CRM 1 - Credit Risk Management

Question 1

Ratings approach to Default Probabilities

Answer 1

• Ratings are expample of Ordinal scale
• Maps a continuous quantity like prob of default into ratings bucket
• Not intended for PD calculation originally
• Meant to have risk on an ordinal scale

Question 2

Causal Rating Systems approach to Default Probabilities

Answer 2

• Preferred approache
• Rely on a relationship b/w underlying credit risk drivers and default events
• Forces modeler to understand true mechanism of default intead of just relying on various ratios
• Requires customized, specific approaches
• Very powerful and preferred by author

Question 3

Balance sheet scorings approach to Default Probabilities

Answer 3

• Map balance sheet ratios into scores into PD

Question 4

Private Client Scorings approach to Default Probabilities

Answer 4

• Conceptually similar to balance sheet scorings
• Except that ratios will computed on different metrics
• Example: wealth, income situation, family context

Question 5

Expert Rating Systems approach to Default Probabilities

Answer 5

• More complicated situations may require further analysis
• Example: Swiss municipalities had almost no default in a data set analyzed

Question 6

Overview of Calibration of Default Probabilities to Ratings

Answer 6

• Calibration is the process of assigning default probs to ratings
• Uses historical table of corp bonds defaults by ratings class
• Often best rating classes will have no observed defaults
• Not surprising since expected default prob is very low

Question 7

Steps in the “quick-and-dirty” calibration of Default Probabilities to Ratings

Answer 7

1. Calculate the mean and standard deviation of historical annual default probs
   
   • ​Mean is first guess for a default prob
2. Plot mean values on a coordinate system, with x-axis for rating classes
   
   • use log scale to fit mean default probs to a line since default frequencies grow exponentially w/ decreasing creditworthiness
3. Use regression equation to estimate default probs
   
   • Smooth out sampling errors and ensure positive default probs for even best rating classes

Question 8

Draw-Down Factor (DDF) for Exposure at Default

Answer 8

Analyzes how much of the commitments will be used and is the product of two quantities:

• Prob of commitments getting used?
• If used, how much of the commitments are drawn upon?

Question 9

Cash Equivalent Exposure Factor (CEEF) for Exposure at Default

Answer 9

• Conversion factor quantifiying the conversion of the specific contigent liability into cash
• Prob of CL generating cash exposure

Question 10

Overview of contingent liabilities in Exposure at Default

Answer 10

• May not necessarily lead to cash exposure (e.g. an insurer selling guarantees)
• Guarantee has no real exposure as of today, but might in the future
• Prob of contigent liab generating cash exposure = CEEF

Question 11

Expected Exposure at Default of Contigent Liab

Answer 11

Product of:

• Draw down factor (DDF) of contigent liab
• and, cash equivalent exposure factor (CEEF)

Question 12

Loss Given Default (LGD)

Answer 12

• 1 minus recovery rate
• Random variable to stimulate severity of a default

Question 13

Factors impacting recovery rates

Answer 13

• Quality of collateral
• Seniority of bank’s claims

Question 14

Describe Unexpected Loss when the severity and default event D are uncorrelated

Answer 14

Question 15

Why is the lack of correlation of severity and default event an unrealistic assumption?

Answer 15

• Default rates spike during bad economies, which is normally when recovery rates drop
• Collateral could also decrease when market drops

Question 16

Expocted Loss Formula for Portfolio

Answer 16

Question 17

Unexpected Portfolio Loss

Answer 17

Question 18

Three correlation cases for portfolio unexpected loss

Answer 18

• If the losses are uncorrelated , then UL attains its minimum
• If the losses are positively correlated, the concentration risk will increase
• If losses could be perfectly negatively correlated, then the UL could be forced equal to zero (unrealisitc in credit risk)

Question 19

Economic Capital

Answer 19

• Similar to VaR, in that it measures a percentile loss
• Usually quoted in excess of the expected loss

Question 20

Economic Capital based on confidence interval

Answer 20

• Company may need risk capital for more than one standard deviation of portfolio

Question 21

Components of Loan Pricing

Answer 21

1. Costs of administering loan along with some potential upfront fees
2. Expected losses based on the customer credit rating
3. Unexpected losses
   
   • dependends on the portfolio because of diversification benefits

Question 22

Methods to generate credit loss distribution

Answer 22

• Monte carlo simulation:
  
  • Get empirical loss distribution (loss of exposure) from simulations
  • Derive risk quantities from empirical distribution
  • better captures correlation in portfolio, but takes long time to run
• Analytical approximation:
  
  • Maps an unknown loss distribution to an equivalent portfolio with a known loss distribution
  • works well for homogeneous portfolio (e.g. no exposure concentration)

Question 23

Analytical Approximation steps to generate credit loss distribution

Answer 23

• First choose a family of distributions characterized by its first and second moment (such as a beta distribution)
• From known characteristics of the original portfolio, calculate the first moment (expected loss) and estimate the second moment (unexpected loss)
  
  • Need an average default correlation to calculate the second moment
• Then choose a distribution from the family that most closely matches the first and second moments
  
  • The average asset correlation is critical and difficult to determine
  • Can use experience from known portfolios (25% in Moody’s universe of rated corp bonds)
• Calculate the quantiles of the loss distribution as the quantiles of the chosen distribution

Question 24

Modeling Default Correlations by Means of Factor Models

Answer 24

Identify underlying drivers
Reduces computational efforts for correlated losses
Common factors could include industry or country factors
Express correlation between loans via correlations between factors
The part of the firm’s risk that can be explained by the factors is systematic risk; the other portion of the risk is specific or idiosyncratic risk

Question 25

Three levels of the KMV factor model

Answer 25

1. The first level decomposes the firm’s variance into systematic and specific parts
2. The second level decomposes the systematic risk into industry and country risk
3. the third level, a weighted sum of independent global factors is constructed for representing industry and country indices

Question 26

Differences between KMV and CreditMetrics

Answer 26

1. KMV is calibrated with asset value processes, while CreditMetrics uses equity
   correlations as a proxy for asset correlations
2. KMV considers industries and countries separately, while CreditMetrics uses indices that are a combination of industry and country.