University of Amsterdam
Master Thesis
How Learning about Future
Profitablility affects Stock Valuation
Author:
Kristian Ndokaj
Supervisor:
Dr. Liang Zou
A thesis submitted in fulfillment of the requirements
for the degree of MSc Business Economics: Finance Track
in the
Finance Group
Amsterdam Business School
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Declaration of Authorship
I, Kristian Ndokaj, declare that this thesis titled, “How Learning about Future Profitablility affects Stock Valuation” and the work presented in it are my own. I confirm that:
• This work was done wholly or mainly while in candidature for a Master’s degree at this University.
• Where any part of this thesis has previously been submitted for a degree or any other qualification at this University or any other institution, this has been clearly stated.
• Where I have consulted the published work of others, this is always clearly attributed.
• Where I have quoted from the work of others, the source is always given. With the exception of such quotations, this thesis is entirely my own work.
• I have acknowledged all main sources of help.
• Where the thesis is based on work done by myself jointly with others, I have made clear exactly what was done by others and what I have contributed myself. • The Faculty of Economics and Business is responsible solely for the supervision
of completion of the work, not for the contents. Signed:
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UNIVERSITY OF AMSTERDAM
Abstract
Faculty of Economics & Business Amsterdam Business School MSc Business Economics: Finance Track
How Learning about Future Profitablility affects Stock Valuation by Kristian Ndokaj
I study the relationship between Learning about average future profitability and the firm value. The Market-to-Book ratio is found to increase with uncertainty about average profitability. The M/B is also predicted to decline over a firm’s lifetime because of the learning process. The data support that this effect is stronger for stocks that don’t pay any dividends whatsoever. There is also strong indication that the effect of learning is weaker for firms with dual share structure. Future firm profitability and initial valuations after companies list on stock exchanges have attracted much attention over the years and the results of this thesis could help explain why over-estimated valuations happen.
vii
Acknowledgements
I would like to thank my supervisor Dr. Liang Zou for his helpful comments and recommendations.
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Contents
Declaration of Authorship iii
Abstract v Acknowledgements vii 1 Introduction 1 2 Background 5 3 Methodology 9 3.1 Data Construction . . . 9 3.2 Hypotheses . . . 10 3.3 Model . . . 10 4 Summary Statistics 13 4.1 Data . . . 13 4.2 Descriptive Statistics . . . 13 4.3 Figures . . . 16 5 Results 22 6 Robustness Checks 29 7 Conclusion 34 8 Appendix 37
8.1 Autoregressive Integrated Moving Average Model (ARIMA) . . . 37
xi
List of Figures
4.1 M/B ratio in the years after listing . . . 17
4.2 Return Volatility in the years after listing . . . 18
4.3 M/B ratio in calendar time . . . 19
4.4 Return Volatility in calendar time . . . 20 4.5 M/B ratio for Dual Share Structure Firms in the years after listing . 20 4.6 Return Volatility for Dual Share Structure Firms in the years after listing 21
xiii
List of Tables
4.1 Mean by Age . . . 15
4.2 Median by Age . . . 15
4.3 Cross-correlation Table . . . 16
5.1 Determinants of Market-to-Book Ratio . . . 24
5.2 The lnAGE coefficients for Dividend Payers versus Non-payers 25 5.3 The lnAGE coefficients for Dual Class Firms versus Non-Dual Class . . . 26
6.1 The lnAGE coefficients for Dividend Payers versus Non-payers (Stock Repurchase counted as dividend) . . . 30
6.2 Determinants of the 1st difference of the M/B ratio . . . 31
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1
1
Introduction
OVER THE PAST YEARS A WAVE OF ACADEMIC WRITING about Initial Pub-lic Offerings has risen. All of these authors focus on IPOs under-performance, the returns around the date of the IPO of a firm and other relevant subjects. Little has been done on how actually these initial valuations turn up through the years, meaning how learning more about a firm affects the value of that company. More specifically, there have been observed very high valuations during the first months of a firms life. The main explanation for this occurrence could be that young firms are expected to be very profitable and also that investors are on average more optimistic than usual about the future profitability of young firms. Of course, after some con-siderable time those high valuations tend to drop and thus what is actually taking place is learning. Learning more about a firm is done after many years of observation on major corporate announcements, analysts’ reports, financial statements, mergers and acquisitions, new investments etc. The basic idea is that investors attempting to value newly listed firms are faced with a lot of uncertainty about a company and most importantly about its future profits.
