Market Risk Aggregation Using Copula and Its Application to Financial Practice

Abstract

We investigate how a copula between risk factors takes portfolio diversification effect on market risk in both stressed and normal situations when the portfolio is comprised of stock and bond securities. In Japanese market over the past ten years, the movement of stock price and interest rate had shown positive correlation; in this situation a financial industry-standard practice of risk aggregation (such as variance-covariance method) provides large diversification effect on portfolio market risk, compared with the simple sum of stock risk and bond risk. In the European debt crisis since 2009, however, stock price plunge and interest rate surge occur at the same time; in such a stressed situation the diversification effect is considered to be limited. Hence, we consider copulas representing the dependency between risk factors in a stressed situation within the industry-standard framework of time series models. Devising copulas to capture the stressed situations even in normal periods as well as examining data in stressed both periods and areas, we measure the impact of the copulas in a stressed situation on the diversification effect and carry several implications.