Techniques for Data Analysis

Home/Techniques for Data Analysis
Techniques for Data Analysis 2016-11-10T15:00:31+00:00

Project Description

1. Introduction

Market efficiency refers to the ability of the market to reflect all the information that are of interest to the stock in the stock price. A highly efficient market not only prices in the information continuously but also accurately (Barnes, 2009). However market efficiency has been a controversial topic in financial economies with several contradicting theories and empirical evidences that have been produced by the researchers. The efficient market hypothesis, which is considered the most important theory in this area of study asserts that an efficient market includes all the possibly available information including the privately-held information in the stock prices (Dothan, 2008). The semi-strong form of the efficient market hypothesis asserts that the price of a security adjusts instantaneously to any new information that is released to the market. Due to this reason no investor may be able to earn significant positive returns acting on the basis of new information that is released (Jarrow and Larsson, 2011). This brief research attempts to study the impact of stock-specific information on the movement of share prices of the company and consequently upon the returns generated by the stock. This research uses market model as the theoretical basis and event study as the empirical method for accomplishing this objective.

2. Research Aim and Hypothesis

The primary aim of this research is to analyse the impact of firm-specific information on the stock returns of the firm. From an analytical perspective, this research attempts to ascertain if stock-specific information could have significant impact on the returns provided by the company’s shares over short-term.

 

This research uses Virgin Media Inc as the company to be studied and the event of acquisition of Virgin Media by British Sky Broadcasting as the case study (Reuters, 2010). Four events related to this acquisition are identified and the stock returns surrounding these events are analysed. Following is the hypothesis that are identified and tested in this empirical research for each one of the four events separately.

 

H1: The information related to acquisition of Virgin Media by British Sky Broadcasting has significant impact on the stock returns of Virgin Media’s shares.

3. Methodology

3.1. Market Model

The previous chapter has identified the important aim and the hypothesis to be tested for this research. In order to analyse the impact of specific information on the performance of the stocks of Virgin Media, this research uses empirical research. It is necessary for the empirical research to have a theory as its foundation and an appropriate method for testing the hypothesis (Eckbo, 2008). The theory that is used in this case is the market model. What explains the returns generated by the stocks of a company has remained an important question for several years in academic research as well as in investment practice. Capital Asset Pricing Model (CAPM) is widely considered the origin of the market model. CAPM (Capital Asset Pricing Model) asserts that the expected return of a stock contains a risk free rate of return and a part that represents the undiversified risk of the security (Elton et al., 2009). This is calculated as the product of the beta of the security and the return from the market portfolio. CAPM has been a popular model for explaining the returns of the security. It asserts that he investors are compensated in the form of returns not for bearing overall risks but only the non-diversifiable risks of the security. Due to this reason beta, which measures the sensitivity of the returns of the stock to the market returns, is taken as the slope of the linear equation. However there are some important limitations of CAPM model. The biggest limitation of CAPM has been that the model has failed to hold its group during empirical tests (Kürschner, 2008). It is notorious for its empirical invalidity. Researchers have attempted to identify alternative theories that can also withstand the empirical tests. Market model, APT and Fama-French three factor models are some of the most popular alternatives that have been identified (MacKinlay, 1995).

 

Market model decomposes the stock returns into two parts (Li and Pincus, 2008). The first part consists of a term that represents the part of return that can be attributed to the association of the security with the market index. Beta is used as the measure of the sensitivity of stock returns to returns of market index. The second part of the model contains the return that is attributable to the stock-specific or company-specific risks. Thus according to market model there are two kinds of information that may be considered pertinent to a stock’s price movement. They are the information related to the market as a whole and the information that are directly related only to that particular company (Keller, 2008). The market model can be shown through the following expression.

 

Rj = aj + ßj Rm + ej

Where

Rj is the return from stock j

ßj is the slope which is the sensitivity of change in stock returns to change in Rm

Rm is the returns from market index

aj is the constant term

ej is the error term

 

In this research the above given model is used as the basis for modelling the stock returns of Virgin Media.  In this research market model is used to classify the stock-specific information from the other information. This helps this research is to ascertain if the stock-specific information has a significant influence on the overall stock returns.

