1. Credit Risk § Types of Loans § Return on Loans
§ Models of Credit Risk measurement

7. 金融機構逾放比例

8. Types of Loans in Taiwan

9. Types of Loans in Taiwan

11. Commercial & Industrial Loans
◆Term
◆Amounts
─ Syndicated Loan
◆Secured & Unsecured
◆Spot Loan & Loan Commitment
Is Commercial Loan still important ??

12. Real Estate Loans
◆Mortgage Loans
◆Revolving Home Equity Loans

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

15. Individual Loans ◆Nonrevolving e.g : Auto Loans ; Mobile Home Loans
e.g : Credit Card
Other Loans

17. Credit Card in Taiwan

19. Return on Loans Influence Factor : ◆ Interest Rate ◆ Fees
◆ Credit Risk Premium
◆ Other Factors

20. ROA per dollar lent 1+k=1+｛〔f+(BR+m)〕/〔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

21. Expected Return on a Loan
＊ E (r) = p (l+k)
p: probability of repayment of the loan

22. Credit Risk Two Dimensions to Control Credit Risk
◆1+k: price or promised return
◆quantity or credit availability

23. Credit Decisions Retail ◆accept or reject ◆sorted by loan quantity
Wholesale
◆Both interest rates &
credit quantity

25. Default Risk Models – Qualitative Models
Market-specific Factors
◆Business Cycle
◆Level of interest rates
Borrower-specific Factors
◆Reputation
◆Leverage
◆Volatility of Earnings
◆Collateral

26. Default Risk Models – Credit Scoring Models
◆Linear Probability Model
Z i = ∑n j=1βj X ij + error
◆Logit Model
F(Zi) =1/(1+e-z)

27. Default Risk Models – Credit Scoring Models
◆Linear Discriminant Models
Z=1.2X1+1.4X2+3.3X3+0.6X4+1.0X5
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

28. Discriminant Model Problems ◆discriminate between extreme behavior
◆Are the weights and Xi constant?
◆Ignore hard-to-quantify factors
◆No centralized database

29. 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

30. 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

31. Probability of default on a one –period debt instrument
p = the probability of repayment
= the risk premium
Example 11-4

32. Probability of default on a one –period debt instrument
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 , p , ( k - i )
= k - i = 5.8%

33. = the proportion of the loan’s principal and interest that is collectible on default. > 0
and are perfect substitutes for each other.
An increase in collateral a decline in

34. i = 10%
p = 0.95
r = 0.9
k = 10% % = %

35. Probability of default on a multiperiod debt instrument
Cumulative Default probability: The probability that a borrower will default over a specific multiyear period
: the probability of the debt surviving in the ith year
Example

36. Probability of default on a multiperiod debt instrument
Marginal Default Probability
No arbitrage
Forward Rate
Example

37. Advantages and Problems
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

38. Mortality Rate Derivation of Credit Risk
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.
Total value of grade B bonds defaulting in year i of issues
Total value of grade B bonds outstanding in year i of issues =

39. 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

40. 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.

41. RAROC (Risk-Adjusted Return of Capital) Models
One year income on a loan
Loan (asset) risk or capital at risk
RAROC =
RAROC > ROE the loan should be made

42. RAROC Models The first problem in estimating RAROC
The measurement of loan risk

43. 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.

44. RAROC Models Example 11-6 = 10% AAA borrower = 2.7
Spread = 0.2% * $1m = $2’000
Fees = 0.1% * $1m = $1’000
Example 11-6
AAA borrower
400 publicly traded bonds (AAA)
The range of Risk Premium is from -2%~3.5%
$ $1000
-(2.7) * ($1m)(0.11/1.1) =
11.1% =

45. RAROC Models One-year income on loan
One-year income per dollar loaned
RAROC Models
Unexpected default rate
One-year income on loan
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%

46. RAROC Models RAROC = Add more interest income or fees
One year income on a loan
Loan (asset) risk or capital at risk
RAROC =
Add more interest income or fees
Curtail the size of the loan
Shorten the duration of the loan

47. Option Models of Default Risk
The Borrower’s Payoff from Loans
buying a call option on the assets of the firm
The Debt Holder’s Payoff from Loans
Writing a put option on the value of the borrower’s assets with B, the face value of debt, as the exercise price.

