Overconfidence and Asset Pricing
By Kent Daniel, Columbia Business School and NBER and David Hirshleifer, University of California at Irvine and NBER
- Empirical research has identified anomalous behaviors in stock, bond, and other asset markets: overaggressive trading and overreaction and correction patterns in prices.
- This article discusses how the overconfidence approach provides an integrated explanation for these puzzles and a rich set of new insights.
Some notable patterns of trading and pricing in asset markets seem to reflect investor overreaction to information. There is evidence that trading volume is high in asset markets, that individual investors trade aggressively and on average lose money thereby, and that asset returns show patterns of overreaction and reversal.
A natural possible explanation is investor overconfidence, which we define as a belief on the part of investors that their valuations are more precise than they actually are. This overestimation of the accuracy of one’s beliefs has very strong and consistent confirmation in the psychology literature and is sometimes stronger for experts. It has been documented among corporate financial officers (Ben-David, Graham, & Harvey, 2013) and among professional traders and investment bankers (Glaser, Langer, & Weber, 2013). Overconfident beliefs are supported by self-attribution bias, in which people give credit their own talents and abilities for past successes, while blaming their failures on bad luck.
Disagreement, Speculation, and Trading Volume
Economic theorists have shown that under reasonable assumptions, rational investors should not agree to disagree. Intuitively, suppose two investors start with the same prior beliefs, but end up disagreeing about the prospects of a firm. Then, at least one party has information that the other party should be taking more fully into account (Aumann, 1976). This suggests that rational investors should not place speculative bets. If another investor is willing to trade against me, I should conclude that this investor knows something important that I do not. So, in the simplest perfectly rational models, trading occurs primarily to diversify and share risk rather than to speculate, and the volume of trade should be quite limited. In reality, in 2014, the total dollar trade in the top 500 US stocks was $29.5 trillion (Collin-Dufresne & Daniel, 2014), which was close to twice GDP. Trade in foreign exchange is extremely heavy (Froot & Thaler, 1990).
Individual investors on average lose money from their bets on individual stocks, and the more they trade, the more they lose (Barber & Odean, 2000). Such losses can be immense (Barber, Odean, & Zhu, 2009). Furthermore, individuals invest in high-fee actively managed mutual funds instead of low-fee index funds, despite the documented net performance differential (French, 2008; Malkiel, 2013). Overconfidence is the natural explanation for overaggressive trading (Odean, 1998). Trading behavior is also consistent with bias in self-attribution, which is an underpinning of overconfidence. In an investment context, this is the belief that high returns are the result of high skill, boosting overconfidence, whereas low returns are the result of bad luck (see the models of Daniel, Hirshleifer and Subrahmanyam (1998) and Gervais and Odean (2001)).
Consistent with bias in self-attribution, individual investors tend to trade more after they experience high stock returns. For example, investors moved to online trading platforms after experiencing superior personal performance, and then proceeded to trade more aggressively than before (Barber & Odean, 2002; Choi, Laibson, & Metrick, 2002). Griffin, Nardari, and Stulz (2007) document that stock market trading volumes increase after high returns around the world.
Rather than just overreaction in either direction, overconfidence should systematically induce overpricing when short-selling is difficult or costly. Short-selling constraints make it harder for pessimists about a stock to trade on their views. If optimists overconfidently stick to their views instead of taking into account that sidelined pessimists have important information as well, the optimists will overvalue the stock. This implies overpricing on average. So when investors are overconfident, the greater the disagreement; the more severe are short sales constraints, the more a security becomes overpriced (see Miller, 1977), when considering the theory of bubble formation of Scheinkman and Xiong (2003) and the evidence of Diether, Malloy, and Scherbina (2002).
Since high volatility creates greater scope for disagreement, we also expect greater over-pricing of more volatile stocks. This provides an explanation for the anomaly that high idiosyncratic-volatility stocks earn lower subsequent returns (Ang et al., 2006). Overconfident disagreement can also explain the clear-cut mispricing episodes that occurred during the high-tech boom at the turn of the millennium (Lamont & Thaler, 2003).
