Introduction
There are many market anomalies observed in financial markets that efficient-market hypothesis (EMH) and standard asset-pricing models cannot explain. Many academics think of a new theory to explain market anomalies found. However, due to a lack of agreement among academics about the proper theory, many academics refer to market anomalies without a reference to a benchmark theory (Daniel and Hirshleifer, 2015; Barberis, 2018) and then they simply refer to anomalies as return predictors, avoiding the problem of defining a benchmark theory (McLean and Pontiff, 2016). Some market anomalies are briefly summarized below.
Contrarian Effect / Reversal Effect
De Bondt, Werner and Thaler (1985, 1987) found that investors are too pessimistic about the past loser portfolio and too optimistic about the past winner portfolio. Consequently, past losers (stocks with low returns in the past three to five years) will win positive excess returns than past winners (stocks with high returns in the past three to five years) which will have negative excess returns, when the market is finally adjusted to the fundamental value. This is known as the Contrarian Effect (or the Winner-Loser Effect). This market anomaly can be used to predict stock returns and use the reversal strategy to buy the loser portfolios in the past and sell the winner portfolios in the future.
The representative heuristic (Tversky and Kahneman, 1974), for example, shows that people tend to rely too heavily on small samples and too little on large samples. Then, it inadequately discounts both for the regression phenomenon, and for selection bias in the generation or reporting of evidence (Hirshleifer, 2001). Due to the existence of representative heuristic, investors signify excessive pessimism about the past loser portfolios and excessive optimism about the past winner portfolios. Consequently, investors overreact to both good and bad news. This leads to the underestimation of the loser portfolio prices and the overestimation of the winner portfolio prices, leading to deviations from their fundamental values.
Momentum Effect
Jegadeesh and Titman (1993) found that recent past winners (portfolios formed on the last year of past returns) outperform recent past losers, known as the Momentum Effect. If stock returns are examined over a period of 6 months, the average return of the winner portfolio is about 9% higher than that of the loser portfolio. Chan, Jegadeesh and Lakonishok (1996) enlarged upon the research samples of Jegadeesh and Titman (1993) and obtained the same results. Schwert (2003) found that the Momentum Effect seems quite large and reliable using both CAPM and the three-factor model.
Asness, Frazzini, Israel and Moskowitz (2014), however, challenge the existence of the Momentum Effect. They prove that momentum return is small, fragmentary, in danger of disappearing and only applicable in short positions. Also, there is no theory to support the Momentum Effect. Moreover, the Momentum Effect may not exist or may be limited by taxes or other transaction costs, and it may provide various results depending on different momentum measures in any given period.
Lam, Liu, and Wong (2010, 2012), Fung, Lam, Siu, and Wong (2011), Guo, McAleer, Wong, and Zhu (2017), and others have developed the Bayesian models that can be used to explain both contrarian and momentum effects while Fabozzi, Fung, Lam, and Wong (2013) have developed 3 different tests to test whether there are any contrarian and momentum effects.
Wong, Chow, Hon, and Woo (2018) have conducted a survey to examine whether Hong Kong small investors’ behaviors are due to conservative and representative heuristics on both momentum and contrarian trading strategies. Fong, Wong, and Lean (2005) find that the search for rational asset pricing explanations for the momentum effect may be a futile one and confirm the market is not efficient. Lam, Chong, and Wong (2007) use the trading rules based on 1-day and intraday momentum are estimated for major world stock indices and find that the trading rules perform well in the Asian indices but not in those of Europe and the United States.
Calendar Anomalies
January Effect
The January Effect was first discovered by Wachtel (l942). Rozeff and Kinney (1976) found that the return of NYSE’s stock index in January from 1904 to 1974 was significantly higher than that of the other 11 months. The studies of Gultekin and Gultekin (1983) and Nippani and Arize (2008) found similar evidence of the January effect. However, according to Riepe (1998), the January effect is weakening. Moller and Zilca (2008) investigated the evolution of the daily pattern of the January effect across size deciles and confirmed its existence. However, from Zhang and Jacobsen (2013), well-known monthly seasonals in returns such as January effect, are sample specific revealed by over 300 years of UK stock returns so that monthly seasonals might be in the eye of the beholder.
