UNIVERSITY OF AMSTERDAM AMSTERDAM BUSINESS SCHOOL BSc Economics and Business
Bachelor Specialisation Finance and Organisation
IS THERE EVIDENCE OF AN ISSUANCE EFFECT IN THE LSE?
Seasoned equity offerings as a predictor of short-term future returns.
Author: G. Chiarelli Student number: 11084847
Thesis supervisor: Dr. J. J. G. Lemmen Finish date: 06/2018
STATEMENT OF ORIGINALITY
This document is written by Student Giulia Chiarelli who declares to take full responsibility for the contents of this document.
I declare that the text and the work presented in this document are original and that no sources other than those mentioned in the text and its references have been used in creating it.
The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.
ABSTRACT
When companies announce a seasoned equity offering it is has been observed that often their share price is negatively affected. Nevertheless, the research on this so called issuance effect is still inconclusive and some papers find no proof of it. However, most research is conducted using samples of U.S. SEOs. Therefore, this paper will provide an out of sample observation by analysing a sample UK seasoned equity offerings. In particular, the short-term abnormal returns produced by SEOs are analysed. First, an event study is performed and an analysis of cumulative abnormal returns shows evidence of short-term underperformance following the SEO. Secondly, a regression analysis is also performed. However, none of the explanatory variables have a significant effect on abnormal returns.
Keywords: Asset Pricing, Stock Price, Issuance Effect, Firm Financing, Seasoned Equity Offerings, London Stock Exchange.
JEL Classification: G12, G14, G32.
TABLE OF CONTENTS
PREFACE AND ACKNOWLEDGEMENTS……….. 2
ABSTRACT……….. 3
TABLE OF CONTENTS……….. 4
LIST OF TABLES……….5
LIST OF FIGURES………6
CHAPTER 1 Introduction………..7
CHAPTER 2 Literature Review……….9
CHAPTER 3 Method………16
CHAPTER 4 Data……….…22
CHAPTER 5 Results……….23
CHAPTER 6 Conclusion………...27
REFERENCES………..29
APPENDIX………31
LIST OF TABLES
Table 2.1 Overview of relevant Studies 9
Table 4.1 Sample Description 20
Table 5.1 Overview of cumulative abnormal returns over different event periods. 24
Table 5.2 Average AR and average CAR for Repurchase and Non-Repurchase SEO’s 25
Table 5.3 Regression analysis for the whole sample. The dependent variable is the CAR(-1,1) 26
Table 5.4. Regression analysis for each quartile. 28
LIST OF FIGURES
Figure 2.1 Timeline 17
Figure 4.1 Distribution of SEO’s per year 22
Figure 5.1 Magnitude and direction of the average abnormal returns 24
Figure 5.2 Cumulative Abnormal Returns of Repurchase and non-Repurchase SEOs 24
CHAPTER 1 Introduction
In the current economic system a company facing an investment opportunity can raise capital in several ways. For instance, capital can be raised by issuing debt or by issuing equity. However, a company is able to issue debt only when its financial conditions are sound such that it can credibly commit to fully repay the loan. Alternatively, a manager can decide to issue equity. If a company issues equity for the first time it does so via an Initial Public Offering (IPO). Later on, it can raise further amounts of equity through a Seasoned Equity Offering (SEO) (Berk and DeMarzo, 2014). In particular, an SEO can be of two kinds: a sale of shares to existing shareholders is defined as a rights issue while a sale of shares to all investors at large is referred to as a cash issue. Also, new shares being sold in the market are referred to as primary shares while shares sold by existing shareholders are called secondary shares (Berk and DeMarzo, 2014). Logically, issuing equity also comes at a cost. In fact, a company is bound to make regular dividend payments to its shareholders however, the magnitude and timing of the dividends can vary. Considering the specific characteristics and consequences of different ways to raise capital past literature has argued that financing decisions can be interpreted as a signal of management’s private information about the company. More consistently, Bayless et al. (1996) point out that a manager is likely to be more informed about the situation of the company than the market and he might decide to issue equity, rather than debt, when he believes that the former is overvalued. Furthermore, in the Myers and Majluf’s (1984) adverse selection model, rational investors presume that on average managers approve stock offerings when, based on their superior information, they believe that the stock is overvalued. Therefore, rational investors will lower their assessment of the stock current value whenever a stock offering is announced resulting in a decrease in share price. Moreover, agency theory models developed by Jensen and Meckling (1976) predict that if managers hold a large percentage of company’s stock the conflicts of interest between managers and shareholders is decreased. In fact, managers seek to maximise their own utility while shareholders seek maximisation of the share value. Therefore, any increase in outstanding shares which decreases management percentage of shareholdings is predicted to have a negative effect on the stock price. Then, Masulis (1983) argues that if managers adjust financial leverage to maximise firm value, changes in management information regarding a firm’s expected cash flows is signalled to investors through change in leverage. Thus, rational investors infer that a decrease in leverage, caused by an equity offering possibly coupled with a decrease in outstanding debt, is a negative signal of firm value.
In past decades, scholars have investigated whether equity issuance is actually a predictor of poor future stock returns. In particular, Brav et al. (2000) find that actually the stock performance of issuing firms is not different from the performance of non-issuing firms of comparable size and book-to-market ratio. On the other hand, Daniel and Titman (2006) and Pontiff and Woodgate (2008) find that share issuance is actually a predictor of poor future returns in the U.S.. However, other studies such as Fama and French (2008) sorts analysis find that this anomaly is present in the U.S. only for very large stock issuances (20% to 26% of market capitalisation) while abnormal returns after less extreme issuances are
usually positive. One important remark about past literature is that it mostly uses samples of firms from the NASDAQ or NYSE. Few scholars such as McLean et al. (2009) perform an analysis using non-U.S. stocks. As pointed out by McLean et al. (2009) there is a need for an out-of-sample analysis to prove that the past findings are not simply the result of data mining.
Therefore, this paper will investigate to what extent seasoned equity offerings (SEOs) predict poor future performance using a sample of firms listed in the London Stock Exchange (LSE). Certainly, after the referendum of June 2016 when the British population voted for the UK leaving the European Union a great deal of attention has been devoted to the English stock market. Therefore, in this years of change and uncertainty this paper will contribute to achieve a greater understanding of the price effects and short-term future performance of a company’s shares after a seasoned equity issuance in the UK. More consistently, the research hypothesis is that an issuance effect is present in the companies listed in the LSE for all kind of issuance levels and the null hypothesis is that the effect of SEOs on abnormal returns is not significantly different from zero. The reasoning behind the formulation of the hypothesis follows the paper by McLean at al. (2009) who found a robust issuance effect in a sample of 41 non-U.S. countries during a period that ranges from the beginning of the 90s till 2006. Furthermore, the research will be structured as an event study. In particular, the Adjusted Market Model will be applied as explained by De Jong et al. (1992).
