While most researchers agree on the existence of intermediate-term momentum and long-term reversals in stock returns, their source has been the subject of controversy.
Traditional asset pricing models seem to fail to explain the intermediate-term momentum phenomena. For instance, Jegadeesh and Titman (1993) show that changes in market beta
cannot be the source of the intermediate-term momentum and Fama and French (1996) show that the Fama-French three factor model cannot explain the intermediate-term price momentum. Also, the long-term reversals described in the previous subsection persist even after controlling for the Fama-French three-factor risk (Lee and Swaminathan, 2000, and Jegadeesh and Titman, 2001).
Jegadeesh and Titman (1993) initially conjectured that intermediate-term momentum might be driven by investor underreaction to firm-specific information. Since then, many theories to explain intermediate-term momentum and long-term reversals in stock returns based on behavioral models have been suggested. See Barberis, Shleifer, and Vishny (BSV, 1998), Daniel, Hirshleifer, and Subrahmanyam (DHS, 1998), Hong and Stein (HS, 1999) and Barberis and Shleifer (2003). BSV and DHS attribute momentum to investor cognitive biases while HS argue that momentum is due to slow diffusion of firm-specific information to the public. Finally, BS attribute momentum profits to investors’ style investing behavior (details in next subsection).
Some explanations for momentum are consistent with the efficient markets hypothesis.
There are two classes of such explanations. One argues that momentum strategies
systematically buy high-risk stocks and sell low-risk stocks. (See Conrad and Kaul, 1998) The other suggests that momentum strategies tend to buy stocks when the expected
returns of the stocks is high and sell stocks when the expected returns of the stocks is low.
(See Berk, Green, and Naik, 1999, and Chordia and Shivakumar, 2002) Conrad and Kaul (1998) argue that stocks with high realized returns will be those that have high expected
returns, suggesting that the momentum strategy’s profitability is a result of cross-sectional variability in expected returns. However, Grundy and Martin (2001) show that the profitability cannot be explained as a reward for bearing risk as measured by the three factors of the Fama-French (1996) model, nor by cross-sectional variability in stocks’
average returns. Jegadeesh and Titman (2001) argue that reversals in the post-holding period reject the claim of Conrad and Kaul that momentum profits are generated by dispersion in unconditional expected returns. Furthermore, Jegadeesh and Titman argue that the results in Conrad and Kaul are driven by estimation errors in the estimation of expected return variance.
It is plausible that intermediate-term momentum profits are due to time-varying risk and hence, due to systematic changes in expected returns. Chordia and Shivakumar (2002) show that the expected returns of momentum portfolios can be predicted by four
macroeconomic variables and argue that the macroeconomic variables might be related to risk factors that are not yet identified. However, Part 2 of this dissertation shows that that a spurious relation between persistent macroeconomic variables and predicted returns from the macroeconomic variables falsely appears to explain the momentum.
Behavioral Models for the Intermediate-Term Momentum and Long-Term Reversals Barberis, Shleifer, and Vishny (BSV, 1998), Daniel, Hirshleifer, and Subrahmanyam (DHS, 1998), and Hong and Stein (HS, 1999) present theoretical models that attempt to explain the coexistence of intermediate-term momentum and long-term reversals in stock returns. In sum, under BSV and HS, momentum occurs because traders underreact when
new information arrives and long-term reversals occur because they overcorrect previous mispricing. In DHS, momentum occurs because traders overreact to prior information and the subsequent correction of this overreaction results in long-term reversals.
Barberis, Shleifer and Vishny (BSV, 1998)
BSV explain intermediate-term price momentum and long-term price reversal using a parsimonious model of investor sentiment. Their behavioral model is based on two psychological constructs: conservatism and the representativeness heuristic.
Conservatism states that individuals are slow to change their beliefs in the face of new evidence. Individuals subject to conservatism might disregard the full information content of an earnings announcement, perhaps because they believe that it contains a large temporary component, and still cling, at least partially, to their prior estimates of earnings. As a consequence, they might underreact to new information when evaluating stocks.
