Long‐Term Market Overreaction or Biases in Computed Returns?

Abstract

We show that the returns to the typical long‐term contrarian strategy implemented in previous studies are upwardly biased because they are calculated by cumulating single‐period (monthly) returns over long intervals. The cumulation process not only cumulates “true” returns but also the upward bias in single‐period returns induced by measurement errors. We also show that the remaining “true” returns to loser or winner firms have no relation to overreaction. This study has important implications for event studies that use cumulative returns to assess the impact of information events.

Is the Mean Return of Hotel Real Estate Stocks Apt to Overreact to Past Performance?

“…Other competing explanations include "microstructure biases" hypothesis of Ball et al (1995), "upward bias in cumulating single-period returns" hypothesis of Conrad and Kaul (1993), "book-to-market equity effect" hypothesis proposed by Chan et al (1991), Lakonishok et al (1994) and Fama and French (1995), and "cash flow reversion" hypothesis of Yoshida (2008).…”

Removing biases in computed returns

“…13 Although both Blume and Stambaugh (1983) and Roll (1984) show that observed returns are upward biased, to date no studies have proposed a method for removing the bias that allows for frequent rebalancing. Conrad and Kaul (1993) suggest that studies examining long-term returns use annual (or longer) buy-and-hold returns. Canina et al (1998) agree with Conrad and Kaul (1993) and suggest that researchers construct long holdingperiod buy-and-hold portfolios when they are concerned with long-run performance.…”

“…Conrad and Kaul (1993) suggest that studies examining long-term returns use annual (or longer) buy-and-hold returns. Canina et al (1998) agree with Conrad and Kaul (1993) and suggest that researchers construct long holdingperiod buy-and-hold portfolios when they are concerned with long-run performance. 14 However, an annual holding period is not suitable for event studies, which typically examine returns in the days following an event.…”

“…1 Frequently re-balanced, equally-weighted indexes (or portfolios) are especially prone to the bias, which is known to be cumulative (Conrad and Kaul 1993). However, equal weighting is the method used in virtually all event studies and is the preferred method of forming an index when there are disproportionate market capitalization weights among representative stocks., 23 Also, since the bias is cumulative, it can potentially affect the relative rankings of stock performance, especially over longer periods of time.…”

“…See Roll (1983) for a comparison of rebalanced and buy-and-hold portfolio returns. 5 For example Blume and Stambaugh (1983) examine one-year investment horizons and Conrad and Kaul (1993) examine 3-year investment horizons. 6 Blume and Stambaugh (1983) and Bessembinder and Kalcheva (2007) note that while short horizon continuous-compounded rates of return contain no bias, they also possess certain properties that limit their use in many tests.…”