Abstract
The traditional portfolio selection model seriously overestimates its theoretic optimal return. Aiming at this problem, two portfolio selection models are proposed to modify the parameters and enhance portfolio performance based on Bayesian theory. Firstly, a Bayesian-GARCH(1,1) model is built. Secondly, Markov Chain is applied to curve the parameters’ state transfer, and a Bayesian Markov regime-Switching-GARCH(1,1) model is constructed. Both the two models can handle the overestimation problem and can obtain self-financing portfolios. In the numerical experiments, both the models are examined with data from China stock market, and their performances are compared and analyzed. The results show that BMS-GARCH(1,1) model is superior to the Bayesian-GARCH(1,1) model.
Highlights
Portfolio optimization and diversification have been instrumental in the development and understanding of financial markets and financial decision-making. e major breakthrough came in 1952 with the publication of Harry Markowitz theory of portfolio selection. e theory is popularly referred to as modern portfolio theory
More and more parameter uncertainties have been analyzed in Bayesian Framework. e Bayesian method has advantages: first of all, it can fully use prior information; secondly, it explains the uncertainties of estimated risks and models; thirdly, it makes the computation in simulating complicated variables easy
The Bayesian method has advantages: first of all, it can fully use prior information; secondly, it explains the uncertainties of estimated risks and models; thirdly, it makes the computation in simulating complicated variables easy
Summary
Portfolio optimization and diversification have been instrumental in the development and understanding of financial markets and financial decision-making. e major breakthrough came in 1952 with the publication of Harry Markowitz theory of portfolio selection. e theory is popularly referred to as modern portfolio theory. E Bayesian method has advantages: first of all, it can fully use prior information; secondly, it explains the uncertainties of estimated risks and models; thirdly, it makes the computation in simulating complicated variables easy In this way, investors firstly set the parameter prior; they use Bayesian rules to get the posterior. The Bayesian method has advantages: first of all, it can fully use prior information; secondly, it explains the uncertainties of estimated risks and models; thirdly, it makes the computation in simulating complicated variables easy. The Bayesian theory is used in model analysis [35], risk measurement or return-risk trade off [36], portfolio optimization [37, 38], and so on
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