Credit Risk§ Types of Loans

§ Return on Loans

§ Models of Credit Risk measurement

全體金融機構資產類別

--

5,000,000

10,000,000

15,000,000

20,000,000

25,000,000

30,000,000

35,000,000

81 年 83 年 85 年 87 年 89 年 91 年

資料來源：金融統計月報

單位：百萬元

庫存現金

不動產投資

證券投資

國外資產

放款

全體金融機構負債類別

0

5000000

10000000

15000000

20000000

25000000

30000000

35000000

81年 83年 85年 87年 89年 91年 資料來源：金融統計月報

單位：百萬元央行發行之國庫券、定存單金融債券

人壽保險準備

信託資金

政府存款

企業及個人存款通貨發行額

國外資產

金融機構存放款利差比較

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

86 87 88 89 90 91 92資料來源：金融統計月報

%本國一般銀行

外國銀行在台分行中小企業銀行

信用合作社

農漁會 信用部

信託投資公司

放款機構額度比較

--

2,000,000

4,000,000

6,000,000

8,000,000

10,000,000

12,000,000

14,000,000

16,000,000

81 82 83 84 85 86 87 88 89 90 91 92資料來源：金融統計月報

單位：百萬元

信託投資公司

信合社

農漁會

中小企銀

本國一般銀行

外國銀行

放款期限別

0.00%

5.00%

10.00%

15.00%

20.00%

25.00%

30.00%

35.00%

40.00%

45.00%

84年 86年 88年 90年 92 ( 8 )年至 月資料來源：金融統計月報

一年以下

超過一年至三年

超過三年至五年

超過五年至七年

超過七年

金融機構逾放比例

0.001.002.003.004.005.006.007.008.009.00

10.0011.0012.0013.0014.0015.0016.0017.0018.00

84年 86年 88年 90年 92 ( 6 )年 至 月資料來源：財政部金融局

單位：百分比總體逾放比率

本國銀行(含信託投

)資公司外國銀行在華分行

基層金融機構

Types of Loans in Taiwan

貸款部門別

0.00%

5.00%10.00%

15.00%

20.00%

25.00%30.00%

35.00%

40.00%45.00%

50.00%

84年 86年 88年 90年 92 ( 8 )年 至 月資料來源：金融統計月報

公營事業民營事業個人等政府機關

Types of Loans in Taiwan

貸款用途別

0.00%5.00%

10.00%15.00%20.00%25.00%30.00%35.00%40.00%45.00%50.00%55.00%60.00%

84年 86年 88年 90年 92 ( 8 )年至 月

資料來源：金融統計月報

購置不動 產

購置動產

企業投資

週轉金

Types of U. S Bank Loans(March 2001)

0.00%

5.00%

10.00%

15.00%

20.00%

25.00%

30.00%

35.00%

40.00%

45.00%

C&I Real estate Consumer Other

Commercial & Industrial Loans

◆Term

◆Amounts

─ Syndicated Loan

◆Secured & Unsecured

◆Spot Loan & Loan Commitment

Is Commercial Loan still important ??

Real Estate Loans

◆Mortgage Loans

◆Revolving Home Equity Loans

Real Estate Loan i n Tai wan

--

500,000

1,000,000

1,500,000

2,000,000

2,500,000

3,000,000

3,500,000

4,000,000

4,500,000

5,000,000

84 85 86 87 88 89 90 91 92(8)

