c15.0021 money, banking, and financial markets

Copyright 1999 A. S. Cebenoyan 1

Money, Banking, and Financial Markets

Professor A. Sinan CebenoyanStern School of Business - NYU

Set 3


Credit Risk - Chapter 11• Measurement of credit Risk:

– Pricing of loans

– credit rationing

• Japanese FI’s over-concentration in real estate and in Asia

– bad loans of 20 trillion yen in 1998

– Japanese Life insurers exposed to these banks by about 14 trillion Yen in loans


• C & I Loans

•Different size and maturities

•Secured or unsecured

•Fixed or floating

•Spot Loans or Loan Commitments

•Commercial paper (large corporations, directly or via investment banker, sidestepping banks, lower rates)

•Real Estate Loans

•various features


•Individual (Consumer) Loans

•Revolving loans

•High default rates (3-7 %)

•Return on a Loan•Interest rate

•fees

•credit risk premium

•collateral

•nonprice terms (compensating balances, reserve requirements)


•Prime Rate most commonly used for longer-term loans, fed-funds for shorter term

•LIBOR

The gross return on loan, k, per dollar lent is

)]1([1)(11

RbmLfk

Numerator is fees plus interest…promised cash flows

Denominator is net outflow from the bank


•Expected return on the Loan•Default risk

)1()( kprE

Retail versus Wholesale Credit decisions

•Retail

•Accept-Reject decisions

•credit rationing…….quantity restrictions rather than price or interest rate differences


•Wholesale

•Interest rate and credit quantity used to control credit risk

•Prime plus a markup for riskier borrowers, BUT

•Higher rates don’t necessarily imply higher return

Measurement of Credit Risk•Need to measure probability of default

•Information

•Covenants


Default Risk ModelsThree Broad Groups, Qualitative, Credit-Scoring, Newer Models

•Qualitative Models (Expert systems)

•Lack of public information leads to assembly of :

•Borrower Specific information

•Reputation, Long-term relationship, implicit contract

•Leverage, or capital structure (D/E), threshold beyond which probability of default increases

•Volatility of earnings (stable v.s. high-tech)

•Collateral

•Market Specific Factors (Business cycle, Interest rates)


•Credit Scoring Models

either calculate default probabilities or sort borrowers into different risk classes, Thus:

•Numerically establish the factors that explain default risk

•Evaluate the relative importance of these factors

•Improve pricing of default risk

•Better screening of bad loan applicants

•better position to calculate reserves needed to meet expected future loan losses

•Linear Probability Model

errorX ij

n

jjiZ

1


Example:

Suppose there were two factors influencing the past default behavior of borrowers: the leverage or D/E and the sales/assets ratio (S/A). Based on past default (repayment) experience, the linear probability model is estimated as:

iii ASEDZ )/(1.)/(5.

Assume a prospective borrower has a D/E=.3, and a S/A=2.0, its expected probability of default (Zi ) can then be estimated as:

35.)0.2(1.)3(.5. iZ

)1()( ii pZE Also, P is repayment probability


Problem is probabilities can lie outside of 0 to 1. Logit Model fixes this by:

iZie

ZF

1

1)(

The left hand side is the logistically transformed value of Zi

The Probit Model is an extension of Logit which considers a cumulative normal distribution rather than a logistic function.

•Linear Discriminant Models

•Altman’s (of NYU) Z-score, uses various financial ratios in classifying borrowers into high and low default risk classes:

54321 0.16.03.34.12.1 XXXXXZ

Where, X1=WC/TA, X2=RE/TA, X3=EBIT/TA, X4=MVEq./BVLtd, and X5=Sales/TA, Low Z means high risk


Altman’s Z has a switching point at 1.81.Problems:

•Only two extreme cases discussed

•Are the coefficients stable over time?

•Are the ratios relevant over time?

•Qualitative factors ignored

•Lack of dataNewer Models•Term Structure Derivation

We extract implied default probabilities on loans or bonds using the spreads between risk-free discount Treasury bonds and discount bonds issued by corporations of different risks


Probability of default on one-period Debt Instrument

Assume risk-neutrality, and that the FI would be indifferent between the corporate and the Treasury of same maturity discount bonds:

p(1+k) = (1+i)

p = (1+i) / (1+k) with i = 10% and k = 15.8%

p = (1.1) / (1.158) = .95 probability of repayment

thus, 5% is the implied probability of default given the market rates, a 5.8% risk premium ( goes along with it.

