The optimal combination of investment in assets in different conditions of the stock market using the Mean-VaR model

اقتصاد پولی مالی

Articles in Press, Accepted Manuscript, Available Online from 12 June 2024

Document Type: Original Article

DOI: 10.22067/mfe.2024.79777.1259

Authors

faramarz tahmasebi^{* 1}; alireza tamizi²

¹payam noor

²Faculty member of Payame Noor University Department of Economics

Abstract

Introduction
Harry Markowitz’s portfolio selection theory is the pioneer of new theories (Markowitz, 1952). Markowitz’s mean-variance analysis is the most common method to solve the asset selection problem. In this method, the variance of asset returns is the only criterion for risk assessment. Unfavorable risks and their measurement are considered in the new financial theories about risk. Value at risk (VaR) is one of the most commonly used indicators in this field (Jorion, 1997, 2000). For the first time, Bamol (1963) proposed the concept of VaR as a new model for risk assessment (Alexander and Baptistab, 2002). But since the early 1990s, it has been widely used as a tool to assess risk. Hanifi (2010), in his first research on the model of VaR in Iran, calculated and compared VaR of different companies in Iran and several foreign countries. In the conducted studies, the portfolio risk of joint-stock companies was calculated by the VaR approach and using different models. The research results were compared with the variance criterion in some of these studies (i.e. a research by Karimi).
Financial markets are among the most important and influential markets of any country. Stock market is considered as one of the important components of financial markets. On the other hand, stock asset is one of the important components of people's asset portfolio; its price usually changes due to the economic fluctuations. It is believed that the demand for maintaining other assets will be influenced by changing the return in one of the components of the asset portfolio; therefore, the people's asset portfolio composition will be changed. In this study, the effect of changes in the stock market returns on the people’s asset portfolio composition was condsidered by using the VaR criterion and the mean-VaR model in different periods of the stock market.

Theoretical framework
In general, two theories are considered more in the literature of financial economics and topics on optimal portfolio determination; Modern portfolio theory and ultra-modern portfolio theory. Optimal asset allocation and optimal portfolio recognition are done according to the optimization based on the mean and variance of asset returns in modern portfolio theory, which was first introduced by Markowitz. Markowitz's mean-variance model, based on a specific level of return rates, obtains optimal values of risk based on minimizing the variance of the total assets in the portfolio (Markowitz, 1952)
In another theory, optimal asset allocation and optimal portfolio recognition are done based on the relationship between return and unfavorable risk criteria. Ultra-modern portfolio theories explain the behavior of investors and portfolio selection based on the relationship between return and unfavorable risk. In this theory, unfavorable risk (fluctuations lower than the investor's target rate of return) is defined as a risk measurement index. From the viewpoint of the theory, risk as an emotional status is more representative of the fear of an unfavorable event such as loss or less performance than expectations or lack of access to the desired goal. So, unfavorable risk measures can explain it mathematically in a better way (Adami, 2012). Value at risk (VaR) is one of these measures. The risk of assets is calculated using VaR approach in the Mean-VaR model and it is used in the model.


Research Methodology
The study’s population was consisted of the price of assets, such as land, housing, gold coins, currency, stocks, bonds and bank deposits. These assets’ prices were extracted from the website of Iranian Central Bank and Statistics Center from 1991 to 2021. Then, the return and standard deviation of return on assets were calculated and used in the study. Dickey-Fuller test was used to review the stationarity of time series. Most macroeconomic variables are correlated of the first degree (integrated of 1). It is expected that data to be fixed after one time differentiation. Since the data used in this study is in the form of growth rate, it is expected that the data to be fixed. The results indicated that all the data are fixed as expectations. In order to conduct the research, after calculating the return, expected return and correlation coefficients of return on assets by Markowitz model, the asset risk with the 95% confidence level and the short-term (one-year), medium-term (10-year) and long-term (30-year) time horizons. year) were estimated using the VaR model (parametric method). Statistical calculations were performed and the results were extracted by using mean-VaR model.

Conclusion
In order to select the optimal portfolio, the results of the statistical analysis indicated that the asset portfolio composition is changed due to the change in the ratio of return to risk during the entire period with respect to different time horizons. People's asset portfolio mostly includes stocks and housing during the period when stock returns are positive. Although there is a very high risk for investing in stocks, but it has a high share in people's investment portfolio due to the higher risk-return ratio in this period. At the same time as the stock returns become negative, a most change is occured in asset portfolio composition. So that stocks are completely removed from people's portfolios and are replaced by bonds and bank deposits. Under this condition, the entire asset portfolio almost consistes of the bonds and bank deposits in the short-term period.
These two assets, in addition to low risk, have consistent returns for investors. The results represented that the change in stock returns lead to changing the asset portfolio composition in different periods. Since there is not a study to investigate and determine the people’s asset portfolio composition in different conditions of the stock market, it is not possible to compare this study’s results with other studies

Keywords

return; expected return; risk; optimal portfolio; Mean-Var model

References