Predictability of stock market indexes following large drawdowns and drawups.
| Autor | Brandi, Vinicius Ratton |
Disclaimers The views expressed in this paper are those of the author and do not necessarily represent those of the Banco Central do Brasil or the Superintendencia de Seguros Privados.
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Introduction
In 2008, when Queen Elizabeth II asked a group of professors at the London School of Economics why nobody had noticed the financial crisis coming, (1) Her Majesty was probably unaware she was addressing one of the most important and controversial topics in Finance: the predictability of the financial markets. The origin of this debate dates back at least to Bachelier (1900), who developed the mathematics of Brownian motion as a model for stock price variations and concluded they followed a random walk. Since then, the randomness of the financial markets has become a subject of great interest and scrutiny among academics and market participants.
Half a century ago, Prof. Eugene F. Fama published his first broad review of the theoretical and empirical literature on this subject. Even at that time, he already recognized the area was "so bountiful" that he apologized for any missing references (Fama, 1970). He consolidated and popularized the concept of an efficient market as one "in which prices always fully reflect available information" and defined the classic taxonomy that distinguishes the three different forms of market efficiency: weak (past return), semi-strong (public information) and strong (public and private information), according to the type of information used to predict future prices.
Since then, the academic debate has been driven around what is now well-known as the "efficient market hypothesis" (EMH), which evolved from the random walk theory of asset prices (Fama, 1965; Samuelson, 1965). As Ball (2009) explains, the idea behind the hypothesis merges the insight that competition among rational agents reduces trading margins close to zero with another one stating that asset price fluctuations are driven solely by the arrival of new and relevant information. Rational expectation plays a central role in explaining how transaction prices remain as best estimates for market equilibrium. When all investors are rational, no one would be willing to enter into a mispriced transaction. Even with the presence of some irrational agents, the competition among rational arbitrageurs would prevent prices from diverging from market equilibrium (Friedman, 1953).
Amini et al. (2013) offer a broad and detailed review on the short-term predictability of stock markets after the observation of large price variations, comparing different markets, time periods and methodologies used in the empirical research. They suggest that future research could benefit from using different ways to define large returns, such as looking at those conditional on other factors.
Following that idea, we propose using drawdowns and drawups as triggers, in order to investigate the existence of short-term abnormal returns in stock markets, using ten different stock price indexes from developed and emerging markets. Drawdowns and drawups are defined as the cumulative price variation on a sequence of negative or positive returns, respectively. Unlike fixed-time measures such as daily, weekly or monthly returns, the duration of drawdowns and drawups varies randomly according to investor behavior. As these measures are not computed within a fixed time horizon, they are flexible enough to capture subordinate, time-dependent processes (local dependence) that could drive investors' under- or overreaction.
As emphasized by Mandelbrot (1963), for price return distributions with infinite second moment, the total price variation is usually concentrated in a few trading days. According to Clark (1973), these turbulent cascades could be explained by some subordinate, time-dependent process. The process could be related to market microstructure variables, such as trading volume or number of trades, which are ultimately related to investor behavior. Dacorogna et al. (1996), Levitt (1998), Weron and Weron (2000), and Gerhard and Hautsch (2002) give examples of alternative ways to capture the dynamics of financial time series using the concept of elastic time. Using drawdowns and drawups may better enable us to understand market behavior, compared to fixed time statistics, especially those related to the occurrence of large returns (Mandelbrot, 1972; Johansen and Sornette, 2001; Mendes and Brandi, 2004).
We estimate abnormal returns following the dummy variable approach, similar to Karafiath (1988) and Mazouz et al. (2009), for time periods from 1 to 21 business days after the event ending date. Residual variance is assumed to follow the GJR-GARCH model proposed by Glosten et al. (1993), which captures both GARCH structure and asymmetries in the data and, therefore, circumvents some restrictive assumptions on standard OLS estimation. As pointed out by Mazouz et al. (2009), GARCH methods lead to higher estimation efficiency, avoiding invalid inference caused by failure to capture market uncertainty variations close to event periods.
Our results show a great variety of estimates across the different stock market indexes in the sample. This variety is evidence that price behavior after large drawdowns and drawups varies according to country-specific market features. Similarly to previous empirical literature, we do not provide conclusive evidence on short-term predictability of stock market returns following large price variations. The majority of estimates support the efficient market hypothesis. Results also provide stronger support for the underreaction hypothesis than for overreaction, with a higher prevalence of return continuations than reversals. Evidence for the uncertain information hypothesis (UIH) is present in some markets, mainly after events of lower magnitude.
The remainder of the paper is organized as follows. The next section discusses the related literature. Section 3 presents the data and Section 4 discusses the methodology. Section 5 describes the empirical results, while the conclusion is presented in the last section.
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Related literature
With the development of cognitive and social psychology, (2) economists gained a better understanding of how biases in judgments and beliefs can affect the individual decision-making process, as well as market behavior as a whole. The field of "behavioral economics" also added many insights to the market efficiency debate, by incorporating new evidence on how human behavior departs from the hypothesis of rationality. Inspired by evidence from Kahneman and Tversky (1979) that individuals tend to underweight base rate (prior) data and overweight recent information, DeBondt and Thaler (1985), in widely-known early research, find empirical evidence of long-term overreaction in the US stock market.
In a further review, Fama (1998) argues in favor of the efficient market hypothesis. He points out that observed anomalies tend to disappear over time or with improved research methodology. This would clearly make it impossible to obtain excessive and easy profits through stock market transactions.
Shiller (2003), in contrast, states that behavioral finance research may contribute to understanding markets' sometimes-irrational behavior. Perhaps market-efficiency interpretations of abnormal events can lead to incorrect answers. As the author concludes, researchers may "distance ourselves from the presumption that financial markets always work well and that price changes always reflect genuine information." From this perspective, studying market anomalies may help to support, for instance, improvements in information transparency (Healy and Palepu, 2001).
The first studies on short-term overreaction, however, yielded quite controversial results. While Arbel and Jaggi (1982) and Atkins and Dyl (1990) find no evidence to reject the EMH, Bremer and Sweeney (1991) find that large negative daily returns are followed, on average, by significant, abnormal positive returns. Overall, the literature presents different theories to explain price behavior following large price variation events, and lacks consensus on which of them prevails. Besides overreaction, another behavioral explanation, known as the underreaction hypothesis (3), assumes that new information is not immediately incorporated into market prices, causing near-term future returns to follow the direction of prior large price changes.
It is also possible that abnormal returns may be explained by no anomaly at all, based on the conventional rational expectations framework. Under the UIH, the systematic risk of stocks tends to increase concurrently with large price variations, which leads to a demand for higher expected returns from risk-averse rational investors (Brown et al., 1988). As a result, this hypothesis predicts return continuation after large price increases, and reversals after large drops. In addition, some explanations relate to market microstructure, such that spurious serial correlation may be caused by unsynchronized trading or bid-ask bounce effects (Cox and Peterson, 1994).
For Brazil's stock market, Dourado and Tabak (2014) compare results from different studies and conclude that this topic is controversial in this country, as well. Using the most popular national stock index as the price reference, they provide evidence supporting market efficiency, in accordance with most recent results in the literature. Similar results were found by Saffi (2003), who concludes in favor of a weak form of the efficient market hypothesis, after observing predictions from technical analysis investment strategies. In contrast, Gaio et al. (2009) use time series techniques to show that the Brazilian market does not display a weak form of market efficiency.
Da Costa Jr. (1994) presents one of the earliest studies of overreaction in the Brazilian stock market. He investigates the period from 1970 to 1989, and finds evidence of price reversals in 2-year...
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