Do unobservable factors explain the disposition effect in emerging stock markets?

Abstract

In a previous paper, we utilized panel data methods to explore both cross-sectional variations and time series effects within the post-event period for losers' stocks. Some of these effects are not observable, but ignoring them lays the estimation open to bias from concealed heterogeneity amongst firms and periods (Hsiao, 2004). In this article we re-examine our methodology to test whether past losers outperform past winners. Using daily data from the Egyptian stock market on a sample of 20 companies which experienced dramatic 1-day price change over the period 2005 to 2008, a two way Fixed Effects (FE) model reveals strong evidence of price reversal with period FE. Results support the disposition effect by selling winners short and buying losers. Firm size is negatively correlated with post-event Abnormal Returns (ARs) consistent with the argument that small firms have a greater tendency to price-reverse. However, temporary, unobservable time-specific phenomena common to all companies, together with permanent, unobservable company-specific factors are more important in explaining price reversals. We also find that, unobservable company-specific factors account for a much larger percentage of post-event variations in stock prices. These company effects are sufficiently large to suggest a profitable trading strategy.

Notes

¹ These firm-specific effects may possibly be proxy unobservable quality for any given size of a company; this will be explored in a future paper.

²They found that there was little evidence of price reversal (a positive coefficient on event day returns) and that, insofar as it existed, it could be explained by the bid–ask bounce and market liquidity effects.

³ For a −10% trigger, the average day 1 rebound was 1.8%, and by day 2 the cumulative rebound was approximately 2.2%.

⁴ They found that when size was controlled for the previously negative coefficient on event day, returns for days 1–3 disappeared suggesting that the apparent reversal was actually a small firm effect.

⁵ They used Generalized Autoregressive Conditional Heteroscedasticity (GARCH) model to estimate the ARs as they argue that Capital Asset Pricing Model (CAPM) βs are not constant over time.

⁶ The Capital Market Authority (the regulator) imposed a symmetric price limit on fluctuations of individual stock prices which should be within the range of ±5% daily and ±20% weekly. On 21 July 2002, EGX commenced a new price ceiling system, whereby the daily price limits were widened to 20% for the most active stocks, limits which encompassed 101 stocks at the end of April 2008.

⁷ The EGX30 index (formerly known as CASE30–Cairo and Alexandria Stock Exchange), a free-floated market capitalization weighted index, was introduced on 2 February 2003 and retroactively computed as of 1 January 1998 with a base value of 1000 points. EGX30 is weighted by each company's adjusted market capitalization (listed shares adjusted by free float).

⁸ Other measures were also tried, namely the market index (CAPM with β of 1) and the time average return for the company, but qualitatively the results remained the same. This is also in line with the literature.

⁹ We also used 5 days estimation window, and got similar results regardless of the autocorrelation.

¹⁰ We used GARCH model to estimate the ARs and got similar results.

¹¹ As mentioned above, we use a 10-day time unit so that, e.g. t = 2 means 20 trading days (4 working weeks) from the event.

¹² Consistently with Egypt's new era of economic reform, starting in 1997, a number of Initial Public Offerings (IPOs) of the state-owned companies were executed through the EGXs in the privatization programme. Formerly, public companies are companies that were privatized via an IPO.

¹³ Turnover ratio (TR) equals trading volume/number of shares outstanding.

¹⁴ This is known as the LSDV regression (Hsiao, 2004, p. 15).

¹⁵ An FE model allows that the effects may be correlated with the regressors (covariates) whilst an RE model does not, as REs are part of the error term and hence any correlation with the covariates implies an endogeneity problem.

¹⁶ This is evident in the Hausman (1978) test for random versus fixed firm effects which has as the null E(α _i |x_it ) = 0, where x_it is the vector of covariates for firm i at time t. If the null is rejected, the fixed firm effects model is appropriate.

¹⁷ It is assumed in the FE models that the terms α _i , λ _t are fixed numbers. For the RE models (not estimated for reasons spelled out below) the terms α _i , λ _t , u_it have the following properties (Hsiao, 2004): 

¹⁸ and is i.i.d. N(0, σ²).

¹⁹ We qualify this statement later. It is important to note that whilst it is conceivable that bid–ask bounce or transactions costs might eliminate ARs to the average winners and losers, we shall show that this is highly unlikely to be the case for those stocks with (absolutely) large unobservable company effects.

²⁰ The correlation matrix (not presented but available on request from the authors) reports that there is no potential multicollinearity.

²¹ A similar result was found by CP (1994), Larson and Madura (2003) and Ma et al. (2005).

²² Removing private made virtually no difference to the remaining coefficients. Finally, as we shall see, as a dummy variable private has to be dropped for other reasons from the panel data regressions.

²³ Another reason (as is well known) is that dummy variables present estimation problems for panel data analysis, e.g. producing perfect collinearity in FE models.

²⁴ The simplest exposition of how this kind of bias arises is to be found in Hsiao (2004, Section 1.2).

²⁵ Not presented but available from authors upon request.

²⁶ Both one-way models are well-specified and the null of redundant FEs are decisively rejected (both F-statistics have p ≪ 1%). In particular, the covariates of both models are highly significant models and the signs of ln mcap and ln trvol are negative and positive, respectively. Adjusted R ² are 21 and 16%, respectively, for the company and period FE models.

²⁷ We finally note that in the combined model the adjusted R ² at 12 and 14% for winners and losers, respectively, is higher than either of the one-way models (not reported here, but available from the authors).

²⁸ As mentioned above, the company FE may possibly be interpreted as unobservable measures of company quality. A future paper will explore this issue.