Niveles de lectura

Many previous studies investigated the weekend effect by regressing returns on four daily dummy variables (e.g. French, 1980; Jaffe and Westerfield, 1985; Smirlock and Starks, 1986). However, the use of this methodology has two drawbacks and could give misleading inferences (Kiymaz and Berument, 2001, 2003). First, errors in the model may be autocorrelated and second, error variance may be heteroskedastic. French, Schwert and Stambaugh (1987) and Nelson (1991) also emphasize these characteristics of autocorrelation and conditional heteroskedasticity. To address the first issue, we include lagged values of the returns in equation (i). To avoid the second limitation, we allow the variance of errors to be time-dependent. This conditional heteroskedasticity will capture any time variation in stock returns variance (Kiymaz and Berument, 2001, 2003). As Connolly (1989) mentions, there is much evidence that stock returns have time varying variance and many previous studies of market anomalies failed to take that into consideration.

We therefore model our returns using the following stochastic model: 𝑅_𝑡= 𝑎₀+ 𝑎₁𝐷_1𝑡+ 𝑎₂𝐷_2𝑡+ 𝑎₃𝐷_3𝑡+ 𝑎₄𝐷_4𝑡+ ∑𝑛 𝑏_𝑖

𝑖=1 𝑅𝑡−𝑖+ 𝜀𝑡 (i)

16_{As of December 2012, the 17% holdings of traded stocks by the institutional investors are distributed}

among 19 industries and 236 listed companies (out of 283). The percentages of each sectoral investment by these investors are given in Appendix B (see page 335). The figures in Appendix B shows that institutional investors generally have greater holdings in firms with higher market capitalizations; which mean in DSE, institutions prefer larger companies for investments. For example, they hold an average of around 25% traded stocks of banks and the banks have the highest percentage (i.e. 26.72%) of market capitalizations in the market. Similarly, institutional investors hold around 20% traded stocks of Pharmaceuticals, Cements and Fuel and Power industries. The market capitalizations of these three sectors are also higher in the DSE than others industries. Altogether, data reported in Appendix B indicates that institutional/foreign investors mostly target large cap stocks in DSE.

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Where 𝑅_𝑡 is the daily return, 𝐷₁, 𝐷₂, 𝐷₃, and 𝐷₄ are dummy variables for Sunday, Monday, Wednesday and Thursday at time t, and n is the lag order. 𝜀_𝑡 is the error term that follows the Generalised Error Distribution (GED) with mean zero and with a time changing variance, ℎ_𝑡 [𝜀_𝑡~𝐺𝐸𝐷(0, ℎ_𝑡)]. The dummy variable for Tuesday is excluded from the equation to avoid the dummy variable trap. Tuesday is selected as it is middle of the week and we are examining trading pattern around the weekend.

We next apply the generalized autoregressive conditional heteroskedasticity (GARCH) model to investigate the weekend effect in terms of volatility. The GARCH model, developed by Bollerslev (1986), has been a major tool to capture the three empirical features most often observed in stock returns data: leptokurtosis, skewness and volatility-clustering. Here the assumption is that conditional variance, ℎ𝑡 is a function of three terms – a constant (𝜔), shocks or news-impact from the previous period (𝜀𝑡−12 ) measured as the lag of the squared residual from the mean equation, and last period forecast variance (ℎ𝑡−12 ). A simple time varying variance model using a GARCH (1,1) process is:

ℎ_𝑡 = 𝜔 + 𝛼𝜀_𝑡−12 _{+ 𝛽ℎ} 𝑡−1

2 _(ii)

Engle (2001) states, “GARCH (1, 1) is the simplest and most robust of the family of volatility models” and it is also the most widely applied. We therefore use the GARCH (1, 1) model to investigate the weekend effect on volatility. However, many previous papers have included exogenous variables in the variance equation to check their significance for the returns volatility (e.g. Choudhry, 2000; Balaban, 2001; Berument and Kiymaz, 2001 and 2003; Baker et al., 2008). Following those studies, some exogenous variables are allowed in the GARCH (1, 1) model, which could possibly affect the variance. To be specific, this study allows the constant term of the conditional variance equation to change for each day of the week to check the weekend effect on volatility. Thus the specific GARCH (1,1) model becomes:

ℎ𝑡 = 𝜔 + 𝛼𝜀𝑡−12 + 𝛽ℎ𝑡−12 + ∑𝑛𝑚=1𝐷𝑚𝜋𝑚 (iii) Where D represents the exogenous variables, particularly each weekday and 𝜋 is the corresponding weight for D. Therefore, if 𝜋 is found statistically significant for any weekday then we can assert that the weekend effect exists in the variance equation. We determine the structural shift in the daily data using the Bai and Perron (1998) method and exclude those date from the series to increase the persistence of GARCH (1,1) model.

The study uses a GARCH process under the assumption that the conditional distribution of the error term, 𝜀_𝑡, follows a Generalized Error Distribution (GED hereafter) as suggested in Nelson

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(1991). The GED includes the normal as a special case, along with many other distributions, some more fat tailed than the normal and some thin tailed such as the uniform distribution (Nelson, 1991). Therefore to capture the distributional characteristics of equity returns we apply GED in this study to model the GARCH process.