Although overconfidence induces arguably overaggressive trading, overconfidence has potential positive externalities as well. It can induce investors to investigate more or to trade more aggressively based on their private information signals, leading to a more efficient market price (Hirshleifer, Subrahmanyam, & Titman, 1994; Odean, 1998; Hirshleifer & Luo, 2001). It can also encourage greater participation in asset classes such as international stock markets, which investors might otherwise mistakenly avoid. At the managerial level, there is evidence that firms with overconfident CEOs spend more on R&D, and have greater innovative success, in the sense of generating more patents, even after controlling for R&D (Hirshleifer, Low, & Teoh, 2012).
There are many return anomalies, or patterns of predictability of stock returns not obviously explained by rational theories. As argued by Daniel and Hirshleifer (2015), the high premia earned by a combination of anomaly-based strategies is too large to be explained plausibly by rational risk premia.
The size effect (Banz, 1981) is the finding that low-market-capitalization firms on average earn higher returns than large firms. Stronger predictability is obtained when the firm’s market capitalization (size) is scaled by a measure of the firm’s fundamental value. The book-to-market ratio—that is, the book-value of equity, scaled by the firm’s market capitalization—is a strong positive return predictor (Fama & French, 1992). Value firms—those with high book-to-price ratios—substantially outperform growth firms, or those with low book-to-price ratios. There is also long-term reversal of returns from the preceding few years (DeBondt & Thaler, 1985). Past returns are closely related to the book-to-price ratio, since low past returns reduce the current price.
Momentum is the tendency for returns over the past 3-12 months to continue in the same direction in the next year. There are strong value and momentum anomalies in non-U.S. data and in other asset classes including currencies, commodity futures, government bonds (Asness, Moskowitz, & Pedersen, 2013) and even sports betting venues (Moskowitz, 2015). Consistent with the model in Daniel, Hirshleifer, and Subrahmanyam (2001), Moskowitz (2015) finds that higher uncertainty is associated with stronger momentum and value returns, though Daniel and Moskowitz (2015) find that low past market returns, combined with higher market volatility, are associated with a lower momentum premium.
For many kinds of corporate events, there is continuation in the sense that events for which there is a positive average announcement return are on average followed by high subsequent abnormal returns, while “bad news” events are on average followed by negative post announcement returns (see the summary in Hirshleifer, 2001). A major example is the issuance of new securities, which on average convey bad news about future cash flows. Similarly, the repurchase of existing securities tends to convey good news. Consistent with return continuation, equity and debt issues in many countries are on average followed by negative abnormal returns for long periods, and repurchases tend to be followed by high returns (Loughran & Ritter, 1995; Spiess & Affleck-Graves, 1995; Henderson, Jegadeesh & Weisbach, 2006; Ikenberry, Lakonishok, & Vermaelen, 1995; Daniel & Titman, 2006; Pontiff & Woodgate, 2008).
A portfolio which exploits simultaneously various return anomalies generates an exceptionally high reward-to-risk ratio, as discussed in Daniel and Hirshleifer (2015). This suggests looking to a psychological explanation such as overconfidence.
Overconfidence-Based Models of Trading and Asset Pricing
Return anomalies have encouraged researchers and practitioners to consider behavioral theories of asset pricing. There are several approaches, but our focus here is on overconfidence.
A Simple Overreaction Setting
To build intuition, we first consider a setting that captures overreaction by an overconfident investor to a signal that the investor perceives as private. The signal may be shared with many other investors, but not with everyone. Since the signal is not common to everyone, the investor has some sense of personal ego connection to the signal, resulting in an unwarranted overestimate of the precision of the signal.
The group of investors who get this signal thus overreact to it, resulting in overreaction and eventual correction. This is consistent with evidence of long-run return reversals and with the value effect. We discuss below how generalizations of this basic setting can generate many other anomalies described above.
Suppose that there are three dates, t = 0, 1, and 2. There are two assets, a risk-free asset with a return of zero, and a risky asset which pays an uncertain liquidating dividend at time 2. To start with, suppose that the representative overconfident investor is risk-neutral. So, the investor is willing to trade very aggressively on his beliefs, and we can ignore the trades of investors who are not overconfident about the signal or who don’t observe it.
The investor starts at date 0 with some prior expectation of the terminal dividend, which implies a market price P0 equal to the expectation of the liquidating dividend. At t = 1, the investor observes a signal and updates by taking a weighted average of the prior expectation and the signal. Since the investor is overconfident about the signal, he puts too much weight on it. The market price is equal to his expectation, so at date 1 the market price overreacts to the signal. This results in overly aggressive trading as well (e.g., against risk averse investors, or arbitrageurs, who do not overreact to the signal, or perhaps do not even see it).
