The gambler’s and hot-hand fallacies: Empirical evidence from trading data☆
Introduction
People who are affected by the gambler’s or the hot-hand fallacy misinterpret random sequences. The gambler’s fallacy or “Law of Small Numbers” describes the empirical observation that many people expect systematic reversals in outcomes of random sequences based on a small sample size (Rabin, 2002, Tversky and Kahneman, 1971). In contrast, the hot-hand fallacy describes the observation that people expect excessive persistence in random sequences rather than reversals (Camerer, 1989, Gilovich et al., 1985). In an effort to reconcile the two fallacies, Rabin and Vayanos (2010) propose a model that predicts a belief in reversals following short streaks and a belief in continuation of streaks following long streaks.
In this paper, I exploit a unique empirical setting that allows me to test this prediction using trader-level financial market data. I infer retail investors’ beliefs on future stock prices from their investment decisions using a novel data set, which contains the trading records of a large brokerage service. The broker alerts investors of sequences of stock price increases and decreases—so-called streaks—by sending standardized push notifications to its clients. I observe which investors read the push notifications and trade on them. As the broker allows investors to take long and short positions by means of contracts-for-difference (CFDs) at the same costs, they can take positions that allow them to profit from a continuation or a reversal of the reported streak, depending on their beliefs. Thus, this setting provides me a nice financial markets playing field to test the empirical predictions of Rabin and Vayanos (2010).
As noted by Stöckl et al. (2015), the “hot-hand fallacy and the gambler’s fallacy are two important behavioral biases in financial markets” (p. 327). Yet, to date the predictions of Rabin (2002) and Rabin and Vayanos (2010) have not been tested directly in a financial market setting on an individual level. Loh and Warachka (2012) study streaks of consecutive earnings announcements and subsequent aggregate market reactions. They document that the post-earnings-announcement drift has a significant time-series component consistent with the gambler’s fallacy, but they do not find evidence in support of the hot-hand fallacy following longer streaks. Related studies have used experimental data (Asparouhova et al., 2009), state lottery data (Suetens et al., 2016), or college football betting markets (Durham et al., 2005) to shed light on the these important biases. I extend prior research and contribute empirical evidence using individual level trade data.
Section snippets
Data and methodology
I use transactional-level brokerage data from an online broker that allows its customers to trade CFDs on a large set of stocks. CFDs are financial futures contracts designed such that their price always equals that of the underlying security (Brown et al., 2010). CFD trading provides an important advantage for my analysis, as CFDs allow investors to implement trading strategies involving short positions. The broker charges transaction costs through a portion of the bid/ask spread of the trades
Results
I present the results of the formal test in Table 1. Column (1) considers the analysis on novel positions, Column (2) considers the analysis on existing positions. The results show that, on average, investors’ tendency towards the hot-hand fallacy increases in the duration of the streak. The coefficients in Column (1) ( −0.0045, -statistic 1.23; 0.0005, -statistic 1.92) provide evidence in support of a non-monotonic relationship between Streak Duration and the hot-hand fallacy,
Discussion
Rabin and Vayanos (2010) predict a belief in reversals following short streaks and a belief in continuation of streaks following long streaks. I contribute empirical evidence in support of this prediction using individual-level brokerage data. The analysis indicates that investors’ are more likely to trade in line with the hot-hand fallacy as the duration of the streak increases. In particular, while I observe a small tendency of investors to take positions in line with the gambler’s fallacy
References (14)
- et al.
A model of investor sentiment
J. Financ. Econ.
(1998) - et al.
The hot hand in basketball: On the misperception of random sequences
Cogn. Psychol.
(1985) - et al.
Hot hand and gambler’s fallacy in teams: Evidence from investment experiments
J. Econ. Behav. Organ.
(2015) - et al.
Inference from streaks in random outcomes: Experimental evidence on beliefs in regime shifting and the law of small numbers
Manage. Sci.
(2009) - et al.
Exchange traded contracts for difference: Design, pricing, and effects
J. Futures Mark.
(2010) Does the basketball market believe in the ‘hot hand’?
Am. Econ. Rev.
(1989)- et al.
The market impact of trends and sequences in performance: New evidence
J. Finance
(2005)
Cited by (2)
Crash-based quantitative trading strategies: Perspective of behavioral finance
2022, Finance Research LettersCitation Excerpt :Based on the aforementioned studies, a price crash can be caused by investors’ cognitive biases, such as herding bias and overconfidence bias. Even though such cognitive biases can result in mispricing of securities, investors may theoretically expect excess returns generated from a stock market crash as long as they rationally use certain behavioral deviations (Conrad et al., 2014; Jang and Kang, 2019; Pelster, 2020). Therefore, it is highly possible to realize excess returns from a stock market crash.
A Dissociation Between Two Cognitive Biases in Acute Stress Disorder: Preliminary Evidence for the Reverse Gambling Fallacy
2021, Cognitive Therapy and Research
- ☆
Data were obtained under a non-disclosure agreement with a financial institution. I thank the data provider for use and explanations of their data. I thank Costas Meghir (the editor), an anonymous reviewer, John Beshears, and Maik Dierkes for valuable comments and suggestions. Any errors, misrepresentations, and omissions are my own.