Risk Aggregation by a Copula with a Stressed Condition

This paper examines the marginal distributions of stocks and bonds, and a copula between the movement of stock prices and interest rates. Because some widely used aggregation methods such as variance-covariance tend to underestimate the risk of an aggregated portfolio, a copula is utilized for risk aggregation, which captures various dependencies in the median and the tail of marginal distributions, unlike a linear correlation. In this study, various types of copula, including one that simultaneously captures both positive and negative linear correlations, are analyzed under several time periods. We examine data related to the Euro crisis and the post-bubble period in Japan. Our analyses show that widely used risk aggregation methods may overestimate the diversification effect.