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The efficient-market hypothesis (EMH) is a hypothesis in financial economics that states that asset prices reflect all available information. A direct implication is that it is impossible to "beat the market" consistently on a risk-adjusted basis since market prices should only react to new information. Because the EMH is formulated in terms of risk adjustment, it only makes testable predictions when coupled with a particular model of risk. As a result, research in financial economics since at least the 1990s has focused on market anomalies, that is, deviations from specific models of risk. The idea that financial market returns are difficult to predict goes back to Bachelier, Mandelbrot, and Samuelson, but is closely associated with Eugene Fama, in part due to his influential 1970 review of the theoretical and empirical research. The EMH provides the basic logic for modern risk-based theories of asset prices, and frameworks such as consumption-based asset pricing and intermediary asset pricing can be thought of as the combination of a model of risk with the EMH. Many decades of empirical research on return predictability has found mixed evidence. Research in the 1950s and 1960s often found a lack of predictability (e.g. Ball and Brown 1968; Fama, Fisher, Jensen, and Roll 1969), yet the 1980s-2000s saw an explosion of discovered return predictors (e.g. Rosenberg, Reid, and Lanstein 1985; Campbell and Shiller 1988; Jegadeesh and Titman 1993). Since the 2010s, studies have often found that return predictability has become more elusive, as predictability fails to work out-of-sample (Goyal and Welch 2008), or has been weakened by advances in trading technology and investor learning (Chordia, Subrahmanyam, and Tong 2014; McLean and Pontiff 2016; Martineau 2021). Theoretical background Suppose that a piece of information about the value of a stock (say, about a future merger) is widely available to investors. If the price of the stock does not already reflect that information, then investors can trade on it, thereby moving the price until the information is no longer useful for trading. Note that this thought experiment does not necessarily imply that stock prices are unpredictable. For example, suppose that the piece of information in question says that a financial crisis is likely to come soon. Investors typically do not like to hold stocks during a financial crisis, and thus investors may sell stocks until the price drops enough so that the expected return compensates for this risk. How efficient markets are (and are not) linked to the random walk theory can be described through the fundamental theorem of asset pricing. This theorem provides mathematical predictions regarding the price of a stock, assuming that there is no arbitrage, that is, assuming that there is no risk-free way to trade profitably. Formally, if arbitrage is impossible, then the theorem predicts that the price of a stock is the discounted value of its future price and dividend: P t = E t [ M t + 1 ( P t + 1 + D t + 1 ) ] {\displaystyle P_{t}=E_{t}[M_{t+1}(P_{t+1}+D_{t+1})]} where E t {\displaystyle E_{t}} is the expected value given information at time t {\displaystyle t} , M t + 1 {\displaystyle M_{t+1}} is the stochastic discount factor, and D t + 1 {\displaystyle D_{t+1}} is the dividend the stock pays next period. Note that this equation does not generally imply a random walk. However, if we assume the stochastic discount factor is constant and the time interval is short enough so that no dividend is being paid, we have P t = M E t [ P t + 1 ] {\displaystyle P_{t}=ME_{t}[P_{t+1}]} . Taking logs and assuming that the Jensen's inequality term is negligible, we have log ⁡ P t = log ⁡ M + E t [ log ⁡ P t + 1 ] {\displaystyle \log P_{t}=\log M+E_{t}[\log P_{t+1}]} which implies that the log of stock prices follows a random walk (with a drift). Although the concept of an efficient market is similar to the assumption that stock prices follow: E [ S t + 1 | S t ] = S t {\displaystyle E[S_{t+1}|S_{t}]=S_{t}} which follows a martingale, the EMH does not always assume that stocks follow a martingale. Empirical studies Research by Alfred Cowles in the 1930s and 1940s suggested that professional investors were in general unable to outperform the market. During the 1930s-1950s empirical studies focused on time-series properties, and found that US stock prices and related financial series followed a random walk model in the short-term. While there is some predictability over the long-term, the extent to which this is due to rational time-varying risk premia as opposed to behavioral reasons is a subject of debate. In their seminal paper, Fama, Fisher, Jensen, and Roll (1969) propose the event study methodology and show that stock prices on average react before a stock split, but have no movement afterwards. Weak, semi-strong, and strong-form tests In Fama's influential 1970 review paper, he categorized empirical tests of efficiency into "weak-form", "semi-strong-form", and "strong-form" tests. These categories of tests refer to the information set used in the statement "prices reflect all available information." Weak-form tests study the information contained.... Discover the Travis Christofferson popular books. Find the top 100 most popular Travis Christofferson books.