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Chapter 10

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Overview

This chapter discusses types of loans, and the analysis and measurement of credit risk on individual loans

Important for purposes of:

– Acceptance/Rejection decision

– Pricing loans and bonds

– Setting limits on credit risk exposure

Credit Quality Problems

Problems with junk bonds, LDC loans, and residential and farm mortgage loans

Late 1990s, credit card and auto loans

Crises in other countries such as Argentina, Brazil, Russia, and South Korea

2006-2007: Mortgage delinquencies and subprime loans

Emphasizes importance of managing credit risk

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Nonperforming Asset Ratio for U.S. Commercial Banks

Types of Loan

Commercial and industrial loans,

Real estate loans,

Individual (consumer) loans,

Other loans (e.g. government loans, margin loans, farm loans).

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Commercial and Industrial Loans

Loans for business purposes Short-term loans: to finance working capital needs and other

short-term funding needs,

Long-term loans: to finance purchase of real assets, new venture start-up costs and permanent increases in working capital.

Syndicated loans: Finance provided by a group of lenders,

Usually to finance large C&I loans.

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Commercial and Industrial Loans (cont.) Credit risk:

Loan rating: external credit rating.

Secured (asset-backed) loan: loan backed by first claim on certain assets.

Unsecured loan (junior debt): loan with a general claim only.

Other characteristics Fixed rate or floating rate

Spot loan or loan commitment (line of credit) which is a revolving credit facility with a maximum size and a maximum period of time

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Commercial and Industrial Loans (cont.) Commercial paper and disintermediation

Commercial papers: unsecured short-term debt instrument

Large corporations with good credit rating can get direct access to funds in capital markets by issuing commercial papers.

Changes: Decline in C&I loans originated by commercial banks and

growth in commercial paper market

Effect of financial crisis on commercial paper market

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Real Estate Loans Loans to individuals and families to finance property

purchase. Long maturities, often 25 - 30 years. Periodic payments typically cover both interest payments

and partial repayment of principal. Changing trend: in the 1990s most real estate loans were

granted for owner-occupation; today a larger proportion of loans are for investment purposes.

Competitive market through new entrants: RAMS, Aussie Home Loans, Wizard…

Fixed-rate, ARM Mortgages can be subject to default risk when loan-to-

value rises

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ARMs’ Share of Total Loans Closed, 1987-2012

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Individual (Consumer) Loans

Personal loans, automobile, mobile home loans Non-revolving loans

Credit cards A revolving loan facility

Growth in credit card debts

Risks affected by competitive conditions and usury ceiling

Other loans

Other loans include a wide variety of borrowers and types Farm loans

Other banks

Nonbank FIs: Broker margin loans

Foreign banks and sovereign governments

State and local governments

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Calculating the Gross Return on a Loan

Factors affecting the promised loan return: Loan interest rate = base lending rate (BR) + credit risk

premium or margin (m).

Direct fees, eg. loan origination fee (f),

Indirect fees, eg. Compensating balance requirements (b),

Reserve requirement (R).

Other non-priced items, eg. collateral,

Gross return on loan (k) per dollar lent:

1+k = 1 + [f + (BR+m)] / [1- b(1-R)].

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Calculating the Expected Return on a Loan

Expected return might differ from promised return because of default risk.

Expected return:E(1+r)=1+E(r) = p(1+k).

Where:

p = probability of loan repayment.

If p < 1:

Default risk exists,

Control credit risk: set risk premium and limit the exposure (credit rationing)

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Retail Versus Wholesale Credit Decisions

Retail:

Characteristics Small dollar size loans,

Higher cost associated with collection of information,

Decision: Usually accept or reject decision,

Standard loan rate is usually charged,

Credit risk controlled through credit rationing: limit the total exposure to the sector/individual

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Retail Versus Wholesale Credit Decisions

Wholesale:

Credit risk controls: the use of differential interest rates to compensate for

different levels of risks

Limit credit exposure through credit rationing.