I argue that uncertainty contributes to high valuation multiples and that the process of learning reduces that ambiguity and that in turn reduces valuations. There
2 1. Introduction is a very simple idea behind this. Let B denote a firm’s book value of equity at the present and g its long-term growth rate, so the value of book equity at some future time T is B = egT . Based on the conjecture that a highly competitive market eliminates the firm’s expected abnormal earnings by T, the firm’s market value at T equals its book value, and the market value today is equal to the expected book value at T discounted at some known rate r. If g is not known to the majority of investors and assumed to be normally distributed with mean g and variance σ2, the
Market-to-Book ratio (M/B) today is
M/B = E[e(r−g)T] = e(¯g+σ2−r)T
The M/B ratio is an increasing function in the uncertainty about book equity growth, σ2. I assert that uncertainty is decreased over a firm’s lifetime because of learning. Therefore, younger firms have greater σ2 and thus also greater M/B ratios, holding other variables (such as ¯g and r) constant. My empirical analysis confirms the previous statements on a large panel of data comprising the years from 1962 to 2015. Due to the fact that uncertainty declines over a firm’s life because of learning a younger company should have a higher M/B ratio than an otherwise identical older firm. Veritably, I find a significantly negative cross-sectional association between firm age and M/B, even when controlling for other widely used determinants of M/B. For instance, I find a difference of around 5% between the appraisals of a typical two-year old firm and a one-year old firm. Among firms that pay no dividends I find a valuation difference of over 15%.
A new addition to the current literature studied in this thesis is how learning affects Dual Class Share Structure firms relative to the others. None has attempted to analyse such firms until now and it seems really interesting to do so because of many such companies listing on stock exchanges and doing very well financially like Facebook, Alibaba etc. Typically, firms listing with this sort if structure are high-tech
1. Introduction 3 start-ups or firms with a very special product. Because their founders tend to have a vision for the future they try to hold control of their companies even if the have the minority of the share by imposing the structure mentioned. This insight came from various observations on internet stocks. One particular example is that of Facebook, which went public on 18/05/2012 on the Nasdag Composite opening at a first day adjusted price of $38.23 and then followed having a stock price of $53.32 on December 2013 and currently trading at $113.02. As we can clearly observe even after fours years the stock price is on an uprising movement. Of course, this is in absolute terms and we also need to watch how these results change in relative terms. In relative terms, the trend is the same and this important observation is what inspired to check on those type of firms. My empirical analysis strongly indicates that learning effects are weaker on Dual Class Share Structure firms. For example, a typical 5-year old Dual Class firm has a 7% more positive learning effect on its valuation than a typical 5-year old regular firm.
The basic methodology used in this thesis is a time-series average cross-sectional regression or the so-called Fama Mac-Beth regression. All the key variables are com-puted as ratios or logarithms so as to relate them to the valuation multiples such as the Market-to-Book ratio. All data used are going to be firm fundamentals and stock data.
The thesis is outlined as follows. Fist, I am going to establish the current literature on my topic and review what other authors have found till now. Next, my methodol-ogy is going to be explained extensively so it will be easy to follow the remaining of the dissertation. Thereafter, a summary statistics section is shows including descriptive statistics such as tables with the mean and median of major variables in a way that one can see how they are affected by ageing. Moreover, many figures showing how the M/B ratio and the uncertainty changes through ageing including sub-samples like
4 1. Introduction dividend paying firms and dual share class structure firms. Following, the main results of my empirical research are shown in various alterations in order to show the effects on the sub-samples mentioned just before. Continuing after the results, robustness checks take place in order to prove the soundness of the empirical strategy I chose to implement. Last but not least, the conclusion of my thesis proceeds, summarizing the main findings and how I came to find those results.
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2
Background
It is crucial for my analysis to define first what learning is and the key variables interacting with it and of course what other authors have worked on learning and its implications. Without any mathematical formulations learning can be defined as the filtering process of estimating unobservable parameters about future profitability of a firm. These unobservable parameters can be learned with realized returns. Let’s also explain two concepts of high importance, risk and uncertainty. Risk is when given a description of the state-space, the value we are willing to pay to be insured against adverse events. We have uncertainty when the expected return (i.e. the model) is not known/some states are hidden/we do not know how to assign probabilities 1.
Let’s consider the dividend discounted model which states that the value of a company is given by
P = D/(r − g),
where r is the discount rate, g is the dividend growth rate and D is the next period’s dividend. This well known formula holds also for when g is not constant.
