This paper discusses a novel explanation for asymmetric volatility based on the anchoring behavioral pattern. Anchoring as a heuristic bias causes investors focusing on recent price changes and price levels, which two lead to a belief in continuing trend and mean-reversion respectively. The empirical results support our theoretical explanation through an analysis of large price fluctuations in the S&P 500 and the resulting effects on implied and realized volatility. These results indicate that asymmetry (a negative relationship) between shocks and volatility in the subsequent period indeed exists. Moreover, contrary to previous research, our empirical tests also suggest that implied volatility is not simply an upward biased predictor of future deviation compensating for the variance of the volatility but rather, due to investors' systematic anchoring to losses and gains in their volatility forecasts, it is a cointegrated yet asymmetric over/under estimated financial instrument. We also provide results indicating that the medium-term implied volatility (measured by the VIX Index) is an unbiased though inefficient estimation of realized volatility, while in contrast, the short-term volatility (measured by the recently introduced VXST Index representing the 9-day implied volatility) is also unbiased and yet efficient.Keywords: Anchoring; Implied volatility; Realized volatility; Asymmetric volatility; VIX; VXST JEL classification: G02; G14; C53; C58; Acknowledgements: We are grateful to the conference participants at the Workshop on Behavioural Economics and Industrial Organization at Corvinus University, 2014. We would like to gratefully acknowledge the valuable comments and suggestions of the anonymous referee that contribute to a substantially improved paper. Mihály Ormos acknowledges the support by the János Bolyai Research Scholarship of the Hugarian Academy of Sciences. Dusán Timotity acknowledges the support by the Fundation of Pallas Athéné Domus Scientiae.This paper is appearing in the Economic Systems. Please cite this article as: Ormos, M., Timotity, D., Unravelling the asymmetric volatility puzzle: A novel explanation of volatility through anchoring, Economic Systems (2016), DOI: 10.1016DOI: 10. /j.ecosys.2015 This is the pre-print version of our accepted paper before typesetting. 2 Unravelling the Asymmetric Volatility Puzzle A Novel Explanation of Volatility Through Anchoring AbstractThis paper discusses a novel explanation for asymmetric volatility based on the anchoring behavioral pattern. Anchoring as a heuristic bias causes investors focusing on recent price changes and price levels, which two lead to a belief in continuing trend and mean-reversion respectively. The empirical results support our theoretical explanation through an analysis of large price fluctuations in the S&P 500 and the resulting effects on implied and realized volatility. These results indicate that asymmetry (a negative relationship) between shocks and volatility in the subsequent period indeed exists. Moreover, contrar...

We implement a market microstructure model including informed, uninformed and heuristicdriven investors, which latter behave in line with loss-aversion and mental accounting. We show that the probability of informed trading (PIN) varies significantly during 2008. In contrast, the probability of heuristic-driven trading (PH) remains constant both before and after the collapse of Lehman Brothers. Cross-sectional analysis yields that, unlike PIN, PH is not sensitive to size and volume effects. We show that heuristic-driven traders are universally present in all market segments and their presence is constant over time. Furthermore, we find that heuristic-driven investors and informed traders are disjoint sets.

This paper provides a theoretical explanation for the heteroscedasticity of asset returns. In line with existing empirical results, our model yields an asymmetric relationship between stock return and volatility. Based on the simple assumptions that investors behave according to Prospect Theory and are subject to mental accounting in a dynamic setting, we analytically derive the unit-root versions of two of the best fitting heteroscedasticity models (EGARCH and TGARCH). The model is supported by our empirical results from two different sides: first, analysis of individual trading data shows that investors indeed become risk-seeking right after losses and more risk-averse subsequent to gains; second, the parameter estimation of our volatility model yields the predicted negative relationship between abnormal returns and subsequent volatility.Keywords: Asymmetric volatility; Risk seeking; Prospect theory; TGARCH; EGARCH; Volatility dynamics; Market microstructure; Heuristic-driven trader JEL classification: C58; C93; G02; G11; G12 Acknowledgements: We gratefully acknowledge the help of Terry Odean, who provided us the individual trading dataset. We also would like to express our gratitude for the thoughtful remarks of Adam Zawadowski, which have significantly contributed to our paper. We thank Zsolt Bihary and Niklas Wagner for their comments and suggestions of at the 6th Annual Abstract This paper provides a theoretical explanation for the heteroscedasticity of asset returns. In line with existing empirical results, our model yields an asymmetric relationship between stock return and volatility. Based on the simple assumptions that investors behave according to Prospect Theory and are subject to mental accounting in a dynamic setting, we analytically derive the unit-root versions of two of the best fitting heteroscedasticity models (EGARCH and TGARCH). The model is supported by our empirical results from two different sides: first, analysis of individual trading data shows that investors indeed become risk-seeking right after losses and more risk-averse subsequent to gains; second, the parameter estimation of our volatility model yields the predicted negative relationship between abnormal returns and subsequent volatility.

We introduce an equilibrium asset pricing model, which we build on the relationship between a novel risk measure, the Expected Downside Risk (EDR) and the expected return. On the one hand, our proposed risk measure uses a nonparametric approach that allows us to get rid of any assumption on the distribution of returns. On the other hand, our asset pricing model is based on loss-averse investors of Prospect Theory, through which we implement the risk-seeking behaviour of investors in a dynamic setting. By including EDR in our proposed model unrealistic assumptions of commonly used equilibrium models -such as the exclusion of risk-seeking or price-maker investors and the assumption of unlimited leverage opportunity for a unique interest rate -can be omitted. Therefore, we argue that based on more realistic assumptions our model is able to describe equilibrium expected returns with higher accuracy, which we support by empirical evidence as well.

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