# Vilhelm Niklasson: Bayesian Quantile-Based Portfolio Selection

**Time: **
Wed 2020-05-13 15.15 - 16.00

**Location: **
Zoom, Registration Required

**Participating: **
Vilhelm Niklasson, Stockholms universitet

### Abstract

In this paper, we study the optimal portfolio allocation problem from a Bayesian perspective using value at risk (VaR) and conditional value at risk (CVaR) as risk measures. By applying a stochastic representation of the posterior predictive distribution for the future returns, we are able to find relevant quantiles and express the optimal solution in terms of observed data. This is in contrast to the conventional method where the optimal solution is based on unobserved quantities which are estimated, leading to suboptimality. We also derive expressions for the global minimum VaR and CVaR portfolios and give conditions for their existence. It is shown that these portfolios may not exist if the confidence level used for VaR or CVaR are too low. Moreover, analytical expressions for the mean-VaR and mean-CVaR boundaries are presented.

By using simulation and actual market data from S&P500, we compare our Bayesian approach to the conventional method. The sample efficient frontiers are compared to the population efficient frontier and the performance of the global minimum VaR and CVaR portfolios are analysed. In these comparisons, it is shown that our Bayesian approach usually outperforms the conventional.

### How to register

Since recently all events at Matstat require preliminary registration. In order to get registered for this event, please send an email to Dmitry Otryakhin, otryakhin@math.su.se .