Summary:
The recent discovery of the MAX anomaly poses a challenge to the effectiveness of the factor pricing model. In-depth analysis of the MAX anomaly and clarification of the reasons for its formation are of great importance for improving the factor model and increasing market efficiency. From a review of the literature, this paper finds that studies of the causes of MAX anomaly have approached the problem from a variety of perspectives, but few have given a systematic theoretical explanation of its formation and persistence. This paper argues that the MAX anomaly occurs due to the speculative trading of investors and is subject to arbitrage restrictions in the stock market. First, investors' gambling preference drives them to buy winners and sell losers. The pursuit of a small probability of abnormal returns leads to large fluctuations in stock prices in the short term. Second, mispricing breeds market anomalies, but arbitrage trading among investors causes asset prices to return to equilibrium and eliminates market anomalies. Therefore, when investors face tight restrictions on arbitrage, stock mispricing will be ongoing and ultimately strengthen the market anomaly. Based on this analysis, this paper empirically examines the MAX anomaly in the A-share market by using the public data of Chinese A-share listed companies from year 1995 to 2017, and analyzes the impact of investors' gambling speculation on the MAX anomaly. To prove that the MAX anomaly originates from the gambling trading behavior of investors rather than value investment behavior, this paper further examines the impact of firm value on the anomaly. By constructing an index of arbitrage restriction, this paper further analyzes the strengthening effect of arbitrage restriction on the MAX anomaly. The main conclusions of this paper are as follows. First, there is a significant MAX anomaly in China's A-share market, which is statistically significant after controlling different MAX construction periods and company characteristics. Through a combined long-short strategy, investors can achieve an annualized return of 15.72%. Second, due to investors' gambling psychology, MAX has the characteristics of inertia transmission in the short term. However, the positive transfer probability of MAX decreases gradually and tends to become equal with the passage of time. There is no alternation change between high MAX and low MAX, which means that the MAX anomaly is different from the volatile aggregation anomaly. In addition, there is a positive correlation between speculative characteristics and the MAX anomaly. The MAX anomaly of stocks with low value, high gambling risk, and high retail shareholding ratio is significantly stronger than that of high value, low gambling risk, and low retail shareholding stocks. Lastly, due to arbitrage constraints, the stock price deviation caused by investors' irrational speculation cannot return to equilibrium in the short term, which significantly strengthens the MAX anomaly. However, in terms of the excess portfolio returns generated by short selling, the impact of arbitrage restrictions is limited. This paper makes three major contributions. First, it confirms the existence of the MAX anomaly, which is robust to many factors. In terms of the construction period for MAX, this paper finds that the best construction term in the Chinese A-share market is five days. The construction criterion for the MAX period is based on the marginal return of portfolios, which gives a quantitative basis for the construction of the MAX index, and can effectively avoid the need for data mining. Second, from the perspective of probability transfer and a nonlinear probability model, this paper proves that the transfer of extreme returns has the characteristic of time-varying attenuation, and the probable transfer of the MAX index cannot be observed in the long run. Overall, the stronger the degree of gambling speculation is, the more significant the MAX anomaly becomes, while the higher the investment value is, the less evident the MAX anomaly is. This paper also confirms that the gambling trading behavior of retail investors is significantly stronger than that of large investors and institutional investors. Finally, this paper expands the explanation of the MAX anomaly from the perspective of limited arbitrage.
Aboulamer A and Kryzanowski L, 2016. “Are Idiosyncratic Volatility and MAX Priced in the Canadian Market”, Journal of Empirical Finance, 37(3):20～36.
[11]
Ang A, Hodrick R J and et al, 2009. “High Idiosyncratic Volatility and Low Returns: International and Further U.S. Evidence”, Journal of Financial Economics, 91(1):1～23.
[12]
Annaert J, Ceuster M D and Verstegen K, 2013. “Are Extreme Returns Priced in the Stock Market？ European Evidence”, Journal of Banking & Finance, 37(9):3401~3411.
[13]
Bali T G, Cakici N and Whitelaw R F, 2011. “Maxing Out: Stocks as Lotteries and the Cross-section of Expected Returns”, Journal of Financial Economics, 99(2):427~446.
