# Vilhelm Niklasson: Bayesian portfolio selection and risk estimation

**Time: **
Wed 2022-06-01 15.15 - 16.00

**Location: **
Kräftriket, House 6, Room 306

**Doctoral student: **
Vilhelm Niklasson

**Opponent: **
Andreas Stephan (Linnéuniversitetet)

**Supervisor: **
Taras Bodnar

### Abstract

This thesis concerns portfolio theory from a Bayesian perspective and it includes two papers related to this theme. In the first paper, optimal portfolio weights are derived from a Bayesian perspective to the problem of minimizing the portfolio risk in terms of value at risk (VaR) or conditional value at risk (CVaR) given a certain level of expected return. The so called efficient frontiers, i.e., the set of optimal portfolios with the highest possible expected return given a certain level of VaR or CVaR, are also presented. Both a noninformative prior and an informative prior are considered and the resulting portfolios are compared to the ones obtained from the conventional method which is based on the sample estimates. Using simulated and empirical stock returns, we conclude that the Bayesian approach outperforms the conventional method in terms of out-of-sample VaR estimation when the global minimum VaR portfolio is considered. Moreover, we show within a simulation study that the efficient frontiers obtained from the Bayesian procedure are generally more conservative and closer to the true efficient frontier when the latter is known. In the second paper, we consider the problem of determining VaR or CVaR of a portfolio when market conditions are quickly changing. When the market conditions are stable over time, it is possible to model future returns by using an equal belief in all historical observations. However, it is well known that volatility tends to cluster, particularly when considering daily or more frequent data observations. We use a Bayesian approach to create a model where the prior belief about returns resembles the recent period and where the degree of belief depends on how much the recent period deviates from the long term period. The new model is compared to some classical homoscedastic and heteroscedastc models in terms of VaR estimation using both simulated and empirical stock returns. We conclude that the new model performs well in the Basel backtest, particularly during turbulent market conditions where other models struggle.