Portfolio Model Based on Bayesian Method

Asset investment theory was first used by well-known American economist Harry Markowitz who is the founder of portfolio theory systematic proposed in 1952. In 1952, he published the historic paper "Portfolio Selection", describes the main principles and methods of the security returns and risk analysis, established the basic framework of the Mean-variance portfolio model.

<strong>Mean-variance theory mainly depends on the assumptions: </strong>
Rational investors based on rates of return and risk as the basis for the risk investment. The classical framework uses the sample estimates of the mean and the covariance of returns as if they were true parameters. If the data is not estimation error, Markowitz model can be effectively guaranteed portfolio.

However, the expected data is unknown, need to be statistical estimation, therefore, these data would not be without error. The other question is Markowitz model failure to account for parameter uncertainty leads to optimal portfolio weights that are too sensitive to small changes to small changes in the inputs of the portfolio optimization problem. Solution instability limit the application of Markowitz model at the development of asset allocation policy. As we all know, Bayesian statistics is based on general information, sample information, and a priori information in statistical inference. The mainly difference with the classical statistical is whether use the prior information to Bayesian statistics attention to the sample observations have emerged, the observation of the samples have not yet taken place will not be considered, Bayesian statistics attached great importance to a priori information's data mining and processing, make it quantitative, inform the prior distribution, participate in statistical inference, so that improve the quality of statistical inference.

Therefore, we put the Bayesian theory applied to the portfolio model, using Bayesian methods derived the Bayesian estimation of rate of return, could be further determine the factors of the portfolio that weights.

<strong>Put the Bayesian theory into the economy can provide the following three advantages:</strong>

(1) can provide a theoretical framework for the combination of a variety of information resources,
(2) can provide a precise contains a reasonable estimate of the risk scenario,
(3) can be flexible to handle complex and realistic models.

After use the Bayesian Theory in the portfolio model portfolio derive the coefficients that weights, in this paper, we use the real data from the stock market to proved that the coefficient was derived by Bayesian portfolio was more effective than the coefficient derived by maximum likelihood estimation.