Fitting asset returns to skewed distributions: Are the skew-normal and skew-student good models?

Vernic (2006), Bolancé et al. (2008), and Eling (2012) identify the skew-normal and skew-student as promising models for describing actuarial loss data. In this paper, we change the focus from the liability to the asset side and ask whether these distributions are also useful for analyzing the investment returns of insurance companies. To answer this question, we fit various parametric distributions to capital market data which has been used to describe the investment set of insurance companies. Our results show that the skew-student is an especially promising distribution for modeling asset returns such as those of stocks, bonds, money market instruments, and hedge funds. Combining the results of Vernic (2006), Bolancé et al. (2008), Eling (2012), and this paper, it appears that the skew-student is a promising actuarial tool since it describes both sides of the insurer’s balance sheet reasonably well.