For the GED errors, the contribution to the log-likelihood function is:

lt= - 1₂ log ( Γ(1_𝛾)3 Γ(3_γ)(γ₂)2) - 1 2log ht - ( 𝛤(3_𝛾)(𝑅𝑡−𝑋𝑡́ )𝜃 2 ℎ𝑡𝛤(_𝛾1) ) 𝛾/2

(iv)

where 𝑅_𝑡 is the endogenous variable, X́_t is a vector of exogenous variables and 𝛾 is a tail- thickness parameter. The GED is a normal distribution if 𝛾 = 2, fat-tailed if 𝛾 < 2 and thin- tailed if 𝛾 > 2. The Marquardt technique is used to maximize the log likelihood function of the GED.

To investigate the degree to which the weekend effect is related to firm size, we follow the methodology of Keim (1985) and Brusa et al. (2000). We initially divide all the listed firms on the DSE into ten deciles. We then create three sub-portfolios from them based on ranking firms’ market values. The firms in the first and second deciles are the “smallest group”, the third to seventh deciles are the “medium sized group” and the last two deciles are the “largest group”. We apply the time varying conditional variance model to judge the significance of returns and volatility of each value weighted sub-portfolio on Sunday. The returns equation is as follows: 𝑅_𝑠𝑡= 𝛼₀+ 𝛼₁𝜓_1𝑡+ 𝛼₂𝜓_2𝑡+ 𝛼₃𝜓_3𝑡+ 𝛼₄𝑅_𝑠𝑡−1+ 𝜀_𝑡 (v) Where 𝑅𝑠𝑡 is the Sunday return, 𝜓1, 𝜓2 and 𝜓3 are the value weighted returns of the largest, mid- sized and smallest firms at time t, and 𝑅_𝑠𝑡−1 is the one period lag value of Sunday returns to minimize the autocorrelation problem. 𝜀_𝑡 is the error term that follows the Generalised Error Distribution (GED) with mean zero and with a time changing variance, ℎ_𝑡 [𝜀_𝑡~𝐺𝐸𝐷(0, ℎ_𝑡)]. Based on the statistical significance of each sub-portfolio, i.e. 𝜓, we should be able to assert which category of investors and their trading activities influence the Sunday returns.

Next, we use a modified variance equation to examine how the volatility of each sub-portfolio affects the variance of Sunday returns:

ℎ_𝑡 = 𝜔 + 𝛼𝜀_𝑡−12 _{+ 𝛽ℎ} 𝑡−1 2 _{+ ∑ 𝜉} 𝑚 𝑝 𝑚=1 𝜋𝑚 (vi)

Where 𝜉 is the exogenous variable, i.e. each sub-portfolio, and 𝜋 is the corresponding coefficient. Therefore, if 𝜋 is found to be statistically significant for any portfolio then we can state that the

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weekend effect on volatility is the result of trading patterns of a certain group of investors; since investors have different preferences for risk holding.

Further, we investigate how the dividend preference of equity investors influences the weekend effect. If individuals’ trading activity determines the pattern of returns and variance on Sunday then it should be reflected in lower dividend paying firms. Therefore we further break down all the listed firms on the DSE into two portfolios (i.e. high and low dividend yield portfolios) based on the daily value weighted dividend yield from January 2000 to December 2012. We use median dividend yield to define the categories, where high dividend yield firms have larger annual median dividend yields than low dividend yield firms. The use of the value weighted dividend yield helps us to control the size effect and make the estimation unbiased17_{. Finally, we run the time varying}

conditional variance model as stated in equations (vii) and (viii) for each portfolio to see which type of stock activity influences the returns and variance on Sunday:

𝑅_𝑠𝑡= 𝛼₀+ 𝛼₁𝛿_1𝑡+ 𝛼₂𝛿_2𝑡+ 𝛼₃𝑅_𝑠𝑡−1+ 𝜀_𝑡 (vii) ℎ_𝑡 = 𝜔 + 𝛼𝜀_𝑡−12 _{+ 𝛽ℎ} 𝑡−1 2 _{+ ∑ ∅} 𝑚 𝑞 𝑚=1 𝜃𝑚 (viii)

Where 𝑅𝑠𝑡 is the Sunday returns and 𝛿1𝑡, 𝛿2𝑡, and ∅𝑚 are the portfolios (low and high) based on dividend yields. To minimize the problem of autocorrelation between returns we use the one period lag of Sunday returns, 𝑅𝑠𝑡−1. We assume that the error term 𝜀𝑡 follows the Generalised Error Distribution (GED) with mean zero and a time changing variance ℎ_𝑡 [𝜀_𝑡~𝐺𝐸𝐷(0, ℎ_𝑡)]. Based on the statistical significance of each coefficient for the sub-portfolios, i.e. 𝛼₁ and 𝛼₂ in the returns equation and 𝜃𝑚 in the variance equation, we should be able to compare the influence of institutions’ and individuals’ trading patterns on Sunday.