資料來源：金融統計月報

單位：百萬元

非營利團體

政府機構

公民營企業

私人

Residential Mortgage-Lending Process

Function Rewards Risks

Origination Fees Limited

Funding/underwriting

SpreadLiquidity , interest

rate , credit

SellingFees &

commissionsLiquidity , interest

rate , credit

Servicing Fees Limited

Investor Interest & principalLiquidity , interest

rate , credit

Individual Loans

◆Nonrevolving

e.g : Auto Loans ; Mobile Home Loans

◆Revolving

e.g : Credit Card

Other Loans

消費性貸款類別

0.00%

5.00%

10.00%

15.00%

20.00%

25.00%

30.00%

35.00%

40.00%

45.00%

50.00%

55.00%

60.00%

86年 87年 88年 89年 90年 91年 92 ( 7 ) 年至 月

購置住宅貸款

房屋修繕貸款

汽車貸款

機關團體職工福利貸款

其他消費性貸款

信用卡循環信用餘額

建築貸款

Credit Card in Taiwan

信用卡業務統計

05000

10000150002000025000300003500040000450005000055000600006500070000

77年 81年 83年 85年 87年 89年 91年資料來源：財政部金融局

單位：千張

發卡數（千張）

流 通 卡 數

（千張）

信用卡業務統計

0

100,000

200,000

300,000

400,000

500,000

600,000

700,000

800,000

900,000

1,000,000

76年 80年 82年 84年 86年 88年 90年 92 8年 月

單位：百萬元

簽帳金額

預借現金

循環信用餘額

信用卡循環利率 平均利率 最高 最低本國老銀行 18. 001 19. 893(新竹國際商銀） 13. 14( )台銀本國新銀行 19. 47318 20(中國信託、台新） 18( )誠泰外商銀行 19. 9735 20( )花旗、渣打 19. 929(HSBC)

Return on LoansInfluence Factor :

◆ Interest Rate

◆ Fees

◆ Credit Risk Premium

◆ Other Factors

ROA per dollar lent1+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

Expected Return on a Loan

＊ E (r) = p (l+k)

p: probability of repayment of the loan

Credit Risk

Two Dimensions to Control Credit Risk

◆1+k: price or promised return

◆quantity or credit availability

Credit DecisionsRetail

◆accept or reject

◆sorted by loan quantity

Wholesale

◆Both interest rates &

credit quantity

Default Risk Models – Qualitative Models

Borrower-specific Factors

◆Reputation

◆Leverage

◆Volatility of Earnings

◆Collateral

Market-specific Factors

◆Business Cycle

◆Level of interest rates

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)

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

Discriminant Model

Problems

◆discriminate between extreme behavior

◆Are the weights and Xi constant?

◆Ignore hard-to-quantify factors

◆No centralized database

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

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

Probability of default on a one –period debt instrument

p = the probability of repayment

= the risk premium

Example 11-4

ikp 1)1(

ik

k

i

1

1

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 )

95.0158.1

100.1

1

1

k

i

= k - i = 5.8%

= 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

ii

ik

11

ikk 1111

i = 10% p = 0.95 r = 0.9

%55276.0

005527638.0

100.1995.0

100.1

%10195.09.095.09.0

%101

k = 10% + 0.55276% = 10.55276%

n

iipC

1

1

Probability of default on a multiperiod debt instrument

: the probability of the debt surviving in the ith year i

1165.093.095.0193.0

95.0

2

1

C

Example

Cumulative Default probability:

The probability that a borrower will default over a specific multiyear period

Probability of default on a multiperiod debt instrument

Marginal Default Probability No arbitrage Forward Rate

112

2 111 ckk

Example

12.1

1.1

11.11

2

1 f 112

2 111 fii

202.1

158.1

18.11

2

1 c

112 1)1( fcp 9318.02

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

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.Total value of grade B bonds defaulting in year i of issues

Total value of grade B bonds outstanding in year i of issuesiMMR =

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

Mortality Rate Derivation of Credit Risk Problems

historic or backward-looking measures. Implied future default probabilities tend t

o 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.

RAROC (Risk-Adjusted Return of Capital) Models RAROC =

RAROC > ROE the loan should be made

One year income on a loanLoan (asset) risk or capital at risk

RAROC Models The first problem in estimating RAROC

The measurement of loan risk

R

RD

L

LL

1

RRLDL L 1

RAROC Models

: The change in the yield spread between corporate bonds of credit rating class i (Ri) and matched durationmatched duration treasury bonds (RG) over the last year.

Max [ ] : only consider the worst-case scenario.

