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(0)2 = 0 ? (X2j X2)2 (.15)2 = .0225 (.05)2 = .0025 ? (X3j X3)2 ()2 = .01 (.4)2 = .16 ? (X4j X4)2 ()2 = .01 ()2 = .0025 ? ___________ ______________ ______________ ? ? (Xjj Xi)2 ? = .045 ? = .285 ? ?A = % ?B = % ? ________________________________________________________ IV. Partial Applications of Portfolio Theory ? Loan Loss RatioBased Models: ? This model involves estimating the systematic loan loss risk of a particular sector relative to the loan loss risk of a bank39。s total loan portfolio. This systematic loan loss can be estimated by running a time series regression of quarterly losses of the ith sector39。s loss rate on the quarterly loss rate of a bank39。s total loans: ? (Sectoral losses in the ith sector/Loans to the ith sector) = ? + ? (Total Loan Losses/Total Loans) 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 ? sectorssince low ? loan sector risks (loan losses) are less systematic, that is, are more diversifiable in a portfolio sense. 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 quantitativetype models, although the development of models like KMV, as well as CreditMetrics and Credit Risk+, may make bank regulators change their minds. IV. Partial Applications of Portfolio Theory ? Life and propertycasualty insurance regulators have also been concerned with excessive industry sector and borrower concentrations. ? These general diversification limits are set at 3 percent for lifehealth insurers and 5 percent for propertycasualty insurers implying that lifehealth panies must hold securities of a minimum of 33 different issuers, while for PC panies the minimum is 20. ? The rationale for such a simple rule es from modern portfolio theory, which shows that equal investments across approximately 15 or more stocks can provide significant gains from diversification.