1Andrea Buraschi, 2010, Asset Pricing with Uncertainty and Learning, Imperial College Business
6 2. Background Things of high interest happen when g in the previous equation is unknown. Paśtor and Veronesi (2003, 2006) argue that uncertainty about g increases the stock price and also Leipold et al (2007) stress out the same. Intuitively, uncertainty about the growth rate makes the allocation of future dividends right-skewed, thereby increasing expected future dividend payments (Paśtor and Veronesi (2009)). Speaking in a widely relaxed form, a firm with some probability of failure (a very low g) and some probability of becoming the next Facebook (a very high g) is very valuable. When r is endogenously determined in equilibrium with a power-utility representative agent, uncertainty about g may increase or decrease r, but its overall effect on P/D is positive (Paśtor and Veronesi (2006)). Rather than focusing on P/D, which does not apply for non-dividend-paying firms, Paśtor and Veronesi use a different valuation multiple and focus on the market-to-book ratio (M/B). This ratio increases with uncertainty about the firm’s average profitability, which can be viewed as uncertainty about the average growth rate of book value. Since uncertainty declines over time due to learning, the Paśtor and Veronesi (2003) model predicts that M/B declines over a typical firm’s lifetime, so that younger firms should have higher M/B’s than otherwise identical older firms. This prediction is confirmed in U.S. stock data: the median M/B falls in a monotonic way from a figure of 2.25 for 1-year-old firms to 1.25 for 10-year-old firms, and the cross-sectional relation between firm age and M/B is consistently negative. The model also insinuates that the effect that age has on M/B should be stronger for younger firms and non-dividend-paying firms. Additionally, M/B ought to fall with expected return and rise with both the level and the volatility of profitability. All of these predictions are confirmed empirically using time-series averages of cross-sectional regressions. Another empirical confirmation is also done by Fereira et al (2007). Even though they study the relationship of corporate governance policy and idiosyncratic risk, the empirical models they use are very similar to that of Paśtor and
2. Background 7 Veronesi (2003). Mostly they use information measures as their dependent variable and they find that age is negatively correlated with measures like amount of private information trading and of course this tells us that older firms tend to have much more disclosed information to the public and the fact that the Market-to-Book ratio included in their regression is also negatively correlated with the information measure mentioned lead to the indirect implication that learning about future profitability, grasped by ageing, leads to lower valuations.
As for the predictability of future returns, we could say that those returns can be predicted with a good accuracy. When the aggregate Price-to-Dividend (P/D) ratio is low, future stock market returns tend to be high (Leipold et al (2007)). Timmermann (1993) explains that such predictability can be attributed to learning about g. When the current estimate of g, is below the “true” value of g, investors are pessimistic about future dividends, so P/D is low. The future returns are likely to be high, though, because the current estimate is likely to be revised upwards. As a result, low P/D predicts high future returns.
Going through all of these papers and getting the main elements out of them, I can formulate my hypotheses. It is clear from what has been read till now that learning has a negative effect on valuations and that effect is of higher magnitude for younger firms. Thereafter, uncertainty seems to have a positive effect on the market price of a company suggesting that the more the uncertain the prospect for a company the more it could be potentially overvalued. Paśtor and Veronesi also went deeper into seeing stronger effects for dividend paying firms. This is a very nice inspiration for me, which leads me to search for the opposite, weaker effects. After very much thought and reading, I came up with the idea to test that for firms that have Dual Share Structure, meaning that some "special" shares can control the company even if they are the minority. This tends to happen with high-tech firms and companies
8 2. Background having influential founder that want to execute a long-term vision they have for the company they created.
One would expect that there would a wider literature on this topic. The truth is that this subject hasn’t been touched upon a lot and most papers are theoretical and very few empirical ones. The main explanation of this could be attributed to the high level difficulty of such analyses which use a lot of continuous-time finance, Bayesian updating, highly sophisticated mathematical and statistical techniques etc. Of course, the current literature is sufficient for me to forge an empirical strategy and the results to follow are quite interesting.
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3
Methodology
3.1
Data Construction
In this part I will explain how the main variables are constructed. First and foremost, the age of a company is constructed by taking into account the first appearance of the firm in the database and hence age will be one for the year that the company first showed. Hereinafter, following Fama and French (1993), book equity is constructed as stockholders’ equity plus balance sheet deferred taxes and investment tax credit minus the book value of preferred stock. Depending on availability, stockholders’ equity and preferred stock are also included. Market equity is computed by multiply-ing the stock price at fiscal year-end by common shares outstandmultiply-ing. Earnmultiply-ings are calculated as income before extraordinary items, available to common stockholders, plus deferred taxes from the income statement plus investment tax credit. Debt is total long-term debt, Assets are total assets, and Dividends are dividends available to common stockholders. M/B ratio is computed as market equity divided by book equity, return on equity is earnings divided by last year’s book equity, and leverage is debt divided by total assets. I eliminate the values of market equity, book equity, and total assets smaller than $1 million, as well as M/B ratios smaller than 0.01 and larger
10 3. Methodology than 100. Last but not least, volatility of profitability (V OLP ) is calculated as the residual standard deviation of an ARIMA(2,1,0)1 model, meaning an first differences
autoregressive model of order two, on the stock return. The technical contribution of this thesis is to develop the previously mentioned model in order to obtain the stock return volatility and extent the the previously used method by the other authors and it is also crucial I point out that this process is highly sophisticated and was a difficult exercise to perform but of course it is very important to me to put my personal touch in the methodology and differentiate from the model used in the paper of Paśtor and Veronesi (2003).
3.2
Hypotheses
In order to give a clear idea on how this dissertation is going to unfold the main hypotheses are being stressed. Firstly, I assert that high uncertainty about average profits increases the valuation of a firm. Secondly, as companies age their M/B ratio declines because of learning. Learning about Non-Dividend paying firms has a stronger negative effect on valuation multiples than learning about Dividend-Payers has. Last but not least, learning about Dual Share Structure firms has a weaker influence on the value of those firms.
