ACHIEVE OF POSITIVE SEMI-DEFINITENESS AND STUDY IN ASSET ALLOCATE AT MINIMUM RISKS A CASE STUDY OF RATE OF RETURNS OF SET50

Abstract

                ABSTRACT

 The purpose of this study is to study covariance matrices that are estimated from sample data may not be positive semi-definite (PSD), as theoretically required. We consider the sample covariance matrices of the daily rate of return of common stocks traded in the Stock Exchange of Thailand during December 2, 2016 to December 29, 2017. When the sample size is small, relative to the size of the covariance matrix, it may not be PSD. However, as sample size increases, it generally becomes PSD. In addition, semi-definiteness does not depend on type of industry a stock is in. We compare the methods of adjusting sample covariance to achieve PSD. Those methods are Modified Matrix Factorization (MMF), and Semi-Definite Programming (SDP). By using the relative errors criteria to be computed from 1-norm and 2-norm (Euclidean norm). We find that SDP gives the smallest 1-norm and 2-norm relative errors, with 95% confidence. Moreover, MMF is computationally faster than SDP

From the study to analyze the returns and risks of securities of each stock in the SET 50, the returns of the most valuable securities is EA. The lowest risk securities are the securities SCB which have the risk (SD) as 0.92 The securities which has risks per one unit returns (CV) with the best value for money is the securities BLA is -0.33 per unit.

In the study to measure the correlation of each stock, including the ability to diversify in finding the pairs of the most correlated securities in the opposite side. So this can help spread the risk, by the first five securities pairs are ADVANC - BDMS, CPALL - INTUCH, RATCH – MTLS and AOT – BEM, and the securities and the study to determine the optimal proportion of investment in securities in the SET 50 Index. As well as the proportion of investors as types of investors by consider cause and effect of decision and it can be used for real. Based on the study, the lowest returns of CV of securities in SET 50 are securities ADVANC, INTUCH, RATCH, TMB and GLOW which got cv value as 0.0293