CREDIT RISK OF LOAN PORTFOLIOS

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CREDIT RISK OF LOAN PORTFOLIOS

• FIN 653 Lecture Notes
• From Saunders and Cornett
• Ch. 12

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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.

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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.

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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.

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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
• ________________________________________

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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.

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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.

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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

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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.

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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.

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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).

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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 - 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).

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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
  loss given default or LGDi.

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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.

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III. Loan Portfolio Diversification and Modern
Portfolio Theory (MPT)

• Risk of the Loan (?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. That
  is
• ?Di ( EDF) (1-EDF)1/2.

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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!

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III. Loan Portfolio Diversification and Modern
Portfolio Theory (MPT)

• 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.

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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
• ________________________________________

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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

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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.

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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
• __________________________________________________
  ______

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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)

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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.

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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.

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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.