Market overreaction and underreaction: tests of the directional and magnitude effects

Abstract

We investigate whether the US equity market exhibits underreaction or overreaction. More specifically, we study the directional and magnitude effects associated with abnormal market reaction. The directional effect is the phenomenon that an extreme price movement will be followed by a price movement in the opposite (overreaction hypothesis) or same (underreaction hypothesis) direction. The magnitude effect is the phenomenon that the more extreme the initial price movement is, the greater the subsequent adjustment will be. In this article, we study both effects by considering extreme, medium and mild winner–loser portfolios. The directional effect is assessed by the profits generated by these portfolios, and the magnitude effect is assessed by comparing the difference in profits between these portfolios. Three tests are developed and applied to test the magnitude effect. Empirically we find support for both of these effects for extreme, medium and mild winner–loser portfolios.

Keywords:

• overreaction hypothesis
• underreaction hypothesis
• momentum strategy
• contrarian strategy
• directional effect
• magnitude effect
• winner portfolio
• loser portfolio

JEL Classification:

• G10
• G14

Notes

1 See, for example, Barberis et al. (1998), Daniel et al. (1998), Hong and Stein (1999), Gervais and Odean (2001), Brav and Heaton (2002) and Friesen and Weller (2006).

2 Their approach differs from that of Barberis et al. (1998), although they draw some similar conclusions.

3 Since the S&P500 stocks are big (in terms of market cap), liquid and relatively high-priced, our results do not suffer from potential microstructure and related issues raised by Bali et al. (2005) and Bali and Cakici (2008), who emphasize the effect of interaction between size, liquidity and idiosyncratic volatility on future stock returns.

4 For more information about this issue, see, for example, Lo and MacKinlay (1988) and Chan et al. (2000).

5 We follow the literature for the construction of winner and loser portfolios. This construction may result in the problem of survival bias.

6 We note that in our model setup, we do not consider trading costs or other issues such as different market conditions. Lesmond et al. (2004) find that the profit from a momentum strategy becomes insignificant after taking into account the high trading costs. McLean (2010) provides reasons why transaction costs may not eat up long-term contrarian profits. In contrast, Cooper et al. (2004) report that the profits are in fact confined to periods following up markets, whereas Asem and Tian (2010) find that the profits are higher when the markets continue in the same state than when they transition to a different state.

7 See Hollander and Wolfe (1973) regarding the consistency and efficiency of the test.

8 The proof is as follows. Letting X be a random variable with cumulative distribution function F(T), we have P(F(T) < c) = P(T < F ⁻¹(c)) = FF ⁻¹(c) = c for any c in [0,1]. Thus, F(T) is a random variable with uniform distribution [0,1]. Moreover, because the distribution of any -value of any random variable can be expressed as a cumulative function of the random variable such that , this allows us to conclude from the aforementioned derivation that the -value has a [0,1] uniform distribution. It is obvious that if has a [0,l] uniform distribution, then –2ln(Y) has a chi-square distribution with 2 degrees of freedom.

9 The tables with the estimated values for the tests are available upon request.

10 We will illustrate the data problem for constructing a sample of 4 years for the second subperiod here. To construct the first transformed data used for testing, we use the first four years (2000–2003) as the formation period and the second four years (2004–2007) as the holding period to obtain the first transformed data. To get the second transformed data, we need to use the second four years as the formation period (2008–2011) and use data from 2012 to 2015 to form the second transformed data. However, because we only have data from 2000 to 2009, we could only obtain the first transformed data for testing the 4-year period. Thus, it is not possible to conduct the test for this period. Similarly, we could not obtain enough data to test for the 3- and 3.5-year periods.

11 Since the plots for the subperiods are similar to the plots in Figs. 1–3, to conserve space, we have not presented those figures here. However, the figures are available upon request.