Microfoundations of Heteroscedasticity: A Loss-Aversion-Based Explanation of Asymmetric GARCH Models

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.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.

The Case of “Less is More”: Modelling Risk-Preference with Expected Downside Risk

“…It means that practically every investor picks portfolios from the EDR=rf-0.08E(r) line, and therefore, we see a negative relationship between EDR and E(r) at the daily frequency. This negative relationship between risk and reward in the short term is well in line with recent literature, which confirms the existence of investors increasing portfolio risk immediately subsequent to negative asset price shocks (Ormos and Timotity, 2016d;Ormos and Timotity, 2016e).…”

Market microstructure during financial crisis: Dynamics of informed and heuristic-driven trading

“…We apply this probability (PH) as a defining measure of market microstructure. This inclusion of PH in our microstructure model is based on the following idea by Ormos and Timotity (2016a): investors that are sensitive to loss-aversion and mental accounting, when they lose (gain) money, tend to aggregate in time, and therefore, their required return increases (decreases) in the subsequent period; then, this raised (lowered) expected return can be obtained by investing in riskier assets or increasing leverage, hence, their demand for risky assets increases (decreases). Altogether, therefore, this behavior leads to a negative relationship between order imbalance and previous market returns.…”

“…Furthermore, we extend our analysis to another type of investors. According to Ormos and Timotity (2016a), due to loss-aversion and intertemporal mental accounting, investors tend to follow contrarian strategies: they invest into riskier (less risky) assets or increase (decrease) leverage subsequent to previous negative (positive) market shocks. We introduce this latter pattern into market microstructure by including a class of heuristic-driven traders in the base model consisting of informed and uninformed traders and specialists.…”