Rule-Based LTV and Penalty Function for Concentration Risk

Abstract

This paper implements a simple and transparent procedure for setting loan-to-value (LTV) ratio based on the market risk of the underlying collateralized portfolio. The loan hair cut (i.e. 1-LTV) is closely related to value-at-risk (VaR) which is very sensitive to model assumptions and complicated to estimate in the non-Gaussian multi-variate case. Our calculation first employs a Rule-Based LTV based on the sum of the individuals VaRs, which in turns is individually calibrated to historical volatility-VaR relationship. Next, in order to correct for the concentration-diversication effect of the portfolio, we propose a variance adjusted concentration measure which generalizes the Herndahl-Hirschman index by weights reflecting the variance of the individual assets. Furthermore, to adjust for the correlation relationship, we adopt a multi-factor framework where the correlations are driven by the regional and industry sectors. The combined adjustment factor is derived in closed form. In the empirical tests, we collect 10-day returns of the most frequently pledged stocks from 1998 and 2010 and group them into 10 regions and 10 industries sectors. The MSCI country and industry indices are used to construct region and industry risk factors. Our empirical tests show the accuracy of the Rule-Base value-at-risk is greatly improved by our adjustment factor in both in-sample and out-of-sample periods.