Copulas and Coherence

Abstract

Traditional portfolio theory assumes that risk factors are elliptically distributed, when most real-world risk factors do not satisfy this condition. The lack of ellipticality poses two problems: First, correlation-based approaches to statistical dependence become unreliable, and second, conventional risk measures such as the standard deviation and value at risk also become unreliable. These problems can be dealt with by using copulas to handle dependence and by using coherent risk measures. The advantages of using copulas are demonstrated in an example that shows that traditional portfolio theory can also be misleading in a non-elliptical context.