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nt 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 lowerquality loans (., those rated 2 and 3), concentrating more of its portfolio on grade 1 loans. 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. ? ., suppose management is unwilling to permit losses exceeding 10 percent of an FI39。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 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 bank39。s capital. III. Loan Portfolio Diversification and Modern Portfolio Theory (MPT) ? The FI manager can pute 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. 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). III. Loan Portfolio Diversification and Modern Portfolio Theory (MPT) ? KMV measures