Recall: expected return on loan E(1+r)= p(1+k) Pricing tool (increase k) does not fully address the problem

of credit risk Why?

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Measuring Credit Risk

Qualitative credit risk models

Credit scoring models

Term structure based methods

Mortality rate models

RAROC models

Option models (for your knowledge only)

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Qualitative credit risk models

Borrower-specific factors include: Reputation: implicit contract,

Leverage (capital structure),

Volatility of earnings,

Covenants,

Collateral.

Market-specific factors include: Business cycle,

Level of interest rates.

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Credit Scoring Models

Quantitative models that use observed borrower characteristics to: Calculate score as a proxy of borrower’s default probability,

or Sort borrowers into different default classes.

A scoring model needs to: Establish factors that help to explain default risk Evaluate the relative importance of these factors

Major types of credit scoring models: Linear probability model,

Logit model,

Linear discriminant models.

Credit Scoring Models (cont)

Linear Probability Model

Statistically unsound, since the Zs obtained are not probabilities at all.

Since superior statistical techniques are readily available, little justification for employing linear probability model.

Logit Model overcomes weakness of the linear probability model using a

transformation (logistic function) that restricts the probabilities to the zero–one interval.

n

jjiji XZ

1, error

exp( ) /(exp( ) 1)i i iP Z Z

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Credit Scoring Models: Linear Discriminant Models Altman’s Z score model for manufacturing firms

Z=1.2X1 + 1.4X2 + 3.3X3 + 0.6X4 + 1.0X5

Critical values of Z = 1.81 and Z = 2.99.

X1 = Working capital/total assets.

X2 = Retained earnings/total assets.

X3 = EBIT/total assets.

X4 = Market value equity/book value LT debt.

X5 = Sales/total assets.

Critical values suggested by Altman Z >= 2.99, high quality loans, low default risk

Z < 1.81, very low quality loans, high default risk

1.81 <= Z < 2.99, hybrid

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Credit Scoring Models: Linear Discriminant Models

Weaknesses: Models ignore hard-to-quantify factors such as

borrower reputation, Variables in any credit scoring model unlikely to be

constant over longer periods of time, Weights in any credit scoring model unlikely to be

constant over longer periods of time, There is no centralised database on defaulted business

loans for proprietary or other reasons – hard to test the validity of any model or develop new models.

Broad distinction between borrower categories, i.e. good and bad borrowers.

Term structure (of credit risk) model

If we know the risk premium we can infer the probability of default.

Under the market equilibrium, expected return of a risky loan should be equal to the risk-free rate after accounting for probability of default (1-p).

Assuming a zero default recovery rate: p (1+ k) = 1+ i

Adjust for varying default recovery rates. Assume that γ is the proportion of the loan’s principal and

interest that is collectible on default:

[(1 - p) γ(1 + k)] + [p(1 + k)] = 1 + i

(1-p) γ(1+ k) = the payoff the FI expects to get in case of default.

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Term structure model: Key ideas/ relationship

The equality of expected returns over any horizon or in any single period.

The relation between cumulative probability of payment and marginal probability of payment:

Probability of payment for two periods (P) =

probability of payment in period 1 (P1)

* probability of payment in period 2 (P1-2)

The relation between cumulative return and single period return: Return for two periods (1+k) = (1+k2)2 = (1 + k1)*(1+k1-2)

where k1 and k2 are 1-year and 2-year spot rates (the annual interest rate on a zero-coupon bond)

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Term structure model (Cont)Cumulative PD on a multi-period debt

Approach 1: infer from the equality of expected returns: [(1 - p) γ(1 + k)] + [p(1 + k)] = 1 + i

1-p – cumulative PD,

k – cumulative return for debt,

i – cumulative risk-free return

Approach 2: infer from marginal PD in individual periods.

