Title: CREDIT RISK OF LOAN PORTFOLIOS
1CREDIT RISK OF LOAN PORTFOLIOS
- FIN 653 Lecture Notes
- From Saunders and Cornett
- Ch. 12
2I. Introduction
- Credit risk of a loan (asset) portfolio should
take into account both the concentration risk and
the benefit from loan portfolio diversification. - Portfolio credit risk can be used to set maximum
loan concentration limits for certain business or
borrowing sectors. - The FDIC Improvement Act of 1991 requires bank
regulators to incorporate credit concentration
risk into their evaluation of bank insolvency
risk.
3I. Introduction
- Banks will be allowed to use their own "internal"
models, such as CreditMetrics and Credit Risk
and KMV's Portfolio Manager, to calculate their
capital requirements against insolvency risk from
excessive loan concentrations. - The National Association of Insurance
Commissioners (NAIC) has developed limits for
different types of assets and borrowers in
insurers' portfolios - a so-called pigeonhole
approach.
4II. Simple Models of Loan Concentration Risk
- 1.Migration Analysis Lending officers track
SP, Moody's, or their own internal credit
ratings of certain pools of loans or certain
sectors. If the credit ratings of a number of
borrowers in a sector or rating class decline
faster than has been historically experienced,
then lending to that sector or class will be
curtailed.
5II. Simple Models of Loan Concentration Risk
- TABLE A Hypothetical Rating Migration or
Transition Matrix Risk Grade at End of Year - _______________________________________
- 1 2 3 Default
- ________________________________________
- Risk grade at 1 .85 .10 .04 .01
- Beginning of 2 .12 .83 .03 .02
- Year 3 .03 .13 .80 .04
- ________________________________________
6II. Simple Models of Loan Concentration Risk
- A loan migration matrix (or transition matrix)
seeks to reflect the historic experience of a
pool of loans in terms of their credit-rating
migration over time. As such, it can be used as a
benchmark against which the credit migration
patterns of any new pool of loans can be
compared. - E.g. For grade 2 loans, historically 12 percent
have been upgraded to 1, 83 percent have remained
at 2, 3 percent have been downgraded to 3, and 2
percent have defaulted by the end of the year.
7II. Simple Models of Loan Concentration Risk
- Suppose that the FI is evaluating the credit risk
of its current portfolio of loans of grade 2
rated borrowers and that over the last few years
a much higher percentage (say, 5 percent) of
loans has been downgraded to 3 and a higher
percentage (say, 3 percent) has defaulted than is
implied by the historic transition matrix. The FI
may then seek to restrict its supply of
lower-quality loans (e.g., those rated 2 and 3),
concentrating more of its portfolio on grade 1
loans.
8II. Simple Models of Loan Concentration Risk
- 2. Setting External Limits For management to set
some external limits on the maximum amount of
loans that can be made to an individual borrower
or sector. - E.g., suppose management is unwilling to permit
losses exceeding 10 percent of an FI's capital to
a particular sector. If it is estimated that the
amount lost per dollar of defaulted loans in this
sector is 50 cents, then the maximum loans to a
single borrower as a percent of capital, defined
as the concentration limit, is
9II. Simple Models of Loan Concentration Risk
- Concentration limit Maximum loss as a
- percent of capital (1/Loss
- rate)
- 10 1/.5
- 20
- Bank regulators in recent years have limited loan
concentrations to individual borrowers to a
maximum of 10 percent of a bank's capital.
10III. Loan Portfolio Diversification and Modern
Portfolio Theory (MPT)
- The FI manager can compute the expected return
(RP) and risk (?P2) on a portfolio of assets as - RP ? Xi Ri
- ?P2 ? Xi2 ?i2 ? ? Xi Xj ?ij ?i ?j
- If many loans have negative default covariances
or correlations, the sum of the individual credit
risks of loans viewed independently will
overestimate the risk of the whole portfolio. FIs
can take advantage of the law of large numbers in
their investment decisions.
11III. Loan Portfolio Diversification and Modern
Portfolio Theory (MPT)
- KMV Portfolio Manager Model
- Any model that seeks to estimate an efficient
frontier for loans and thus the optimal or best
proportions (Xi) in which to hold loans made to
different borrowers needs to determine and
measure three things - 1. the expected return on a loan to borrower i
(Ri), - 2. the risk of a loan to borrower i (?i), and
- 3. the correlation of default risks between loans
made to borrowers i and j (?ij).
12III. Loan Portfolio Diversification and Modern
Portfolio Theory (MPT)
- KMV measures each of these as follows
- Ri AISi - E(Li) AISi - EDFi LGDi
- ?i ULi ?Di LGDi EDFi (1 - EDFi)1/2
LGDi - where
- AIS All-in-spread Annual fees earned on the
loan The annual spread between the loan rate
paid by the borrower and the FI's cost of funds -
The expected loss on the loan E(Li). - E(Li) The Expected Loss (The expected
probability of the borrower defaulting over the
next year or its expected default frequency
(EDFi)) (The amount lost by the FI if the
borrower defaults the loss given default or
LGDi).
13III. Loan Portfolio Diversification and Modern
Portfolio Theory (MPT)
- Return on the Loan (Ri)
- Measured by the so-called annual all-in-spread
(AIS), which measures annual fees earned on the
loan by the FI plus the annual spread between the
loan rate paid by the borrower and the FI's cost
of funds. Deducted from this is the expected loss
on the loan E(Li). - This expected loss E(Li) is equal to the
product of the expected probability of the
borrower defaulting over the next year, or its
expected default frequency (EDFi) times the
amount lost by the FI if the borrower defaults
the loss given default or LGDi.