Next, Chapter 2 will consists of a Literature Review of relevant papers related to the topic of seasoned equity offerings and future stock returns. Then, Chapter 3 will illustrate the Research Method and Chapter 4 will describe the Data. Finally, Chapter 5 and 6 will report the Results and Conclusion respectively.
CHAPTER 2 Literature Review
This chapter will consist of a summary of the previous findings on the topic of SEOs and future stock performance will be given. First, an overview of the relevant studies is given in Table 1.1. Secondly, a detailed discussion of the results of previous studies is reported in Chapter 2.1. Then, Chapter 2.2 summarises the main arguments in support of information asymmetry as a possible cause for the issuance effect. Finally, Chapter 2.3 explores two alternative explanations and Chapter 2.4 consists of a brief conclusion and discussion.
Table 2.1 Overview of relevant studies.
Author(s)
(publication year) Region Time Period Method Result
Affleck-Graves, Spiess
(1995) U.S.
1975-1989
Compare abnormal returns with industry,
B/M ratio and size matched firms
Underperformance
Asquith, Mullins
(1986) U.S.
1963-1981 Mean model Underperformance
Bayless, Chaplinsky
(1996) U.S
1968-1990 OLS regression There are windows of
opportunity for SEOs
Billet, Xue (2007)
U.S. 1985-1996 Market Model
Share repurchases prior to issuance have a positive
effect on SEO-announcement day abnormal
reruns.
Booth, Chang
(2011) U.S.
1975-2002 OLS regression
Dividends payers face a smaller price drop after
Brav, Geczy, Gompers
(2000)
U.S. 1975-1992
Fama and French three factor model with
extra factor No underperformance Daniel, Titman (2006) U.S. 1968-2003 Fama-MacBeth analysis Underperformance Dierkens (1991) U.S. 1980-1983 Market Adjusted Model Information asymmetry related to drop in price after
SEOs Fama, French (2008) U.S. 1963-2005 Sorting No Underperformance for Issuance < 20% of Market Cap. Lerskualla wat (2011)
Thailand 1999-2006 Market Adjusted
Model Negative Market Reaction
Mahmood, Shahid, Usman, Xinping
(2010)
China 1998-2008 Market Adjusted
Model Underperformance
Masulis, Korwar
(1986)
U.S. 1963-1980 Comparison period
return Underperformance McLean, Pontiff, Watanabe (2009) Africa, Asia, Australia, Europe 1981-2006 Cross-sectional analysis Underperformance
Pontiff, Woodgate (2008) U.S 1932-1969 Fama-MacBeth analysis No Underperformance Prior to 1970 Teoh, Welch, Wong (1998) U.S. 1970-1989 Regression of abnormal returns on earnings accruals Negative Relation of Accruals and Price
2.1 Results in Previous Studies
As it can be inferred from Table 1.1 most of the existing literature on the issuance effect focuses on U.S. firms. Asquith and Mullins (1986) analyse the announcement day and issue day price effects of seasoned equity offerings. They use a sample of U.S. seasoned equity offerings between 1963 and 1981. More consistently, they point out four possible causes of the post-SEO negative price effect:
1. The demand curve for a firm’s shares is downward sloping so an increase in supply causes a permanent price reduction.
2. The change in corporate structure (e.g. debt-to-equity ratio) reduces tax advantages and makes debt less risky resulting in a transfer of wealth from shareholders to debt holders. Also since issuing debt results in a binding constraint it is seen by the market as a positive signal of management’s expectation of future cash flows. On the other hand, issuing equity can be seen as a negative signal. 3. Managers are better informed on the situation of the firm than the market. Therefore, it is logical to
assume that they will only choose to issue equity when the stock is overvalued. 4. Large transaction costs associated with equity issues.
They investigate each of these hypothesis by analysing abnormal returns. In the two years following the issue the sample of industrial firms underperforms the market by 6%. Furthermore, in the two-day announcement period they find that firms have an average of 3.0% abnormal return and a median of -28.0% dilution. Where, dilution is defined as the aggregate reduction in firm’s equity value as a percentage of the planned proceeds of the SEO. Also, it is shown that on average firms outperform the market prior to SEOs which is consistent with the hypothesis that managers only issue equity when shares are overvalued. Moreover, a significant negative relation between price and size of the issuance is found. On the other hand, changes in capital structure seem to have no significant effect on price reduction. The change in price is independent from the market which has positive returns both before and after the issuance. Finally, they find no conclusive evidence in support of the hypothesis that the demand curve for firm’s shares is downward sloping or that negative price reaction is caused by large transaction costs.
Similarly, Masulis and Korwar (1986) investigate the effects of SEO using a sample of common stock issuances of U.S. firms between 1963 and 1980. They point out that stock offerings have two major effects on a firm. First, they increase equity capital which results in a decrease of the firm’s leverage ratio. Second, they usually result in an increase of capital expenditures. Also, they conduct a separate analysis for public utilities and for industrial firms. This is motivated by the fact that public utility stock issuances are highly regulated suggesting greater market anticipation and smaller announcement day price reaction. Their, results are consistent with the prediction and the average announcement period return for industrial firms is -3.25% while for public utilities it is -0.68% which is quite smaller. In light of the findings by Masulis (1983) a possible explanation for the magnitude of these returns is consistent with a positive effect of contemporaneous announcement of capital expenditure increase that partially offsets the negative issuance effect. In fact, Masulis (1983) finds that when a common stock exchange is announced to retire debt, such that no increase in capital expenditure is to be expected, then the average announcement day return is -9.91%. Also equity issuances are easier to predict since they usually occur after a sustained increase in stock price or after the announcement of a major increase in capital expenditures so their announcement day return is biased towards zero. Furthermore, a greater negative effect in stock price is found when as a result of the issuance. management fraction of ownership in the firm decreases. More consistently, the portfolio of SEOs that do not involve management sales of stock has an average significant announcement period return of -2.22% compared to a return of -4.54% when combination offerings involve management sales. Furthermore, Masulis et al. (1986) runs a series of cross sectional regressions which show that the effect on stock price is proportional to the change in the fraction of company’s share owned by management which is consistent with Jensen and Meckling (1976).