= k - i = 5.8%If all is not lost at default, if is the proportion of the loan that can be collected, then

(1+k)(1-p) + p(1+k) = 1 + i

the first term is the payoff to the FI if default occurs.


The fact that there will be partial recovery reduces

)1()(

)1( ipp

iik

With i= 10%, and p=.95, and =.9, risk premium = 0.6

MULTIPERIOD WILL BE COVERED IN CLASS!!!!!!

Mortality rate derivation of credit risk

Focus on historic default risk experience. Substitute mortality rates for default rates.

MMR1= Ratio of total value of bonds of a certain grade defaulting in year 1 of issue TO total value of same bonds outstdg. in year1 of issue

MMR2= Ratio of year 2 defaults TO total value of survivors in year2

Problems : backward-looking, period-sensitive, volume+size sensitive.

1

11

ki

por


RAROC Models

Risk-adjusted return on capital, RAROC, is the ratio of loan income to loan risk. A loan is approved if RAROC exceeds a FI established benchmark rate (cost of capital)

Estimating loan risk is possible using a Duration-type approach

RRD

LL

L

1

)1( RRLDL L

Replacing interest-rate shocks with credit quality shocks]0)([ Gi RRMaxR

Do example in book, pages 233-234.


Credit Risk Continued

• Option Models of Default Risk• Borrower always holds a valuable default or

repayment option. If things go well repayment takes place, borrower pays interest and principal keeps the remaining upside, If things go bad, limited liability allows the borrower to default and walk away losing his/her equity.

• KMV corporation (www.kmv.com) has developed a model called Expected Default risk Frequency EDF used now by largest US banks.


Payoff to stockholders

0 BA1 A2-S

Assets

This is the borrower’s payoff function, s is the size of the initial equity investment, B is the value of Bonds, and A is the marketvalue of the assets of the firm.


BA1 A2 Assets

Payoff todebt holders

The payoffs to the bond holders are limited to the amount lent Bat best.


Merton’s model:

debtrisky on yield Required)()]()/1()(ln[)/1()(premiumrisk default mequilibriu get thecan We

borrower ofrisk asset h exceedingdeviation of )(

/)]ln(2/1[/)]ln(2/1[

)/( ratio leverage sborrower'

)]()()/1[()(

12

2

22

21

21

khNdhNik

yprobabilithNdhdh

ABedtT

wherehNhNdBeF

i

i


On the last equation variance and leverage ratio would affect the riskpremium. But NOTICE that the key variables are A, market value ofassets, and asset risk

An Option Model Example is given on page 237.

2 Neither of which are directly observable.

The KMV model uses the OPM to extract the implied market value ofassets (A), and the asset volatility of a given firm. This is done byviewing equity as a call-option on the firm’s assets and the volatilityof a firm’s equity value will reflect the leverage adjusted volatility ofits underlying assets. We have in general form:

)(

),,,,(

gand

iBAfE

E

Where, the bars (-) denote variables that are directly observable.Since we have 2 equations with 2 unknowns (A,), we can solve..


The following is a graph that depicts the superior accuracy ofKMV-EDF over agency ratings in capturing expected default probabilities.

Source KMV Corp.


Loan Portfolio Risk- Chapter 12

• We move beyond default risk measurements to more aggregate contexts, i.e. portfolios.

• I will focus on two models that are not treated in detail in the current edition of the Saunders book.– A simple model : Migration Analysis– A more sophisticated model: KMV Corporation’s

“Portfolio Manager Model”


Migration Analysis

• A Loan Migration Matrix measures the probability of a loan being upgraded, downgraded, or defaulting over some period. Historic data is used, as such it can be used as a benchmark against which the credit migration patterns of any new pool of loans can be compared.

• In a Loan migration matrix the cells are made up of transition probabilities.

• The number of grades are generally around 10 for most FI’s.


Risk Grade at end of year1 2 3 D=Default

Risk Grade 1 0.85 0.1 0.04 0.01at beginning 2 0.12 0.83 0.03 0.02of year 3 0.03 0.13 0.8 0.04

A Hypothetical Rating Transition Matrix:

If the FI is evaluating the credit risk of of grade 2 rated borrowers,and observes that over the last few years a much higher %, say 5%,have been downgraded to3, and 3.5% have defaulted, the FI may then seek to restrict its supply of lower quality loans (grades 2 and3), concentrating more on grade 1. At the very least it should seekhigher credit risk premiums on lower quality loans. Migration ana-lysis is used on commercial, credit card, and consumer loan portfolios.


