Chapter 7: Credit Risk

Question 1

What is credit risk?

Answer 1

• Credit risk is the risk of financial loss due to failure of counterparty to fulfill obligations.
• Managing credit risk is challenging because of high complex nature:
  
  • There are three determinants of credit risk that all need to be modelled: probability of default, exposure at default and loss given default
  • It is a long-lived risk: it involves long term instruments that can not easily be liquidated
  • There are legal issues: credit risk is often a breach of contractual obligations
  • For many institutions it is a real risk: traditional banks have large exposures to credit risk

Question 2

What are the different aspects of credit risk?

Answer 2

1. Settlement risk: arises at the execution of a transaction as a result of:
   
   1. Counterparty default
   2. Liquidity constraints
   3. Operational failure
2. Presettlement risk arises over the full life of the contract
   
   • Traditional concept of credit risk
   • Captures any change in credit quality: not only by default, but any upward or downward revision of creditworthiness.
   • Focus of this course is on the general presettlement risk.

Question 3

What are the determinants of credit risk?

Answer 3

1. Probability of default (PD): default is a discrete state that occurs with a certain probability PD:
   
   • within the ’no default state’: different levels of creditworthiness can arise (where any chance in credit quality can be modelled)
2. Loss given default (LGD): fraction of claim that cannot be recovered:
   
   • LGD = 1-recovery rate = (1 − f )
   • collateral significantly reduces LGD
3. Credit exposure (CE): amount of money at stake:
   
   • CE equals the market value of the claim
   • At default this CE is labelled exposure at default (EAD)

Question 4

How is modeling credit risk in practice?

Answer 4

• Much more challenging:
  
  1. What about the credit loss distribution of a portfolio of instruments?
  2. What about other credit quality changes?
  3. What about random credit exposures and recovery rates?
• To be realistic, the above simple example needs to be modified, but the question then raises how we should deal with this.

Question 5

Can we proceed along the same approach of market risk where we can choose between the empirical distribution or normal distribution approach?

Answer 5

• The credit loss distribution is highly skewed (we have limited upside, and a large downside). Imposing a parametric distribution is then not straightforward, and thus we need to simulate the credit loss distribution.
• In addition, computing credit risk losses at the level of a porfolio is much more challenging than computing losses in the context of market risk.
• The portfolio distribution should reflect diversification benefits, and thus should account for correlations between PD (and potentially also correlations between LGD and CE)

Question 6

What is the main component of probability of default and how do we estimate this?

Answer 6

• The main component of credit risk is the probability of default (PD) and most attention goes to modelling this likelihood of default.
• 2 main approaches to estimate PD:
  
  1. Historical methods: allow us to derive PDs by analyzing the factors that are associated with historical default rates
  2. Market price methods: allow us to derive PDs by analyzing market prices of instruments subject to default risk = more forward looking.

Question 7

What are the historical methods to forecast default rates?

Answer 7

• Historical methods focus on the determinants that explain or forecast default rates based on a sample of historical data.
• 2 main approaches to estimate default risk:
  
  1. Altman Z-score probabilities of default
  2. Ratings’ based probabilities of default

Question 8

What is the Altman Z-score?

Answer 8

• Z-score predicts creditworthiness of a firm based on financial statement data.
• Model was developed in 1968, with extensions in 2000.
• Formally, we use a multiple discriminant analysis to predict PD from 5 accounting ratios:
  
  • working capital/total assets (X1)
  • retained earnings/total assets (X2)
  • EBIT/total assets (X3)
  • market value of equity/book value total liabilities (X4)
  • sales/total assets (X5)
• For Z higher, the PD is lower:
  
  • Defaulting firms: Z < 1,8
  • Grey zone: 1,8 < Z < 2,99
  • Non-defaulting firms: Z > 2,99
• Apart from the standard Z-score model, revised Z)score models exist that use different account ratios/cutoff scores and classification criteria for private firm and for non-manufacturing firms.

Question 9

What are some variations to the Z-score model that have been introduced in the literature?

Answer 9

• Ohlson O-score is a 9-factor model using financial disclosure statement data
• CHS model is a 10-factor model combining financial disclosure statement data and stock price data.

Question 10

What are the ratings based PD?

Answer 10

• Rating agencies as well as financial institutions have developed their proprietary rating models to capture the likelihood of default. Such models are rather sophisticated and combine a broad set of information:
  
  • Quantitative analysis
  • Qualitative analysis
  • Legal analysis
• Four rating agencies (S&P, Moody’s, Fitch, DBRS) are recognized by the ECB to determine collateral requirements for banks to borrow from the ECB (which makes them indispensable and powerful)
• Credit ratings correspond to descriptive definitions, no strict probabilities.
• Importantly, ratings between different agencies are similar, but not identical! Significant differences between S&P and Moody’s!
• While part of differences can be explained by the use of a different methodology, differences are maybe too large to be meaningful:
  
  • The role of judgement is very large and we have no information on specifics of methodologies used
  • There are conflicts of interest: rating agencies are not independent as the firms pay to obtain a rating

Question 11

What are average cumulative default rates?