Also, announcement period stock returns are positively related to changes in leverage and evidence is consistent with a positive effect of capital expenditure increase that offsets negative issuance effect leading to small announcement day negative returns. Subsequently, Affleck-Graves and Spiess (1995) analyse a sample of seasoned equity offerings between 1975 and 1989 initiated by companies listed on the NYSE and NASDAQ. In particular, they match issuing firms with similar non-issuing firms on the basis of industry, size and book-to-market ratio and then compare their performance. As a result, they find that issuing firms did have positive returns after equity issuances but these were significantly lower than the returns of matched similar firms. Furthermore, 59.6% of the firms in the sample underperformed their counterparts in the 3-year post issuance period while 61.7% of the firms in the sample underperformed their counterparts in the 5-year period.
Subsequently, Daniel and Titman (2006) investigate the relation between stock issuances and excess returns in the following 5 years by means of a Fama-MacBeth analysis. As well as previous studies, they use data on a sample of U.S. firms between 1968 and 2003 and they find that share
Woodgate (2008) perform a cross-sectional-analysis on share issuance and long-run stock returns using a sample U.S. pre-1970 share issuances. This way, the authors are able to perform an out-of-sample test of the explanatory power of share issuance. Interestingly enough, they find no underperformance in issuing firms before 1970. Then, McLean et al. (2009) performed a similar study using a sample of stocks from 41 non-U.S. countries between 1981 and 2006. The sample of SEOs included African, Asian, Australian and European firms. Their results differ from Pontiff and Woodgate (2008) as a robust issuance effect is found in their sample. However, as pointed out by Fama and French (2008) 60% of the firms listed on the NYSE count for only 2% of its total market capitalisation. Therefore, there is a need to control for the plausibly stronger effects of SEOs on this so called “microcaps”. For this reason they perform a study on abnormal returns using sorts. First, their sample of U.S. firms is divided by market capitalisation. Then, their sample of stock issuances is separated by relative size into quintiles. The results show that in their sample underperformance is limited to stock issuances of more than 20% of shares outstanding. On the other hand, controlling for B/M ratio lower issuances tend to have small positive effects on share price.
Furthermore, also Lerskuallawat (2011) performs an out-of-sample study using a sample of 126 common stock issuances between 1999 and 2006. His main findings are that also in Thailand there is a negative market reaction to SEOs. Similarly, Mahmood, Shahid, Usman, and Xinping (2010) perform an out-of-sample study using SEOs in the Chinese market between 1998 and 2008. In particular, they analyse the differences in market reactions between cash issues and rights issues. Their results show that the market reacts negatively to cash issue announcements while it reacts positively to rights issue. Their results are in accordance with the argument of Jensen and Meckling(1976) that a decrease in the percentage shareholding of the manager is considered as a bad news because it entails an increase in agency problems.
2.2 Information asymmetry hypothesis
Given the inconclusiveness of studies regressing abnormal returns on measures of stock issuance a substantial number of scholars have explored the hypothesis that underperformance is caused by information asymmetries and by the signals entailed in a stock issuance rather than by the issuance itself. For example, Dierkens (1991) studies the relation between information asymmetry and SEOs. She argues that information asymmetry exists because managers have access to firm-specific information that is not available to the market. Therefore, she regresses abnormal return for a sample of U.S. SEOs between 1980 and 1983 on four different empirical proxies for information asymmetry. Her results show that the greater the information asymmetry the greater the price drop. Furthermore, by means of time-series and timing tests she finds that information asymmetry is significantly decreased after equity issuances and that managers time issuances to when asymmetry is relatively low. On similar lines, Bayless and Chaplinsky (1996) investigate plural whether there are widows of opportunity for equity issuances. More consistently, they try to identify periods in time when information costs are reduced for all firms such that a firm can correctly signal its value and the pricing errors following SEOs are minimised. In
particular, they define periods when it is favourable to issue equity as “hot” and periods when it is unfavourable to issue equity as “cold”. Their results show that hot market issuers raise approximately an extra 2% (or $13 million) in equity than if they would have issued in a cold market. Also Daniel and Titman (1996) investigates information asymmetry. In particular, he analyses the relation between stock issuances and intangible information. According to the authors, stock issuances are a realisation of intangible information held by the managers of the firm who only issue when they perceive equity to be overpriced. Once the intangible information becomes tangible via the SEO then the market will react accordingly and the share price will decrease. In support of their hypothesis they find that future returns are indeed negative related to issuance and to realisation of intangible information. On the other hand, no evidence is found to support a significant relation between future returns and past tangible returns. Furthermore, Booth and Chang (2011) investigate whether market reaction to SEO announcements differs among dividend and non-dividend payers. Their reasoning follows the argument that asymmetry is lower for firms that pay dividends because changes in the latter entail a signal to the market about the current situation of the firm. Therefore, since asymmetry decreases and also price drop post-issuance should be lower. Interestingly enough, their results show that previous to mid-1980s the market did not differentiate between dividend payers and non-dividend payers. However, since then a significantly less negative market reaction for dividend payers than for non dividend payers is found following SEO announcements. This is most likely motivated by the fact that the number non-dividend paying firms has sharply increased after mid-1980s as identified by Fama and French(2001). Furthermore, Booth and Chang (2011) run a series a robustness tests that yield some results worth mentioning. First, there is the issue of sample self-selection. In fact, dividend payers are found to be mostly larger firms with lower growth opportunities. Also, an industry effect is found meaning that firms are more likely to pay high dividends if the percentage of dividend payers in the same industry is high. Secondly, the dividend status variable remains significant even after controlling for other information asymmetry proxies and share repurchases. Furthermore, firms with increasing dividends are found to have higher SEO announcement day return and vice versa. One last interesting point made by Booth and Chang (2011) is that dividend decreases of public utility firms result in stronger market reactions to SEOs announcements. Interestingly enough, Billet and Xue (2007) investigate whether there is a possibility for firms to reduce the post-issuance price drop. In fact, undervalued firms which plan to raise capital through equity in the future can eliminate the undervaluation by repurchasing shares prior to the SEO announcement. This way they can send a positive signal to the market and potentially overcome the adverse selection problem illustrated by Myers and Majluf (1984). In particular, Billet and Xue (2007) investigate their hypothesis by matching repurchase and non-repurchase SEOs and comparing their post-issuance abnormal returns and evidence in support of their argument. Namely, they find out that post SEO abnormal returns are 1.7% are higher for firms that
asymmetric information in which they combine repurchases with subsequent equity issue to show that firms can profit from repurchases and by doing so they can improve the terms of the subsequent SEO. In accordance with Billet and Xue f(2007) their model predicts that firms which conduct a share repurchase previous to the SEO have better investment opportunities than firms who don’t. Concluding, there is substantial evidence that seasoned equity offerings have a signalling feature that results in a decrease of information asymmetry between insiders in the firm and the market. As a result prices adjust and often decrease because the signal entailed by SEOs on the financial condition of the firm is a negative one (Masulis, 1983).
