Semi-parametric Model of Idiosyncratic Volatility Pricing by Explaining the Arbitrage Risk

The relationship between idiosyncratic volatility and expected return in finance has become a puzzle. While, based on modern portfolio theory, the relationship between risk and expected return is positive, many studies find a negative relationship between these variables. In addition, many studies have examined the factors affecting this relationship. In this paper, we have examined the relationship between idiosyncratic volatility and the expected return through explanation of the arbitrage risk as a factor affecting the relationship in the period from 2007-2017.

In this study, a five-factor Fama-French model has been used to estimate idiosyncratic volatility. In order to answer the research question and hypothesis testing, portfolio analysis and Fama-Macbeth regression methods have been used.

The idiosyncratic volatility was estimated using the Fama-French five-factor model, which was implemented based on the local polynomial kernel regression. Also, for estimating the arbitrage risk index, a trading limit on the Iran stock exchange and other common variables of arbitrage risk measurement are also used.

The results show that in addition to idiosyncratic volatility pricing, the relationship between idiosyncratic volatility and expected return is negative. Also, the arbitrage risk is confirmed as an effective variable on the severity and significance of the relationship between idiosyncratic volatility and expected return.