 

3.2. Research Method

Empirical research requires a suitable research method to carry out the analysis of data and to draw observations on the basis of the data. As stated in the previous section this research uses market model as the basis for studying the stock returns. This research uses event study analysis as the research method for calculating abnormal returns during and after the event. Event study is a popular method of research often used when specific events such as dividend announcements, stock splits, mergers and acquisitions etc., are studied closely by the researchers (Campbell et al., 2010). The event study method involves the use of an initial estimation period to model the relationship between the returns of the market and the returns of the stock. The parameters estimated are used as the basis for calculating the expected returns of the stock in the event period and the post-event period. The difference between the actual observed returns and the expected returns is taken as the movement that is due to that specific information that is released into the market.  Thus event study involves the definition of there periods – estimation period, event period and post-event period.

 

In this case four events related to acquisition are considered. They are as follows:

 

Event Date Event
Event 1 4-Jun-10 British Sky Broadcasting buys virgin media channel for £160 million (Announcement).
Event 2 13-Jul-10 British Sky Broadcasting completes virgin media TV deal.
Event 3 20-Jul-10 British Sky Broadcasting deal for Virgin media goes to OFT.
Event 4 5-Oct-10 The OFT has approved the acquisition of Virgin media’ TV channel business by British Sky Broadcasting.

 

For all the four events, only one estimation period is used. In this case the estimation period spans for 2 years preceding the first event. Therefore the estimation period is from 4 June 2008 to 3 June 2010. The event period and the post-event period have to be identified separately for the four events. The event period is taken as the three days beginning with the actual day of event. Two additional days includes because it is possible that the impact of the news event may have lasted for a few more trading sessions. The post-event period begins on the fourth day of the event and last till the end of the 3 months following the event day. Following table shows the event period and the post-event period for each event in the sample.

Event Event Date Event Period Post-Event Period
Event 1 4-Jun-10 4-Jun-10 to 6-Jun-10 7-Jun-10 to 4-Sep-10
Event 2 13-Jul-10 13-Jul-10 to 15-Jul-10 16-Jul-10 to 13-Oct-10
Event 3 20-Jul-10 20-Jul-10 to 22-Jul-10 23-Jul-10 to 20-Oct-10
Event 4 5-Oct-10 5-Oct-10 to 7-Oct-10 8-Oct-10 to 5-Jan-10

 

Using the estimation period from 4 June 2008 to 3 June 2010, the intercept and slope are estimated employing the following market model.

Rj = aj + ßj Rm + ej

For the event period and the post-event period, a and ß from the above model are applied and the expected returns are calculated as follows.

 

Abnormal return is calculated as the difference between expected return and the observed returns during the event period and the post-event period.

ARj = Rj – E(Rj)

In order to calculated the cumulative abnormal returns, the total return generated by an investment of $1 made the day before the event day till the end of post-event period is calculated. This is known as the cumulative abnormal return (CAR). Average Abnormal Return (AAR) is calculated as the simple average of the AR for the entire period from event till the end of post-event period.

 

The hypothesis that is tested in this case is that the mean of abnormal returns generated by the stock during the event period and post-event period is significantly different from zero. If it is found to be valid then it is concluded that the stock-specific information has a significant impact on the stock returns. If this hypothesis fails then the conclusion would be that the events considered in this research have not had a significant impact on the stock returns.

 

3.3. Data

This research requires stock price information related to Virgin Media as well as a suitable market index. In this case NASDAQ 100 index is taken as the market index. Virgin Media is traded on the NASDAQ stock exchange. All the data are taken on a daily periodicity to ensure sufficient observations to perform the calculations. One of the important concerns while obtaining data of Virgin Media was that the returns had to be adjusted for dividends. Therefore the adjusted closing price, which takes into account the dividend adjustments, is used as the basis for calculation of the returns.

 

The daily returns are calculated using the following formula.

Rt = ln(St) – ln(St-1)

This presents the continuously compounded rate of return for the stock price, which is considered appropriate for the empirical studies.

 

The next section of the report presents the observations from the analyses performed on the data sample.

