Prueba de Hipótesis

The following sections explain the dependent variables used to carry out the empirical analysis.

i. Indicator Variable for Rights Issues, Open Offers, and Private Placement The study compares rights issues with open offers on one hand, and rights issues and private placement on the other. Thus, for the first part the dependent variable is 1 for rights issues and 0 for open offers. In the second part, the dependent variable is 1 for rights issues and 0 for private placement.

ii. Long term abnormal returns

Long-term returns estimation presents important statistical issues that need to be considered in order to avoid biased estimates. Unlike short-run abnormal returns with limited stock price volatility over short estimation window, long run abnormal returns can be affected by the estimation method used and produces biased estimates and misspecified test statistics. Kothari and Warner (1997) and Barber and Lyon (1997) both analyse extensively the properties of long-run abnormal returns. Both studies find significant statistical problems

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with long-run abnormal returns depending on the method of estimation. Cumulative abnormal returns, buy-and-hold abnormal returns and Fama and French (1993) three-factor models have been employed to estimate long-run abnormal returns in the empirical literature. Ritter (1991), for example, note that the use of CAR and BHAR depends on the specific question to be

answered. Thus, it is more likely that CAR and BHAR will produce different

estimates.

Moreover, Barber and Lyon (1997) assert that empirical power and specification of test statistics are affected by the method of estimation and the approach for developing benchmark. Long-run abnormal returns benchmarks used in the literature include reference portfolio (market index or size decile portfolios), control firms approach and the three-factor model of Fama and French (1993). Fama (1998) states that long-term return anomalies are sensitive to methodology. Further, Lyon et al. (1999) recognise the problems associated with analysis of long-run abnormal returns. Bias estimates and test statistics misspecification stem from new listing bias, rebalancing bias and skewness bias (Barber and Lyon, 1997). They argue that new listing bias occurs because new firms are allowed to the market index that is benchmark for the sample firms‟ long-run abnormal returns. Again, compound returns of market index are computed with implicit periodic rebalancing whereas returns of sample firms do not involve rebalancing. Finally, long-run abnormal returns are positively skewed.

Control firm approach to calculating abnormal returns is able to offset the sources of bias and misspecification depending on whether CAR or BHAR is

the estimation method. Without the reference portfolio benchmark such as the market index, the bias from new listing, rebalancing and skewness are eliminated. Control firm and sample firm are identical in several respects and experience comparable effects when measured against the market index. CAR

is also associated with measurement bias. Barber and Lyon (1997) contend that

BHAR using the control firm approach produces unbiased and well-specified

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skewness and measurement. The current study follows this approach that has been applied in a number of studies in the literature.30

a. Cumulative Abnormal Returns (CAR)

To estimate cumulative abnormal returns for each cross section firm, the expected returns, using market model that regresses stock returns on market return, is computed. Market returns are defined as the total return on the FTSE ALL SHARE index. The relationship of the market model is thus stated as follows: (1) (2) Where: (3)

The parameters in equation (1) are the stock returns for each firm, ; the market return defined as , and is the idiosyncratic risk associated with the stock returns. and are the alpha and beta coefficients of the regression model to be estimated. Both stock returns and market returns are the daily returns associated with the stock and market index respectively. The estimation window of 250 days prior to the announcement date is used.

The cumulative abnormal returns (CAR) are estimated as the sum of the

abnormal returns (AR) within a specified event window. This is stated as follows:

30 _{Loughran and Ritter (1995), Spiess and Affleck-Graves (1995), Veld and Veld-Merkoulova} (2004), Hertzel et al (2002) and Capstaff and Fletcher (2011) all use the control firm approach in calculating long-run abnormal returns.

it mt i i it R R ) ( _it it it R E R AR mt i i it R R E( ) it R mt R _it i i

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Following Barber and Lyon (1997), the t-test is defined as the ratio of the cumulative abnormal returns to the standard deviation of the CAR of the firms divided by the root of number of firms.

b. Buy-and-Hold Abnormal Returns (BHAR)

Buy and hold abnormal returns measure the difference between compounded actual return and the compounded predicted return. The compounding feature associated with better simulates the effect of an

event on an investor‟s portfolio. Again, provides a good measure of the long run investor experience under the long run event studies (Loughran and Ritter, 1995). and both complement each other due to their peculiar limitations. Whereas fails to capture the compounding effects, can also yield incorrect statistically significant abnormal performance due to short-term return fluctuations. Therefore, the problems of extreme skewness occasioned by are curtailed when double-checked with . Similarly, the BHAR is computed after estimating the expected or predicted returns from the regression of stock returns and market returns. Buy and hold return is the daily compounded return on the equity security for each firm over a specified time period in days.

The buy and hold return (BHR) of each firm is given as .

In same fashion, the expected or predicted buy and hold return is calculated as

T t it it AR CAR 1 N CAR CAR test t iT T CART ) ( ) (BHAR BHAR BHAR CAR BHAR CAR BHAR BHAR CAR 1 ] 1 [ 1 T t it iT R BHR 1 ] ) ( 1 [ ) ( 1 T t it iT E R BHR E

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Finally, BHAR, the difference between the buy and hold returns and the expected buy and hold returns , is computed using the equation below.

Test of statistical significance of the mean returns is computed using the standard t-test as follows: