Market efficiency has been a topic of interest and debate central amongst financial economists for more than five decades. Indeed, two of the recipients of the Nobel Memorial Prize in Economic Sciences in 2013, Eugene Fama and Robert Shiller, have debated about the efficiency of markets since the 1980s. Concerns about market efficiency were catapulted to prominence most recently by the financial crisis of 2007-8. Efficient capital markets are foundational to economic theories that posit the allocative efficiency of free markets, which requires informationally efficient capital allocation markets, such as those for equity and fixed income trading. An extended line of research has uncovered evidence of various anomalies which seem to challenge notions of market efficiency, and has also attempted to explain the causes of one such anomaly, the so-called "size effect." Though there appears to be substantial evidence that the size effect is real and persistent, violating the efficiency market hypothesis, no substantial evidence supports the size effect as violating market efficiency.
Market Efficiency Refers to the efficiency with which markets allocate savings amongst competing investments.
"In an allocationally efficient market, scarce savings are optimally allocated to productive investments in a way that benefits everyone" (Copeland, et al., 2005, p. 353). To provide optimal investment allocation, capital prices must provide market participants with accurate signals, and therefore prices must fully and instantaneously reflect all available relevant information (Copeland, et al., 2005). In advanced economies, secondary stock markets play an indirect role in capital allocation by revealing investment opportunities and information about managers' past investment decisions (Dow & Gorton, 1997). For secondary stock markets, and other formal capital markets, to efficiently and effectively fulfill these two roles, securities prices must "be good indicators of value" (Fama, 1976, p. 133). Therefore, allocative market efficiency requires capital market prices to be informational efficient. Informational efficiency implies no-arbitrage pricing of tradeable securities and entails several defining characteristics that form the basis of the efficiency market hypothesis. Generally, "A market is efficient with respect to information set Î˜_t if it is impossible to make economic profits by trading on the basis of information set Î˜_t" (Jensen, 1978, p. 98), where economic profits are defined as risk-adjusted returns minus trading and other costs. If security prices reflect all available relevant information, such as P/E ratios and past return variances, then it would be impossible to to use such information to profitably trade these securites. Therefore tests of the possibility of using publicly available information to earn economic profits constitute tests of infomational effiency. Tests of informational market efficiency generally take three forms, and comprise the elements of the efficient market hypothesis. Fama (1969) defined the three forms of market efficiency as the weak, semi-strong and strong form, with each form characterised by the nature of the information central to its application. Weak form efficiency tests are tests of the viability of using past price history of the market to predict future returns (which is a necessary, but not sufficient, condition for trading for economic profits). The semi-strong form of the efficienct market hypothesis tests whether all publicly available information could be used by traders to earn economic profits. And finally, the strong form of market effiency tests the viability of using all information, public as well as private, to generate economic profits. In the literature and amongst practicioners, it is the semi-strong form which "represents the accepted paradigm and is what is generally meant by unqualified references in the literature to the 'Efficient Market Hypothesis'" (Jensen, 1978, p. 99). And though some references to 'market efficiency' allude to the allocative efficiency of markets, the term market efficiency usually refers to informational efficiency as operationally defined by Fama's efficiency market hypothesis, specifically the semi-strong formulation. Since its formulation in the late 1960s, researchers have conducted thousands of tests of the efficiency market hypothesis and have found various anomalies, such as the size effect, which appear to violate the market efficiency. Banz (1981) examined NYSE-listed common stock returns between 1936 and 1975 and found stocks with the smallest market capitalisaation earned a risk-adjusted return 0.40% per month higher than the remaining firms in his sample, which was the first evidence that the 'size effect' posed a challenge to semi-strong form efficiency. Analysing a sample of 566 NYSE and AMEX stocks over the 1963â€“1977 period, Reinganum (1981) found that portfolios constructed based on size exhibited predicatability of future returns, with the smallest sized portfolio outperforming the largest decile by 1.77% per month. Keim (1983), testing NYSE and AMEX stocks over the 1963-1979 period, reported a size premium of approximately 2.5% per month. Lamoureux & Sanger (1989) found a size premium for NASDAQ stocks (2.0% per month) and for NYSE/AMEX stocks (1.7% per month) over the 1973 to 1985 period. Fama & French (1992, p.438) concluded, "The size effect (smaller stocks have higher average returns) is robust in the 1963-1990 returns on NYSE, AMEX, and NASDAQ stocks." Though evidence continued to mount of a size effect, which entails that average stock returns of firms with small market capitalisation were significantly higher than the average returns for large capitalisation firms, Fama and French's paper preceded decades of research regarding explanations for the size effect and its possible implications. Over the years researchers have offered a variety of empirical explanations, some of them mutually exclusive, for the size effect. Robert Merton (1987) argued that smaller firms have smaller investor bases and are less likely than larger firms to enjoy an institutional following amongst investors, making smaller firms less liquid and cheaper, which resulted in greater risk-adjusted returns. Chan & Chen (1991) asserted that smaller firms are more likely than large firms to either be distressed or only marginally profitable, and therefore small firms' prices are more responsive to changing business conditions, which loaded the size effect. Fama & French (1993, p.5) formed 25 portfolios of securities based on size and book-to-market