The future returns from date 1 to 2 are predictable in this setting—there are anomalies. Consider, for example, the case of a positive signal. Then P1 is too high. In consequence, it higher than the (rationally) expected dividend. So expected returns are negative. Similarly, following a negative signal at t = 1, and negative returns from t = 0 to t = 1, expected returns will be positive. That is, there is reversal: price changes negatively predict future price changes. This is the basic overreaction-correction pattern implied by overconfidence.
To put this another way, when the price at date 1 is high, it is too high, and when it is low, it is too low. This means that if we were to benchmark the price against some measure of fundamentals, the scaled price would also predict returns. For example, suppose (somewhat unrealistically) that at date 0 book values were an unbiased measure of the expected terminal dividend, and that book values do not change at date 1. Then the ratio of P1 to book value would negatively predict future returns. When the ratio is high, that means that P1 is too high, so future returns will be low; when the ratio is low, P1 is too low. So, this model implies a value effect as well. This simple reasoning captures part of the argument of Daniel, Hirshleifer, and Subrahmanyam (1998, 2001).
To capture other anomalies, we move to a richer model.
A Setting with a Public Signal
Suppose now that there is also a public signal that arrives after the overconfident investor gets his private signal. The overconfident investor is assumed to properly estimate the precision of the public signal. This is the “static-overconfidence” setting of Daniel, Hirshleifer, and Subrahmanyam (1998). Specifically, we now extend the model by assuming that a public signal arrives at t = 2, and the terminal dividend is paid at t = 3. As in the basic setting, the market overreacts to the private signal, so there is “long run” reversal of the price change from t = 0 to 1. Since the investor thinks the precision of his t = 1 signal is higher than it really is, he overweighs it relative to the t = 2 public signal. This causes the investor to put too little weight on the public signal at t = 2.
This extension of the model helps us to understand managerial actions. For example, a firm can undertake new issues or repurchases as a response to mispricing. Since firm management presumably has private information about the firm value, this action—the new issue or repurchase—serves as an indicator to investors of firm value. For example, a firm may announce a new equity issue to take advantage of overvaluation. In this model, the firm is more likely to be overvalued when investors have received a positive private signal.
Firms do indeed tend to issue equity more when they are overvalued (Loughran & Ritter, 1995; Dong, Hirshleifer, & Teoh, 2012) and repurchase when they are undervalued (Ikenberry, Lakonishok, & Vermaelen, 1995). Such public signals are undertaken in opposition to the mispricing, in the sense that overpricing triggers a bad news event (issuance) and underpricing a good news event (repurchase).
Owing to overconfidence, there will be return continuation after such a selective event. A new issue follows overpricing at date 1 and triggers a partial downward correction at date 2. But the correction is too small because the overconfident investors are stubbornly optimistic about their favorable signal. So, the return is often negative after the public event. Similarly, after a repurchase (good news event), returns are often high.
The model explains why there is return continuation after corporate events. It also explains why this does not happen for all such events. Some events are not selective, and for these events, there will be no continuation. This reasoning also reveals that it is too simple to call the return predictability based on corporate events underreaction. It is true that there is price underreaction to the event. But this is a consequence of investor overreaction to the private signal. So, a valid understanding recognizes that overconfidence can lead to both under- and overreactions to different kinds of information.
This setting, however, still does not explain how to reconcile long-term return reversal with short-term price momentum (Jegadeesh & Titman, 1993). For this, we need to consider the dynamics of overconfidence.
Dynamically Shifting Confidence
In revising their beliefs about their own abilities, such as the ability to accurately value securities, investors incorporate feedback in a biased way. Self-attribution bias is the tendency of people to treat successes as reflecting their own skills, and failures as reflecting bad luck—the “heads I win, tails it’s chance” fallacy (Langer & Roth, 1975). Owing to bias in self-attribution, an overconfident investor can remain overconfident even in the face of disappointment. To capture this, following Daniel, Hirshleifer, and Subrahmanyam (1998), we now allow for an unlimited number of public signals arriving at times 2, 3, 4, and so on. Suppose that when a public signal arrives that is consistent with the investor’s overconfident beliefs, the signal causes the investor to substantially upwardly revise his estimate of the precision of his private signal; but, when an inconsistent public signal arrives, he only minimally revises downward his estimate of his signal precision. (There are different possible ways to define the idea of a public signal being consistent with the investor’s beliefs, but we won’t get into these details.)
