Credit Risk

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Credit Risk

• Types of Loans
• Return on Loans
• Models of Credit Risk measurement

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Types of Loans in Taiwan
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Types of Loans in Taiwan
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Commercial Industrial Loans

• ?Term
• ?Amounts
• - Syndicated Loan
• ?Secured Unsecured
• ?Spot Loan Loan Commitment
• Is Commercial Loan still important ??

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Real Estate Loans

• ?Mortgage Loans
• ?Revolving Home Equity Loans

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Residential Mortgage-Lending Process
Function Rewards Risks
Origination Fees Limited
Funding/underwriting Spread Liquidity , interest rate , credit
Selling Fees commissions Liquidity , interest rate , credit
Servicing Fees Limited
Investor Interest principal Liquidity , interest rate , credit
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Individual Loans

• ?Nonrevolving
• e.g Auto Loans Mobile Home Loans
• ?Revolving
• e.g Credit Card
• Other Loans

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Credit Card in Taiwan
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Return on Loans

• Influence Factor
• ? Interest Rate
• ? Fees
• ? Credit Risk Premium
• ? Other Factors

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ROA per dollar lent

• 1k1?f(BRm)?/?1-?b(1-R)??
• k Gross Return on the Loan
• f Loan Origination fee
• BR Base Lending Rate
• m Credit Risk Premium
• b Compensating Balance Requirement
• R Reserve Requirement

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Expected Return on a Loan

• E (r) p (lk)
• p probability of repayment of the loan

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Credit Risk

• Two Dimensions to Control Credit Risk
• ?1k price or promised return
• ?quantity or credit availability

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Credit Decisions

• Retail
• ?accept or reject
• ?sorted by loan quantity

• Wholesale
• ?Both interest rates
• credit quantity

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Default Risk Models
Qualitative Models

• Market-specific Factors
• ?Business Cycle
• ?Level of interest rates

• Borrower-specific Factors
• ?Reputation
• ?Leverage
• ?Volatility of Earnings
• ?Collateral

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Default Risk Models Credit
Scoring Models

• ?Linear Probability Model
• Z i ?n j1ßj X ij error
• ?Logit Model
• F(Zi) 1/(1e-z)

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Default Risk Models Credit
Scoring Models

• ?Linear Discriminant Models
• Z1.2X11.4X23.3X30.6X41.0X5
• X1 Working capital /total assets ratio
• X2 Retained earnings/total assets ratio
• X3 EBIT/total assets ratio
• X4 Market value of equity/book value of
  long-term debt
• ratio
• X5 Sales/total assets ratio

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Discriminant Model

• Problems
• ?discriminate between extreme behavior
• ?Are the weights and Xi constant?
• ?Ignore hard-to-quantify factors
• ?No centralized database

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New Models of Credit Risk Measurement and Pricing

• Term Structure Derivation of Credit Risk
• Mortality Rate Derivation of Credit Risk
• RAROC Models
• Option Models of Default Risk

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Term Structure Derivation of Credit Risk

• The spreads between risk-free discount bounds
  issued by the Treasury and discount bounds issued
  by corporate borrowers of differing quality
  reflect perceived credit risk exposures of
  corporate borrowers for single payments at
  different times in the future.
• Probability of default on a one period debt
  instrument
• Probability of default on a multiperiod debt
  instrument

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Probability of default on a one period debt
instrument

• p the probability of repayment
• the risk premium
• Example 11-4

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Probability of default on a one period debt
instrument

• i 10
• k 15.8
• In this case, a probability of default of 5 on
  the corporate bond requires the FI to set a risk
  premium of 5.8.
• p , 1-p , ( k - i )
  

k - i 5.8
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• the proportion of the loans principal and
  interest that is collectible on default.
  gt 0
• and are perfect substitutes for each
  other.
• An increase in collateral a decline in

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• i 10
• p 0.95
• r 0.9

k 10 0.55276 10.55276
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Probability of default on a multiperiod debt
instrument
Cumulative Default probability The probability
that a borrower will default over a specific
multiyear period
Example
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Probability of default on a multiperiod debt
instrument

• Marginal Default Probability
• No arbitrage
• Forward Rate

Example
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Advantages and Problems

• Advantages
• Clearly forward looking and based on market
  expectations.
• Liquid markets for Treasury and corporate
  discount bonds.
• Problems
• Treasury markets _ deep
• Corporate markets_ small
• Discount yield curve

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Mortality Rate Derivation of Credit Risk

• Mortality Rate
• Historical default rate experience of a bond or
  loan
• Marginal Mortality Rate
• The probability of a bond or loan defaulting in
  any given year of issue.