3.3
Model
The econometric method to be used is cross-sectional multiple regression for each year and following Fama and MacBeth (1973) the coefficients are going to be time-series averages of the estimated cross-sectional slope coefficients. Residual correlation can be dealt with in each regression by robust errors or clustering.
3.3. Model 11 The variable capturing the Valuation is going to be the multiple of the Market-to-Book ratio because as I already mentioned in the Introduction, I assume that the Market value equals the Book value in the long term. Therefore, it seems reasonable to have the M/B ratio as the dependent variable. Except for the proxy for learning, which is Age, following Paśtor and Veronesi (2003), other known determinants of the Market-to-Book ratio are included. One alternative proxy could be the dispersion of security analysts’ profitability forecasts, constructed from the earnings forecast in the IBES database of Thomson Financial. As shown by Asquith Paul et al (2005), analysts’ forecasts have information never revealed before and thus seems plausible to also use this kind of variable as a proxy for learning. However, there is a concern about selection bias as the sample mentioned is heavily tilted towards big and well established stocks.
Furthermore, Vuolteenaho (2000) shows a linear model where the log M/B is equated with a infinite discounted sum of future returns and profitability. A mean of all future values could also be included but putting a number of future values can be useful to see how many are actually needed.
The main empirical model to be used is a cross-sectional regression for each year. ln(M/B)i = α + β1lnAGEi+ β2DDi+ β3LEV ERAGEi+ β4SIZEi+ β5V OLPi+
γCLASSi + δ0ROEi + δ1ROEi,t+1 + · · · + δpROEi,t+p + ζ0RET U RNi,t+1 + · · · +
ζpRET U RNi,t+p+
Where, ln(M/B) is the Logarithm of Market-to-Book ratio, lnAGE is the natural logarithm of the Age of the firms, DD is a Dividend Dummy showing whether a firm paid dividends or not , LEV ERAGE is the Long term Debt divided by Total Assets , SIZE is the natural logarithm of Total Assets, V OLP is the Volatility of
12 3. Methodology Stock Returns taken by the ARIMA(2,1,0) model, ROE is a proxy for future profit predictability (Return on Equity), RET U RN is proxy for future return predictability (Stock Return), CLASS is Class of Share Structure and is white noise.
The coefficient of lnAGE is expected to be negative as was also found by Paśtor and Veronesi (2003)2 and Fereira et al(2007) and that’s what I need in order to verify my first hypothesis. Here, it is of importance to stress out that the model used in my methodology is adjusted to be simpler than the theoretical models created by the authors previously mentioned but without losing the insight from theory. The second part of the hypothesis can be validated if the coefficient of V OLP is positive. The second hypothesis and third hypothesis can be tested by dividing into sub-samples and running the regression as shown above. LEV ERAGE is expected to have a negative impact on M/B whereas SIZE is foreseen to have a positive one. Future ROEs are expected to have a positive effect as found by Paśtor and Veronesi (2003) and Fereira et al(2007). If you think that higher future profits are already grasped in the M/B, which is a forward looking measure then it makes perfect sense for these coefficients to be positive. Finally, future stock RET U RN s are expected to have a negative effect as shown in Paśtor and Veronesi (2003) and Fama and French (1993).
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4
Summary Statistics
4.1
Data
The data used in this empirical approach are firm fundamentals and stock data which are going to be combined in order to create a panel of firms and years. We can already see briefly how this data are used in the equation previously shown in the Methodology Chapter.
As for the database, annual data from the merged CRSP/COMPUSTAT database from January 1962 to December 2015 were used for my empirical research. The year span is so big because of the future returns on equity and stock returns needed, i.e. if I use 25 future annual stock returns, then I need to go way back in time in order to have future observations. The kind of data to be used are mostly firm fundamentals.