14III. Loan Portfolio Diversification and Modern
Portfolio Theory (MPT)
- Risk of the Loan (?i)
- The risk of the loan reflects the volatility of
the loan's default rate (?Di) around its expected
value times the amount lost given default (LGDi).
- The product of the volatility of the default rate
and the LGD is called the unexpected loss on the
loan (ULi) and is a measure of the loan's risk or
?i. - To measure the volatility of the default rate,
assume that loans can either default or repay (no
default) then defaults are "binomially"
distributed, and the standard deviation of the
default rate for the ith borrower (?Di) is equal
to the square root of the probability of default
times 1 minus the probability of default ( EDF)
(1-EDF)1/2.
15III. Loan Portfolio Diversification and Modern
Portfolio Theory (MPT)
- Correlation of Loan Defaults (?ij)
- To measure the unobservable default risk
correlation between any two borrowers, the KMV
Portfolio Manager model uses the systematic
return components of the stock or equity returns
of the two borrowers and calculates a correlation
that is based on the historical comovement
between those returns. - According to KMV, default correlations tend to be
low and lie between .002 and .15. This makes
intuitive sense. For example, what is the
probability that both IBM and General Motors will
go bankrupt at the same time? For both firms,
their asset values would have to fall below their
debt values at the same time over the next year!
16III. Loan Portfolio Diversification and Modern
Portfolio Theory (MPT)
- A number of large banks are using the KMV model
(and other similar models) to actively manage
their loan portfolios. Nevertheless, some banks
are reluctant to use such models if it involves
selling or trading loans made to their long-term
customers. In the view of some bankers, active
portfolio management harms the long-term
relationships bankers have built up with their
customers. As a result, gains from
diversification have to be offset against loss of
reputation.
17IV. Partial Applications of Portfolio Theory
- Loan Volume-Based Models
- Table Allocation of the Loan Portfolio to
Different Sector - National Bank A Bank B
- ________________________________________
- Real estate 10 15 10
- CI 60 75 25
- Individuals 15 5 55
- Others 15 5 10
- ________________________________________
18IV. Partial Applications of Portfolio Theory
- To calculate the extent to which each bank
deviates from the national benchmark, we use the
standard deviation of bank A's and bank B's loan
allocations from the national benchmark. - We calculate the relative measure of loan
allocation deviation as - ? (Xij - Xi)21/2
- ?j -----------------------
- N
19IV. Partial Applications of Portfolio Theory
- Bank B deviates significantly from the national
benchmark due to its heavy concentration in
individual loans. - The standard deviation simply provides a manager
with a measure of the degree to which an FI's
loan portfolio composition deviates from the
national average or benchmark. - This partial use of modem portfolio theory
provides an FI manager with a feel for the
relative degree of loan concentration carried in
the asset portfolio.
20IV. Partial Applications of Portfolio Theory
- TABLE Measures of Loan Allocation Deviation
from the National Benchmark Portfolio - __________________________________________________
______ - Bank A Bank B
- __________________________________________________
______ - (X1j - X1)2 (.05)2 .0025 (0)2 0
- (X2j - X2)2 (.15)2 .0225 (.05)2 .0025
- (X3j - X3)2 (-.10)2 .01 (.4)2 .16
- (X4j - X4)2 (-.10)2 .01 (-.05)2 .0025
- ___________ ______________ ______________
- ? (Xjj - Xi)2 ? .045 ? .285
- ?A 10.61 ?B 26.69
- __________________________________________________
______
21IV. Partial Applications of Portfolio Theory
- Loan Loss Ratio-Based Models
- This model involves estimating the systematic
loan loss risk of a particular sector relative to
the loan loss risk of a bank's total loan
portfolio. This systematic loan loss can be
estimated by running a time series regression of
quarterly losses of the ith sector's loss rate on
the quarterly loss rate of a bank's total loans - (Sectoral losses in the ith sector/Loans to the
ith sector) ? ? (Total Loan Losses/Total
Loans)
22IV. Partial Applications of Portfolio Theory
- Where ? measures the systematic loss sensitivity
of the ith sector loans. - The implication of this model is that sectors
with lower ?s could have higher concentration
limits than high ? sectors--since low ? loan
sector risks (loan losses) are less systematic,
that is, are more diversifiable in a portfolio
sense.
23IV. Partial Applications of Portfolio Theory
- Regulatory Models
- The method adopted is largely subjective and is
based on examiner discretion. The reasons given
for rejecting the more technical models are that
(1) current methods for identifying concentration
risk are not sufficiently advanced to justify
their use and - (2) insufficient data are available to estimate
more quantitative-type models, although the
development of models like KMV, as well as
CreditMetrics and Credit Risk, may make bank
regulators change their minds.
24IV. Partial Applications of Portfolio Theory
- Life and property-casualty insurance regulators
have also been concerned with excessive industry
sector and borrower concentrations. - These general diversification limits are set at 3
percent for life-health insurers and 5 percent
for property-casualty insurers implying that
life-health companies must hold securities of a
minimum of 33 different issuers, while for PC
companies the minimum is 20. - The rationale for such a simple rule comes from
modern portfolio theory, which shows that equal
investments across approximately 15 or more
stocks can provide significant gains from
diversification.