In this paper, we attempt to provide a behavioral explanation to the observed asymmetric return-volatility relationship. In some cases, the affect heuristic, mental accounting and extrapolation bias may not be adequate to explain return-volatility dynamics. We build up three hypotheses to establish whether return-volatility relationship is influenced by cognitive dissonance. We observe that both positive and negative relationships exist for return-volatility dynamics. We show that cognitive dissonance is responsible for return-volatility relationship and which can explain their observed negative and positive relationships. Our third hypothesis relates to significance of volatility feedback theory. We find that it is rejected, which confirms that volatility feedback theory is not always tenable for explaining asymmetric return-volatility relationship.

Two important theories that are intended to explain the negative correlation between changes in the volatility and the changes in the stock price are ‘leverage theory’ and ‘volatility feedback theory’. The ‘leverage’ theory, first propounded by Black (1976), underlines that decrease (increase) of the stock price would cause increase (decrease) of the leverage of the firm. An increased leverage of the firm would increase the risk of the firm, thereby increasing its volatility. A number of empirical studies by Christie (1982), Cheung and Ng (1992), Duffee (1995) and Whaley (2000) support the hypothesis. In other words, the leverage theory predicts that at firm level there would be a negative correlation between changes in volatility and the changes in stock price. However, the leverage theory is not sufficient to explain the phenomenon. For instance, the theory fails to explain return asymmetry in declining and rising market, as also stronger relationship is documented on index return, which as per the theory, should be on individual firm return. On the other hand, the volatility feedback theory considers that volatility is a measure of market risk, and accordingly, if the volatility increases it points to higher risk. With higher risk, the investor would ask for higher return. In order to achieve this higher return, the investors should pay lower price for the stock. Thus, an asymmetric relationship arises between changes in volatility and changes in stock prices. The essential difference between the two theories is that leverage theory suggests that changes in stock price would change volatility and feedback theory implies that changes in volatility would lead to changes in the stock prices. The leverage and the volatility feedback theories have certain drawbacks. In order to overcome these drawbacks, several hypotheses are floated, including the behavioral hypothesis. For instance, an alternate argument put forward in this regard is based on the heterogeneous expectation of risk-averse investors on good news and bad news. The market ‘bad news’ (responsible for downward movement of stock prices) induces more dominant changes in portfolio composition than changes in the same portfolio as a consequence of ‘good news’ (responsible for upward movement of stock prices). From another viewpoint, Bouchaud et al. (2011) posit that the price discovery process can be conjectured to be dependent on the moving average of the past prices rather than on the instantaneous price.

Applied Finance Journal, Application, Concept of Dissonance, Cognitive Dissonance, United States (VIX), South Korea (VKOSPI), Japan (VNKY), Regression Results, Return-Volatility Relationship.