Introduction
Early Developments
In 1900, French mathematician Louis Bachelier published his PhD thesis, Théorie de la Spéculation (Theory of Speculation) (Bachelier, 1900). He recognized that “past, present and even discounted future events are reflected in market price, but often show no apparent relation to price changes”. Hence, the market does not predict changes in asset prices. Moreover, he deduced that ‘The mathematical expectation of the speculator is zero’, which is consistent with Samuelson (1965) in explaining efficient markets in terms of a martingale. The implication is that asset prices fluctuate randomly, and then their movements are not predictable.
Pearson (1905) introduced the term ‘random walk’ to describe the path taken by a drunk with the drunk staggering in an unpredictable and random pattern. If prices follow a random walk, then it is difficult to predict the future path of asset prices. Kendall (1953), in examining weekly data on stock prices finds that they essentially move in a random walk pattern with near-zero autocorrelation of price changes. Working (1934) and Roberts (1959) find that the movements of stock prices look like a random walk. Cowles (1933 and 1944) and Working (1949) document that market participants cannot successfully forecast, and investors cannot beat the market.
Recent Developments
Eugene Fama, the Nobel laureate in 2013, made influential contributions to theoretical and empirical investigation for the recent development of market efficiency. Fama (1965a) defines an efficient market as a market in which there are a lot of rational, profit-maximizing, actively competing traders, who try to predict future asset values with current available information. In an efficient market, competition among many sophisticated traders leads to a situation where actual asset prices, at any point in time, already reflect the effects of all available information and therefore, they will be good estimates of their intrinsic values. The intrinsic value of an asset depends upon the earnings prospects of the company under study, which is not known exactly in an uncertain world, so that its actual price is expected to be above or below its intrinsic value. If the number of the competing traders is large enough, their actions should cause the actual asset price to wander randomly about its intrinsic value through offsetting mechanisms in the markets, and the resulting successive price changes will be independent. A market in which the prices of securities change independently of each other is defined as a random-walk market (Fama, 1965a). Fama (1965b) links the random walk theory to the empirical study on market efficiency. The theory of random walk requires successive prices changes to be independent and to follow some probability distribution.
When the flow of news coming into the market is random and unpredictable, current price changes will reflect only current news and will be independent of past price changes. Hence, independence of successive price changes implies that the history of an asset price cannot help in predicting its future prices and profits. It is then consistent with the existence of an efficient market. Using serial correlation tests, run tests and Alexander’s (1961) filter technique, Fama (1965b) cannot reject the independence of successive price changes and concludes that history of price changes would not help make the expected profits of market traders more than buy-and-hold.
The random-walk theory does not specify the shape of the probability distribution of price changes. Fama (1965b) finds that a Paretian distribution with characteristic exponents less than 2 fit the stock market data better than the Gaussian distribution, which is in line with the findings of Mandelbrot (1963). Hence, the empirical distributions have more relative frequency in their extreme tails than would be expected under a Gaussian distribution while the intrinsic values change by large amounts during very short periods of time.
Efficient-market Hypothesis (EMH)
A comprehensive review of theory and evidence on market efficiency was first provided by Fama (1970). He defines an efficient market in which asset prices at any time fully reflect all available information, and then further introduces three kinds of tests of EMH that are concerned with different sets of relevant information.
Weak form tests
Weak-form tests are used to examine whether investors can earn abnormal profits from the past data on asset prices. If successive price changes are independent and then unpredictable, it is impossible for investors to earn more than buy-and-hold. In literature, there is evidence of random walk and independence in the successive price changes in support of weak-form market efficiency (e.g., Alexander, 1961; Fama, 1965a, b; Fama and Blume, 1966).
