A Comparative Study Of Several Portfolio Models Based On Mean-Variance Framework

Portfolio management can be divided into three stages as the estimation of asset risk and expected return, the construction of optimal portfolio and the evaluation of portfolio performance respectively. Till now, mean-variance theory has been widely acknowledged in the portfolio optimization and configuration process. However,"extreme weights" phenomenon caused by the parameter-instability towards outliers, and the drawback that numerous variables needed to be estimated in the covariance matrix in the theories, are one of the main problems that can restrict their empirical results. In the view of this situation, a lot of scholars home and abroad are trying to introduce some frontier methods like Bayesian estimation, moment restriction, robust control approach, and etc. in reducing the sample risk of the optimal portfolio.Then, by using these estimation improving technologies, will the performances of portfolio models based on the mean-variance criteria in Chinese stock market be ameliorated? To be one of the emerging lands in the international capital system, Chinese security market bears the defects as short developing history, insufficient research data as well as significant non-random fluctuations. Compared with those mature markets in Europe and the United States, Chinese market has shown its unique characteristics. Therefore, it is rather meaningful to discuss the applicability of those portfolio models in Chinese stock market based on the mean-variance framework.In this paper, we choose the constituent stocks in SSE50Index as the investment area, and Shanghai Composite Index as well as the SSE50Index as the market benchmark. By using sample data ranging from January1,2008to December31st,2012, we develop the whole empirical work of the optimal portfolio. By introducing the investor risk aversion coefficient gama γ, with two specific values to be chosen, we construct the portfolio with mean-variance methodology and the global minimum variance strategy respectively. Begin with the primitive sampling MV and Min models, whose parameter estimation are based on the historical data, we consider eight distinct models by including Bayesian diffuse prior, Stein shrinkage estimation, single-index model, constant correlation model, robust estimation etc.. Provided with three derivatives for each primitive model, and added with equally weighted portfolio, we, thus, generate9different optimal portfolios, holding them with periodic adjustment and constant rolling sample strategy.Abide by portfolio management process, this article further compares the performance pros and cons as well as the improving efficiencies of the estimation errors under formation periods of6months, between each portfolios, also, between benchmark index and portfolios. The evaluation indicators used are Sharpe ratio, certainty equivalent (CEQ), and transaction cost, from the angles of portfolio risk and return, investors’ utility, and trading cost correspondingly. Based on the above empirical work, we can then analysis the applicability and effectiveness of these models in Chinese security market. Furthermore, we also take into consideration the impact of weights restriction and risk aversion coefficient variation toward the portfolio.The empirical results are shown as followed.(a) Without weight restriction conditions, among all the optimal portfolios gained through these nine models, equally weighted portfolio is the best with most of the holding period. The primitive sampling Min model and Bayes-Stein shrinkage model rank second. Besides, the evidences are collected in the empirical work about the correctness of the conclusion that by ignoring the high sensitivity to outliers for mean parameter, minimum variance portfolio construction method reduces the estimated errors as well as improves the investment performance compared with mean-variance approach.(b) The introduction of weights constraint, including short sales constraint, in every model, help portfolios perform better in aspects of returns and risks. Those portfolios calculated from the minimum variance method whose gama γ=∞outperform the Shanghai Composite Index as the representative of benchmark, while the others generated from the mean-variance strategy with γ=50, on the other hand, cannot be better than the market. At this moment, constant correlation model performs best, and equally weighted portfolio still bears the good property and superiority.(c) Based on the sample period from2008to2012in our paper, the efficiency to reduce estimation errors and enhance performance of Missing Factor model, which are the shrinkage combination of single index model and unit matrix approach, rank highest, while single index model, Bayes-Stein shrinkage model, constant correlation model all to some extent make the effort to improve the primitive model. However, diffuse prior and Robust estimation strategy cannot be well applied in Chinese Stock market according to our result.(d) Investor risk aversion coefficient gama γ maintains a monotonous influence towards primitive sampling MV model, diffuse prior model and Robust estimation model, thus, the bigger of the coefficient, the better of the model effect. Meanwhile, this phenomenon cannot be significantly observed in Bayes-Stein shrinkage model.