Research On Capital Asset Pricing Based On Deep Learning

Since the CAPM model was produced in 1965,it has developed to the now-famous q5 model,the Fama-French six-factor model,a large number of Firm characteristics and factors have been continuously mined,the model's anomaly interpretation capabilities have been continuously enhanced,and the multi-factor pricing model has always maintained a very High energy and vitality.However,traditional capital asset pricing models are inseparable from the linear assumption that asset returns are linearly related to factors.This assumption is inconsistent with the numerous noises of the financial market and the complexity of the real world.And with the advent of the era of big data,it is difficult for linear models to extract information from massive amounts of data usefully.Therefore,linear factor models are destined to be less and less able to meet the needs of research with the development of time.In recent years,machine learning,especially deep learning methods based on neural networks,can fit all complex nonlinear relationships through nonlinear activation functions and target minimization principles.As Cochrane(2011)emphasized,we should apply different tools to study the financial market,and the domestic deep learning method is still in its infancy for systematic research in this area,so combined with deep learning's super relational characterization ability And multi-factor pricing theory.This paper studies the non-linear Firm characteristics and stock expected returns on the A-share market.In this paper,452 anomalies in the existing literature are screened and based on the A-share data from January 1,1997 to December 31,2019,73 valid Firm characteristics are obtained.Based on these characteristics,this article first examines the nonlinearity between the expected stock returns implied by the Firm characteristics in the A-share market;Secondly,this paper extracts the information of Firm characteristics and constructs in-depth pricing factors to study the expected return of stock cross-section;finally,it considers the impact of changes in Firm characteristics to test and enhance the conclusions of this article.Based on a series of research and empirical research,this article draws the following conclusions:The research on the expected return information of stocks implied by Firm characteristics has important value for the selection of asset pricing risk factors and optimal portfolio management.Using deep learning methods,we apply 73 Firm characteristics to predict stock returns,and construct investment portfolios based on the results of the income forecasts,and use the performance of the portfolio to study the expected return information of stocks implied by the Firm's characteristics.The results show that the investment portfolio can obtain significant risk-adjusted excess returns.The research on the expected return information of stocks implied by Firm characteristics has important value for the selection of asset pricing risk factors and optimal portfolio management.Using deep learning methods,we apply 73 Firm characteristics to predict stock returns,and construct investment portfolios based on the results of the income forecasts,and use the performance of the portfolio to study the expected return information of stocks implied by the Firm's characteristics.The results show that the investment portfolio can obtain significant risk-adjusted excess returns.The investment portfolio constructed by the long-short-term memory neural network has the largest excess return,followed by the feedforward neural network,and the linear model has the smallest.Few types of trading friction,value growth,and momentum include most of the information about the expected return of stocks.The non-linear relationship between Firm characteristics and the expected return of stocks,the interaction between Firm characteristics and the dynamic trend of Firm characteristics imply the information of expected return of stocks that cannot be ignored.The depth factor model based on deep learning is better than the benchmark three-factor model in terms of the statistical performance of the model,interpretation of anomalies,and the performance of the investment portfolio based on the model.First of all,in terms of the performance of pricing error,the pricing error of the pricing model with depth factor is much smaller than the pricing error of the three-factor model in order of magnitude.On the whole,the pricing error based on the three-factor model is almost the same as the pricing error of the depth factor model.100 to 1000 times;Secondly,from the perspective of anomaly interpretation,the number of bivariate and univariate anomalies that the three-factor model can explain is 29 and 33.When the depth factors is added,the model can explain up to 71 and 72 anomalies.This explains almost all the anomalies;finally,from the perspective of the annualized Sharpe ratio of the model-based portfolio,the Sharpe ratio of the depth factor portfolio has a significant improvement compared to the Sharpe ratio of the benchmark three-factor model,The improvement ratio ranges from 130% to 471%.Although the overall performance of the LSTM model considering the dynamic changes of the characteristics over time is better than the ordinary neural network model,the result is not obvious,which also shows that the depth factor pricing model has been able to steadily capture the market's The influence model of information on stock returns.