Nevertheless, Fama (1970) recognizes that rejection of the random walk model does not imply market inefficiency. Market efficiency does not require the independence assumption, which is too restrictive, but only requires the martingale process of asset returns (Samuelson, 1965) with zero expected profits to the investors. Guo, Jiang, and Wong (2017) show that stochastic dominance and Omega ratio can be used to examine whether the market is efficient while Bai, Li, Liu, and Wong (2011), Bai, Li, McAleer, and Wong (2015), Ng, Wong, and Xiao, (2017), and Chan, Clark, Guo, and Wong (2020) have developed statistics that can be used to test for market efficiency. There are many applications to examine whether the market is efficient, see, for example, Lean, McAleer, and Wong (2010), Chan, De Peretti, Qiao, and Wong (2012), Tsang, Wong, and Horowitz (2016), Zhu, Bai, Vieito, and Wong (2019), Woo, Mai, McAleer, and Wong (2020), Wong (2020, 2021), Hon, Moslehpour, and Woo (2021), Lv, Tsang, Wagner, and Wong (2022), Chan, Chow, Guo, and Wong (2022), Wong, Yeung, and Lu (2022), Lakshmi (2022), Archer, Owusu Junior, Adam, Asafo-Adjei, and Baffoe (2022), Wong, Broll, Qiao, and Ma (2023), and many others. Furthermore, if investors can make significant abnormal profits using any tools in technical analysis based on past data, the weak-form efficiency is also violated. For instance, Wong, Chew, and Sikorski (2001), Wong, Manzur, and Chew (2003), Lam, Chong, and Wong (2007), McAleer, Suen, and Wong (2016) and Chong, Cao, and Wong (2017) propose new trading rules or indicators to earn abnormal profits in the markets. However, Kung and Wong (2009 a, b) find that the use of trading rule in technical analysis may have been useful in the past but may not be able to generate significant profit currently.
Semi-strong form tests
Semi-strong form tests involve an event study which is used to test the adjustment speed of asset prices in response to an event announcement released to the public. An event study averages the cumulative abnormal return of assets under investigation over time, from a specified number of pre-event time periods to a specified number of post-event periods. Fama, Fisher, Jensen, and Roll (1969) provide evidence on the reaction of share prices to stock split in support of semi-strong form market efficiency. Other event studies on earnings announcements (Ball and Brown, 1968), announcements of discount rate changes (Waud, 1970) and secondary offerings of common stocks (Scholes, 1972) generally provide supportive evidence for semi-strong forms of market efficiency.
Strong-form Tests
Strong-form tests are used to assess whether professional investors have monopolistic access to all private as well as public information so that they can outperform the market. Jensen (1968) indicates that professional investors of mutual funds cannot beat the market in favor of the strong-form market efficiency. Malkiel (2005) also finds that the performance of professional investment managers in domestic and foreign capital markets does not exceed the corresponding index benchmark so that market prices already reflect all available public and inside information.
Evolution of EMH
Besides market risk that exists in tradition asset pricing models, some propose additional risk factors in factor models to explain cross-section expected returns of securities, so the excess returns are considered as compensations for additional sources of risk (Beard and Sias, 1997; Fama and French, 2008).
Fama-French Three-Factor Model
Fama and French (1993) provide evidence that a three-factor model can explain stock returns. The three-factor model considers that the excess returns of a stock portfolio can be explained by its exposure to three factors: market risk premium (RMRF), market value factor (SMB, Small market capitalization Minus Big market capitalization), and book-to-market ratio factor (HML, High book-to-market ratio Minus Low book-to-market ratio).
Carhart Four-Factor Model
Some factors, like short-term reversal, medium-term momentum, volatility, skewness, gambling, and others are not considered or included in the three-factor model. Carhart (1997) develops a four-factor model which includes the momentum factor (PRIYR, the return for the one-year momentum in stock returns) in addition to RMRF, SMB and HML. Carhart (1997) provides evidence that it can explain large cross-sectional variation of the average returns stock portfolios.
Fama-French Five-Factor Asset Pricing Model
Fama and French (2015) further examine profitability and investment factors, as well as RMRF, SMB and HML, which is called a five-factor asset pricing model, to absorb the patterns in average returns and explain more anomalies. Fama and French (2017) tested the five-factor model. They found that average stock returns for markets of North America, Europe, and Asia Pacific increase with HML and profitability factor and are negatively related to the investment factor. The relation between average returns for the market of Japan and HML is strong but there is little relation between average returns and profitability or investment factor.
Liu-Stambaugh-Yuan Factor Models
Liu, Stambaugh and Yuan (2019) propose a Chinese version of the three-factor model which consists of EP (earning-price ratio) as well as RMRF and SMB, of the four-factor model which consists of turnover factor PMO (Pessimistic minus Optimistic) as well as EP, RMRF and SMB, and of the seven-factor model which consists of trading volume and turnover rate factors in addition to RMRF, SMB, HML, profitability and investment factors. These Chinese versions of factor models can empirically explain the returns on China’s A-share market. Bian, McAleer, and Wong (2013) develop a modified maximum likelihood (MML) estimator for the multiple linear regression model with underlying student t distribution and demonstrate that the MML estimator is more appropriate for estimating the parameters of the Capital Asset Pricing Model. This approach could also be used to get better estimations for all the factor models, including Fama-French Three-Factor Model, Carhart Four-Factor Model, Fama-French Five-Factor Asset Pricing Model, Liu-Stambaugh-Yuan Factor Models, and others.
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