A quantitative study of optimal asset allocation in a mean-CVaR & mean-variance framework

Sammanfattning: Optimal portfolio selection has been an area of great focus ever since the inception of modern portfolio theory as proposed by Harry Markowitz. This project has applied Markowitz modern portfolio theory to an invest- ment universe created from the output of an economic scenario genera- tor. This project is a collaboration between the author and the Swedish reinsurer Sirius International. The investment universe stems from Sir- ius International’s own modeling of assets. In this universe, a frame- work for extracting optimal portfolios is developed using the risk mea- sures Conditional-Value-at-Risk (CVaR) and the variance. The project analyses how a set of efficient portfolios perform in terms of risk versus reward, creating both a mean-CVaR and a mean-variance framwork. The project also analyses the cost of constraints enforced in the optimization of efficient portfolios. Its main findings conclude that the mean-CVaR framework is prefer- able for an insurance company for several reasons. The mean-CVaR frame- work is more reliable than a mean-variance framework because it relies on the modeling of the tails of the loss distribution, whereas the mean- variance optimization will only capture the variance of a loss distribution. The mean-variance framework will as such only reflect the risks in their entirety for an underlying normal distribution. Furthermore, the mean- CVaR framework offers more stability, making it favorable for a dynamic investor who may want to adjust their portfolio holdings according to shifting market conditions. The report also concludes that the additional constraints enforced in the optimization can be quantified in terms of a limited return tradeoff.