2.3 Alternative Explanations
Simultaneously to research on information asymmetry some scholars pursued alternative ways to explain the negative post-issuance returns. For example, in the attempt to make sense of the contradicting empirical evidence some scholars such as Teoh, Welch and Wong (1998) took a very different perspective and studied whether underperformance of firms could actually be caused by accounting manipulations made by managers prior to stock issuances. Namely, under the generally accepted accounting principles (GAAP) firms are allowed to recognise earnings before cash flows to reflect better the situation of the firm independently of cash transfers. Therefore, managers can recognise the proceeds an SEO before the shares are actually sold as “accrued earrings”. Through this accounting manipulation managers can increase earnings right before the SEOs such that investors overstate the actual value of the shares being issued. Logically, when the level of earnings cannot be sustained they become disappointed and sell the shares causing a drop in the stock price. To test their hypothesis the authors define “discretionary current accruals” as the part of earnings subject to management manipulation and they match issuer with non-issuer firms. As expected, issuers with high discretionary current accruals underperform their matched firms more than issuers with more conservative accruals. So much as, that firms with very low discretionary accruals actually outperformed their matched firms by 0.99%.
On the other hand, Brav, Geczy and Gompers (2000) expand on previous literature by exploring the hypothesis that issuer underperformance might be driven by a model misspecification problem. For example, they use a variation of the Fama-French (1993) three factor model that includes an extra factor related to momentum to investigate whether it is possible to better price equity issuing firms. Contrary to most of the past literature, they find evidence to support their hypothesis that no underperformance occurs. In particular, they point out that in their portfolio the returns of issuing firms covary with the return of non-issuing firms suggesting that stock issuance itself is not the cause of underperformance. Instead, other management decisions which are actually responsible for the anomalous returns might have been more heavily weighted in the firms that underperform.
2.4 Discussion and Interpretations
Concluding, the topic of anomalous post issuance returns has been studied in depth by scholars. In summary, there is evidence that seasoned equity issuance is a predictor of poor future returns but there is equally strong evidence that asymmetric information or accounting manipulations are the true causes of the anomalous returns. Even more so, scholars such as Teoh et al. (1998) refute the occurrence of an anomaly at all. On the other hand, they find proof suggesting that by adjusting the model it is possible to correctly price issuing firms. However, most studies perform their tests using the same 1970s till 2000 sample of SEOs from U.S. firms. A minority of studies such as Pontiff and Woodgate (2008) and McLean et al. (2009) focuses on out-of-sample tests. Still, their results are mixed. Therefore, there is a need for more out-of-sample studies and future research should focus on analysing post-SEO abnormal returns using samples from different time periods or different countries.
CHAPTER 3 Method
In this chapter the research methodology will be presented. The results and conclusions of this study are based on an analysis of abnormal returns. More consistently, the methodology of an event study explained by De Jong et al. (1992) will be applied. Furthermore, the event period will span from one day before to one day after the seasoned equity offering. First, an analysis of the cumulative abnormal returns will be conducted. Then, abnormal returns will be regressed against a measure of issuance.
3.1 Abnormal Returns
De Jong et al. (1992) defines abnormal returns as the realised returns (R) minus a benchmark or normal return (NR)
𝐴𝑅#$ = 𝑅#$− 𝑁𝑅#$
where i represents the specific event and t belongs to the interval [t1,t2] which is defined as the event period. Namely, there are two relevant periods to an event study which are the estimation period [T1;T2] and the event period mentioned above. The estimation period is the time span in which the coefficients to calculate the normal returns are measured and it can be any interval of time surrounding but excluding the event date. On the other hand, the event period contains the event date (t=0) and it is the time frame of the abnormal return analysis. In this paper an estimation period of [T1;T2] = [-350,-2] is adopted while the event period is set at [t1,t2] = [-1,1]. Figure 2.1 provides a graphical explanation of the time windows.
More consistently, the benchmark can be estimated using different models. In particular, some of the past literature such as Asquith and Mullins (1986) uses the average returns of the company in the estimation period as a proxy for normal returns. This particular approach is referred to as the Mean
Figure 2.1 Timeline
T
1T
2t
2t
2Estimation Period Event Period
Event t=0 AR1, -1 … ARN,-1 AR1,0 … ARN,0 AR1,1 … ARN,1 cross-section time series
Market Adjusted Model. This model corrects for market wide price movements by approximating abnormal returns to the residuals (𝜖 ) of the CAPM model as follows:
𝑅#$ = 𝛼#+ 𝛽#𝑅,$+ 𝜀#$ (2)
where the normal returns during the event period are computed using the OLS estimates 𝛼 and 𝛽
estimated using the returns during the estimation period. Such that:
𝑁𝑅#$ = 𝛼#+ 𝛽#𝑅,$ (3) 𝐴𝑅#$ = 𝜀#$ (4)
In the US a commonly used market proxy is the S&P 500 index which is based on the 500 largest companies by market capitalisation that are listed either in the NYSE or NASDAQ (Berk and De Marzo,2014). Therefore, for the UK the FTSE 100 will be used as market proxy because it comprises the 100 largest companies by market capitalisation listed on the London Stock Exchange. Concluding, once the analysis is completed the abnormal returns ( ) over the event period can be summarised in the following matrix such that every column consists of a time-series of returns while each row consists of a cross-section of returns.
Although abnormal returns can be quite informative per se, they are usually never analysed separately. In fact, Falk et al. (1992) study the cumulative abnormal returns (CARi) generated by the event. In particular, cumulative abnormal returns are defined as the sum of abnormal returns in the time-series for each event.
𝐶𝐴𝑅# = 𝐴𝑅#$1+. . . +𝐴𝑅#$2 = $0 𝐴𝑅#$
$1$2 (5)
Logically, if the event had no defined effect the abnormal returns will tend to cancel each other out and the CARi will not be significantly different from zero. On the other hand, a CARi different from zero suggests that there is indeed an effect. However, to study the general event effect throughout the sample it is more appropriate to analyse the cumulative abnormal returns in the cross section by computing the cumulative average abnormal returns (CAARi):
𝐶𝐴𝐴𝑅 =32 3 𝐶𝐴𝑅#
#11 (6)
As well, if the cumulative average abnormal return is significantly different from zero there is evidence of an event effect in the sample.