 

4. Findings and Analysis

4.1. Estimation of Market Model

The first step in event study method used in this research is to estimate the market model and to estimate the values of a and ß of the stock. The model used is already shown in the previous section. Using the daily returns data pertaining to 4 June 2008 till 3 June 2010, the market model is estimated using Ordinary Least Squares (OLS) method of linear regression. The important results of the estimation are shown below.

 

R 0.78587
R Square 0.61759
Adjusted R Square 0.61683
Standard Error 0.03183
Total Number Of Cases 504
Ri = 0.0004 + 1.8338 * Rm
ANOVA
d.f. SS MS F p-level
Regression 1. 0.82141 0.82141 810.71826 0.0000
Residual 502. 0.50862 0.00101
Total 503. 1.33003
Coefficients Standard Error LCL UCL t Stat p-level
Intercept 0.0003 0.0014 -0.0024 0.0031 0.2612 0.7940
Rm 1.8338 0.0644 1.7072 1.9603 28.4731 0.0000

 

From the above table it can be seen that the coefficient of Rm, which is beta is 1.8338. The beta value of more than 1 indicates that the stock can be considered significantly high risk in nature. The t-statistic of the coefficient is 28.4731, which falls outside the area covered between the lower limit and upper limit at 95% confidence level as shown in the table. On the basis of this observation, the null hypothesis that beta is equal to zero can be rejected at 5% significance. The intercept, which is the alpha, has a value of 0.0003. Since the p-value of alpha is 0.7940 and it is more than 0.05, the null hypothesis that alpha is equal to zero is not rejected at 5% significance level. In other words, the alpha is insignificant while beta is significantly positive.

 

The overall validity of the model can be tested using F-test. The F-statistic is 810.7182 and the associated p-value is 0.000. Since the p-value is less than 0.05, the null hypothesis that all the coefficients are equal to zero can be rejected at 5% significance level. The R-squared value shown in the table indicates the extent to which the market return is capable of explaining the changes in the stock returns. In this case the R-squared value of 0.6175 indicates that Rm is able to explain about 61.75% of the changes in Rj. This can be considered fairly high. Thus the model is found to be able to significantly model the stock returns. The estimate model is shown below.

 

Ri = 0.0004 + 1.8338 * Rm

 

Since the data used in this estimation is time series, there is a risk of heteroskedasticity and autocorrelation (Hamilton, 1994). These two have to be checked before finalising the estimation model. The autocorrelation can be tested using the Durbin-Watson statistic.

 

The Durbin Watson statistic is estimated using the following formula.

 

The value of d is calculated as 2.0372. Since this value is not significantly different from 2, it is concluded that there is no significant autocorrelation in the residuals. The heteroskedasticity can be observed from the following chart showing the residuals and the Rm in scatter plot.

 

The above chart clearly shows that there is no pattern that can be observed from the distribution of residuals about the Rm. Therefore it can be concluded that the residuals do not have different variances. In other words, they are homoskedastic in nature.

 

On the basis of the above tests, it is concluded that the model estimated using the linear regression analysis is suitable for estimation of the expected returns during the event period and the post event period. The next section is concerned with the calculation and analysis of abnormal returns.

Oops! We could not locate your form.

 

4.2. Abnormal Returns Analysis

The most important part of this research is the analysis of the abnormal returns. Using the parameters, a = 0.0004 and ß = 1.8338, the expected returns are calculated for each day of the event period and the post-event period for each one of the four events considered. These are deducted from the observed returns and the abnormal returns are arrived at. Following chart shows the daily abnormal returns during event period and post event period for the four events.

 

From the above chart it is noted that the daily returns have varied between 6% to -4%. Event 1 is the most volatile among the four as it has the most number of spikes on either side of the mean. Event 4 appears to be the least volatile among the four. However not many observations can be made from the above chart. Therefore it is helpful to study the cumulative abnormal returns. The CAR are calculated as the compounded returns generated using the abnormal returns calculated. In other words, CAR represents the overall abnormal return made from the period by investing $100 at the beginning of the period. Following chart shows the overall abnormal return from the entire period starting from the announcement of acquisition in the first event till the end of the post-event period following the fourth event.

