*3.4. Book-to-Market E*ff*ect*/*Value Anomaly*

Many studies have been undertaken on the Book-to-Market (BM) effect by scholars around the world. Fama and French (1992) studied all stocks listed in NYSE, AMEX and NASDAQ from 1963 to 1990 and found that the combination with the highest BM value (value portfolio) had a monthly average return of 1.53% over the combination with the lowest BM value (charm portfolio). Wang and Xu (2004) took A-share stocks in Shanghai and Shenzhen stock markets from June 1993 to June 2002 as samples, calculated the return data of holding one, two, and three years, and considered that the BM effect exists. The same conclusion was drawn by Lam et al.'s (2019) study covering data from July 1995 to June 2015 in Chinese stock markets.

Black (1993) and MacKinlay (1995) argued that BM e ffect exists only in a specific sample during a specific test period, and is the result of data mining, which is not the same as what Kothari et al. (1995) found: It is the selection bias in the formation of BM combination that causes the BM e ffect. However, Chan et al. (1991), Davis (1994), and Fama and French (1998) tested the stock market outside the United States or during the extended test period, and still found that the BM e ffect existed significantly, negating the argumentation of Black (1993) and MacKinlay (1995).

Fama and French (1992, 1993, 1996) asserted that BM represents a risk factor, i.e., financial distress risk. Companies with high BM generally have poor performance in profitability, sales, and other fundamental aspects. Their financial situation is also more fragile, making their risk higher than that of companies with low BM. What is also considered is that the high return obtained by companies with high BM is only the compensation for their own high risk, and is not the unexplained anomaly. Furthermore, for the BM e ffect on the international level, Fama and French (1998) confirmed that a Two-Factor Model with a relative distress risk factor added could explain it rather than an international CAPM.

De Bondt and Thaler (1987) and Lakonishok et al. (1994) agreed that the BM e ffect is caused by investors' overreaction to company fundamentals. On the premise of confirming the positive correlation between BM and the company's fundamentals, as investors are usually too pessimistic about companies with poor fundamentals and too optimistic about companies with good fundamentals, when the overreaction is corrected, the profits of high BM companies will be higher than those of low BM companies.

## *3.5. The Size E*ff*ect*

Banz (1981) found 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 especially in January, as size of the firm and arrival of January are regarded as public information. Lakonishok et al. (1994) found that, since the stock with high P/E ratio is riskier, if P/E ratio is presumed to be known information, then this negative relationship between P/E ratio and return rate provides a considerable prediction on the latter, bringing a serious challenge to EMH.

On the contrary, Daniel and Titman (1997) claimed that BM and size only represent the preference of investors, not the determinants of returns. Due to the poor fundamentals of high BM companies and good fundamentals of low BM companies, while investors prefer to hold value stocks with good fundamentals rather than those with poor fundamentals, the return rate of companies with high BM is higher.
