The Evaluation of Return and Risk on Investment in Stocks based on the Integration of Asset Pricing Multi-Factor Model and Penalty Function

Evaluation of stocks based on return and risk related to capital assets is one of the important issues of this field. The majority of multifactor models are defined based on the assessment of one of the return and risk criteria. Nevertheless, the model presented in this study evaluated return and risk simultaneously. The multifactor patterns are static and do not express dynamic changes during time intervals affected by latent factors. In this research, unpredicted fluctuations in stock return were defined as latent factors in the penalty function. A more accurate estimate was provided by using the simulation of Fama–MacBeth regression in the estimation of effective parameters and separation of the effects of latent and manifest factors affecting stock return and risk. According to the analysis of the field of knowledge and content analysis, factors affecting the stock return were recognized, and the most effective factors including market measures were refined as manifest factors based on the tolerances. Finally, the model proposed(P-PCA) was exploited in risk prediction (at risk value). According to the results of the study, the mentioned model more efficiently showed the effects of latent and manifest factors on stock return over a long period. In addition, it was able to predict the risk of investment with proper accuracy and similar to patterns of conditional variance, such as ARCH and GARCH.