Asset Allocation:Nonparametric Bayesian Approach

Asset allocation involves dividing an investment portfolio among different asset categories, such as stocks, bonds, and cash. Many financial experts say that asset allocation is an important factor in determining returns for an investment portfolio. Asset allocation problem is not easy to solve. On the one hand, asset return generation process is of great meaning in optimal allocation policies, but we do not know the real data generation process. On the other hand, Investors have not complete information of all relevant parameters of the asset return model. If ignoring parameter uncertainty and model uncertainty, allocation decision will be sun-optimal.This paper takes nonparametric Bayesian approach to incorporate return generation process uncertainty and incomplete information into the static problem of asset allocation. Namely, by introducing Dirichlet process mixture model and hierarchical Dirichlet process hidden Markov model to stochastic volatility asset return dynamics, we study the expected utility maximization model under the setting of incomplete information. We use the MCMC algorithm for posterior inference and Monte Carlo integration method to simulate the optimal allocation decision between a risky and a riskless asset. The research work is divided into the following three main parts in this dissertation:Firstly, this paper proposes a Dirichlet process mixture stochastic volatility model to accommodate error distribution uncertainty in measurement equation. We use the described MCMC algorithm for posterior inference, then Calculate the mean of function of Multi-period predictive asset returns, and then simulate the optimal decision making behavior with Monte Carlo integration method. Using data from the Chinese stock and inter-bank market, an empirical study suggests that comparing to parametric stochastic volatility model, investors will invest less in risky asset under DPM-SV model, and distribution uncertainty brings negative horizon effect. This is because the predictive distribution of investors accounting for additional uncertainty may be different than any distribution typically considered under parameter uncertainty. To gauge the economic significance of distribution uncertainty, we calculate the certainty equivalent losses of investors who would be forced to allocate their wealth according to the model ignoring distribution uncertainty. If ignoring distribution uncertainty, the presence of such distribution uncertainty gives 1.7% welfare costs under high risk aversion.Secondly, we apply the infinite hidden Markov model to describe the regime switching of investment opportunity set and propose a hierarchical Dirichlet process Markov switching stochastic volatility model, and then construct the discrete time asset allocation model. The empirical results show that under incomplete information, introducing regime uncertainty leads to significantly different allocations to the risky asset. Comparing to parametric stochastic volatility model, investors will also invest less in risky asset under HDP-MSSV model but more than DPM-SV model, and distribution uncertainty and regime uncertainty together bring negative horizon effect. Aversion to regime uncertainty leads to the hedge demand for additional risky asset to hedge against the uncertainty risk about market states. If ignoring market regimes, the presence of such regimes gives 2.2% substantial welfare costs even under high risk aversion.Furthermore, risk-adverse investor may find the optimal dynamic weights of the selected assets according to time-varying investment opportunity set. We construct the volatility timing strategy in case of hierarchical Dirichlet process Markov switching stochastic volatility, and find that the volatility timing strategy outperform the open end equity fund portfolios.