Moreover, the hypothesis of cumulative abnormal returns being different from zero can be tested. In this study the hypothesis test is the following
𝐻0: 𝐸(𝐶𝐴𝑅#$) = 0 (7)
𝐻1: 𝐸(𝐶𝐴𝑅#$) < 0
The hypothesis can be tested using a simple t-test. First, the cumulative abnormal returns must be assumed to be independently and identically distributed as well as normally distributed with mean zero and variance 𝜎2. Of course, the population variance is not know but it can be estimated from the sample as follows
𝑠 = 3<1 1 3 (𝐶𝐴𝑅#− 𝐶𝐴𝐴𝑅)0
#11 (8)
The the test statistic is computed as
𝐺 = 𝑁?@@AB ≈ 𝑁(0,1) (9)
More consistently, in this paper the cumulative abnormal returns from the day before the issuance (t1= -1) till the day after the issuance (t2=1) will be analysed. The reasoning for choosing this window is related to noise. In fact, when measuring CAR over a longer time span the risk of measuring effects other than issuance is quite high. Therefore, to minimize the risk of mixed results a three-day event window is considered. However, it is possible that the announcement is not priced in right away because for example it occurred outside of trading hours or not during a working day. In this cases, the price could take up to one day to adjust. Therefore, the CAR (-1,2) is examined as well. Furthermore, larger event windows up to [t1,t2] = [-10,10] will also be taken in account. This way, it will be possible to get a better overview of the distribution of abnormal returns. In particular, an event window of [t1,t2] = [-5,5] will be used to make considerations on the implementation and leakage effects. In fact, it is reasonable to expect some investors to have private information about the firm and be informed of the issuance prior to the market. If this is indeed the case they will have the chance to speculate on the share price and some abnormal returns are likely to be detected even before the event date. Such leak of information will be measured by computing the cumulative abnormal returns starting five days before the issuance and ending on the event day. In fact, a significantly negative CAR (-5, 0) would suggest that a substantial part of the market was already speculating on the event before it actually occurred. On the other hand, the implementation effect can be isolated by computing the CAR (0,5).
3.3 Repurchase and Non-Repurchase SEOs
Billet and Xue (2007) argument that firms who repurchase shares previous to SEOs send a positive signal to the market. As a result, announcement day abnormal returns of issuing firms are higher, as in less negative, for repurchase-SEOs tan for non-repurchase SEOs in their sample. As a follow up to their investigation this paper will also analyse the possible differences in abnormal returns among Repurchase and non-Repurchase SEOs. More consistently, the separation criteria will be whether the issuing firm has repurchased shares in the 2 years prior to the SEO announcement date. If a firm executes more than one seasoned equity offering following a share repurchase only the closest SEO will be considered as a repurchase-SEO. The remaining issuances will be studied as a non-repurchase SEO. In particular, the time window was chosen according to Billet and Xue (2007) who find a strong positive effect on abnormal returns when repurchases take place less than 716 days prior to the SEO. First, the average AR and CAR will be compared in an event window of 21 days spanning from ten days before the issuance till ten days after. In other words [t1,t2] = [-10,10]. Then, a difference-in-difference test will be used to check for variations among the two subgroups. The difference-in-difference estimator is computed as follows ( Stock and Watson, 2011):
𝛽1E#FFB<#G<E#FFB= 𝐴𝑅HIJKHLMNBI,NF$IH− 𝐴𝑅HIJKHLMNBI,OIFPHI −
The estimator above can be used to test whether either CAR and AR are significantly different among the two subarus orf SEO with a t-test. However, in order to run a regression a number of new variables must be created:
- AR: variable listing the average AR from [-10,10] for both the Repurchase SEO’s and the non-Repurchase SEO’s
- CAR: variable listing the average AR from [-10,10] for both the Repurchase SEO’s and the non-Repurchase SEO’s
- Aft: dummy variable equal to 1 when the AR or CAR occurred after t=0
- Rep: dummy variable equal to 1 when the AR or CAR is generated by an SEO preceded by a share repurchase.
- AftRep: interaction variable between Aft and Rep that is equal to 1 when the AR or CAR is occurs after t=0 and is generated by an SEO preceded by a share repurchase.
Then, the following regressions will be run:
𝐴𝑅 = 𝛼 + 𝛽1E#FF<#G<E#FF𝐴𝑓𝑡𝑅𝑒𝑝 + 𝛽2𝐴𝑓𝑡 + 𝛽3𝑅𝑒𝑝
𝐶𝐴𝑅 = 𝛼 + 𝛽1E#FF<#G<E#FF𝐴𝑓𝑡𝑅𝑒𝑝 + 𝛽2𝐴𝑓𝑡 + 𝛽3𝑅𝑒𝑝
The variable of interest is AftRep. If this variable is significantly different from zero then the AR and CAR are significantly different from each other in the two subgroups.
3.4 Cross-Sectional Regression
Past literature such as McLean et al. (2009) has explored a different method to study the impact of seasoned equity offerings on future returns. Namely, they tried to quantify the issuance effect by means of a cross-sectional regression of abnormal returns on a measure of issuance. In this paper the following regression will be run
𝐶𝐴𝑅(−1,1) = 𝛾0+ 𝛾1𝐼𝑆𝑆 + 𝛾2ln (𝑀𝐶) + 𝛾3𝐵/𝑀 (10)
Where the dependent variable is the cumulative abnormal returns from the day before till the day after the SEO (CAR (-1,1)) while the explanatory variable is the share issuance computed as follows
𝐼𝑆𝑆# =3K,OIH PF BMNHIB $10 <3K,OIH PF BMNHIB ($1<1)
3K,OIH PF BMNHIB ($1<1) (11)
Also, ui represents the error term. More consistently, control variables are chosen according to economic logic and past literature. For example, Mclean et al. (2009) as well as Fama and French (2008) use log(market capitalisation) and book-to-market ratio as control variables. Similarly, Affleck-Graves and Spiess (1995) match issuing companies with non-issuing companies on the basis of size and B/M ratio to compare their post issuance returns. However, market-to-book ratio was chosen rather than B/M because of its direct availability on DataStream.