KMV Portfolio Manager Model

• KMV Portfolio Manager is a model that applies Modern Portfolio Theory to the loan portfolio.

To estimate an efficient frontier for loans as in the above figure, andthe proportions (Xi), we need to measure :


•Expected return on a loan to borrower i, (Ri)•The risk of a loan to borrower i, (i)•The correlation of default risks between loans to borrowers i and j KMV measures each of the above as follows:Return on the Loan:

][)( iiiiii LGDEDFAISLEAISR

Where,AIS = annual ‘all-in-spread’ on a loan = (Annual Fees earned) + (Loan rate - Cost of Funds)E(L) = expected loss on the loan EDF = expected default frequencyLGD = loss given default


Risk of the Loan:

iiiiDiii LGDEDFEDFLGDUL )1(

The Unexpected Loss (UL) is a measure of loan risk, i. It reflects thevolatility of the loan’s default rate, Di, times LGD. To measure Diwe assume loans either default or repay (no default), then defaults arebinomially distributed, then the of the default rate for the ith borrower Di, is equal to the square root of the probability of default times oneminus the probability of default, as above with EDF, (1-EDF).

Correlation : ij Correlation between the systematic returncomponents of the equity returns of borrower i and j. Generally low.A number of large banks are using this model or variants to activelymanage their loan portfolios. Some are reluctant especially if involvinglong-term customers. Diversification versus Reputation.


Sovereign Risk- Chapter 16

• Large Exposure

JapanUSBritainFranceGermanyOther

Foreign banks’ share of total Asian debt at the end of June 1997 (excluding Singapore and Hong Kong. Source BIS)


•Prior to July 97 Thai crisis, Foreign banks had $389 billion in loans

and other debt outstanding. See slide on page 29.

•This crisis is still unfolding

•Bailouts and loan restructuring packages (South Korea $57 billion IMF organized loan package)•Credit Risk

•Sovereign Risk should dominate

•Repudiation (common before WWII) bonds

•Rescheduling (common since WWII) bank loans

•Relatively small number of banks (1/98 South Korea loans just over 100 banks involved)


•Same group of banks involved

•Cross-default provisions

•Governments view social costs of default on international bonds less worrisome than on loans. Possible incentive problems?

Country Risk Evaluation•Outside Evaluation Models

•Euromoney Index

•Institutional Investor Index

•Internal Evaluation Models

•Similar to our Credit-risk scoring models based on explaining probability of a country rescheduling, like Z-scores


Common variables in CRA:

•Debt Service ratio=(interest+amortization on debt)/Exports

positive relation with probability of rescheduling

•Import Ratio=(Total imports/Total FX reserves)

positive relation

•Investment Ratio= Real Investment/GNP

+/- relation, arguments on both sides

•Variance of Export Revenue=

+ relation

•Domestic Money Supply Growth= M / M

+ relation

2ER


Problems•Measurement

•Population groups (a finer distinction than rescheduler or not)

•Political risk factors

•Portfolio aspects (systematic risk more important)

•Incentive Aspects (Benefits and Costs) Read section

•Stability (of variables)

Use of Secondary market for LDC Debt to measure risk•The structure of the market

•Brady Bonds ($ loans exchanged for $ bonds-US Treasury bonds are used to collateralize the bonds).

•Sovereign Bonds. No US-Tbonds used as collateral


•Performing Loans

•Non-performing loans

LDC Market Prices and CRA

Regression analysis of price changes to key variables. LHS= periodic changes in prices of LDC debt in the secondary markets, RHS= set of key variables.

Once the parameters are estimated, FI can combine these with forecasts of key variables to estimate price changes.

Has problems but hopefully reduces errors.


Dealing with Sovereign Risk Exposure

•Debt-Equity Swaps (Industries like motor, tourism, chemicals have been desirable fo outside investors.)

FI may sell $100 million loan to a company for $93, Company negotiates with foreign gov. And swaps $100 million for $95 million worth equity in local currency. Company has $2million buffer, country gets rid of US$ debt, company has to invest in local markets in local currency.

•MYRA (Multiyear Restructuring Agreements)•concessionality: The amount the bank gives up in present value terms as a result of a MYRA.

example:From appandix of chapter.•Loan sales•Debt for Debt Swaps (Brady Bonds)

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