Modern Applied Science; Vol. 9, No. 11; 2015 ISSN 1913-1844 E-ISSN 1913-1852 Published by Canadian Center of Science and Education 135 Forecasting systematic risk by Least Angel Regression, AdaBoost and Kernel Ridge Regression Mahdi Salehi 1 , Mahdi Moradi 2 & Samaneh Molaei 2 1 Assistant Professor of Accounting, Ferdowsi University of Mashhad, Mashhad, Iran 2 MS.C. Student of Accounting, Mashhad Branch, Islamic Azad University, Mashhad, Iran Correspondence: Mahdi Salehi, Department of Accounting, Ferdowsi University of Mashhad, Khorasan Razavi, Iran. E-mail: mehdi.salehi@fum.ac Received: March 20, 2015 Accepted: April 22, 2015 Online Published: September 30, 2015 doi:10.5539/mas.v9n11p135 URL: http://dx.doi.org/10.5539/mas.v9n11p135 Abstract In according to importance of risk in financial decision and investment is one of issue that helps to investors is existing tools and appropriate models in order to predict systematic risk. Aim of this research was forecasting systematic risk of companies admitted at Tehran stock Exchange by Least Angel Regression (LARS), AdaBoost and Kernel Ridge Regression (KRR) and comparing ability of the algorithms in order to find the best methods of the test. In this study the financial data of (1159 observations) during 2005-2014. We used MATLAB software vision (R2013b). Results indicated that Kernel Ridge Regression (KRR) with 9.65% error (90.35% confidence) in comparison with Least Angel Regression (LARS) with 12.15% error (87.85% confidence) and AdaBoost with 28.91% error (71.09 confidence) has more ability for forecasting systematic risk. Moreover, ability of forecasting systematic risk in Least Angel Regression (LARS) is more than AdaBoost. Keywords: systematic risk, Least Angel Regression, AdaBoost, Kernel Ridge Regression 1. Introduction Investment is fundamental and necessary in processing grow and economic development of country. Among effective factors in selecting investment is paying attention of investors to risk and investment’s return. Investors try to investment their financial resources in where the highest return and the least risk. Thus, companies should instead of focusing on earnings more pay attention to risk as limited factors as maximize return. In contrast of return, risk is mental concept and non-quantitative. Therefore, most of financial and economic experts more focus on measuring and identifying risk. Based on modern portfolio theory, risk is divided into two sections: First section which is related to systematic risk; second section, non-systematic risk which is related to specific condition. In this theory, risk measures by risk of assets with Beta (criteria of systematic risk). Therefore, beta is one of the most applicable and accepted tools of financial and economic experts in order to evaluate and risk management. Additionally, beta in field of various financial and accounting sciences like fair value of equity, related research about measuring market reaction to specific decision of a company and related research of price has specific responsibility (Hong and Arker, 2007). Several believe that an accounting as a notification system and some believe that it provides information in order to decision makers can do prior decision. In according to importance risk in financial decision and investment is one of issue can helps investors and it provides tools and prior models for predicting systematic risk. Aim of this research is comparing various method of systematic risk in order to select optimal method. Aim of this research is forecasting systematic risk in companies admitted in Tehran stock exchange by using Least Angel Regression (LARS), AdaBoost and Kernel Ridge Regression (KRR) and comparing ability of the algorithms in order to find the best methods of the test. Efficiency changes of systematic risk of a particular investment to changes in the market and the investment returns of the index β are measured. The index returns reflect the sensitivity of a stock relative to the market portfolio return. Dividing the covariance between the return on asset i in the market portfolio return and the variance of the portfolio return, the beta of asset i is obtained (βi) and calculate as following (Mahdavi and