نوسانات نامتقارن، VIX و بازده سهام Idiosyncratic volatility, the VIX and stock returns

1. Introduction The relationship between idiosyncratic volatility (IVOL) and returns has attracted a great deal of research attention, yielding, to date, mixed findings. In efficient markets, there should be no interrelation between IVOL and expected returns (Sharpe, 1964; Lintner, 1965; Fama & MacBeth, 1973). In other words, ceteris paribus, portfolios sorted based on IVOL should manifest no difference in their average excess returns (the return of the stock minus the free risk interest rate). However, the literature comes to different and ambiguous conclusions. While earlier studies report either a positive relationship between IVOL and average returns (Malkiel & Xu, 2002; Goyal & Santa-Clara, 2003) or fail to indicate any significant relationship (Tinic & West, 1986; Bali & Cakici, 2008), Ang, Hodrick, Xing, and Zhang (2009) show that stocks around the world with high IVOL tend to have low future average returns. In their study, they rule out explanations based on trading frictions, information dissemination, and higher moments. However, using EGARCH models, Fu (2009) rejects the findings of Ang et al. (2009) and demonstrates a positive relationship between IVOL and returns. In another study, Boyer, Mitton, and Vorkink (2010) report that expected idiosyncratic skewness and returns are negatively correlated. Stambaugh, Yu, and Yuan (2015) claim that part of the IVOL effect is derived from arbitrage asymmetry between holding a long position for underpriced stocks and a short position for overpriced stocks. Combining the fact that IVOL has a negative effect on the return of overpriced stocks and a positive one for underpriced stocks, with the fact that taking a short position in overpriced stocks is less common than taking a long position in underpriced stocks, results in a negative relationship between IVOL and returns. Given the contradictory results in the literature regarding the effect of IVOL on returns, we postulate that some of the difference in returns between high and low IVOL portfolios may also be explained by the VIX. Specifically, months with a positive (negative) change in the VIX will tend to be followed by a negative (positive) relationship between IVOL and future returns. To test this contention, we sort stocks from Chicago’s Center for Research in Security Prices (CRSP) on a monthly basis according to their idiosyncratic volatility and construct five value-weighted portfolios, with Portfolio 1 containing the lowest idiosyncratic volatility stocks and Portfolio 5 the highest. We then compute the excess returns of each portfolio in month t + 1. In line with previous works (e.g., Ang et al., 2009), we track the Portfolio “5 minus 1” (longing the highest IVOL quintile and shorting the lowest) to reflect the relationship between IVOL and future returns. The findings indicate that when the VIX increases in time t, the portfolio of interest (“5 minus 1”) is negatively affected, as reflected in time t + 1. In contrast, when the VIX decreases in time t, Portfolio “5 minus 1” is positively affected in t + 1. These findings indicate that if an increase in the VIX is translated into a decrease in Portfolio “5 minus 1” in the next period, this outcome can likely occur if either Portfolio 5 performs poorly or Portfolio 1 performs well, or both.