Answer 11

• Apart from the credit ratings, rating agencies also report average cumulative default rates. This gives an indication of the fraction of issuers, per rating category, that have defaulted up to a particular year.
• Characteristic of these average cumulative default rates is that they go up over time (they are cumulative) and over decreasing credit worthiness
• Default process: at each nod there are 2 states possible: default or not default so the cumulate default rates can be used to comppute various related probabilities to default.

Question 12

What is the marginal probability during year t?

Answer 12

• Marginal default probability during year t, dt,r (with initial rating r)is the number of issuers that default in year t, mt,r, relative to number of issuers at beginning of year t, nt,r
  
  • This probability is also labelled conditional default probability
  • The conditional default probability for a short period of time ∆t is refered to as λ(t)∆t, with λ(t) the hazard rate or default intensity

Question 13

What is survival probability?

Question 14

What is the unconditional default probability?

Answer 14

• Unconditional default probability​ is the number of issuers that defaulted in year t, relative to the initial number of issuers with rating r (ie as observed at time zero).
• Also called the marginal default rate from start to year t.

Question 15

What is the cumulative default rate?

Answer 15

• Number of issures that have defaulted at any time until year t.

Question 16

How is the accuracy of ratings based PD?

Answer 16

• Part of the variation in default rates can be explained by shortage of data over time/over rating class: we observe few defaults for investment graded bonds or for long horizons
• Such limited observations might lead to imprecise or even inconsistent default estimates: adding/omitting particular data can have large impact our estimates
• A solution to this problem is to consider transition rates: they give the probability of a change in rating, conditional on its rating in the beginning of the period.
  
  • Transition rates are more robust and consistent than cumulative default rates.
  • By assuming that migration rates are independent over time, we can use them to calculate more robust cumulative default rates.

Question 17

How can we evaluate historical methods to PD?

Answer 17

• While widely used, ratings based PDs have some important disadvantages/limitations:
  
  • PDs are based on stale sources: accounting information is only reported on a low frequency
  • PDs are based on a smoothed out and historical representation of financial strength
  • PDs have no formal underpinning: inconsistencies in estimates can therefore arise (e.g. due to data shortage)

Question 18

What are the market price methods to PD?

Question 19

How can we use bond prices to PD?

Answer 19

• Approach is closely linked to credit risk measurement by a credit spread.
• Since the price of a bond is its discounted future cashflows, the ultimate payoff depends on its state of default –> back out the cumulate risk-neutral probability of default.
  
  • Using bonds of different maturities, this allows us to construct a term structure of default probabilities.

Question 20

How can we estimate PD from equity prices?

Answer 20

• Merton model: structural model of credit risk: it models the event of default as the situation where a firm’s assets are sufficiently low as compared to its liabilities
• In particular: default is triggered by a failure of a firm to meet its debt servicing obligations: when assets < debt.
• Probability to default can be estimated as PD = P (Assets < Debt)
• Payoff to the shareholder = European call on the assets of the firm so using Black-Scholes we can value the payoff to the shareholder.
  
  • PD is then derived as a risk-adjusted probability in the Black-Scholes model.
• Advantage: it starts from an intuitive notion of default, and by doing so endogenizes the event of default within the company dynamics.
• Disadvantage: it makes strong assumptions on the dynamics of the firm’s balance sheet.

Question 21

What is the KMV model?

Answer 21

• Application of the equity price implied estimation.
• KMV estimates expected default probabilities (EDF):
  
  • PDs as a function of distance of asset value relative to moving floor of liabilities (cf Merton model)
  • distance reflects likelihood of default
• The advantage of the KMV model is that allows for more complex balance sheet structures as compared to basic Merton model
• The disadvantage is that it is information intense and is best applicable to publicly quoted firms where estimates of equity is available

Question 22

How can you estimate EDFs?

Answer 22

1. Estimate the asset value and asset volatility of the firm (using market value and volatility)
2. Compute the distance-to-default by comparing asset values and liabilities; this gives an index measure of default risk
3. Calculate EDFs by mapping the distance-to-default to actual default rates

• Once the asset value and volatility has been estimated, we estimate the distance-to-default (DD).
  
  • Based on these, probabilities can be derived: these are called expected default frequencies.
  • This is done by mapping the DDs on actual default rates (based on large historical default database): by estimating the number of defaulting firms within each DD band, we obtain EDF’s as the % of defaulting firms
  • These EDFs have a proven track-record as default proxies: they are useful leading indicators (1 year ahead) with a clear link with business cycle

Question 23

How to estimate loss given default?

