Multi–dimensional Portfolio Risk and its Diversification in the Iranian Stock Market

Abstract

One of the criteria that is commonly used to measure portfolio risk is the standard deviation or variance. This criterion cannot properly measure risk in the case that the distribution of stock returns is abnormal, because skewness and kurtosis can increase the risk. Therefore, in the new definition of risk, skewness and kurtosis criteria should also be included. In this research, it has been investigated how the two components of skewness risk and kurtosis risk are reduced by increasing the number of stocks in a well-diversified portfolio. The results of this research show that when the portfolio has skewness and skewness, not only the variance of the portfolio but also the skewness and skewness decrease simultaneously with the increase in the number of stocks in the portfolio, and if the risky assets in a portfolio have correlation As the number of shares increases, three components of risk - variance, skewness and kurtosis - decrease and eventually converge to a non-zero value, this part of risk that does not decrease with the increase of the number of shares represents a multi-dimensional systematic risk. So, it can be said that the multi-dimensional unsystematic risk decreases with the increase in the number of stocks in a well-diversified portfolio. Another important result obtained from this research is that the risk of skewness decreases more slowly than the variance and the kurtosis risk. In fact, it is more difficult to diversify the risk of skewness than the risk of kurtosis and variance.