Predicting the Probability of Extreme Returns with Volatilities and Risk factors using Logistic regression and Neural Network models

Document Type : Original Article

Authors
Felor Ghorashi 1
Ghodratollah Emamverdi 2
Seyedeh Mahboubeh Jafari 3
Ali Baghani 3
Yadollah NouriFard 3
1 Faculty of financial management, South Tehran Branch, Islamic Azad University, Tehran, Iran
2 Faculty of Economics, Central Tehran Branch, Islamic Azad University, Tehran, Iran.
3 Faculty of Accounting, South Tehran Branch, Islamic Azad University, Tehran, Iran.
10.30495/jik.2025.23610
Abstract
Today, due to intense competition between companies and other economic and political factors, returns experience high fluctuations. The purpose of this study is to identify the factors affecting such returns and increase return on investment. This study investigated the relationship between volatility and other risk factors with the probability of expected marginal returns. The purpose of this paper is to find the variables that affect the limit efficiencies. In this study, two types of idiosyncratic volatility and expected shortfall are investigated. Conditional volatility Using the EGARCH model, the idiosyncratic volatility is calculated based on the Fama and French five-factor model, and the expected shortfall is also calculated based on the generalized Pareto distribution. Research data include the period from 1382/01 to 1397/07. This study is based on the logit and probit regression model and neural network. The results of the study show a positive relationship between the three criteria of risk factor volatility and the probability of extreme return. Other characteristics, including firm value, stock price volatility and oil and the dollar, had a significant relationship with the probability of extreme returns, but no significant relationship was found between the firm age variable and extreme returns. The performance of logit, probit and neural network regression methods in predicting extreme returns were compared. The Probit model performs better than the other two models.
Keywords
Extreme returns
Idiosyncratic volatility
Conditional volatility
Expected shortfall
Logit and probit regression
-رادپور میثم، عبده تبریزی حسین، (1388). اندازه‌گیری و مدیریت ریسک بازار رویکرد ارزش در معرض ریسک.
-عباسی ابراهیم، منیژه هادی نژاد، کریمی جعفر، (1394). بررسی اثرات نامتقارن نوسانات قیمت نفت بر روی بازار سهام بورس اوراق بهادار تهران با استفاده از مدل MS-EGARCH، فصلنامه روند، سال بیست و دوم، شماره 27، زمستان 1394، صفحات 105.127
Ang, A. Hodrick, R. J. Xing, Y. & Zhang, X. (2006). The cross-section of volatility and expected returns. Journal of Finance, 61(1), 259–299.
Ang, A. Hodrick, R. J. Xing, Y. & Zhang, X. (2008). High idiosyncratic volatility and low returns: International and further U.S. evidence. Journal of Financial Economics, 91(1), 1–23.
An, Li. (2014). Asset Pricing when Traders Sell Extreme Winners and Losers. Retrieved from SSRN 2355520.
Bali, T. G. (2003). An extreme value approach to estimating volatility and value at risk.
Bali, T. G. & Cakici, N. (2008). Idiosyncratic volatility and the cross-section expected of returns. Journal of Financial and Quantitative Analysis, 43(1), 29–58.
Bali, T. G. Cakici, N., & Whitelaw, R. F. (2011). Maxing out: Stocks as lotteries and the cross-section of expected returns. Journal of Financial Economics, 99(2), 427–446.
Beneish, M., Lee, D., Charles, M. C., & Tarpley R. L. (2001). Contextual fundamental analysis through the prediction of extreme returns. Review of Accounting Studies, 6 (2-3), 165-189.
Berggrun, L., Cardona, E., & Lizarzaburu, E. (2019). Extreme daily returns and the cross-section of expected returns: Evidence from Brazil. Journal of Business Research, 102, 201–211.
Bollerslev, T. (1986). Generalized Conditional Heteroskedasticity, Journal of Econometrics, 31, 307-327.
Campbell, J., Sanford, Y., Grossman, J., & Wang, J. (1993). Trading volume and serial correlation in stock returns (Report No. w4193). National Bureau of Economic Research.
Douglas, George W. (1969). Risk in the equity markets: An empirical appraisal of market Efficiency. Yale Economic Essays 9, 3–45.
Engle, R. F., Lilien, D. M., & Robins, R. P. (1987). Estimating time-varying risk premia in the term structure: The ARCH-M model. Econometrica. 391–407.
Falkenstein, E. (1994). Mutual Funds, Idiosyncratic Variance, and Asset Returns. Ph.D. thesis at Northwestern University.