4.2
Descriptive Statistics
In this part the most important descriptive statistics are going to be shown, which are going to give us some direction on what to expect in the empirical part of this thesis later on. First of all, Table 4.1 is a summary of the M/B ratio, the Return on
14 4. Summary Statistics Equity, the Stock Return, Total Assets and Leverage. In this table only the mean for each variable is shown because I categorize them by the firm age in order to see how these variables are affected by ageing, demonstrating the company age up to ten years . The most important variable of all is the M/B ratio and as we can see there is a huge decline in the second year of a firm’s life and thereafter it keeps decreasing at a steadier rate giving us promising results for the regression analysis following in the Results section in later stages. What is also interesting is the Return on Equity which is really high in the first year of firms’ lives and afterwards it declines and it is most of the time at a number around 0.2-0.25. The Stock return is as expected higher in the first year which is also known in the literature very well as the IPO underpricing, the process at which the stock price goes really high after the first stages of trading the stock, with shareholders baring the cost. Next, Total Assets as expected follow an increasing rate because as companies age, they also grow. Lastly, Leverage seems to follow a slightly increasing rate and that tells us that actually Long-Term Debt is increasing at a very high scale because if you take into account the huge increase in assets then it is reasonable to deduce that Debt is rising really fast as firms become older. This fact is very logical considering that the more a firm is around the more it gets known and trusted by investors and borrowing institutions and hence can borrow more. I also included a similar table with a different statistic measure of that of the average. Table 4.2 is now taking into consideration the median instead of the mean. Median is generally considered more unbiased because it doesn’t get affected by outliers. The results are very similar to those of Table 4.1. The Market-to-Book ratio follows the same pattern again by having a steep decline after the first year and then descending at lower rate. The Return on Equity is now starting with a more moderate number and it slightly decreases through time. Finally, as for Total Assets and Leverage, we can observe more or less the same results as in Table
4.2. Descriptive Statistics 15
Table 4.1: Mean by Age
Age M/B ROE RETURN ASSETS LEVERAGE
1 4.207 3.292 0.464 919.320 0.144 2 3.196 0.246 0.088 1130.549 0.161 3 2.896 0.252 0.173 1315.877 0.170 4 2.748 0.442 0.237 1541.405 0.173 5 2.574 0.228 0.232 1796.218 0.176 6 2.461 0.206 0.214 2081.361 0.179 7 2.435 0.204 0.254 2294.875 0.182 8 2.377 0.207 0.193 2625.497 0.184 9 2.379 0.235 0.221 2800.525 0.183 10 2.295 0.191 0.204 3143.981 0.182 Total 2.916 0.281 0.199 1752.581 0.170
4.1. Hereinafter, a cross-correlation table is also included in my analysis in order to
Table 4.2: Median by Age
Age M/B ROE RETURN ASSETS LEVERAGE
1 2.484 0.211 0.000 44.114 0.065 2 1.909 0.168 -0.105 56.253 0.092 3 1.706 0.150 -0.052 64.218 0.111 4 1.593 0.143 -0.018 71.591 0.120 5 1.479 0.143 -0.027 81.108 0.127 6 1.449 0.142 0.000 89.397 0.135 7 1.414 0.145 0.020 97.801 0.139 8 1.396 0.144 0.008 111.093 0.147 9 1.365 0.142 0.007 121.634 0.142 10 1.341 0.141 0.027 132.972 0.145 Total 1.591 0.143 0.007 129.818 0.135
observe any significant correlation between the main variables to be used in my main methodology. Even though most cross-correlations are statically significant at 5% or more, we don’t see any serious correlation because the largest number seen in the table is 0.4155 and hence we cannot conclude that there is any potential problem of multicollinearity. The other important factor needed to be stressed is that the cross-correlation between the Market-to-Book ratio is negative and significant, endorsing the assertion I made that ageing is negatively correlated with the M/B ratio and also
16 4. Summary Statistics agreeing with the observation made from tables 4.1 and 4.2 that is also about the negative relation of age and M/B.
Table 4.3: Cross-correlation Table
A cross correlation table of the variables, Market-to-Book ratio (M/B), firm age (AGE), total assets (ASSETS), long-term debt over common equity (LEVERAGE), volatility of stock returns (VOLP), return on equity (ROE), and
stock return (RETURN) is shown underneath and in the parentheses the standard errors are shown and the ones with asterisk have statistical significance at 5% or better.
VARIABLES M/B AGE ASSETS LEVERAGE VOLP ROE RETURN
M/B 1.000 AGE -0.059 1.000 (0.000)* ASSETS -0.079 0.415 1.000 (0.000)* (0.000)* LEVERAGE -0.028 0.066 0.275 1.000 (0.000)* (0.000)* (0.000)* VOLP 0.031 -0.035 -0.059 -0.030 1.000 (0.000)* (0.000)* (0.000)* (0.000)* ROE 0.085 -0.007 -0.012 -0.001 0.033 1.000 (0.000)* (0.032)* (0.001)* (0.811) (0.000)* RETURN 0.090 -0.010 -0.040 -0.020 -0.003 0.039 1.000 (0.000)* (0.000)* (0.000)* (0.000)* (0.238) (0.000)*
4.3
Figures
In this section I am going to show some figures crucial to my research in order to get a further idea about the the most important variable to be tested and of course an optical demonstration is always pleasant to see.
The first graph which is Figure 4.1 shows that ageing during a firm’s life tends to be accompanied by a decrease in the M/B ratio. We can see a monotonically decreasing function of age. The solid line represents all firms in the sample while the dashed line is about Non-Dividend Payers and the dotted line represents Dividend Payers. We can see that for all sub-samples the highest M/B ratio is observed at the start of the firm’s life. Noticeable is that Non-Dividend Payers have a highest
4.3. Figures 17 M/B ratio than those companies paying dividends and most importantly they seem to have a blunter decline at initial stages, which is really interesting and of course will be also tested in a regression framework. In general, we can see the M/B ratio has a steep decline after the first years of firms’ life and after that it declines in a smaller rhythm. We could attribute that to learning and of course the huge M/B ratios at the beginning to high uncertainty about a company potential at initial stages.
