Document Type : Research Paper

Authors

• Reza Taleblou ¹
• Parisa Mohajeri ¹
• Morteza Yeganeh ²

¹ Associate Professor of Economics, Allameh Tabataba’i University, Tehran, Iran

² Master's Student in Economics, Faculty of Economics Allamah Tabataba'i University, Tehran, Iran

Abstract

 Volatility analysis is considered a modern and efficient tool for estimating, managing, and hedging risk, valuing and selecting optimal portfolios, and aiding investors in making informed financial decisions. This research aims to present a model for the risk analysis of 30 large companies listed on the Tehran Stock Exchange using the Multivariate Factor Stochastic Volatility Model (MFSVM) within the framework of a non-linear state-space approach. In this framework, the volatility of stock returns is decomposed into two components, "volatility arising from latent factors" and "idiosyncratic risks". The dynamic correlation matrix of the volatility of stock returns is then estimated. In this regard, weekly stock return data from January 10, 2018, to October 7, 2023, were utilized. The results of the research indicate that the first three hidden factors influence the volatility of stock returns. The first factor impacts stocks in the oil products industry, chemical products, basic metals, mining, and investment funds. The second factor predominantly affects banks, while the third factor also influences bank stocks to some extent. Second, the strongest posterior pairwise correlations are observed between “GDIR” and “PTAP” (74%), “PASN” (73%), and “FOLD” (71%). Additionally, “FOLD” shows a 69% correlation with both “PASN” and “PTAP,” and a 66% correlation with “MSMI” and “MADN”. The weakest correlation is between “GDIR” and “BPAS” (-10%). Third- “BPAS” exhibits the lowest correlation within the stock network, whereas “GDIR” shows the highest correlation.
Introduction
The research utilizes a multivariate factor stochastic volatility model to analyze the volatility of stock returns for 30 major companies listed on the Tehran Stock Exchange. Factor models operate on the premise that all systems, even those with high dimensions, are driven by a few random factors. These random factors influence the hidden common interactions among observations. Essentially, these models reduce the number of unknowns by decomposing the dynamic covariance matrix into two distinct matrices: one for the latent factors and another diagonal matrix for the idiosyncratic variances. By employing an orthogonal latent factor space with fewer dimensions, the model effectively reduces the number of unknowns, enabling a more precise representation of stock return volatilities. This approach mitigates the curse of dimensionality and provides an efficient estimate of the dynamic covariance matrix.
The model highlights the crucial role of latent factors in stock return volatility and provides a framework for comprehending dynamic correlations in stock markets, which fluctuate among different stocks over time. It effectively captures potential elements such as clustered volatility and co-movements of volatilities, while remaining resilient against shocks unique to each company’s stock.
Methods and Material
In this research, a multivariate factor stochastic volatility model in R software, along with the relevant packages, based on the Markov Chain Monte Carlo (MCMC) method, has been used to analyze volatilities in the Iranian stock market. The study sample includes weekly return data of 30 large stocks listed on the Tehran Stock Exchange, covering the period from January 20, 2018, to October 7, 2023, extracted using TseClient 2.0 software. The 30 large companies operate in various industries, including banking, insurance, petrochemicals, and other sectors. In this model, based on the Gibbs sampling method in the R software package (Kastner, 2016), the aim is to estimate the parameters and their sampling uncertainty within a Bayesian framework. By quantifying the inherent uncertainty, an appropriate estimate of the sample density distribution is provided.
Results and Discussion
The results indicate the presence of three latent factors. (figure 1) The first latent factor, seemingly rooted in international events, primarily affects export-oriented commodity companies. The second and third latent factors, which appear to have domestic origins, predominantly impact the volatilities of bank returns (figure 2). The studied stock volatilities exhibit clustered and co-movement behaviors, which intensify at certain times. The correlation intensity between the stock return volatilities of the companies under study has increased over time. Initially, during the study period, the correlations were relatively weak and mainly limited to relationships among export-oriented commodity companies. However, these correlations increased across the entire market, peaking from August 2019 to July 2020, before subsequently declining.
The highest posterior pairwise correlations are between Ghadir Investment Company (GDIR) and Oil, Gas, and Petrochemical Investment Company (PTAP), Parsian Oil and Gas Development Company (PASN), and Mobarakeh Steel Company (FOLD) at 74%, 73%, and 71%, respectively. Additionally, FOLD shows correlations of 69% with both PASN and PTAP, and 66% with National Iranian Copper Industries Company (MSMI) and Mines and Metals Development Investment Company (MADN). The weakest pairwise correlation is between Pasargad Bank (BPAS) and GDIR at -10%. BPAS also exhibits the weakest average correlation of approximately (-5%) with the entire stock network, while GDIR has the strongest average pairwise correlation with the entire stock market network at 47.5%.
Figure 1: log Variance of Factors
Figure 2: loading of factors
Given that forming an efficient and diversified stock portfolio requires an understanding of the behavior and correlations between the volatilities of the desired stock returns, the results of this study can provide a clear understanding of the return volatilities of the large companies’ stock network and assist in designing appropriate investment strategies. Additionally, optimizing stock portfolios, valuing options, and calculating value at risk using MFSVM could be subjects for future research, which have not been extensively explored in the domestic research space.
Conclusion
In this article, the Multivariate Factor Stochastic Volatility Model (MFSVM) is used within a non-linear state-space framework to decompose the volatility of stock returns into two components: “volatility arising from latent factors” and “idiosyncratic risks”. Additionally, the dynamic correlation matrix of stock return volatilities is estimated. The results reveal three hidden factors. The first hidden factor, seemingly influenced by international events, primarily affects export-oriented commodity companies. National events are reflected in the second and third factors, which predominantly impact the volatilities of bank returns. The volatilities of stock returns exhibit clustering and co-movement behaviors, which intensify at certain intervals. At the beginning of the investigation period, only the volatilities of export-oriented commodity companies were related to each other. However, during an upward trend, correlations increased across the entire market, peaking from August 2019 to July 2020, before subsequently declining.
Pairwise posterior correlations between stock volatilities were also investigated. The highest posterior correlations were observed between Ghadir Investment Company (GDIR) and Oil, Gas, and Petrochemical Investment Company (PTAP), Parsian Oil and Gas Development Company (PASN), and Mobarakeh Steel Company (FOLD), with correlation coefficients of 74%, 73%, and 71%, respectively. The weakest correlation coefficient was between GDIR and Pasargad Bank (BPAS) at -10%. BPAS exhibited the lowest average correlation of approximately -5% with the entire stock network, while GDIR had the strongest average pairwise correlation with the entire stock market network at 47.5%. The results of this research provide a clear understanding of the volatility of the listed companies’ stocks and can assist in designing suitable investment strategies, optimizing portfolios, and calculating value at risk using MFSVM. These areas could be subjects for future research, which have not been extensively explored in the domestic research space.

Keywords

• Idiosyncratic Risk
• Latent Factors
• Multivariate Factor Stochastic Volatility Model
• Dynamic Correlation
• Stock Market