Excerpt

## Table of contents

1 Introduction

2 Literature Review

2.1 Signaling hypothesis

2.2 Trading-range hypothesis

2.3 Other hypothesis

3 Data and Methodology

3.1 Data

3.2 Calculating Abnormal Returns

3.3 Standardized Residual Test

4 Empirical Results

5 Problems and Extensions of the Standard Market Model

5.1 Assumptions of the Market Model

5.2 GARCH-adjusted Market Model

5.3 Time-varying beta in the Market Model

6 Conclusion

## 1 Introduction

There are many theories in literature which try to examine possible reasons for a stock split. While a stock split seems to be just a cosmetic corporate event, it is often claimed that the motivation to carry out a stock split is to signal future profitability or to bring the share price to a preferred trading-range. Additionally there are many papers published, where the impact of a stock split on liquidity and institutional ownership is examined. Some results of these studies are briefly discussed in the Literature Review.

Most researchers calculate their abnormal returns with the market model by using the most common index in their economy. In this paper, I check whether sectorindices fit the data better than the CDAX does. In some cases, the sector-indices describe the stock returns better.

Another topic of event studies that researchers of the finance area often deal with is whether the assumptions of the market model established by Fama, Fisher, Jensen and Roll (1969) do hold for daily stock returns. I will discuss some of the weaknesses when applied to financial time series and I present two models which can improve the efficiency of the model.

This paper is organized as follows. In section 2 some hypothesis of the reason for stock splits and their empirical results are discussed. Section 3 describes the data and methodology used in this paper. Then the empirical results are presented in section 4. The problems of the assumptions implied by the market model and some extensions of the market model in order to handle these problems are discussed in section 5. The conclusions are in section 6.

## 2 Literature Review

### 2.1 Signaling hypothesis

According to the signaling hypothesis, a manager decides to carry out a stock split to signal a prosperous perspective of the firm’s performance. While Ikenberry et al. (1996) found significant post-split excess returns, Huang et al. (2002) found that the earnings profitability of the firm was negatively related to the stock split. These two results are very contradictory, since having lower earnings should normally not result in higher returns. Most of the papers on stock splits analyze the US stock market. Wulff (1999) mentions that for the German stock market signaling can not be the main reason for a stock split, since legal restrictions hinder the management to use a stock split for signaling.

### 2.2 Trading range hypothesis

The trading range hypothesis suggests that there is an „optimal“ trading range, which is preferred by investors. In a survey of Baker and Gallagher (1980) 94% of the CFO’s answered that bringing the share price to an optimal trading range is the main reason for a stock split. Also Dewing (1953) and Baker, Phillips and Powell (1995) mention that the trading range is the most important driver to carry out a stock split. They even report a trading range in prices which is preferred by investors.

### 2.3 Other hypothesis

Another hypothesis which explains the motivation for a stock split is the liquidity improvement theory. Examining the trading volume as a proxy for liquidity, one can empirically test whether improving the liquidity of a share is an important reason for a stock split. While Easley et. al (2001) cannot confirm the hypothesis for the US stock market - he even observed decreasing trading volume or no change in trading volume - in other countries improving liquidity seems to explain the reason for a stock split quite well. Jing (2003) found for the Hong Kong stock market, and Mishra for the Indian stock market a positive effect on trading volume after the stock split. Also Wulff (1999) detected for the German stock market a positive influence of the stock split on liquidity.

The theory, that managers carry out a stock split to give small investors an incentive to invest in the company, cannot be confirmed by Maloney and Mulherin (1992) and Powell and Baker (1993). For managers it might be advantageous to have less institutional investors, since they tend to have much higher control on the firm. Empircally, it was observed that institutional ownership was even higher after the stock split.

Wulff (1999) found that for the German stock market the neglected firm hypothesis seems to explain the motivation for a stock split best. According to the neglected firm hypothesis, managers carry out a stock split to improve the recognition on the capital market. This may be true especially for lesser known firms, where the share is traded at a discount, because of lack of information about the firm on the capital markets.

## 3 Data and Methodology

### 3.1 Data

For the empirical study I used stock prices of 13 german companies, from large-sized to medium-sized which had a stock split between 1st of January 2006 and 30th of June 2008.

I used exactly the same stocks in the same time period as Zhi (2008) did in her paper, nevertheless there were many deviations in the stock prices, probably due to the fact, that we had stock prices of different stock exchanges. Or maybe this was caused by errors in her data, since I used the more reliable data from Datastream.

As indices I took the CDAX and the sectorDAX indices. The sector indices are sub- indices of the Prime All-Share Index, which contains all stocks listed on the Prime Standard. The sector indices split the Prime All-share into 18 different sectors to make a comparison between two companies of the same sector more precisely.

### 3.2 Calculating Abnormal Returns

To calculate the expected returns I used the market model of Fama, Fisher, Jensen and Roll (1969), where is the return of the stock , the return on the stock market index, in the case of my study either CDAX or one of the sector-indices. and are assumed to be constants which are estimated by Ordinary Least Squares. The estimation period, in which the parameters of the OLS are estimated, is from =-221 to =-21, where =0 is the day of the stock split execution. is the error term of the model.

The abnormal returns (AR) are then calculated by subtracting the actual returns from the returns predicted by the market model from =-20 to =+20.

Summing up the single abnormal returns we can get an overview of how the stock price changed in total during the event period and calculate the cumulated abnormal return (CAR), where to is any time period around the stock split.

To get the cumulated average abnormal return (CAAR), we just divide the CAR’s by the number of firms in each period.

### 3.3 Standardized Residual Test

To detect whether the abnormal returns are significantly different from zero, I use a similar test methodology as Patell (1979), where the abnormal returns are standardized by the standard deviation of the estimation period. Also suggested by Brown and Warner (1985) and Boehmer et al. (1991), this test statistic has two advantages over more commonly used event study tests. First, for the event-period the abnormal returns will have a higher standard deviation than in the estimation period due to the fact, that this is an out-of-sample prediction. The standardized residual test takes this into account. Secondly, when we standardize the abnormal returns during the event period, the sum of the abnormal returns allow for heteroskedasticity in the event period, and single abnormal returns with large variances don’t influence the test in a too large extent. The test is constructed as following. First we standardize the abnormal return by the standard deviation estimated in the estimation period,

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The standard deviation in the estimation perdiod is

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**[...]**

- Quote paper
- David Bosch (Author), 2009, A stock split event study using sector-indices vs. CDAX and some extensions of the standard market model, Munich, GRIN Verlag, https://www.grin.com/document/176261

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