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CREDIT RISK OF LOAN PORTFOLIOS

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Title: CREDIT RISK OF LOAN PORTFOLIOS


1
CREDIT RISK OF LOAN PORTFOLIOS
  • FIN 653 Lecture Notes
  • From Saunders and Cornett
  • Ch. 12

2
I. 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.

3
I. 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.

4
II. 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.

5
II. 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
  • ________________________________________

6
II. 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.

7
II. 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.

8
II. 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

9
II. 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.

10
III. 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.

11
III. 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).

12
III. 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).

13
III. 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.

14
III. 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.

15
III. 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!

16
III. 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.

17
IV. 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
  • ________________________________________

18
IV. 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

19
IV. 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.

20
IV. 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
  • __________________________________________________
    ______

21
IV. 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)

22
IV. 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.

23
IV. 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.

24
IV. 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.
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