Courts handling shareholder class actions and other types of securities litigation have expressed different views about how often stocks should respond to material news. Despite the importance of this issue in determining whether shares trade in an efficient market, these views are not attributed to any empirical evidence. My new study, available here, examines how often companies in the S&P 500 Index exhibit a statistically significant response to earnings announcements, documenting that the typical company has a statistically significant response on either the day of or the day following the earnings announcement only about 50 percent of the time. Thus, if demonstrating market efficiency requires a company’s stock to move in a statistically significant manner following at least half of earnings announcements, approximately half of S&P 500 Index members would fail this test. Further tests based on the size of an earnings surprise yield similar results, while a requirement that the stock-price movement be in the same direction as the earnings surprise reduces the share of S&P 500 Index members that would pass such a test of market efficiency to under 40 percent.
At least two courts have asserted that, if a stock trades in an efficient market, they would expect at least half of most news events to be followed by a statistically significant stock-price movement. In In re Federal Home Loan Mortgage Corp., No. 09 Civ. 832 (MGC) (S.D.N.Y. Mar. 27, 2012), the U.S. District Court stated, “A plaintiff must show that the market price responds to most new, material news.” Similarly, in George v. China Automotive Systems, Inc., No. 11 Civ. 7533 (KBF) (S.D.N.Y. July 3, 2013), the court stated, “Even assuming that the methodology was proper, showing that only seven out of sixteen days resulted in a market reaction is an insufficient foundation upon which to pronounce market efficiency. (Id. at 100.) (To state the obvious, seven out of sixteen is less than 50%.)”
Yet, the opinions provide no theoretical or empirical basis for these expectations. An easy, though informal, proof of why there is no theoretical basis for an argument that a specific share of news days should be associated with a statistically significant price movement can be made by pointing out that statistical significance is determined at various levels, with the 5 percent significance level being the most common in financial economics. Assume that under the 5 percent significance level, some fraction of news days is associated with statistically significant price movements. Under another significance level, say the stricter 1 percent significance level, a different, and smaller, fraction of news events would be associated with statistically significant price movements. Thus, in the abstract, there cannot be some constant expected fraction of news days that should be associated with statistically significant price movements in an efficient market.
Empirical academic literature on this question was stimulated by Richard Roll’s seminal article “R2,” Journal of Finance 43, (1988). An R2 is the fraction of the variance in a variable, here stock-price movements, that is explained by the statistical analysis. The abstract for Roll’s paper begins, “Even with hindsight, the ability to explain stock price changes is modest. R2s were calculated for the returns of large stocks as explained by systematic economic influences, by the returns on other stocks in the same industry, and by public firm-specific news events. The average adjusted R2 is only about .35 with monthly data and .20 with daily data.” A few later studies that examine how stock prices respond to specific news events contain results that, while not designed for this purpose, can be used to demonstrate that less than 50 percent of their selected news events were followed by statistically significant price movements.
In my paper, I address the question of what percent of “news days” is associated with a statistically significant stock-price movement through a number of analyses. The first analysis examines quarterly earnings announcements for members of the S&P 500 Index as of December 31, 2015 over calendar years 2010 through 2015. Two results of this analysis are: (1) for the median company, ranked by frequency of price response, only 54.2 percent of earnings announcements are associated with a statistically significant stock-price movement and (2) only 2.2 percent of companies have statistically significant stock-price movements associated with more than 80 percent of their earnings announcements.
The first result indicates that if we were to test for market efficiency by examining how frequently a company’s stock price responds to earnings announcements, and the requirement is that half of such announcements are associated with a statistically significant stock-price movement, it would appear that nearly half of S&P 500 Index members would fail the test. (In particular, half of the companies would fail if the bar was having 55 percent of earnings announcements be associated with a statistically significant price movement, and somewhat less than half the companies should fail if the bar is lowered to 50 percent of earnings announcements). The second result indicates that if the requirement is that more than 80 percent of earnings announcements are associated with a statistically significant stock-price movement, then 97.8 percent of S&P 500 Index members would fail this test of market efficiency. The paper also shows what happens if we examine different categories of earnings surprises by size, meaning that we exclude earnings announcements where the reported earnings matched analyst expectations. In that case, we find that about 84 percent to 90 percent of S&P 500 Index members would still fail the test of market efficiency if the requirement is that more than 80 percent of earnings announcements are associated with a statistically significant stock-price movement.
Another test I perform is to consider “directionality,” or whether the stock-price movement is in the direction predicted by whether earnings exceeded or fell below analyst expectations. While this can be an objective basis for determining the directionality of the news, it can sometimes lead to an incorrect inference if the earnings announcement contains other information, such as guidance, that goes in the opposite direction as the earnings surprise. For example, suppose that a company announced that earnings were low because the company ramped up spending on recruiting to staff up for much higher future demand. While earnings were below expectations, the market may very well treat this as a positive announcement. Still, this objective definition allows us to examine the thousands of earnings announcements in the study without getting into the subjective review of earnings announcements and their associated news stories and analyst reports.
The primary result here is that for the median member of the S&P 500 Index, again ranked by frequency of price response, only 37.5 percent of earnings announcements are associated with a statistically significant stock-price movement in the “correct” direction. Put differently, if the requirement were that at least half of non-zero earnings surprises should be associated with statistically significant returns in the same direction as the earnings surprise, more than half of the members of the S&P 500 Index would be expected to fail such a test of market efficiency.
Additional results in the paper further support the conclusion that substantial fractions of S&P 500 Index members would fail various market-efficiency tests that require a statistically significant stock-price movement following half or nearly all of various types of earnings announcements. Of course, there may be more precise tests that would result in greater fractions of S&P 500 Index members passing. However, empirical studies are needed to understand how frequently companies pass or fail some particular benchmark, such as that their stock responds in a statistically significant manner to earnings announcements at least half the time. Otherwise, the use of such benchmarks carries a risk that the corresponding test would set the bar for efficiency at an arbitrary level, including, in some cases, one so high that most members of the S&P 500 Index would not pass it.
 See, for example, the Reference Guide on Statistics in the Reference Manual of Scientific Evidence, Third Edition, Federal Judicial Center, 2011, p. 251 (“In practice, statistical analysts typically use levels of 5% and 1%. The 5% level is the most common in social science, and an analyst who speaks of significant results without specifying the threshold probably is using this figure.” Internal footnote omitted.)
 Further details of the analysis, restrictions on the sample group, and more detailed results are provided in the paper. Additional results are available from the author upon request.
This post comes to us from David Tabak, Senior Vice President of National Economic Research Associates. It is based on his recent article, “What Should We Expect When Testing for Price Response to News in Securities Litigation?,” which is available here.