This causes a very interesting and systematic pattern in how investor beliefs and prices evolve after the original private signal. Let’s focus on the case of good news, which causes price to jump at t = 1. We will see that on average, over time, the price continues to rise for a while, and then the average gradually declines. In other words, there is on average a gradual pattern of continuing overreaction followed by correction. The impulse response function after the good news is hump-shaped. Of course, in a similar way, this function is U-shaped after a bad news signal.
To see why, assume that favorable private news was received at t = 1, and consider the first public signal at t = 2. If the public signal is good news relative to the price at t = 1, price goes up. This jump gets an extra kick because the investor concludes that his original favorable signal was more accurate than he had realized, so he has some extra upward updating of his beliefs (away from the prior belief) based on the old signal, too. On the downside, if the public signal is bad news relative to the price at date 1, price falls. But, this fall also get an extra kick, because the investor concludes that his original favorable signal was less accurate than he had realized. That causes the price to drop even more.
But the extra kick on the upside and on the downside is not symmetric because of bias in self-attribution. The extra kick on the upside is larger than on the downside, so on average, at t = 2, price rises. In other words, there is, on average, continuing overreaction to the original favorable private signal. This explains the upward sloping side of the impulse-response function, which we call the overreaction phase.
Such increasing optimism can’t go on forever because, eventually, beliefs would become so optimistic that any new public signal would be almost sure to be a disappointment. In other words, bad public news (relative to the investor’s beliefs and market price) arrives more often than good public news. Even an investor with self-attribution bias does not become infinitely overconfident. Eventually, as more and more public signals accumulate, even the overconfident investor is forced to update beliefs about the security downward, so expectations decline toward true fundamental value on average. This downward-sloping part of the impulse-response function is called the correction phase. Similar reasoning explains the U-shaped impulse response function after bad news.
This pattern implies that there will be return momentum at short lags and return reversal at long lags, consistent with the evidence. To see why, consider the case of a good news private signal, so that the impulse-response function is hump-shaped. Since this is upward sloping in the overreaction phase, during this phase there are, on average, positive returns that are followed by further positive returns. Similarly, since the curve slopes downward slope in the correction phase, during this period, there are on average negative returns that tend to be followed by further negative returns. So, there is return momentum. (Similar reasoning applies if we look at the U-shape after a bad news private signal.)
In contrast, consider now returns that are separated by a long lag. A positive return during the overreaction phase—the left side of the hump—tends to be followed by a negative return in the correction phase. So, there is reversal at long lags. Similarly, after a bad-news private signal, negative returns in the downward arm of the U-shape tend to be followed by positive returns in the upward arm of the U-shape.
It turns out that overconfidence and its dynamic counterpart, bias in self-attribution, reconcile momentum in returns at short lags yet reversal at long lags. Before financial theorists had developed explicit models of mispricing dynamics, this was viewed as very puzzling. How could it be that investors are systematically underreacting (so that returns tend to continue) yet also overreacting (so that returns tend to reverse)? More careful modeling has clarified that momentum and reversal are compatible, which implies a deeper understanding of what momentum means. Continuation of returns does not imply that there is solely underreaction. Instead, momentum can result from a pattern of continuing overreaction and correction.
In this setting, it also turns out that when public signals such as earnings surprise arrive repeatedly, the signals can be positive predictors of future returns. This is consistent with the post-earnings announcement drift anomaly (Bernard & Thomas, 1989, 1990).
What if overconfident investors are risk averse, so that they do not trade so aggressively as to completely dominate price-setting? In such a setting, rational investors who are also risk averse would act as arbitrageurs, pushing prices toward fundamental values.
Daniel, Hirshleifer, and Subrahmanyam (2001) explore such a setting as an extension of the static-overconfidence model discussed earlier. Rational as well as overconfident investors are all risk averse. There are also many securities, and payoffs come both from common factor realizations, common influences on the payoffs of all securities, as well as residual payoff components, components of security payoffs not explained by common factors. Overconfident investors think their signals about these payoff sources are more accurate than they really are. Risk aversion limits how aggressively investors trade, so prices reflect a weighted average between the beliefs of the rational and irrational investors.
