贷款组合信用风险管理

1、CREDIT RISK OF LOAN PORTFOLIOS From Saunders and Cornett1I. IntroductionCredit 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 cert

2、ain 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. 2I. IntroductionBanks will be allowed to use their own internal models, such as CreditMetrics and Credit Risk+ and KMVs

3、 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、.3II. Simple Models of Loan Concentration Risk1.Migration Analysis: Lending officers track S&P, Moodys, 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 historica

5、lly experienced, then lending to that sector or class will be curtailed.4II. Simple Models of Loan Concentration RiskTABLE: A Hypothetical Rating Migration or Transition Matrix Risk Grade at End of Year_ 123Default_Risk grade at1 .85 .10.04 .01Beginning of2 .12 .83 .03 .02Year3 .03 .13 .80 .04_5II.

6、Simple Models of Loan Concentration RiskA 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 o

7、f 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. 6II. Simple Models of Loan Concentration RiskSuppose that the FI is evaluating th

8、e 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

9、 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. 7II. Simple Models of Loan Concentration Risk2. Setting External Limits: For management to set some external limits on the maximum amount of loans that can be m

10、ade to an individual borrower or sector. E.g., suppose management is unwilling to permit losses exceeding 10 percent of an FIs 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

11、 as a percent of capital, defined as the concentration limit, is8II. Simple Models of Loan Concentration RiskConcentration 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 maxi

12、mum of 10 percent of a banks capital.9III. 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 jIf many loans have negative default covariances or correlation

13、s, 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.10III. Loan Portfolio Diversification and Modern Portfolio Theory (MPT)KMV Portfolio Manager Mod

14、el: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 (

15、i), and 3. the correlation of default risks between loans made to borrowers i and j (ij).11III. Loan Portfolio Diversification and Modern Portfolio Theory (MPT)KMV measures each of these as follows:Ri = AISi - E(Li) = AISi - EDFi * LGDii = ULi = Di* LGDi = EDFi (1 - EDFi)1/2 * LGDi whereAIS = All-in

16、-spread = Annual fees earned on the loan + The annual spread between the loan rate paid by the borrower and the FIs 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 frequen

17、cy (EDFi) * (The amount lost by the FI if the borrower defaults the loss given default or LGDi).12III. 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 F

18、I plus the annual spread between the loan rate paid by the borrower and the FIs 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 defaul

19、t frequency (EDFi) times 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)Risk of the Loan (i):The risk of the loan reflects the volatility of the loans default rate (Di) around its expected value

20、 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 loans risk or i. To measure the volatility of the default rate, assume that loans can either default or repay (no default

21、); 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)1/2.14III. Loan Portfolio Diversification and Modern Portfolio Theo

22、ry (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 histor

23、ical 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 hav

24、e to fall below their debt values at the same time over the next year! 15III. 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

25、 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

26、 reputation. 16IV. Partial Applications of Portfolio TheoryLoan Volume-Based Models:Table: Allocation of the Loan Portfolio to Different SectorNational Bank ABank B_Real estate10%15%10%C&I607525Individuals15555Others15510_ 17IV. Partial Applications of Portfolio TheoryTo calculate the extent to whic

27、h each bank deviates from the national benchmark, we use the standard deviation of bank As and bank Bs loan allocations from the national benchmark. We calculate the relative measure of loan allocation deviation as (Xij - Xi)21/2 j = - N18IV. Partial Applications of Portfolio TheoryBank B deviates s

28、ignificantly 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 FIs loan portfolio composition deviates from the national average or benchmark. This partial use of modem portfolio t

29、heory provides an FI manager with a feel for the relative degree of loan concentration carried in the asset portfolio. 19IV. Partial Applications of Portfolio TheoryTABLE: Measures of Loan Allocation Deviation from the National Benchmark Portfolio_Bank ABank B_(X1j - X1)2(.05)2 = .0025 (0)2 = 0(X2j

30、- 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 = .285A = 10.61%B = 26.69%_20IV. Partial Applications of Portfolio TheoryLoan Loss Ratio-Based Models:This model involves estimating the systematic loan loss risk of a par

31、ticular sector relative to the loan loss risk of a banks total loan portfolio. This systematic loan loss can be estimated by running a time series regression of quarterly losses of the ith sectors loss rate on the quarterly loss rate of a banks total loans:(Sectoral losses in the ith sector/Loans to

32、 the ith sector) = + (Total Loan Losses/Total Loans)21IV. Partial Applications of Portfolio TheoryWhere 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.22IV. Partial Applications of Portfolio TheoryRegulatory Models:The method adopted is l