Reduction of Liquidity Proxies by Using Principal Component Analysis in Tehran Capital Markets

Abstract

The purpose of this study was to investigate the possibility of using principal component analysis method as a tool for data reduction of the proxies of stock liquidity in Tehran Stock Exchange (TSE). First, the initial set of proxies of stock liquidity (8 variables) was identified and after the initial validation tests, the method was implemented at 2 levels: 1) all companies and 2) companies with much data. According to the obtained results, applicability of using this method to reduce the initial set of variables was concluded. The results showed that in both levels of analysis, the method could be used successfully for data reduction of liquidity proxies. Depending on the purpose of different researches, the initial set of liquidity proxies could be appropriately reduced by extracting 2 or 3 main components, while explaining the acceptable part of the total data variance.IntroductionSo far, many variables have been introduced as proxies of stock liquidity in the research literature of capital market. It is impossible to use all these variables in regression models for several reasons, such as excessive reduction of the degree of freedom or high correlation of the variables; thus researchers are forced to choose among them. When selecting among the variables, researchers are faced with some econometric problems like the problem of omitted variables. Therefore, data reduction methods, which have fewer econometric problems, are highly regarded in the research literature. The “principal components analysis” is one of the most reliable data reduction methods that have been introduced. The purpose of this research was to investigate the possibility of using the “principal component analysis” method as a tool to reduce the proxies of stock liquidity in Tehran Stock Exchange (TSE). Method and DataTo carry out this research, first, the initial set of variables introduced as proxies of the stock liquidity (8 variables) were created by deeply studying the professional research literature. For more validity, the analyses were performed at two different levels. In the first level, all the companies (515 companies with 47.153 months of data) were used in the analysis. In the second level, the companies that did not have much data were excluded from the analysis and only those with 100 months of data and more were analyzed. The second category of companies included 312 companies (38.458 months of data).By creating correlation matrices and performing Bartlett and MSA tests, the dataset suitability for implementing the “principal component analysis” was tested, and then the “principal component analysis” method was implemented on the two datasets. Finally, sensitivity analyses were carried out to confirm the validity of the obtained results. According to the results, a conclusion was drawn about the possibility of using "principal component analysis" in reducing the proxies of stock liquidity. FindingsIn the validation phase, Bartlett and MSA statistics confirmed appropriateness of the data correlation for implementing the “principal component analysis” method. The MSA statistics of both levels was about 66%, which was interpreted as the data appropriateness for analysis. The results of the implementation of the “principal components analysis” method at the level of ‘all companies’ showed that this method could be successfully used for reducing the liquidity proxies. By forming 3 components (one component had a borderline significance level), the initial set of liquidity proxies could be reduced appropriately, while explaining an acceptable part of the total data variance.Similar to analysis of the first level, the results obtained for companies with more than 100 months of data also confirmed usefulness of the "principal component analysis" method in the reduction of liquidity proxies. In the validation dimension, there was not much difference between the results of the two levels, but only two components were extracted in the implementation dimension.The sensitivity analysis also showed that the correlation matrix of the investigated variables was stable over time and the results could be extended to all studied periods. Conclusion and discussion Considering the multitude of variables introduced as the proxies of stock liquidity and the econometric issue of choosing among them, this research used the method of "principal component analysis" as an efficient tool with strong theoretical foundations for data reduction of liquidity proxies and reported the results of its application. By confirming applicability of the “principal component analysis” and stability of the correlation matrix over time, it was claimed that this method, regardless of time and topic, could be used for reducing liquidity proxies and helping avoid the econometric issues related to the unsystematic selection of variables. Comparison of the method implementations in the two levels of companies showed that it was possible to perform the analyses by extracting fewer components when the “principal components analysis” was performed on the companies with lots of data..

Keywords

• liquidity
• capital market
• data reduction
• principal component analysis