Two most important explanations for the January Effect include the Tax-Loss Selling Hypothesis (Gultekin and Gultekin, 1983) and the Window Effect Hypothesis (Haugen and Lakonishok, 1988). The tax-loss selling hypothesis suggests that people will sell down stocks at the end of the year, offsetting the appreciation of other stocks in that year, in order to pay less in taxes. After the end of the year, people buy back these stocks. This collective buying and selling leads to a year-end decline in the stock market and a January rise in the stock market the following year. 
The window effect hypothesis argues that institutional investors want to sell losing stocks and buy profitable stocks to enhance year-end statements. This kind of trading exerts positive price pressure on profitable stocks at the end of the year and negative pressure on losing stocks. When the selling behavior of institutional investors stops at the end of the year, the losing stocks that were depressed in the previous year will rebound substantially in January, leading to a larger positive trend of price movements. Some such as Chen and Singal (2004), and Starks, Yong, and Zheng (2006) favor the explanation of the tax-loss selling hypothesis.
Weekend Effect and Reverse Weekend Effect
French (1980) analyzed the 1953-1977 US daily stock returns and found that the gain on Monday has a negative trend, while the gains on other days are positive. When one gets higher returns on Friday than on Monday, it is known as the Weekend Effect, whereas when one gets higher returns on Monday as opposed to Friday, it is called the Reverse Weekend Effect. Schwert (2003) found that the weekend effect seems to have disappeared or at least substantially attenuated since French (1980). Nevertheless, other evidence of the Weekend Effect can be found in Bampinas, Fountas and Panagiotidis (2015). There exist various explanations for stock market behaviors on weekends. For example, the regular Weekend Effect has been attributed to payment and check-clearing settlement lags. On the other hand, Brusa, Liu and Schulman (2000, 2003, 2005) and Brusa, Hernández and Liu (2011) found the Reverse Weekend Effect, which can be explained by the reward for higher volatility on Mondays than on Fridays (Chan and Woo, 2012).
Turn-of-the-Month Effect
Specifically, Turn-of-the-Month is defined as beginning with the last trading day of the month and ending with the third trading day of the following month. Studying CRSP daily returns over the 109-year interval of 1897-2005, all returns to equities on the average were found to be positive during the turn-of-the-month interval (McConnell and Xu, 2008).
Holiday Effect
Lakonishok and Smidt (1988) and Ariel (1990) have shown that average returns are higher the day before a holiday than other trading days, which is the so-called Holiday Effect.
Keim (1988) argues that seasonals in returns are anomalies in the sense that asset-pricing models do not predict them, but they may not imply market inefficiency. These seasonals can be explained in terms of market microstructure (Lakonishok and Maberly, 1990 and Keim, 1989).
Calendar Effect
Wong, Agarwal, and Wong (2004) confirm that there are day-of-the-week effects in the Asian Markets. However, Wong, Agarwal, and Wong (2006) find that both the day-of-the-week effect, the turn-of-the-month effect, and the pre-holiday effect have largely disappeared from the Singapore stock market in the 1993-2005 period. Qiao, Qiao, and Wong (2010) find that the day-of-the-week effect is very weak in some financial markets. They find that there are only Wednesday effects in the Chinese A-share and B-share stock markets. On the other hand, Lean, Smyth, and Wong (2007) find the existence of weekday and monthly seasonality effects in some Asian markets, but confirm that the January effect has largely disappeared.
Book-to-Market Effect /Value Anomaly
Many studies have investigated the Book-to-Market (BM). For example, Fama and French (1992) found the BM effect in the US market; Wang and Xu (2004), and Lam, Dong and Yu (2019) confirmed the existence of the BM effect in the Chinese stock markets. Kothari, Shanken, and Sloan (1995) however consider that it is the selection bias. 
Chan, Hamao, and Lakonishok (1991), Davis (1994), and Fama and French (1998) tested the stock markets outside the US or during an extended test period, and they still found the BM effect.