Ex. For a 2-period bond Marginal PD in period 1 is 1-p1, in period 2 is 1-p1-2

Probability of default in two periods: 1 – p1*p1-2

Marginal PD in a period could be inferred from the equality of expected return in that period

Term structure model (Cont): Marginal PD in a future period on a multi-period debt

Approach 1: infer from the equality of expected returns in the future period (called as forward return) Marginal probability of default (1 – p1-2 ):

[(1 – p1-2) γ1-2 (1 + k1-2)] + [p1-2(1 + k1-2)] = 1 + i1-2

Infer forward interest rate from spot rates

Spot rate: the interest rate for a discount bond

k1 for 1-year spot rate, and k2 for 2-year spot rate

Forward rate for the period year 1 to year2:

(1+k2)2 = (1+k1)*(1+k1-2)

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Approach 2: infer from cumulative PD Marginal PD in period 1: 1-p1

cumulative PD in two periods: 1-p

Marginal PD in period 2: 1-p1-2, where p = p1*p1-2

p and p1 can be inferred from equality of expected returns if you know the cumulative return of two periods and the return in 1st period

Term structure model (Cont): Marginal PD in a future period on a multi-period debt

Term structure model: application

Estimate probability of default (PD) over the life of a loan: applying the equality of expected returns to the cumulative

returns of loans and risk-free assets.

Estimate PD over a single period for a loan (whether current period or a period in the future) applying the equality of expected returns to the returns in a

current or future period for loans and risk-free assets.

Why it is useful? We can estimate the PD for a new loan based on the inferred

PD of (existing) loans/bonds with comparable credit quality.

The PD for the (existing) comparable loans could be inferred based on the equality of expected returns.

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Mortality-Rate Models

Essentially a marginal probability of default concept . The probability of default is estimated from past data on defaults.

Marginal Mortality Rates:

MMRt = (Total value of bond/loan defaults in yr t of issue) / (total value of bond/loan outstanding in yr t of issue)

Cumulative Mortality Rate is just the cumulative probability of default.

CMR2 = 1 - (1-MMR1)*(1-MMR2)

Has many of the problems associated with credit scoring models, such as sensitivity to the period chosen to calculate the MMRs

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RAROC Models

All previous models are somewhat backward looking except for the term-structure models.

RAROC Models

RAROC = risk-adjusted return on capital.

Essential idea: modified ROA concept which balances expected interest income against expected loan risk.

Loan approval if RAROC > benchmark return on capital, eg. ROE

one year income on a loan

RAROC loan asset risk or capital at risk

RAROC Models: Measuring net income

Net income = value of loans outstanding * all-in-spread (AIS)

Where AIS = contractually-promised return on the loan (taking into account of interest rate and all explicit and implicit fees) – funding cost

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RAROC Models: Measuring loan risk

Capital at risk (VaR approach): the potential loan loss under adverse credit scenarios

∆L = - D * L * [∆R / (1+R)]

D is the duration of the loan

L is the size of the loan

R is the current level of rate

∆R is the increase in risk premium

under adverse credit scenarios,

such as 95 or 99 percentile value of the distribution

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RAROC Models – Measuring loan risk

Alternatively, estimate loan loss risk from loan portfolios

unexpected default rate × proportion of loan lost on default

Unexpected default rate is the default rate under adverse credit scenarios from historical distributions.

one year income per $ loaned RAROC

PD* LGD

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Option Models of Default Risk (for interests)

KMV-Merton model: use option pricing methods to evaluate the option to default.

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Option Models of Default Risk Merton showed value of a risky loan

F() = Be-i[(1/d)N(h1) + N(h2)]

Written as a yield spread

k() - i = (-1/)ln[N(h2) + (1/d)N(h1)]

k() = required yield on risky debt

i = risk-free rate on debt of equivalent maturity

= time to maturity

d = borrower’s leverage ratio = Be-i/A

σ is the volatility of the rate of change in the value of assets

Problem: unobservable market value of assets and the volatility of asset value

KMV approach: estimate the above two values by applying an option pricing model to equity

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[0.5 ln( )] /

[0.5 ln( )] /

h d

h d

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Option Models of Default Risk