Figure 4.1: M/B ratio in the years after listing.For each age the median M/B ratio is plotted across firms of that age, regardless the year that that age was reached. The solid line is about all firms, the dashed line plots Non-Dividend Payers and
the dotted line is about Dividend Payers.
Figure 4.2 shows that ageing is associated with decline in uncertainty which is grasped by the return volatility calculated from an ARIMA(2,1,0) model. As a firm ages uncertainty gets lower. Again the noticeable thing here is that Non-Dividend Payers have a higher uncertainty than firms paying dividends which makes sense considering that investors think of companies paying dividends as stable firms with the capability to pay out its equity investors due to having enough cash flows for dividend payments. Moreover, Non-Dividend payers seem to have steeper declines in volatility in the first years.
18 4. Summary Statistics
Figure 4.2: Return Volatility in the years after listing.For each age the median return volatility is plotted across firms of that age, regardless the year that that age was reached. The solid line is about all firms, the dashed line plots Non-Dividend
Payers and the dotted line is about Dividend Payers.
In Figure 4.3 we can see how the M/B ratio changes through the years for different categories of firms. Still, we see that Non-Dividend Payers have a higher ratio than that of Dividend Payers. What is also important, though not focused on learning, is the cyclical movements. During crises the ratios tend to go down and as we can see in the graph the most recent crisis in 2008 follows the same pattern.
In Figure 4.4 we see the reverse happening, meaning that during crises and periods with high M/B ratios uncertainty soars which also is in line with current literature. And of course, dividend paying firms have lowers levels of uncertainty than non-dividend paying companies have.
In Figure 4.5 the Dual Share Structure firms-where founders having the minority of shares can still control the firm because those share are of special structure-is being tested. Checking again the Market-to-Book ratio I divide the sample into all firms, Dual Share structure firms and non-Dual Share Structure Firms. As we can see, all firms and non-Dual firms follow exactly the same pattern. The reason is that there are not many observations about the Dual firms but even so it seems interesting to
4.3. Figures 19
Figure 4.3: M/B ratio in calendar time.The graph plots the evolution of the M/B ratio throughout the years regardless age. The solid line is about all firms, the dashed line plots Non-Dividend Payers and the dotted line is about Dividend Payers.
examine them even with limited data. Although Dual Share Structure firms have very high variations in the M/B ratio and we can’t really discern a trend, they seem to be above other firms.
Lastly in Figure 4.6 we check now the Return Volatility in Dual Share Struc-ture firms and again divide the sample into sub-samples as in the previous table. The results are somewhat opposite to Table II.5, meaning that Dual firms have high variations in volatility but they tend to have lower uncertainty than other firms.
This could be because investors think that those firms have a vision for the future and typically do well financially as history has shown.
20 4. Summary Statistics
Figure 4.4: Return Volatility in calendar time.The graph plots the evolution of the return volatility throughout the years regardless age. The solid line is about all firms, the dashed line plots Non-Dividend Payers and the dotted line is about
Dividend Payers.
Figure 4.5: M/B ratio for Dual Share Structure Firms in the years after listing.For each age the median M/B ratio is plotted across firms of that age, regardless the year that that age was reached. The solid line is about all firms, the dashed line plots Non-Dual Share Structure Firms and the dotted line is about Dual
4.3. Figures 21
Figure 4.6: Return Volatility for Dual Share Structure Firms in the years after listing.For each age the median Return Volatility is plotted across firms of that age, regardless the year that that age was reached. The solid line is about all firms, the dashed line plots Non-Dual Share Structure Firms and the dotted line
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5
Results
In this section I am going to run the regression mentioned before in my methodology. Revising, for each year between 1962 and 2015 I regress the log of M/B on a function of firm age and other potential variables determining the M/B. Table 5.1 includes a summary of all the regressions run for every set of future values of the proxies for profitability added. The most important variable in my analysis, which is lnAGE is always having a negative coefficient and is statistical significant except for in the specification that has 10 future values. The magnitude of the coefficients seems to decline when adding more future values and even for the coefficient with 15 future proxies, that actually rose, we can see it is lower than that of the 1st regression run only against the lnAGE. Let’s assume that the model with 5 future values seems more fit (which is the case). There the coefficient is -0.054 and it is statistically significant at 1% meaning that an increase in age of 1 year has a effect of lowering the M/B ratio 5,4%. The economic significance is even stronger because it means that an average firm will lose some of its value due to learning about its future profits most of the time even if that company is currently doing well financially. Moreover, it is crucial to mention that variation in M/B ratios over time (time effects) is controlled for since I run cross-sectional regression year by year. As for the variation in M/B
5. Results 23 ratios over firms, it doesn’t affect the results since the lnAGE effect is always negative with occasional exceptions (if any). Hence, my first hypothesis seems to be firmly backed by the data. The next important variable is the volatility of profitability. The assertion is that high uncertainty leads to high relative valuations. We can see that the coefficient is always positive, backing my hypothesis, but the coefficients are statistically significant in three of the specifications. If we consider again the regression with 5 future values, there the coefficient of V OLP is 0.910 and it is statistically significant at 1% meaning that a positive change of 1%(0.01) in volatility results in a increase of 0.9% in the M/B ratio. There are some really serious things going here. The economic significance is immense. Think of an entrepreneur that wants to invest in a start-up and doesn’t really believe in their project and business plan but knows that high uncertainty lead to higher valuations and thus higher profits for him even if the expectations are low.