Answer 23

• Apart from PDs, a second component of credit risk is the recovery rate f , also referred to as the loss given default (LGD) = 1 − f
• In case of default, a bankruptcy process starts to centralize outstanding claims (this process is often very lengthy)
• A good proxy for future recovery f turns out to be the observed market price immediately after default: this value proxies for the market value of remaining assets and accounts for costs of the bankruptcy procedure

Question 24

What are the factors that are important when estimating how much you can recover?

Answer 24

• Seniority of debt: the more senior the debt, the higher the recovery rate
• Industry effect: the more tangible assets, the higher the recovery rate
• Legal environment: the more power is given to creditors, the higher the recovery rate (eg. more recovery for UK vs Germany)
• Type of default and reorganization: the more informal the solution, the higher the recovery rate (eg. more recovery for chapter 11 (reorganized start-up) vs chapter 7 (liquidation))
• Business cycle: the better the economy, the higher the recovery rate

Question 25

What is a recovery rating?

Answer 25

• Rating agencies also report recovery rates: they give a recovery rating, corresponding to a recovery range
• There is large variation in recovery rates with seniority of the instrument; even within the same seniority class, there is large variation in recovery rates (SDs are high)

Question 26

What has the research shown on the historical recovery rates from Moody’s?

Answer 26

• Research has shown that there is an amplifier effect in credit losses: at times when default rates increase, recovery rates decrease (see Hamilton et al. [2005])
• In particular, this inverse relation between recovery rate and default rate is as follows:
  
  • A 1% increase in the average default rate, decreases the average recovery rate by 7.6%

Question 27

How can we estimate credit exposure?

Answer 27

• The credit exposure equals the amount that is at risk during the life of the contract: this exposure changes over the life of the contract due market risk and due to credit risk and thus needs to be estimated; At default, this exposure is labelled exposure at default (EAD)
• Formally: CE is the positive replacement value of the instrument; CE = Max (V , 0)
  
  • When the instrument is an asset to you: CE > 0
    
    • When the instrument has positive value to you: CE = V
    • When the instrument has zero value to you: CE = 0
  • When the instrument is a liability to you: CE = 0

Question 28

On what does it depend if an instrument has credit exposure?

Answer 28

• Depends on whether it is an asset or a liability:
  
  • If the credit instrument is always a liability: CE = 0 (eg.: short loan/bond, short option)
  • If the credit instrument is always an asset: CE ≥ 0 (eg. long loan/bond, long option)
  • Some credit instruments can either be asset or liability, depending on the evolution of its market value: CE ≥ 0 if V ≥ 0 (eg. forward contract, swap contract)

Question 29

What is the difference of estimating credit instruments based on how complex the instruments are?

Answer 29

• For basic credit instruments, estimating CE is straightforward:
  
  • eg. the CE of a bond or loan equals its market value, given current interest rates; at maturity, the CE equals its face value
• For more complex instruments, estimating CE is more challenging as its CE can vary significantly over the life of the contract:
  
  • eg. the CE of a derivatives contract depends on the evolution of underlying risk factors, and can range between zero, and a very large positive value

Question 30

What are exposure modifiers?

Answer 30

• A gross analysis of CE typically overstates credit risk due to the existence of credit mitigation clauses: they reduce risk by:
  
  1. Allowing for netting arrangements
  2. Collateralization
• In addition to mitigation clauses, exposure limits are often imposed: the CE then is bound by the limit that is imposed.

Question 31

What are netting arrangements?

Answer 31

• The purpose of netting is to reduce credit exposure by netting payments across a set of contracts over a counterparty: this allows to offset obligations into a single claim
• Such netting is a very efficient risk-reducing mechanism and is standard practice in OTC derivatives trading

Question 32

What is collateralization?

Answer 32

• The CE is significantly reduced if the obligation is secured by collateral: this collateral can be seized in case of default, and reduces actual credit losses
• Collateral provisions are often mark-to-market (MTM) on periodic basis:
  
  • This implies that extra collateral needs to be posted if the current collateral is insufficient
  • Depending on contract, this can be 2-way MTM (both parties are secured) or 1-way MTM (only a single party is secured)
• The size of the collateral is typically larger than the funds owed:
  
  • The difference is called a haircut (= % subtracted from par value of contract)
  • This haircut accounts for default risk and market risk of the collateral

Question 33

What are exposure limits?

Answer 33

• On top of mitigation clauses, exposure limits are used to bound overall credit exposure:
  
  • One can set limits on the maximum exposure with regards to counterparties or asset classes
  • If limits are violated, additional transactions will be prohibited and exposure needs to be reduced