 

The above chart shows that after the announcement of the acquisition event, the abnormal returns continued to increase due to which the CAR also increased continuously. However after the first three months, the CAR started to decline and it declined continuously till it reached the beginning of March 2011. During the entire period following the announcement of acquisition information, the stock made an overall CAR of 11.83%. In other words, after the announcement of the acquisition news, the stock earned 11.83% over and above its expected returns in the seven months. This clearly shows that the stock has seen some significant abnormal return due to the news. However it is noted that the CAR was as high as 42.78% in just 3 months following the announcement, which is the first event. In the subsequent period, this abnormal return disappeared and was cut down to just about 1.3rd.

 

Following chart shows the CAR calculated separately for the four events under consideration.

 

 

The first three days in the above chart are of event period and the remaining are the post-event period days. It is seen from the above chart that events 1, 2 and 3 have generated positive CAR by the end of post-event period while event 4 has generated a huge negative CAR of -14.78% by the end of post-event period. Quite interestingly, both event 2 and event 3 saw rise in CAR till about 33-35 days following the event day and then on started to see declines. The trend in these two CARs is very similar. On the other hand for event 1, the CAR continued to increase through out the entire 3 months period. The CAR of the event 4 continued to decline through the 3 months period.

 

Better analysis can be performed by studying the AAR and CAR for event period and post-event period separately. Following chart shows the CAR for these two periods separately for the four events.

 

From the above chart it is seen that event 1 generated the maximum positive CAR during both event period as well as post-event period. During the event period it was 6.48% over the 3-days while the post-event period generated 27.57%. Event 2 saw a negative CAR of -2.78% during the event period but managed to post 9.33% in the post-event period. The event 3 generated an insignificant 0.19% in the event period and 5.26% in post-event period. Event 4 generated negative CAR in both event period and the post-event period. The CAR during post-event period shows a clear declining trend across the four events. Since the four events are connected to the same acquisition decision, it is noted that as soon as the first announcement is made the market reacted by generated significantly large positive CAR. However subsequent announcement could generate only lesser and lesser interest in the market. When the final approval for acquisition was obtained from the regulators the market reacted negatively. During the final event period the stock underperformed the expected returns. This means that by the third event the market had already discounted the information almost completely and the fourth event did not add any positive information to the news. Therefore those who had bought the stock earlier sold and booked their profits. Following chart shows the CAR for both event and post-event periods together.

 

It is evident that event 1 generated the maximum CAR, followed by event 2 and then by event 3. Event 4 generated negative CAR of -14.67%.

 

4.3. Hypotheses Testing

The ARs calculated in the previous section are used as the basis for testing the hypothesis that the stock-specific news caused a significant impact on the stock returns. In this case this hypothesis is tested separately and jointly for the four events considered. T-test is used for the purpose. T-test is used to check whether the mean of the AR for each event is equal to zero. If its is equal to zero then it would mean that the event did not generate any significant AR and so did not have a significant impact on the stock returns. On the other hand if the null hypothesis is rejected it would mean that the mean of AR is significantly different from zero and so the event had significant impact on the stock returns of Virgin Media during the period. This is a two-tailed test.

 

Following is the hypothesis that is tested.

H0: µAR = 0

Ha: µAR ≠ 0

 

The t-statistic is calculated as follows

 

where

is equal to zero

µ is the mean

s is standard deviation

n is the number of observations

 

Following table shows the calculation of t-statistic and the critical t-values for each event and the combined event.