In addition, less levered firms tend to have higher M/B ratios based on the co-efficients which are always negative and highly significant and bigger firms in size tend to have higher ratios. As far as firms that pay no dividends are concerned, they tend to have higher M/B ratios when the model is richer. Moreover, dual class share structure firms tend to have lower M/B ratios but the data for those firms is limited and thus we can’t be sure because the direction changes across the specifications. All coefficients of ROE, current and future are positive and consistent with the model by Paśtor and Veronesi (2000). The coefficients generally decline as we go further in the future, meaning the more in the future we are the less the effect, and the values turn insignificant at lead 6 meaning that values after future year 6 have no effect. Simi-larly, the coefficients of RET U RN are all negative and consistent with the model and the prediction made from Fama and French (1993). They also decline going forward and they also turn insignificant at lead 6. Therefore, the best fit for our model seems
24 5. Results
Table 5.1: Determinants of Market-to-Book Ratio
For every year between 1962 and 2015, the log of the market-to-book ratio (M/B) is regressed cross-sectionally against the log of the firm age (lnAGE), dividend dummy (DD), leverage (LEVERAGE), the log of total assets (SIZE), the volatility of profitability (VOLP), the Class Share Structure (CLASS), return on equity (ROE), and future values of ROE and stock returns (RETURN), up to the number of leads listed in the column headings. The reported slope coefficients and their standard errors are computed from the time-series of the estimated cross-sectional slope coefficients. The t-statistics, adjusted for any significant serial correlation in the time series, are in parentheses. Also given are averages across these years of the R2’s and of the numbers of observations from the cross-sectional regressions. The values in the first column are obtained from the regression of log M/B on log of age only.
Number of future ROE and RETURN included
0 1 5 10 15 CONSTANT 0.760 0.024 -0.029 -0.035 -0.259 -0.128 (11.97)*** (0.21) (0.24) (0.29) (2.05)** (0.40) lnAGE -0.131 -0.054 -0.051 -0.054 -0.018 -0.128 (6.05)*** (2.65)** (3.03)*** (3.56)*** (0.89) (1.82)* DD 0.038 0.006 -0.051 -0.103 -0.145 (2.68)** (0.43) (3.78)*** (3.42)*** (2.71)** LEVERAGE -0.470 -0.549 -0.644 -0.567 -0.518 (8.13)*** (10.32)*** (9.13)*** (6.68)*** (3.75)*** SIZE 0.039 0.030 0.024 0.025 0.034 (4.96)*** (3.99)*** (3.33)*** (3.08)*** (2.34)** VOLP 1.504 0.961 0.910 1.680 2.071 (2.69)** (2.36)** (2.93)*** (1.50) (1.45) CLASS 0.123 0.011 -0.107 -0.045 -0.021 (1.73)* (0.17) (1.98)* (1.83)* (1.47) ROE 1.697 1.120 1.166 1.332 1.168 (11.61)*** (9.67)*** (7.69)*** (7.41)*** (5.99)*** ROEt+1 1.859 1.381 1.557 1.256 (15.83)*** (11.26)*** (8.08)*** (6.79)*** ROEt+2 0.489 0.567 0.857 (2.83)*** (3.88)*** (3.82)*** ROEt+3 0.552 0.421 0.940 (3.37)*** (3.56)*** (5.74)*** RET U RNt+1 -0.277 -0.411 -0.459 -0.554 (10.07)*** (11.45)*** (9.53)*** (10.71)*** RET U RNt+2 -0.289 -0.334 -0.459 (8.12)*** (6.20)*** (5.50)*** RET U RNt+3 -0.211 -0.256 -0.401 (7.58)*** (6.31)*** (5.95)*** Average R2 0.04 0.25 0.42 0.60 0.70 0.84 Observations 198,166 62,168 47,640 19,750 7,186 2,694 Years 54 45 44 40 35 30 Firms 3670 1381 1082 494 206 90 * p < 0.1; ** p < 0.05; *** p < 0.01
5. Results 25
Table 5.2: The lnAGE coefficients for Dividend Payers versus Non-payers
For every year between 1962 and 2015, the log of the market-to-book ratio (M/B) is regressed cross-sectionally on the logarithm of the firm age (lnAGE), dividend dummy (DD), the interaction term lnAGE*DD, leverage (LEVERAGE), the log of total assets (SIZE), the volatility of profitability (VOLP), the Class Share Structure (CLASS), return on equity (ROE), and future values of ROE and stock returns (RETURN), up to the number of leads listed in the column headings. The reported slope coefficients and their standard errors are computed from the time-series of the estimated cross-sectional slope coefficients. The t-statistics, adjusted for any significant serial correlation in the time series, are in parentheses. Also given are averages across these years of the R2’s and of the numbers of observations from the
cross-sectional regressions. The values in the first column are obtained from the regression of log M/B on lnAGE and lnAGE*DD only. To obtain the t-statistics on the coefficients for non-dividend payers, the regression is rerun with DD redefined as its own complement.
