood throughout business cycle (instead of reflecting chance in current eco environment)
 Follows time-homogeneous Markov chain- assumption that history will repeat

Question 20

Outline hw credit portfolio models work

Answer 20

• Estimate credit exposure over many counterparties
• May allow for diversification and aggregation
• Key challenge is allowing for these relationships

Question 21

Give examples of credit portfolio models

Answer 21

• Multivariate structural
• Multivariate credit migration models
• Econometric
• Common shock models

Question 22

Outline how multivariate structural models work

Answer 22

• Multivariate KMV, using correlation matrices to model A values or copulas (t or explicit fat tailed)

Question 23

Outline how multivariate credit-migration models

Answer 23

• E.g. CreditMetrics
• Assumes equity returns can be modelled by country-specific indices and independent firm-specific volatility
• Monte Carlo simulations used to derive potential:
  o Movements in equity values
  o Corr changes in overall value of each org’s assets
  o Associated rating changes
  o Implied change in value of bonds in portfolio (incl. default experience)
• Can apply risk measures to the simulations

Question 24

What are the assumptions underlying the CreditMetrics model

Answer 24

o Each credit rating has associated P(Default)
o Change in rating is function of change in value of org’s assets and volatility value of those assets
o Value of assets of each org in portfolio behaves log-normally
o Correlation between asset values (of diff orgs) can be estimated from correlation between corr equity values
o Equity returns can be modelled by country-specific indices and firm specific volatility

Question 25

Define econometric models, common shoch models and time until default

Answer 25

Econometric/actuarial models
* Don’t model asset value going forward- estiate default rate using external (e.g. economic) or empirical data
Common shock models
* Determine P(no defaults) assuming each bond defaults in line with Poisson process, and considering shocks, each of which cause default of one or more of bonds in portfolio
Time-until-default / survival models
* Survival CDFS (each based on hazard rate determined from implied probability of default) are linked by suitably parametrised copula function, so as to estimate aggregate default rate for bond portfolio.

Question 26

Give an example of credit exposure models

Answer 26

Monte Carlo approach to estimate expected and max credit exposures

Question 27

Give high level problems with modelling credit risk

Answer 27

• Lack of publicly available info/data on credit quality of individual companies- companies may choose not to pay for rating or publish any ratings.
• Skewness of credit loss distributions. Typically have heavy tails where losses are greatest- making it difficult to estimate extreme events
• Dependence of one credit event on others. If one counterparty defaults, often found that other connected companies or those in similar industry also default. Assumptions on dependency have big impact on overall results of models.
• Some economic events have no equivalent in history, data difficult to get.

Question 28

Why is a lack of data a problem

Answer 28

• Difficult to calibrate models

Question 29

What are the effects of not being able to estimate extreme events?

Answer 29

o Makes it difficult to estimate capital requirements

Question 30

Explain why dependence is an issue in modelling

Answer 30

o Dependency caused by economic links between companies, which can be exposed to similar macroeconomic factors. So default events can be triggered by particular set of eco circumstances.
o Obtaining reliable data on the dependency is difficult

Question 31

What determines recoveries

Answer 31

o Seniority of debt
o Rights of other creditors
o Availability of (marketable/liquid) collateral