The second relevant phenomenon is the representativeness heuristic documented by Tversky and Kahneman (1974): “A person who follows this heuristic evaluates the probability of an uncertain event according to the degree to which it is (i) similar in its essential properties to the parent population, and (ii) reflects the salient features of the process by which is generated”.21 When a stock experiences a series of good (poor)
performance in the previous period caused by investors’ conservatism, thus underreaction, investors falsely conclude that the past history is representative of future returns. As a
21 Tversky and Kahneman (1974), p. 33.
Formation Period (Month -11 to month 0)
Momentum Strategy Holding Period (Month 1 to month 12)
Post-Holding Period (Month 13 to month 60) Underreaction Correction of previous
underreaction Overreaction Correction of previous overreaction Conservatism heuristic
bias - Representativeness
heuristic bias -
Figure 3.1 Summary of BSV’s Model
consequence, investors using the representative heuristic might overreact to the history of high (low) returns that is unlikely to repeat itself in evaluating stocks. In summary, they regard the intermediate-term momentum as results of underreaction and the long-term reversals as results of overreaction of the investors.
The empirical findings of intermediate-term momentum and long-term reversals can be explained by BSV in the Figure 3.1, where the holding period starts at month 1.
Daniel, Hirshleifer, and Subrahmanyam (DHS, 1998)
DHS suggest a model that is based on investors’ overconfidence and variations in confidence arising from biased self-attribution. If an investor overestimates his ability to judge information, or to identify the significance of existing data that others neglect, he will underestimate his forecast errors. If he is more overconfident about signals or assessments with which he has greater personal involvement, he will tend to be overconfident about the information he has generated but not about public signals.
Therefore, stock prices overreact to private information signals and underreact to public signals. They show that this overreaction-correction pattern is consistent with long-run negative autocorrelation in stock returns.
According to attribution theory (Bem, 1965), individuals too strongly attribute events that confirm the validity of their judgment to their own high ability, and events that conflict with their judgment to external noise or sabotage. According to the attribution theory, if an investor receives confirming public information, his confidence rises, but conflicting information causes his confidence to fall only modestly, if at all. Therefore, even if an individual begins with unbiased beliefs about his ability, new public signals on average are viewed as confirming the validity of his private signal. This suggests that public information can trigger further overreaction to a preceding private signal. They show that such continuing overreaction causes momentum in security prices, but that such
momentum is eventually reversed as further public information gradually draws the price back toward fundamentals. Thus, biased self-attribution implies that intermediate-term momentum and long-term reversals would be observed. In sum, the authors think of intermediate-term momentum as result of overreaction, and long-term reversals as result of corrections of previous mispricings. Again the empirical findings of intermediate-term momentum and long-term reversals as explained by DHS can be illustrated in Figure 3.2, where the holding period starts at month 1.
Formation Period
(Month -11 to month 0) Momentum Strategy Holding Period
(Month 1 to month 12) Post-Holding Period (Month 13 to month 60)
- Overreaction Correction of previous
overreaction - Overconfidence reinforced
by self-attribution bias -
Figure 3.2 Summary of DHS’s Model
Hong and Stein (HS, 1999)
Alternatively, HS (1999) develop a model that focuses on the interaction between heterogeneous representative agents rather than the psychology of the agents. In other words, less of the action in their model comes from particular cognitive biases, and more of it comes from the way these traders interact with one another. Their model employs two types of investors: newswatchers and momentum traders. The newswatchers rely exclusively on their private information; momentum traders rely exclusively on the information in past price changes. The additional assumption that private information diffuses only gradually through the marketplace leads to an initial underreaction to news.
The underreaction and subsequent positive serial correlation in returns attracts the attention of the momentum traders whose trading activity results in an eventual
overreaction to news. Prices revert to their fundamental levels in the long run. In Hong and Stein (1999), initial momentum comes from underreaction by the news watchers.
Later momentum is the result of overreaction by the momentum traders, and the long-term reversal comes from prices reverting to their fundamental values. In their model, HS restrict momentum traders to have simple strategies, that is, momentum traders at time t base their trades only on the price change over limited prior intervals, so they do not know whether prices of stocks are still undervalued or have already overshot their long-run equilibrium values. Therefore, momentum traders sometimes gain from their trades, but sometimes lose. The empirical findings for intermediate-term momentum and long-term reversals can be explained by HS in Figure 3.3, where the holding period starts at month 1.
Formation Period (Month -11 to month 0)
Momentum Strategy Holding Period (Month 1 to month 12)
Post-Holding Period (Month 13 to month 60) Underreaction Correction of previous
underreaction Overreaction Correction of previous overreaction Slow diffusion of
information - Momentum traders -
Figure 3.3 Summary of HS’s Model
II.C. George and Hwang (2004) and Fama-MacBeth Style Cross-Sectional Regression
II.C.1. 52-week high strategy
George and Hwang (2004, hereafter GH) find that the nearness of the current price to the 52-week high price as measured by the ratio of the current price to the 52-week high explains a large portion of the profits from the JT momentum strategy. GH define the 52-week high strategy as follows