Furthermore, Fama and French (2008) find out that a significant negative effect of share issuance is present only for issuances higher than 20% of shares outstanding. Therefore, this paper will also analyse whether the effect of SEOs differs according to their size. To do so, the sample of share issuances will be divided in quartiles according to magnitude and four different regressions as in (10) will be run for each quartile.
Moreover, one issue that should be taken in account when running the regressions in STATA is heteroskedasticity of the error term ui. Stock and Watson (2011) define errors as heteroskedastic when their variance depends one or more variables of the regression. Namely, defining Xi as any independent variable in the regression heteroskedasticity of the errors terms occurs when var(u|X)≠0. Otherwise, the errors are defined as homoskedastic. This is relevant because in case of heteroskedasticity it is important to use a heteroskedastic robust standard error. A common way to test for heteroskedasticity of the error terms is by performing a White-test. In his paper White (1980) develops a simple test to check for this property. First, the fitted 𝑦 = 𝛾^+ 𝛾2𝑥2 + 𝛾0𝑥0+ 𝛾`𝑥` have to be calculated for every observation in the sample. Then, the argument advanced by White is that if the errors are correlated to the independent variables, or the product of them, they will also be correlated to 𝑦. Therefore, by regressing the errors on the fitted values it is possible to assess whether there is sufficient evidence to assume that errors are homoskedastic. In fact, according to Stock and Watson (2011) in economics it is always better to assume that the errors are heteroskedastic unless there is a strong reason to assume otherwise. The regression for the test is as follows
𝑢2 = 𝛿
0+ 𝛿1γ + 𝛿2𝛾2 (12)
Then, using an F-test it is possible to test the joint hypothesis H0: 𝛿1=𝛿2= 0 to assess whether there is sufficient evidence to rule out the hypothesis of homoscedasticity. This method is very convenient because it allows for testing on heteroskedasticity without having to perform a very long regression with few degrees of freedom. In fact, regression of the form 𝑢2 = 𝛿
0+ 𝛿1𝑥1+ 𝛿2𝑥2+. .. would need to include also quadratic, cubic and possibly higher grade polynomial terms to rule out any possible relation
CHAPTER 4 Data
In this chapter an accurate description of the data will be given. First of all, The final sample consists of 185 seasoned equity offerings from October 2014 till February 2017. Figure 4.1 shows the frequency of observations per year. Furthermore, Seasoned equity offerings where selected according to the following criteria:
(a) the issuing firm is listed in the London Stock Exchange
(b) data on share price, market capitalisation and book to market ratio are available on DataStream for the event day as well as for the ten days before and after.
(c) data on number of shares is available for the two years before the issuance as well as for the ten following days.
In particular, 49% of the companies issued only once, 10% issued twice, 5% issued three times while the remaining 36% issued four or more times. The maximum frequency of SEO per company in our sample is seven. Furthermore, companies from 25 different sectors are included in the sample and none of them are no public utilities companies. As shown in Table 4.1, 28% of the companies included in the sample are active in the mining industry, 17% are Oil & Gas producers and 8% are General Financial companies while the remaining sectors make up for less than 5% of our sample. Furthermore, a summary of the main statistics is given in Table 4.2. More consistently, the average cumulative abnormal returns is -0.01 with a maximum of 0.30 and a minimum of -0.28. Furthermore, issuance is reported as a percentage of outstanding shares the market capitalisation is reported in millions of pounds. In particular, the smallest seasoned equity offering in our sample is from a company that issued just one share. On the other hand, the maxim issuance is 99.14% from a company that nearly duplicated its outstanding shares.
94 81 30 40 50 60 70 80 90 100 Fr eq u n cy o f S EO
Figure 4.1. Distribution of SEOs per year. The majority of observations are concnetated in the years 2016 and 2017 because the full year was sampled.
CHAPTER 5 Results
In this chapter a detailed description of the main findings will be given. First, the results of the cumulative abnormal returns analysis are be illustrated. Then, the outcomes of the regression analysis will be reported and explained.
5.1 General Abnormal Returns Analysis
Cumulative abnormal returns analysis shows evidence in support of the hypothesis that seasoned equity offerings are a predictor of underperformance in the short term. As shown in Table 5.1 the CAR(-1,1), CAR(-1,2), CAR(-1,0) are all negative and significant. This results are in line with the findings of Daniel and Titman (2006), Mahmood (2010) and Lerskuallawat (2011). Quite surprisingly, the CAR (0,1) is not significantly different from zero which is consistent with a weak implementation effect. Given that the overall abnormal returns are significantly negative this could be motivated by a substantial leakage effect. Therefore, to check whether information about the announcement was actually disclosed prior to the announcement date the daily average AR(-5,5) are graphed in Figure 5.1. As shown, some negative abnormal returns are already visible starting two days before the event date with a peak of negative returns in t=-1. This is indeed consistent with a leakage effect on abnormal returns. However, other studies on non-U.S. SEOs such as McLean et al. (2009) find no evidence of such a strong effect even though, their samples include observations from African and Asian countries which are usually more corrupted than European ones. Therefore, it is possible that this strong leakage effect is unique to our sample and could have been caused for example by sample selection.
Concluding, the evidence is consistent with an issuance effect in the overall sample with significant negative abnormal returns around the event date. However, it appears that much of the underperformance occurred prior to the issuance date suggesting a strong leakage effect. Nevertheless, the latter appears to be only related to our sample and possibly caused by sample selection.
5.2 Repurchase SEO vs Non-repurchase SEO
In the following subchapter the AR and CAR of SEOs that were preceded by a share repurchase will be analysed separately and compared to the rest of the sample. More consistently, the events were separated according to whether a share repurchase occurred in the two years prior to the SEO announcement Table 4.1. Summary Statistics
CAR[-1,1] ISS (%) MV (M£) MB
Mean -0.01 0.77 2.28 2.54
Std. Dev. 0.08 8.09 1.9 5.41
Min -0.28 4.00E-07 -1.66 -1.51
resulting in a sample 58 Repurchase SEO’s and 128 Non-repurchase SEO’s. For each subgroup the average abnormal returns and the average cumulative abnormal returns where computed for the 21 days surrounding the issuances. The results are plotted in Table 5.2 and graphed in Figure 5.2.
