Selecting an optimal portfolio of consumer loans by applying the state preference approach

Internal models like CreditMetrics and Kealhofer–McQuown–Vasicek (KMV), implemented by banks to manage credit risk and assess regulatory capital, are significant examples of how practitioners apply modern portfolio theory (MPT) to the management of bank loan-portfolios. From a theoretical perspective there are several reasons for suggesting to be careful in extending MPT to the case of bank loan-portfolios selection in order to avoid misleading results. Specifically, loans' log-returns are non-normally distributed random variables, furthermore, decision-makers do not necessarily perform a quadratic utility function. Because of both of those reasons the traditional mean–variance approach is inadequate in building up optimal loan-portfolios. Such a conclusion is even more relevant if specific categories of loans are considered. In our paper we deal with the problem of selecting optimal portfolios of consumer-loans by developing a state preference model. It allows us not to explicitly consider the distributional properties of loans' log-returns. The model is a static one having the objective to select the loan-portfolio maximizing the expected utility of wealth allocated by the bank managers, subject to a number of constraints accounting for fundamental strategic choices implemented by the bank managers. Our results show that flexibility is the main characteristic of our model. In fact, adding constraints gives new optimal portfolios without reducing the expected utility of the decision maker. We will explain that such a result does not depend on constraints' misspecification but on the risk structure implied in the state preference approach.