48. Call option -S
Assets (A)
Payoff to stockholders A1
B (debt) A2

49. Put option
Payoff to debt holders A1
B (debt) A2
Assets (A)

50. Option Models of Default Risk
Applying the Option Valuation Model to the calculation of Default Risk Premium

51. Option Models of Default Risk
,T: the maturity date ; t: today
the borrower’s leverage ratio
the probability that a deviation exceeding the calculated value of h will occur
the asset risk of the borrower t = d = = ) ( h N = 2 s

52. Option Models of Default Risk
Required yield on risky debt
The lender should adjust the required risk premium as leverage and asset risk change
@ Example 11-7

53. Example 11-7
B = $100,000
= 1 year
= 12%
i = 5%
d = 90%

54. The required risk spread or premium is
5%+1.33%=6.33%

55. The lender’s decision matrix :
Result
Good loan
Decision
Yes No
Bad loan
Loan repaid
Type 1 error
Type 2 error
Loan denied
Reject H0
Accept H0
H1 is true
H0 is true
Type 1 error
Type 2 error

56. H0:the customer would default H1:the customer could repay
Not Grant
H1:the customer could repay
Grant
TypeⅠ: reject the true H0
Bankrupt
Type Ⅱ: accept the wrong H0
Damage reputation

57. CreditMetrics Credit Risk+

58. CreditMetrics---Introduction
Introduced by J.P. Morgan & its co-sponsors, 1997
Based on the conception of VaR
The difficulties to attain the P and σ of loans & Methods to solve this problem
Rating Migration---changing credit spread
1.The borrower’s credit rating
2.The rating Migration matrix
3.Recovery rate of default loans
4.Yield spreads in the bond market

59. CreditMetrics---Rating Migration
Eg. 5yr $100m 6% loan for BBB borrower
Rating Migration Probabilities
Valuation
P=6+6/(1+r1+s1)+6/(1+r2+s2)2+
6/(1+r3+s3)3+106/(1+r4+s4)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%

60. 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

61. CreditMetrics---VaR & Capital Requirements

62. 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

63. 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

64. Credit Risk---pdf 1.Prob. of n defaults=e-m*mn n!
m: Historic #of defaults for loans of this type
n: # of defaults
2.Severity of Losses---average $ loss per loan defaults

65. Credit Risk---calculations
E.g.. A FI makes 100 loans, each of $10,0000
M=3
Severity of loss:20 cent per$1
Prob. of 4 loans defaulting = e-3*34 4!
Dollar loss of 4 loans defaulting=4*20C*$100,000=$80,000
Possible Drawbacks of this model

66. Loan Portfolio and Concentration Risk

67. 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
0.85
0.10
0.04
0.01
0.12
0.83
0.03
0.02
0.13
0.80
Concentration limit=Maximum loss(% of capital) 1
* Loss rate

68. KMV Portfolio Manager Model---Conceptions

69. MPT Applied to Bank Lending
Modern Portfolio Theory
ALM LINE
Purchasing
Fed Funds
Selling
Fed
Funds

70. FI Portfolio Diversification
Rp=∑ Xi Ri
i=1 C
Σσp2=∑Xi2σi2+
∑∑XiXjσij A B
Σσp2=∑Xi2σi2+
∑∑XiXjρijσiσj

71. KMV Portfolio Manager Model
σi=ULi=σDi* LGDi=√EDFi(1-EDFi) *LGDi
Ri=AISi-E(Li)=AISi -(EDFi*LGDi)

72. Comparing with Benchmark
National
Bank A
Bank B
Real Estate
10%
15%
C&I
60%
75%
25%
Individuals 5%
55%
Others 4
σj= ∑(Xij-Xi)2
i=1 N
σA=10.61% σB=26.69%

73. 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 FI’s total loan portfolio
=α+βi( Total loan losses/Total loans)
Sectoral losses in the ith sector
Loans to the ith sector

74. 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.Cash Settlement
2.Physical Delivery
1.The notional amount
2.The term or maturity
3.The reference party whose credit is being traded
4.Reference Assets

75. Promised int. + Mkt Value Loss
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

76. Credit Derivates(3/3)
Hedge ratio=LIED 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 rate=70%)
Reference asset: a Bond with 50% recovery rate
Hedge ratio=(1-0.7)/(1-0.5)=60%
$10m*60%=6m

77. Thanks for Paying Attention