As shown, the average cumulative abnormal returns are strictly positive after the event date for the Repurchase SEO’s. Furthermore, the difference -in-difference test rejects the null hypothesis that the CAR are not significantly different from each other in favour of the one-sided alternative hypothesis that the CAR are higher for the Repurchase-SEO. On the other hand, the average abnormal returns in the two subgroups are not significantly different from each other. This result is consistent with an unequal distribution of positive and negative abnormal returns among the different Repurchase SEO during event
Table 5.1. Overview of cumulative abnormal returns over different event periods. Event
Periods
Cumulative Abnormal Returns Analysis
n=185 CAAR Std. Dev. t -1,0 -0.011** 0.062 -2.540 -1,1 -0.012** 0.081 -2.179 0,1 -0.004 0.062 -0.949 -1,2 -0.014* 0.099 -1.960 -5,5 -0.007 0.157 -0.621
**Significant at the 1% confidence level *Significant at the 5% confidence level
-1,0% -0,8% -0,6% -0,4% -0,2% 0,0% 0,2% 0,4% 0,6% 0,8% 1,0% -5 -4 -3 -2 -1 0 1 2 3 4 5 Da il y av er ag e ab n or m al r et u rn s
repurchase SEO’s. Overall, our results are in line with the findings of Billet and Xue (2007) and support the theory of Bond and Zhong (2016) that firms can limit the price drop following an SEO by performing a share repurchase prior to it.
Table 5.2 Average AR and average CAR for Repurchase and Non-Repurchase SEO’s Event Day Repurchase SEO
n=58 Non-Repurchase SEO n=128 AR CAR AR CAR -10 0.53% 0.53% 0.02% 0.02% -9 -0.72% 0.19% 0.24% 0.26% -8 -0.03% 0.21% 0.29% 0.03% -7 -1.14% 0.93% 0.34% 0.37% -6 0.97%% 1.90% 0.46% 0.83% -5 -0.31% 1.59% 0.07% 0.76% -4 0.39% 1.98% 0.13% 0.89% -3 -1.04% 0.94% 0.56% 0.33% -2 -1.14% 0.21% 0.19% 0.14% -1 -0.53% 0.74% 1.01% 1.14% 0 -0.24% 0.98% 0.31% 1.45% 1 1.33% 0.34% 0.80% 2.26% 2 0.17% 0.51% 0.25% 2.50% 3 -0.42% 0.09% 0.14% 2.37% 4 1.81% 1.90% 0.26% 2.11% 5 -0.17% 1.73% 0.32% 1.80% 6 -0.11% 1.84% 0.15% 1.95% 7 -0.20% 1.64% 0.13% 1.82% 8 -0.51% 1.13% 0.02% 1.84% 9 0.43% 1.56% 0.21% 1.63% 10 -0.20% 1.36% 0.19% 1.44%
5.2 Cross-sectional regression outcomes
In this section the results of five cross-sectional regression are reported. First, the results of a regression of the abnormal returns on issuance is performed using the whole sample. The cross-sectional regression finds no evidence of an issuance effect in the sample. As shown in Table 5.3 not the explanatory variables nor the control variables are significant. In fact, all variables have p-values higher than 0.05 such that the null hypothesis of no effect is not rejected with confidence level of 5%. In addition, an F-test also fails to reject the null hypothesis of joint significance suggesting that the model has a poor explanatory power for the abnormal returns. Furthermore, a White test for heteroscedasticity has been carried out on the sample. Surprisingly enough, the outcome of the tests is that the null hypothesis is not rejected meaning that there is not enough statistical evidence to reject the null hypothesis of homoscedasticity. Nevertheless, robust standard errors, which are valid both in the case of homoscedasticity and in the case of heteroscedasticity, where used throughout the study.
Secondly, four different regressions are run for each quartile of issuance. As shown in table 5.4 all coefficients are negative but none of them is significantly different from zero. Also in this case F-test for joint significance fail to reject the null hypothesis. One possible explanation for such results is that issuance, size and book-to-market ratio are not determinants of abnormal returns in the sample. On the other hand, another possible explanation for the poor performance of the model is the limited number of observations. As a matter of fact, most studies in the past literature such as Fama and French (2008) or Daniel and Titman (2006) employ samples of more than a thousand observations while in this study uses sample of 185 seasoned equity offerings.
However, there is a third possible reason for the apparent lack of an issuance effect. In fact, Fama and French (2008) argue that post-issuance underperformance is present in their sample only for issuances of 20% or more of shares outstanding. As a matter of fact, the sample studied contains only 5 issuances greater or equal than 20% of shares outstanding. Therefore, our findings are indeed in line with Fama and French as no issuance effect is found.
Table 5.3. Regression analysis for the whole sample. The dependent variable is the CAR(-1,1) Variables
𝛾 Std. Err. t p-value
ISS - 0.002 0.006 -0.36 -0.72
CHAPTER 6 Conclusions
Previous work on seasoned equity offerings and their effect on company’s stock price has produced mixed results. Furthermore, most papers are based on the same sample of U.S. issuances between 1960 and 2000. Some studies such as McLean et al. (2009) have tried to provide new insights by using a sample of non-U.S. SEOs but overall the literature is quite limited. Therefore, this study adds to previous findings by providing an out-of-sample observation from the UK. In particular, a sample of seasoned equity offerings between 2014 and 2017 is analysed. The main condition being that the issuing company is listed on the London Stock Exchange(LSE).
More consistently, previous literature such as Daniel and Titman (2006), Pontiff (2008) and McLean et al. (2009) find that issuing firms consistently underperform the market after the SEO. Daniel and Titman (2006) as well as Billet and Xue (2007) and Booth and Chang (2011) motivate this findings on the basis of information asymmetry and adverse selection. As first explained by Myers and Majluf (1984) and Masulis (1983), rational investors only expect managers to issue equity only when they believe that the latter is undervalued. Therefore, a share issuance is signal of bad news about the firm which is logically followed by decrease in stock price. This hypothesis is supported by the fact that any action undertaken by the firm to decrease information asymmetry between the management and the market result in less severe price drops as a consequence of SEO. For example, Billet and Xue show that some firms perform share repurchases previous to the seasoned equity offerings. This way, a very strong positive signal is sent to the market resulting in significantly higher post-issuance abnormal returns than in the case of non-repurchase SEOs.
However, other studies find no evidence of issuance effect. Brav et al. (2000) arguments that the seemingly consistent underperformance observed in previous studies is actually the result of a model Table 5.4. Regression analysis for each quartile. The dependent variable is the CAR(-1,1) and robust standard errors are reported below the coefficients in parenthesis.
