A Nonparametric Regression Factor Model Is Used To Estimate The Distribution Of Asset Returns And To Conduct An Empirical Study On Portfolio Optimization

Abstract:Mean-Variance model derived by Markowitz is a good framework when analyzing revenue and risk of a portfolio and making asset allocation de-cisions. However, if we simply use historical price data to estimate mean and covariance matrix of all the stocks and use the estimated parameters in making optimal portfolio selection, the empirical result in Chinese stock market is dis-appointing. The performance of the "optimal" portfolio we choose is beaten by simply averaging the weight of all assets. We have two method to improve our strategy. One is to introduce other risk measures since the distribution of stocks may not be normally distributed, the other is to make better forecast of the asset returns. In the first approach, we use VaR and CVaR as risk measures instead of volatility. In the second one, we build a factor model, using the information ac-quired now as factors and stock returns in the next term as dependent variables. During each term, the conditional mean and covariance matrix of all the stocks is estimated using K-Nearest-Neighbors regression method. The empirical result shows that the performance will improve dramatically if we choose the proper factors.