In this setting, scaling market value or price by a fundamental measure can improve return predictability because it can help disentangle two reasons why a firm can have high price: fundamental reasons and mispricing. This may explain why the value effect is stronger than the size effect.
Overconfidence, Arbitrage, and Predictability
In the model, we suggest reasons why mispricing is most likely to persist in factors and is likely to remain large for only a small fraction of the security-specific payoff components. This is consistent with the finding that the mispricing associated with stock characteristics such as return momentum or book-to-market is almost always associated with return co-movement. In other words, we usually identify that entire factors are mispriced, rather than finding just security-specific mispricing. However, a few stocks (perhaps Tesla?) could have severe stock-specific mispricing. Of course, in reality, some stocks and other assets are illiquid, which greatly increases the scope for asset-specific mispricing.
The model also implies excessive disagreement between overconfident investors and the rational arbitrageurs. This causes an excessively large volume of trade. Overconfidence can explain the puzzle of the high trading volumes discussed earlier.
Overconfidence can also help explain mispricing and return predictability of bonds. In a foreign exchange context (Burnside et al., 2011), this can explain a prominent anomaly, the forward premium puzzle. This is the finding that high-interest-rate-currencies, which arguably should be expected to depreciate at a rate that offsets the interest rate, do not do so. If overconfident investors overreact to their information about future inflation, this will tend to cause greater overshooting in long-term instead of short term bonds, which causes severe overshooting in the forward rate. In effect, short-term bonds act as fundamental benchmarks for long-term bonds.
The spot exchange rate partakes of the same mispricing, though not by as much as the forward rate. The mispricing identified by the forward premium (e.g., relatively heavy overestimation of inflation for a country, resulting in a high forward interest rate and low forward value of its currency) predicts future correction of the mispricing, so that the spot price later appreciates. This overconfidence theory also helps explain the profitability of well-known carry trade strategies.
We have argued that overconfidence provides a simple and unified perspective on investor behavior and asset pricing. It has an extremely strong backing from psychological evidence and powerful implications for financial markets. It helps explain known anomalies and offers rich implications for further empirical testing.
Overconfidence also promises to help integrate other conceptual elements of behavioral finance theory. For example, the Miller (1977) model discussed earlier was originally framed in terms of investor disagreement rather than overconfidence, and a continuing literature focuses on disagreement in financial markets. But why should investors disagree so stubbornly? Overconfidence explains why. Some psychological foundation is important both for ensuring validity of inferences and for suggesting additional empirical implications.
Limited investor attention has been proposed as the key to understanding various empirical patterns in trading and prices. Even where limited attention is central to an anomaly, overconfidence is usually a key contributing factor. This can make an investor be less careful in paying attention to other information and less concerned that the information that the investor is neglecting might be important. This explains why investors who neglect important information nevertheless trade aggressively enough to produce prices that do not reflect all available information.
To sum up, overconfidence is a foundational element of behavioral finance.
About the Authors
Dr. Kent Daniel currently serves as the William Von Mueffling Professor of Business in the Division of the Columbia Business School at Columbia University. He also serves as a Research Associate at the National Bureau of Economic Research. Between 2004 and 2010, Kent was with the Quantitative Investment Strategies group at Goldman Sachs Asset Management. In 2005, he became a managing director and head of the QIS equity research effort and became a co-chief investment officer in 2009. Dr. Daniel’s award-winning academic research focuses primarily on behavioral finance and asset financing. His professional service includes appointments as an associate editor for the Journal of Finance, a director of the American Finance Association, and a director of the Western Finance Association.
Dr. David Hirshleifer works at the University of California at Irvine as Merage Chair and Distinguished Professor of Finance and Economics in the Merage School of Business. Dr. Hirshleifer is a Fellow and former president of the American Finance Association, and he has previously held leadership roles such as director of the Western Finance Association and associate editor of Behavioral and Brain Sciences. He is a Research Associate at the National Bureau of Economic Research and a Senior Fellow in the Asian Bureau of Finance and Economic Research. His research interests include social economics and finance, risk management, corporate finance, and psychology and markets.
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