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CREDIT RISK OF LOAN PORTFOLIOS

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CREDIT RISK OF LOAN PORTFOLIOS

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

    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 S&P, 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% C&I 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)2]1/2 ?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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