Fama, E. F., & French, K. R. (1992). The cross-section of expected stock returns. Journal of Finance, 47(2), 427–465.
Fama, E. F., & French, K. R. (1993). Common risk factors in the returns on stocks and bonds. Journal of Financial Economics, 25, 23–49.
Fama, E. F., & French, K. R. (2015). A five-factor asset-pricing model. Journal of Financial Economics, 116(1), 1–22.
Fink, J., Fink, K., & He, H. (2010). Idiosyncratic volatility measures and expected return. Retrieved from SSRN 1692315.
Fodor, A., Krieger, K., Mauck, N., & Stevenson, G. (2013). Predicting extreme returns and portfolio management implications. Journal of Financial Research, 36(4), 471–492.
Fu, F. (2009). Idiosyncratic risk and the cross-section of expected stock returns. Journal of Financial Economics, 91(1), 24–37.
Guo, H., & Savickas, R. (2006). Idiosyncratic Volatility, Stock Market Volatility, and Expected Stock Returns. Journal of Business and Economic Statistics, 24, 43-56.
Goetzmann, W., & Kumar, A. (2004). Why do individual investors hold under-diversified portfolios? Unpublished working paper, Yale University.
Han, Y., & Lesmond, D. (2011). Liquidity biases and the pricing of cross-sectional idiosyncratic volatility. Review of Financial Studies, 24(5), 1590–1629.
Huang, W., Liu, Q., Rhee, G., & Zhang, L. (2007). Return Reversals, Idiosyncratic Risk, and Expected Returns. Working Paper, the University of Hawaii at Manoa.
Huang, W., Liu, Q., Ghon, R. S., & Zhang, L. (2010). Return reversals, idiosyncratic risk, and expected returns. Review of Financial Studies, 23(1), 147–168.
Jiang, G., Xu, D., & Yao, T.(2007). The information content of idiosyncratic volatility. The
Journal of Financial and Quantitative Analysis, 44(1), 1-28.
Kumari, J., Mahakud, J., & Hiremath, G. S. (2017). Determinants of idiosyncratic volatility: Evidence from the Indian stock market. Research in International Business and Finance, 41, 172–184
Levy, H. (1978). Equilibrium an imperfect market: A constraint on the number of securities  in the portfolio. American Economic Review, 68(4), 643–658. 
Merton, R. C. (1973). An intertemporal capital asset pricing model. Econometrica, 41(5),                    867–887.   
Merton, R. C. (1987). A simple model of capital market equilibrium with incomplete            information. Journal of Finance, 42(3), 483–510.McNeil, A. J., Frey, R., & Embrechts, P. (2005). Quantitative Risk Management: Concepts, Techniques, and Tools. Princeton: Princeton University Press.
Malkiel, B., Xu, Y. (2004). Idiosyncratic Risk and Security Returns. Unpublished working paper.Princeton University and the University of Texas at Dallas.پ
Nelson, D. B. (1991). Conditional heteroscedasticity in stock returns: A new approach. Econometrica, 59(2), 347–370.
Piotroski, J.D. (2000). Value investing: The use of historical financial statement information to separate winners from losers. Journal of Accounting Research, 38, (3), 1-41.
Sharpe, W. F. (1964). Capital asset prices: A theory of market equilibrium under Conditions of risk. Journal of Finance, 19(3), 425–442.
Spiegel, M. I., & Wang, X.  (2005). Cross-Sectional Variation in Stock Returns Liquidity and Idiosyncratic Risk. Working Paper, Yale School of Management
Switzer, L. N., & Picard, A. (2015). Idiosyncratic volatility, momentum, liquidity, and expected stock returns in developed and emerging markets. Multinational Finance Journal, 19, 169–221.
Switzer. L. N., & Tahaoglu, T., Zhao, Y. (2017). Volatility measures as predictors of extreme returns. Review of Financial Economics, 35, 1–10.
 Switzer. LN,  Wang. J,  Lee. S. (2017). Extreme risk and small investor behavior in developed markets. Journal of Asset Management, 18, 457–475.
Tsay, R. S. (2010). Analysis of Financial Time Series (3rd Edition). New York: Wiley.
-Yang.C.Y,BohuiZhangmB., Zhang.C.,(2020) "Is information risk priced? Evidence from abnormal idiosyncratic volatility "Journal Volume 135, Issue 2, 2020, 528-554.
-Wu,J. Chimezie,P.E. Gilbert V. Nartea & Jing Zhang (2019): Extreme returns and the idiosyncratic volatility puzzle: African evidence, Applied Economics, DOI:10.1080/00036846.2019.1631442