考虑组合预测股价的泛证券投资组合选择策略

Universal portfolio selection strategy based on combination forecasting price

基于过去信息对股价进行预测是无统计假设下在线投资组合的关键问题之一。为了减小市场异常值或白噪声的影响,本文采用多期历史价格信息预测下一期的股价,并结合指数平滑法和L_(1)-中位数估计法构造组合预测模型。在股价预测值的基础上,以期望收益最大化作为目标进行决策。为减少交易费用,在优化目标函数中加入一个惩罚项来调节投资比例的变动幅度,通过求解得到一种新的在线投资组合选择策略。理论分析结果证明,本文所提出的策略与最优定常再调整策略的平均对数收益率渐近相同。数值分析结果进一步表明:该文提出的策略在国内外多个数据集上的表现均优于其他经典的泛证券投资组合策略,能够承受一定范围内的交易费用,并且对其他参数的选择不敏感。

Online portfolio selection is regarded as an important research issue in the field of quantitative finance,which often aims to maximize returns or risk-adjusted returns.Mean-variance model,a classic portfolio model,assumes that the returns on assets obey a certain probability distribution,which characterizes the return and risk by calculating the mean value and covariance matrix of the portfolio,respectively.However,it is difficult to accurately obtain the future return or return distribution of assets,and the only information that can be accurately grasped is historical price data.Therefore,some scholars try to use only historical information to construct portfolio strategy,so they pay more and more attention to online portfolio selection problem.The so-called“online”means that when making decisions in the current period,the updated investment proportion only depends on the historical data obtained up to the beginning of the current investment,and the cycle is carried out until the end of the whole investment.Stock price prediction based on past information is one of the key problems of online portfolio selection without statistical assumption.In this paper,historical price data are used to predict the stock prices,and then a new online portfolio selection strategy is constructed.In the first part of this paper,we design a new online portfolio selection strategy based on the predicted stock prices with the goal of maximizing expected returns.First of all,in order to minimize the influence of market outliers or white noise,we adopt multiperiod historical price information to predict the stock prices for the next period.Secondly,in order to reduce the prediction bias caused by a single prediction model,the exponential smoothing method and L_(1)-median estimation method are combined to construct a combination forecasting model.Then,the stock estimator can be obtained based on the above-mentioned combination forecasting model.Finally,a new online portfolio selection strategy named Combination Forecasting for Exponential Gradient(CFEG)is proposed by taking the maximization of expected return as the goal and adding a penalty term into the objective function to reduce the transaction costs caused by each transaction adjustment.In the second part,the competitive ratio analysis is adopted to analyze the competitive performance of the proposed strategy theoretically,and the Best Constant Rebalanced Portfolios(BCRP)strategy is regarded as a straw man.After a series of derivations,it is proven that the average logarithmic growth rate of CFEG strategy is asymptotically consistent with that of the BCRP strategy,namely,the proposed strategy CFEG is a universal strategy.In the third part,numerical examples are conducted to test the performance of the proposed strategy in terms of final cumulative wealth,statistical t-test,Sharpe ratio,Calmar ratio,transaction cost sensitivity,and other parameter sensitivities.It is necessary to test the performance of our proposed CFEG strategy.Therefore,this paper further demonstrates the performance of CFEG through numerical experiments related to 8 real stock market datasets in China and the United States.First of all,the most important indicator to judge the performance of a strategy is its final cumulative wealth.We compare the final cumulative wealth between the CFEG strategy with 3 benchmark strategies and 6 related online strategies,and compare the difference of the average logarithmic growth rate between CFEG strategy and BCRP strategy.On 8 datasets,the final cumulative wealth of CFEG strategy is stably higher than that of all online strategies,and the difference of the average logarithmic growth rate between CFEG and BCRP is almost zero.The CFEG strategy has a good performance on the whole,and the p-value is very small on each dataset in the statistical t-test.Secondly,the Sharpe ratio and Calmar ratio of CFEG strategy are compared with other strategies.The results show that CFEG strategy can better balance the returns and risks,and obtain higher risk-adjusted returns.Since the transaction costs are an important realistic constraint,the sensitivity analysis of the transaction cost rate of CFEG strategy is carried out subsequently.Meanwhile,4 strategies are also selected for the purpose of comparison.The results show that CFEG strategy can withstand reasonable transaction costs and still obtain high returns.Finally,we conduct the sensitivity analyses of 3 parameters included in the design of CFEG strategy.The results show that the proposed CFEG strategy is stable and insensitive to parameter selection.Although the best parameter values are not selected,the CFEG strategy maintains excellent performance.Therefore,effective parameters can be selected easily in practical applications.In conclusion,the proposed strategy CFEG is suitable for investors to make investment decisions effectively and efficiently.The CFEG strategy is able to update the investment proportion in time without the future stock price information,so as to achieve the goal of maximizing returns,and provide some guidance for online investors.