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Mortality Rate Derivation of Credit Risk

• MMR curve can show the historic default rate
• Any shape to the mortality curve is possible
• The higher Mortality rates
  the lower the rating of the bond

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Mortality Rate Derivation of Credit Risk

• Problems
• historic or backward-looking measures.
• Implied future default probabilities tend to be
  highly sensitive to the period over which FI
  manager calculates the MMRs.
• The number of issues and the relative size of
  issues in each investment grade.

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RAROC (Risk-Adjusted Return of Capital)
Models

• RAROC
• RAROC gt ROE
  the loan should be made

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RAROC Models

• The first problem in estimating RAROC
• The measurement of loan risk

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RAROC Models

• The change in the yield spread
  between corporate bonds of credit rating class i
  (Ri) and matched duration treasury bonds (RG)
  over the last year.
• Max only consider the
  worst-case scenario.

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RAROC Models

• 10
• 2.7
• Spread 0.2 1m 2000
• Fees 0.1 1m 1000

• Example 11-6
• AAA borrower
• 400 publicly traded bonds (AAA)
• The range of Risk Premium is from -23.5

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RAROC Models
One-year income per dollar loaned
RAROC
Proportion of loan lost on default
Expected income per dollar lent 0.3 cents
Unexpected default rate 4
Proportion of loan lost on default 80
RAROC 9.375
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RAROC Models

• Add more interest income or fees
• Curtail the size of the loan
• Shorten the duration of the loan

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Option Models of Default Risk

• The Borrowers Payoff from Loans
• buying a call option on the assets of the firm
• The Debt Holders Payoff from Loans
• Writing a put option on the value of the
  borrowers assets with B, the face value of debt,
  as the exercise price.

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Call option
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Put option
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Option Models of Default Risk

• Applying the Option Valuation Model to the
  calculation of Default Risk Premium

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Option Models of Default Risk

• ,T the maturity date
  t today
• the borrowers
  leverage ratio
• the probability that a deviation
  exceeding the calculated value of h will
  occur
• the asset risk of the borrower

t

d
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Option Models of Default Risk

• Required yield on risky debt

The lender should adjust the required risk
premium as leverage and asset risk
change
_at_ Example 11-7
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• Example 11-7
• B 100,000
• 1 year
• 12
• i 5
• d 90

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• The required risk spread or premium is

51.336.33
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• The lenders decision matrix

Result
Good loan
Bad loan
Loan repaid
Type 1 error
Loan denied
Type 2 error
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• H0the customer would default
• Not Grant
• H1the customer could repay
• Grant
• Type? reject the true H0
• Bankrupt
• Type ? accept the wrong H0
• Damage reputation

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1. CreditMetrics
2. Credit Risk

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CreditMetrics---Introduction

• Introduced by J.P. Morgan its co-sponsors, 1997
• Based on the conception of VaR
• The difficulties to attain the P and s of loans
  Methods to solve this problem
• Rating Migration---changing credit spread

1.The borrowers credit rating 2.The rating
Migration matrix 3.Recovery rate of default
loans 4.Yield spreads in the bond market
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CreditMetrics---Rating Migration

• Eg. 5yr 100m 6 loan for BBB borrower
• Rating Migration Probabilities
• Valuation
• P66/(1r1s1)6/(1r2s2)2
• 6/(1r3s3)3106/(1r4s4)4

