Academic journal article Quarterly Journal of Finance and Accounting

Evaluating Stock Price Behavior after Events: An Application of the Self-Exciting Threshold Autoregressive Model

Academic journal article Quarterly Journal of Finance and Accounting

Evaluating Stock Price Behavior after Events: An Application of the Self-Exciting Threshold Autoregressive Model

Article excerpt

Introduction

After events have occurred, stock returns show a decisive pattern of continuation in semi-annual and annual holding periods while there is evidence of reversal over three to five years. (1) Over a weekly horizon, Lehmann (1990) demonstrates contrarian profits, but subsequent studies attribute his profits to cross-autocorrelation in large and small stocks and bid-ask bounce [e.g., Lo and MacKinlay (1990); Conrad, Gultekin, and Kaul (1997)]. Conditioning on volume, Campbell, Grossman and Wang (1993) and Conrad, Hameed, and Niden (1994) demonstrate reversals following periods of high volume. Cooper (1999) shows reliable evidence of unconditional market overreaction up to a year following large positive and negative weekly returns, with low volume stocks exhibiting greater reversal. This weekly reversal is at odds with the daily horizon where results about reversal/continuation have been inconclusive. This research seeks to shed further light on the subject by reexamining events with a daily horizon using a different model--the self-exciting threshold autoregressive model.

With a daily event window, Atkins and Dyl (1990) and Bremer and Sweeney (1991) present evidence of overreaction, while Brown, Harlow, and Tinic (1988) show predictable variation. When portfolios are unconditionally formed based on large daily declines and/or gains (events), a correction for bid-asked bounce considerably weakens or reverses short-term (up to three or four days) overreaction [e.g., Cox and Peterson (1994); Park (1995); Pritamani and Singal (2001)]. In the longer term (three or four days beyond a negative event), there appears to be a general tendency toward continuation. Cox and Peterson (1994), Park (1995), Pritamani and Singal (2001), and Larson and Madura (2003) find some continuation from day four/five to day 20 after a negative event. By contrast, after a positive event, Park (1995) shows no systematic longer-term variation, Larson and Madura (2003) find a decline up to 20 days, and Pritamani and Singal (2001) show a gain.

The contrast between the post-event performances of daily versus weekly event horizons is puzzling, as large daily returns should coincide with large weekly returns because average daily returns are small. As a result, if overreaction is found in weekly returns, a similar result should be expected after large daily returns. Therefore, stock return behavior following large positive and negative returns warrants further investigation to see if these two streams of literature can be reconciled.

Prior studies have either used fixed thresholds to define events which can yield a sample biased toward high-volatility stocks or have employed a dispersion-based norm that should be free from such a bias. (2) In this study, the self-exciting threshold autoregressive (SETAR) time series model endogenously determines positive and negative event thresholds, thus identifying positive, negative, and non-event regions based on security return characteristics. The method optimally searches for return thresholds that best fit three AR(1) models, one for each region. This allows the detection of those thresholds where the post-event day return is best explained by the event day return in each state. The thresholds are allowed to vary asymmetrically for negative and positive events, as well as across securities and time.

The aggregate period (1/1/63-12/31/03) is divided into eight subperiods to account for changes in volatility, liquidity, and institutional trading. For each subperiod, the event thresholds are estimated using daily returns and several post-event timeframes up to 20 days after the event are analyzed. A within-sample analysis is conducted as well as an examination of a two-year subperiod immediately following each parameter estimation period (to eliminate the look-ahead bias inherent in many trading rules). The model used eliminates the impact of microstructure issues such as bid-ask bounce, non-synchronous trading, and volume related return autocorrelation shown by Chordia and Swaminathan (2000). …

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