Fama and French (1992 and 1993) believe that BM represents a risk factor, i.e., financial distress risk. Firms with high BM generally have poor performance in profitability, sales and other fundamental aspects, and their financial situation is more fragile, making their risk higher than that of firms with low BM. Also considered is that a high return obtained by firms with high BM is only the compensation for their own high risk. BM can then be explained by Fama-French in the three-factor model and is not an unexplained anomaly. Furthermore, Fama and French (1998) confirm that a two-factor model with a relative distress risk factor added could explain the BM effect on the international level.
Size Effect
Banz (1981) showed that the stock market value decreased with the increase of company size. The phenomenon that small-cap stocks earn higher returns than those calculated by CAPM (Reinganum, 1981), and large-cap stocks (Siegel, 1998), clearly contradicts EMH, as the firm size is regarded as public information. Lakonishok, Shleifer, and Vishny (1994) demonstrated that since the stock with high P/E ratio is riskier, if P/E ratio is taken as known information, then this negative relationship between P/E ratio and return rate provides a considerable prediction on the latter, and then challenges EMH.
Disposition Effect
From Shefrin and Statman (1985), the Disposition Effect refers to two phenomena of the stock market. In the first, investors tend to have a strong propensity to hold onto losing stocks and avoid the regret associated with the sale of a losing investment and, in the second, investors tend to sell stocks in order to lock in profits. In these cases, two kinds of psychology describe investors whose regret and embarrassment cause the first phenomenon and whose arrogance leads to the second. 
Hence, investors have a disposition effect which leads them to sell winners and hold losers. The Disposition Effect is one implication of extending Kahneman and Tversky’s prospect theory (1979) to investments.
Barber, Lee, Liu and Odean (2008), Odean (1998, 1999) and Zhao and Wang (2001) found the Disposition Effect in Taiwanese, US, and Chinese stock markets, respectively. They conclude that investors tend to sell profitable stocks and continue to hold losing stocks. On the other hand, Odean (1998, 1999) also found that US stock investors sell more loss-making shares in December, making the Disposition Effect less pronounced because of tax avoidance.
Herd Effect and Ostrich Effect
Herd behavior refers to behavior patterns that are correlated across individuals but could also be caused by correlated prevailing information in independently acting investors. The people with herd behavior will do what others are doing rather than what is optimal based on their own information. Herding is closely linked to expectations, fickle changes without new information, bubbles, fads, and frenzies. Barber, Heath, and Odean (2003) compared the investment decisions of groups (stock clubs) and individuals. Both individuals and clubs are more likely to purchase stocks that are associated with good reasons (e.g., a company that is featured on a list of most-admired companies). However, stock clubs favor such stocks more than individuals, even though such reasons do not improve performance. The previously mentioned seven-factor model by Li, Hu, and Tang (2019) also indicates that herd behavior of the Chinese A-share market is more prevalent in times of market turmoil, especially when the market falls.
Batmunkh, McAleer, Moslehpour, and Wong (2018) confirm the presence of herd behavior in both Taiwan and China’s stock markets, Batmunkh, Choijil, Vieito, Méndez, and Wong (2020) confirm the presence of herd behavior in the Mongolian stock market, and Méndez, Wong, Batmunkh, Choijil, and Vieito (2023) confirm the presence of herd behavior in the Integrated Financial Markets. Choijil, Méndez, Wong, Vieito, and Batmunkh (2022) confirm that there is no consensus regarding the causes of herd phenomenon, but new perspectives have emerged to expand research on herd behavior.
Another market anomaly is the Ostrich Effect. Ostriches deal with obvious risk situations by pretending that risk does not exist, so the ostrich effect is used to describe some investors’ decisions as shown in Galai and Sade (2006). Karlsson, Loewenstein and Seppi (2009) present a theoretical model in which investors collect additional information conditional on favorable news and avoid information following bad news under this effect They also provide empirical evidence to support the existence of the Ostrich Effect in financial markets.
Other Anomalies
There are some other anomalies. For example, Lv, Chu, Wong, and Chiang (2021) confirm that there exists a minimum volatility anomaly such that incorporating both maximum-return and minimum-volatility assets could construct a maximum-return-and-minimum-volatility aggressive-and-yet-defensive trading approach that stochastically dominates most of other assets/portfolios.
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