Variables Quartiles Low 2 3 High ISS (23.199) -24.537 (5.457) -5.877 (2.047) -2.163 (0.007) -0.006 MC (0.010) 0.003 (0.004) -0.001 (0.005) 0.002 (0.012) -0.008 M/B -0.001 (0.002) -0.001 (0.004) 0.003 (0.002) 0.001 (0.002)
misspecification. More recently, Fama and French (2008) perform an in-depth analysis of post-issuance abnormal returns using sorts. Their results are quite relevant as they only find underperformance when issuance exceeds 20% of shares outstanding. For lower levels of issuance they find no abnormal returns.
Similarly, the research conducted in this paper produces mixed results. The event study shows significant underperformance in the short-term following seasoned equity offerings. In particular, significant negative abnormal returns occur around the event date which is consistent with previous findings by Daniel and Titman (2006) and by Mclean et al. (2009). However, the distribution of abnormal returns in the sample is consistent with a strong leakage effect. Given that no such effect has been reported by previous studies on non-U.S. SEOs there is a chance that the effect is specific to this sample and possibly the result of sample selection.
On the other hand, the regression analysis showed no significant short-term underperformance. In fact, none of the coefficients is and the model has poor explanatory power. Similarly, no evidence of a magnitude effect is found. More consistently, none of the per-quartile regressions yield significant results. One important point to be made is that less than 3% of the SEOs in the sample are greater than 20% of shares outstanding. Therefore, the results of the regression are actually consistent with the findings by Fama and French (2008) who argument that no issuance effect is present for SEOs of less than 20% of shares outstanding.
Moving on, our research is limited to the short-term and it not relevant for any long term considerations. Furthermore, the sample is limited to 185 observations which is low compared to other studies such as McLean et al. (2009) or Daniel and Titman (2006) who adopt samples of more than a thousand observations. In addition, the regression analysis methodology uses both market capitalisation and market-to-book ratio as control variables in accordance with past literature. However, these too variables are likely to be correlated such that the regression coefficient could be biased due to multicollinearity.
Concluding, the possibility of the above mentioned leakage effect being specific to the UK market cannot be ruled out and future research should investigate different samples of seasoned equity offerings from this market. Furthermore, this study showed that evidence of issuance effect is not so strong when considering out of sample observations and future research should focus on analysing and comparing post-issuance abnormal returns on samples of non-U.S. stocks.
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APPENDIX
Regression whole sample
Regression Quartile 1 Regression Quartile 2 _cons .0145121 .0472371 0.31 0.761 -.0814853 .1105095 MB -.0005664 .0009613 -0.59 0.560 -.00252 .0013872 MV -.0038205 .0083718 -0.46 0.651 -.0208341 .013193 ISS -24.53729 22.41591 -1.09 0.281 -70.09191 21.01733 CAR Coef. Std. Err. t P>|t| [95% Conf. Interval] Robust Root MSE = .08404 R-squared = 0.0350 Prob > F = 0.6445 F(3, 34) = 0.56 Linear regression Number of obs = 38
_cons .0145121 .0472371 0.31 0.761 -.0814853 .1105095 H -.0005664 .0009613 -0.59 0.560 -.00252 .0013872 G -.0038205 .0083718 -0.46 0.651 -.0208341 .013193 F -24.53729 22.41591 -1.09 0.281 -70.09191 21.01733 CAR Coef. Std. Err. t P>|t| [95% Conf. Interval] Robust Root MSE = .08404 R-squared = 0.0350 Prob > F = 0.6445 F(3, 34) = 0.56 Linear regression Number of obs = 38
_cons -.0066062 .0532957 -0.12 0.902 -.1149162 .1017037 P .0035687 .0015302 2.33 0.026 .0004589 .0066785 O .0022376 .0059818 0.37 0.711 -.0099188 .014394 N -2.163764 2.119374 -1.02 0.314 -6.470849 2.143321 M Coef. Std. Err. t P>|t| [95% Conf. Interval] Robust Root MSE = .08648 R-squared = 0.0870 Prob > F = 0.0869 F(3, 34) = 2.38 Linear regression Number of obs = 38
Regression Quartile 4
Difference-in-difference test of average abnormal returns
Difference-in-difference test of average CAR
_cons .0209321 .0232432 0.90 0.374 -.0263565 .0682207 T .0015882 .003649 0.44 0.666 -.0058358 .0090122 S -.00885 .0090743 -0.98 0.337 -.0273118 .0096118 R -.0069493 .0051581 -1.35 0.187 -.0174436 .003545 Q Coef. Std. Err. t P>|t| [95% Conf. Interval] Robust Root MSE = .08462 R-squared = 0.0422 Prob > F = 0.5624 F(3, 33) = 0.69 Linear regression Number of obs = 37
_cons -.001142 .001932 -0.59 0.558 -.0050531 .002769 AftRep .0017791 .0037751 0.47 0.640 -.0058632 .0094214 Rep .0004035 .0027322 0.15 0.883 -.0051276 .0059346 Aft .0008693 .0026694 0.33 0.746 -.0045347 .0062732 AR Coef. Std. Err. t P>|t| [95% Conf. Interval] Total .001477779 41 .000036043 Root MSE = .00611 Adj R-squared = -0.0356 Residual .001418357 38 .000037325 R-squared = 0.0402 Model .000059423 3 .000019808 Prob > F = 0.6640 F(3, 38) = 0.53 Source SS df MS Number of obs = 42
Rep .0107372 .0032452 3.31 0.002 .0041677 .0173067 Aft -.0150261 .0031706 -4.74 0.000 -.0214446 -.0086076 CAR Coef. Std. Err. t P>|t| [95% Conf. Interval] Total .007659406 41 .000186815 Root MSE = .00726 Adj R-squared = 0.7181 Residual .002000915 38 .000052656 R-squared = 0.7388 Model .005658491 3 .001886164 Prob > F = 0.0000 F(3, 38) = 35.82 Source SS df MS Number of obs = 42
White test for Heteroskedasticity _cons -.0042186 .0022947 -1.84 0.074 -.008864 .0004267 AftRep .0186186 .0044838 4.15 0.000 .0095415 .0276956 Rep .0107372 .0032452 3.31 0.002 .0041677 .0173067 Aft -.0150261 .0031706 -4.74 0.000 -.0214446 -.0086076 CAR Coef. Std. Err. t P>|t| [95% Conf. Interval] Total .007659406 41 .000186815 Root MSE = .00726 Adj R-squared = 0.7181 Residual .002000915 38 .000052656 R-squared = 0.7388 Model .005658491 3 .001886164 Prob > F = 0.0000 F(3, 38) = 35.82 Source SS df MS Number of obs = 42