and found that these "portfolios constructed to mimic risk factors related to size and BE/ME capture strong common variation in returns, no matter what else is in the time-series regressions. This is evidence that size and book-to-market equity indeed proxy for sensitivity to common risk factors in stock returns." Verifying their argument that the size effect was a proxy for common risk factors, Fama & French (1995) found evidence that firm size loaded profitability risk into the cross-section of stock returns. These, and other, empirical findings shed light on possible reasons for the size effect, but a consensus explanation never developed around a single cause. In contrast to the empirical and economic explanations for the size effect, some researchers questioned whether the size effect existed at all. Shumway & Warther (1999) argued that the small firm effect is essentially a statistical illusion, related not to actual share prices but to market microstructure issues which inhibit proper measurement of price movements. They examined prices of NASDAQ-listed firms from 1972 to 1995, a period previous research associated with significant size effect, and found that after considering delisting bias (by accounting for delisted firms' final price movements before removal from the sample), the size effect disappeared completely. Wang (2000) argued along similar lines, contending the size effect resulted from survivorship bias. He argued that small stocks are relatively more volatile and therefore more likely than large firms to be delisted due to bankruptcy or failing to meet listing requirements. These delisted stocks are often excluded from the samples studied for the size effect, which would bias the returns of small stocks upwards. Wang (2000) used simulation experiments to test for the likelihood of the small firm effect under such circumstances and concluded that the effect was spurious. Examining all of the above explanations and others, Dijk (2011, p. 3272) concludes, "The empirical evidence for the size effect is consistent at first sight, but fragile at closer inspection. I believe that more empirical research is needed to establish the validity of the size effect." Though the causes of the size effect are interesting and remain an important topic of debate, more important are the possible implications of the size anomaly for the efficiency market hypothesis. The size anomaly appears to present a violation of efficient markets, especially to those observers who wrongfully presume that market efficiency implies stock prices must follow a random walk; however, no researcher has yet to show that information related to firm size can be leveraged by traders to earn economic profits. Recalling Jensen's (1978) definition of informational efficiency, the size effect violates market efficiency only if such information could be used to generate risk-adjusted abnormal returns. Though the size effect may indicate that stock returns are predictable, "if transaction costs are very high, predictability is no longer ruled out by arbitrage, since it would be too expensive to take advantage of even a large, predictable component in returns" (Timmermann & Granger, 2004, p. 19). Therefore return predictability invalidates market efficiency when it produces risk-adjusted returns that subsume transaction costs. According to Stoll and Whaley (1983), who test whether the size anomaly can be exploited to earn risk-adjusted returns greater than transactions costs, find it is not possible for the sample of NYSE-listed firms examined over the 1960 to 1979 period. This is due in part to the relatively insignificance of small firms in relation to the market as a whole. As noted by Fama (1991, p. 1589), "the bottom quintile [of stocks] is only 1.5% of the combined value of NYSE, AMEX, and NASDAQ stocks. In contrast, the largest quintile has 389 stocks (7.6% of the total), but it is 77.2% of market wealth." So, even if the size effect is granted perfect validity, it does not necessarily negate the efficient market hypothesis. A final set of reasons ameliorating concerns about the size effect's threat to market efficiency is related to model specification. Abstracting from the specific arguments related to size effects, consideration of the joint hypothesis problem dampens concerns that size effects could be determined to violate market efficiency. Roll (1976) noted that the pricing models used to test market efficiency were also necessarily testing the validity of the specification of the market model (specifically, the validity of the market model proxy), which means that researchers' models were necessarily underspecified. Violations seemingly attributable to the size effect, or any other apparent anomaly, can always be attributed to mispecification of the market model or mismeasurement of the market proxy, making it impossible to definitively infer anamolous behavior as evidence of market efficiency. Additionally, this time pointed out by Fama (1991, pp. 1588-9), "small-stock returnsâ€¦are sensitive to small changes (imposed by rational trading) in the way small-stock portfolios are defined. This suggests that, until we know more about the pricing (and economic fundamentals) of small stocks, inferences should be cautious for the many anomalies where small stocks play a large roleâ€¦". Therefore, though there seems to be robust evidence for a size effect, transaction costs overwhelm risk-adjusted returns and model specification concerns generally blunt notions that size effects can be shown to disprove market efficiency. The global financial crisis of 2007-8 renewed prominent calls for dispensation of the notion of efficient markets, as the allocative efficiency of markets seemed in doubt after so much capital appeared to be wasted on ill-advised investments. But efficient market allocation of investments relies not on ex post views of past downturns, but on ex ante decisions about future investment opportunities. Efficient markets imply that all relevant information is impounded in current asset prices, maximising market participants' ability to allocate investment, which necessarily implies that the future is unpredictableâ€”market efficiency prohibited the ability to forecast the financial crisis, as the model predicts. Alternatively, a long line of research has examined the possibility that anomalies, such as the size effect, disprove market efficiency. The size effect, however, though an interesting puzzle regarding the cross-section of stock returns, does not disprove market efficiency.
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