Loading...

The goal of my thesis is to conduct a comparison of advanced **Bayesian models** and the **classical Markowitz optimization** approach. The models will be implemented in a **Probabilistic Programming Language** called **Stan**, which uses **Markov chain Monte Carlo** algorithms to perform inference on those models. I will investigate whether these models perform better and the usage of these advanced techniques is justified in practice.
The **Bayesian** approach of portfolio selection tries to deal with the problems of the classical framework by using advanced models, and gives a more generalized way to approach to the portfolio selection problem.
**Portfolio selection** deals with the problem of selecting the optimal weights for a portfolio of risky financial assets based on investor preferences and constraints.

Harry Markowitz introduced the classical Mean-Variance framework of portfolio selection in 1952, for which he received the Nobel Prize in Economics. Although the theoretical implications are extremely important, several issues when using it in practice have been identified. Parameter uncertainty isn't taken into account, which lead to suboptimal and volatile weight choices, as well as the distribution of returns is assumed to be normal, which is well known to be not the case, especially for short term time horizons. In the general case it is very hard, or even impossible to calculate the posterior using the Bayesian formula because it involves solving the integral of the evidence in the denominator.

**Markov chain Monte Carlo (MCMC)** methods are a set of algorithms which allow to do inference on Bayesian models without solving these models analytically. In recent times not only advanced MCMC algorithms, which allow the usage of highly complex models with a high number of parameters, have been discovered, but also the increasing power of computers allows the practical use of MCMC methods, which are computationally very intensive.

Harry Markowitz introduced the classical Mean-Variance framework of portfolio selection in 1952, for which he received the Nobel Prize in Economics. Although the theoretical implications are extremely important, several issues when using it in practice have been identified. Parameter uncertainty isn't taken into account, which lead to suboptimal and volatile weight choices, as well as the distribution of returns is assumed to be normal, which is well known to be not the case, especially for short term time horizons. In the general case it is very hard, or even impossible to calculate the posterior using the Bayesian formula because it involves solving the integral of the evidence in the denominator.