[14]
Carhart M M, 1997. “On Persistence in Mutual Fund Performance”, Journal of Finance, 52(1):57~82.
[15]
Fama E F and French K R, 1993. “Common Risk Factors in Returns on Stocks and Bonds”, Journal of Financial Economics, 33(1):3~56.
[16]
Fama E F and French K R, 2015. “Dissecting Anomalies with a Five-Factor Model”, Review of Financial Studies, 29(1):69~103.
[17]
Fama E F and Macbeth J D, 1973. “Risk, Return, and Equilibrium: Empirical Tests”, Journal of Political Economy, 81(3):607~636.
[18]
Fama E F, French K R, 2012. “Size, Value, and Momentum in International Stock Returns”, Journal of Financial Economics,105(3):457~472.
[19]
Fong W M and Toh B, 2014. “Investor Sentiment and the MAX Effect”, Journal of Banking & Finance, 46(3):190~201.
[20]
George T J and Hwang C Y, 2010. “The 52‐Week High and Momentum Investing”, Journal of Finance, 59(5):2145~2176.
[21]
Gu M, Kang W and Xu B, 2018. “Limits of Arbitrage and Idiosyncratic Volatility: Evidence from China Stock Market”, Journal of Banking & Finance, 86(1):240~258.
[22]
Herskovic B, Kelly B and et al, 2016. “The Common Factor in Idiosyncratic Volatility: Quantitative Asset Pricing Implications”, Journal of Financial Economics, 119(2):249~283.
[23]
Hou K, Xue C and Zhang L, 2012. “Digesting Anomalies: An Investment Approach”, NBER Working Papers, 28(3).
[24]
Jegadeesh N and Titman S,1993.“Returns to Buying Winners and Selling Losers: Implications for Stock Market Efficiency”,Journal of Finance,48(1):65~91.
[25]
Kumar A, 2009. “Who Gambles in the Stock Market”, Journal of Finance, 64(4):1889~1933.
[26]
Liu L X, Whited T M and Zhang L, 2009. “Investment‐Based Expected Stock Returns”, Journal of Political Economy, 117(6):1105~1139.
[27]
Mclean R D and Pontiff J, 2016. “Does Academic Research Destroy Stock Return Predictability”, Journal of Finance, 71(1):5~32.
[28]
Nartea GV, Kong D and Wu J, 2017. “Do Extreme Returns Matter in Emerging Markets？ Evidence from the Chinese Stock Market”, Journal of Banking & Finance, 76: 189~197.
[29]
Seif M, Docherty P and Shamsuddin A, 2018. “Limits to Arbitrage and the MAX Anomaly in Advanced Emerging Markets”, Emerging Markets Review, 36(3):95~109.
[30]
Stambaugh R F, Jianfeng Y U and Yuan Y U, 2015. “Arbitrage Asymmetry and the Idiosyncratic Volatility Puzzle”, Journal of Finance, 70(5):1903-1948.
[31]
Stambaugh, Robert and Yu Yuan, 2017. “Mispricing Factors”, Review of Financial Studies, 30(4):1270~1315.
[32]
Switzer L N, Tahaoglu C and Zhao Y, 2017. “Volatility Measures as Predictors of Extreme Returns”, Review of Financial Economics, 35(4):1~10.
[33]
Walkshäusl C, 2014. “The MAX Effect: European Evidence”, Journal of Banking & Finance, 42(42):1~10.
[34]
Wan X, 2018. “Is the Idiosyncratic Volatility Anomaly Driven by the MAX or MIN Effect？ New Evidence from the Chinese Stock Market”, International Review of Economics & Finance, 53(1):1~15.
[35]
Yakov Amihud, 2002. “Illiquidity and Stock Returns: Cross-section and Time-series Effects”, Social Science Electronic Publishing, 5(1):31~56.
[36]
Zhong A and Gray P, 2016. “The MAX Effect: An Exploration of Risk and Mispricing Explanations”, Journal of Banking & Finance, 65:76~90.