 

Mean SD n df t-stat Critical Value p-value
Event 1 0.00493 0.02075 65 64 -1.9167 1.9977 0.0597
Event 2 0.00107 0.01839 66 65 -0.4728 1.9971 0.6379
Event 3 0.00097 0.01844 66 65 -0.4290 1.9971 0.6694
Event 4 -0.00233 0.01510 65 64 1.2417 1.9977 0.2189
Event 0.00091 0.01807 150 149 -0.6152 1.9760 0.5393

 

From the above table it can be observed that for event 1 the t-statistic is -1.9167 and the critical value is 1.9977. As the t-statistic is less than the critical value it can be stated that the null hypothesis is not rejected. The p-value associated with t-statistic is 0.0597, which is more than 0.05. Therefore the null hypothesis is not rejected. For event 2 the t-statistic is -0.4728 and the associated p-value is 0.6379. Since the p-value is more than 0.05, it is concluded that the null is not rejected at 5%. Similarly for event 3 and 4 it is seen that the p-values are 0.6694 and 0.2189 respectively, both of which are more than 0.05 and so they lead to conclusions that the null hypothesis is not rejected in each case. In all the four events it is seen that the null hypotheses are rejected. This means that the mean of AR is equal to zero in each one of the four cases. In other words, the events did not have any impact on the stock returns.

 

The final test shown in the table above takes into account the AR for the entire 7-month period following the first announcement made on 4 June 2010. It is seen that the t-statistic is -0.6152 and the p-value of t statistic is 0.5393. This leads to a conclusion that the null hypothesis is rejected and that the event of acquisition as a whole did not have any significant impact on the stock returns of Virgin Media. All the five t-tests performed have produced uniform results and so there are no discrepancies to be explained in this case.

5. Conclusion

The primary objective of this research is to critically examine the impact of stock specific information on the returns produced by the stocks. This research uses the sample of Virgin Media and the event of acquisition of the company by British Sky Broadcasting. This study uses event study analysis method and identifies that three out of the four events related to acquisition have generated positive returns. Specifically when the announcement about the acquisition is first made the 3 month period that followed the announcement saw the highest CAR. Then the subsequent announcement related to the event saw less and less CAR and the final event in the series saw negative CAR. The clearly declining trend over time indicates that the market may have discounted the news completely sometime during the period and so the final announcement did not evoke any positive response from the investors. Quite interestingly when the AR values are subject to statistic tests of significance, it is noted that none of them are significant. In other words, none of the events had a significant impact on the stock returns. This leads to a conclusion that the stock-specific information considered in this case did not have a significant impact on the stock returns of the firm. This raises some important questions about the validity of market efficiency, as it may be reasonable to expect that in efficient markets the fresh news of such important nature as acquisition of the company could have significant impact on the prices and the performance of the stock.

 

 

 

References

 

Barnes, P. (2009) Stock market efficiency, insider dealing and market abuse, Gower Publishing, Ltd.

 

Campbell, C. J., Cowan, A. R. and Salotti, V. (2010) ‘Multi-country event-study methods’, Journal of Banking & Finance, 34(12), 3078-3090.

 

Dothan, M. (2008) ‘Efficiency and Arbitrage in Financial Markets’, International Research Journal of Finance and Economics, 19, 102-106.

 

Eckbo, B. E. (2008) Handbook of corporate finance: empirical corporate finance, Elsevier.

 

Elton, E. J., Grubber, M. J., Brown, S. J. and Goetzmann, W. N. (2009) Modern Portfolio Theory and Investment Analysis, John Wiley and Sons.

 

Hamilton, J. D. (1994) Time series analysis, Princeton University Press.

 

Jarrow, R. A. and Larsson, M. (2011) ‘The Meaning of Market Efficiency’, Johnson School Research Paper Series No. 07-2011.

 

Keller, G. (2008) Statistics for Management and Economics, Cengage Learning.

 

Kürschner, M. (2008) Limitations of the Capital Asset Pricing Model (CAPM): Criticism and New Developments, GRIN Verlag.

 

Li, H. and Pincus, M. (2008) ‘Market Reaction to Events Surrounding the Sarbanes-Oxley Act of 2002 and Earnings Management’, The Journal of Law & Economics, 51.

 

MacKinlay, A. C. (1995) ‘Multifactor models do not explain deviations from the CAPM’, Journal of Financial Economics, 38(1), 3-28.

 

Reuters (2010) Key Developments: British Sky Broadcasting Group PLC (BSY.L), http://www.reuters.com/finance/stocks/keyDevelopments?symbol=BSY.L&pn=2, Date accessed 28/4/2011.

Project Details