Rating Transition Prob
AAA 0.02
AA 0.33
A 5.95
BBB 86.93
BB 5.30
B 1.17
CCC 0.12
Default 0.18
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CreditMetrics---Prob. Distibution
Year- End Rating Loan Value
AAA 109.37
AA 109.19
A 108.56
BBB 107.55
BB 102.02
B 98.10
CCC 83.64
Default 51.13
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CreditMetrics---VaR Capital Requirements
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Credit Risk---Introduction

• Developed by Credit Suisse Financial Products
  (CSFP)
• Derive from the conceptions of fire insurance
• Unlike CreditMetrics, Credit Risk focus on
• 1.The frequency of Defaults
• 2.Severity of Losses

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Credit Risk---Assumptions

• The prob. of any individual loan defaulting in
  the portfolio of loans is random
• The correlation between the defaults on any pair
  of loans is 0
• Poisson Distribution is applied
• More appropriate for analyzing the default
• rate on a large portfolio of small loans
  rather than a portfolio of just a few loans

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Credit Risk---pdf

• 1.Prob. of n defaultse-mmn
• n!
• e2.71828
• m Historic of defaults for loans of this type
• n of defaults
• 2.Severity of Losses---average loss per loan
  defaults

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Credit Risk---calculations

• E.g.. A FI makes 100 loans, each of 10,0000
• M3
• Severity of loss20 cent per1
• Prob. of 4 loans defaulting e-334
• 
  4!
• Dollar loss of 4 loans defaulting420C100,
  00080,000
• Possible Drawbacks of this model

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• Loan Portfolio and Concentration Risk

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Simple Models of Loan Concentration Risk
Risk Grade at Yr End
Risk Grade at yr beginning

• FI widely employed two simple models to measure
  the credit risk of a loan portfolio
• 1.Loan migration matrix
• 2.Concentration limits

1 2 3 D
1 0.85 0.10 0.04 0.01
2 0.12 0.83 0.03 0.02
3 0.03 0.13 0.80 0.04
Concentration limitMaximum loss( of capital)
1
Loss rate
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KMV Portfolio Manager Model---Conceptions
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MPT Applied to Bank Lending

• Modern Portfolio Theory

ALM LINE
Purchasing Fed Funds
Selling Fed Funds
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FI Portfolio Diversification

• N
• Rp? Xi Ri
• i1

C

• Ssp2?Xi2si2
• ??XiXjsij

A
B

• Ssp2?Xi2si2
• ??XiXj?ijsisj

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KMV Portfolio Manager Model

• siULisDi LGDivEDFi(1-EDFi) LGDi
• RiAISi-E(Li)AISi -(EDFiLGDi)

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Comparing with Benchmark
National Bank A Bank B
Real Estate 10 15 10
CI 60 75 25
Individuals 15 5 55
Others 15 5 10
4 sj ?(Xij-Xi)2 i1
N
sA10.61 sB26.69
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Loan Loss Ratio-Based Models

• Involves estimating the systematic loan loss risk
  of a particular section or industry relatives to
  the loan loss of an FIs total loan portfolio
• aßi( Total loan losses/Total loans)

Sectoral losses in the ith sector
Loans to the ith sector
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Credit Derivates---Introduction(1/3)

• Usually OTC, Off-balance sheet contracts
• Banks can use credit derivatives to achieve more
  efficient risk-return combinations without
  hurting customer relationships
• Four Components
• Payment of credit derivatives

1.The notional amount 2.The term or
maturity 3.The reference party whose credit is
being traded 4.Reference Assets
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Credit Derivates(2/3)

• Types of credit derivatives
• Pure-credit (default) Swap
• Total-return Swap

premium
Party1
Party 2
Loss Compensation
premium
Party 2
Party1
Promised int. Mkt Value Loss
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Credit Derivates(3/3)

• Hedge ratioLIED for the loan/LIED for the
  reference assets
• LIED( loss in the event of default)1-recovery
  rate
• e.g.. A Bank holds a 10m,senior, syndicated,
  floating rate loan (estimate recovery rate70)
• Reference asset a Bond with 50 recovery
  rate
• Hedge ratio(1-0.7)/(1-0.5)60
• 10m606m

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• Thanks for Paying Attention