0 Gi RRMaxR

Gi RR

Gi RR

RAROC Models Example 11-6

AAA borrower 400 publicly traded

bonds (AAA) The range of Risk

Premium is from -2%~3.5%

= 10% = 2.7 Spread = 0.2% *

$1m = $2’000 Fees = 0.1% * $1m

= $1’000

AAAR

LD

$2000 + $1000-(2.7) * ($1m)(0.11/1.1)

=11.1%RAROC =

RAROC Models

Proportion of loan lost on defaultRAROC =

Unexpected default rate One-year income on loan

Expected income per dollar lent = 0.3 cents

Unexpected default rate = 4%

Proportion of loan lost on default = 80%

RAROC = 9.375%

RAROC Models

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

RRLDL L 1

One year income on a loanLoan (asset) risk or capital at risk

RAROC =

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.

Call option

0

-S

Assets (A)

Payoff to stockholders

A1

B (debt)

A2

Put optionPayoff to debt holders

A1 B (debt)

A20 Assets (A)

Option Models of Default Risk Applying the Option Valuation Model to

the calculation of Default Risk Premium

211 hNhNdBeF i

/ln22

11 dh

/ln22

12 dh

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

tT

2

)(hN

d ABe i /

Option Models of Default Risk

Required yield on risky debt

@ Example 11-7

121ln1 hNdhNik

k

The lender should adjust the required risk premium as leverage and asset risk change

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

938.0

12.0

9.0ln12.0 22

1

1

h

818.0

12.0

9.0ln12.0 22

1

2

h

174120.01 hN

793323.02 hN

17412.01111.1793323.005127.1

000,100$tL

18.866,93$986788.005127.1

000,100$

The required risk spread or premium is

k

121ln1 hNdhNik

%33.1

]986788.0ln[)1(

5%+1.33%=6.33%

The lender’s decision matrix :

Reject H0

Accept H0

H1 is trueH0 is true

Decision

Yes

No

Good loan Bad loan

Loan repaid

Type 2 error

Type 1 error

Loan denied

Result

1

1Type 1 error

Type 2 error

H0:the customer would default Not Grant

H1:the customer could repay Grant

Type : reject the true HⅠ 0

Bankrupt Type : accept the wrong HⅡ 0

Damage reputation

A. CreditMetrics

B. Credit Risk+

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 loa

ns & Methods to solve this problem

Rating Migration---changing credit spread

1.The borrower’s credit rating2.The rating Migration matrix3.Recovery rate of default loans4.Yield spreads in the bond market

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+s

4)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%

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

CreditMetrics---VaR & Capital Requirements

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

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

Credit Risk---pdf

1.Prob. of n defaults=e-m*mn

n! e=2.71828

m: Historic #of defaults for loans of this type

n: # of defaults

2.Severity of Losses---average $ loss per loan defaults

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

Loan Portfolio and Concentration Risk

Simple Models of Loan Concentration Risk 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

Risk Grade at Yr End Risk G

rade a

t yr

begin

nin

gConcentration limit=Maximum loss(% of capital)

1

* Loss rate

KMV Portfolio Manager Model---Conceptions

MPT Applied to Bank LendingModern Portfolio Theory

ALM LINE

SellingFed

Funds

PurchasingFed Funds

FI Portfolio Diversification

B

C

A

N

Rp=∑ Xi Ri

i=1

Σσp2=∑Xi

2σi2+

∑∑XiXjσij

Σσp2=∑Xi

2σi2+

∑∑XiXjρijσiσj

KMV Portfolio Manager Model

σi=ULi=σDi* LGDi=√EDFi(1-EDFi) *LGDi

Ri=AISi-E(Li)=AISi -(EDFi*LGDi)

Comparing with Benchmark

National Bank A Bank B

Real Estate

10% 15% 10%

C&I 60% 75% 25%

Individuals

15% 5% 55%

Others 15% 5% 10%

σA=10.61% σB=26.69%

4

σj= ∑(Xij-Xi)2

i=1

N

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 iSectoral losses in the ithth sector sector

Loans to the iLoans to the ithth sector sector

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 maturity3.The reference party whose credit is being traded4.Reference Assets

Credit Derivates(2/3)

Types of credit derivatives Pure-credit (default) Swap

Total-return Swap

Party1 Party 2

premium

Loss Compensation

Party1Party 2

premium

Promised int. + Mkt Value Loss

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

Thanks for Paying Attention