Number of future ROE and RETURN included
0 1 5 10 15 Non-payers -0.183 -0.172 -0.169 -0.209 -0.145 -0.621 (7.26)*** (5.89)*** (6.23)*** (6.54)*** (2.75)*** (2.67)** Payers -0.125 0.007 -0.001 -0.010 0.002 -0.122 (5.59)*** (0.33) (0.05) (0.62) (0.10) (1.48) Difference 0.058 0.179 0.168 0.199 0.147 0.5 (1.72)* (4.95)*** (4.98)*** (5.56)*** (2.60)** (2.02)** Average R2 0.06 0.25 0.42 0.59 0.70 0.83 N : Non-payers 111,120 38,230 29,167 12,014 4,371 1,629 N : Payers 87,046 29,948 22,917 9,441 3,435 1,281 Observations 198,166 68,178 52,084 21,455 7,806 2,910 Years 54 45 44 40 35 30 * p < 0.1; ** p < 0.05; *** p < 0.01
to be the specification with 5 future values included in the regression, as was also mentioned before.
Following my 2nd hypothesis that non-dividend paying firms have stronger effects on their M/B ratio due to learning I run a regression segregating into 2 sub-samples in order to find the effect for dividend paying firms and non-paying ones. This is done by including a cross product of lnAGE and the dividend dummy DD, on the right-hand side of the equation. In the table 5.2 you will find the coefficients of non-payers and payers together with the difference and their t-statistics. In all specifications
26 5. Results
Table 5.3: The lnAGE coefficients for Dual Class Firms versus Non-Dual Class
For every year between 1962 and 2015, the log of the market-to-book ratio (M/B) is regressed cross-sectionally on the logarithm of the firm age (lnAGE), dividend dummy (DD), the interaction term lnAGE*CLASS, leverage (LEVER-AGE), the log of total assets (SIZE), the volatility of profitability (VOLP), the Class Share Structure (CLASS), return on equity (ROE), and future values of ROE and stock returns (RETURN), up to the number of leads listed in the column headings. The reported slope coefficients and their standard errors are computed from the time-series of the estimated cross-sectional slope coefficients. The t-statistics, adjusted for any significant serial correlation in the time series, are in parentheses. Also given are averages across these years of the R2’s and of the numbers of observations
from the cross-sectional regressions. The values in the first column are obtained from the regression of log M/B on lnAGE and lnAGE*CLASS only. To obtain the t-statistics on the coefficients for non-dividend payers, the regression is rerun with CLASS redefined as its own complement.
Number of future ROE and RETURN included
0 1 5 10 15 Non-Dual Class -0.132 -0.053 -0.051 -0.054 -0.018 -0.128 (6.10)*** (2.62)** (2.99)*** (3.57)*** (0.89) (1.82)* Dual Class 0.232 0.616 0.177 0.016 -0.022 -0.005 (2.60)** (2.61)** (1.02) (0.26) (1.91)* (0.89) Difference 0.364 0.669 0.228 0.07 0.004 0.123 (3.06)*** (2.82)*** (1.30) (1.10) (0.17) (1.73)* Average R2 0.04 0.24 0.41 0.59 0.69 0.83 N : Dual Class Firms 190 190 190 190 190 190 N : Non-Dual Class Firms 197,976 67,988 51,894 21,265 7,616 2,720 Observations 198,166 68,178 52,084 21,455 7,806 2,910 Years 54 45 44 40 35 30
* p < 0.1; ** p < 0.05; *** p < 0.01
the lnAGE coefficients are negative and statistically significant for non-payers. As for payers, the coefficient is only statistically significant in the first specification and they are not always negative. We can see that in all regression the effect is stronger (more negative) for non-dividend paying firms than for paying ones and this is also backed by the differences which are all statistically significant. The differences are all statistically significant, which is really important because it also backs my hypothesis in the statistical significance level. As an interpretation, consider a typical firm that doesn’t pay dividend and is 2 years old. It’s M/B ratio is approximately 2.2. Taking
5. Results 27 the value of -0.145 of the lnAGE coefficient an otherwise identical firm that is just one year younger is expected to have a M/B of 2.519. Thus, a one-year difference in age tends to lead in a valuation difference of 14.5%. A similar task for a typical 5-year old firm which has a M/B ratio of 1.66 shows that the valuation for a identical one-year old firm is higher by almost 72.5%.
Continuing on my third and last hypothesis, which states that Dual Class firms tend to have weaker effects on their M/B ratios because of learning I run a regression by including an interaction term, which is the cross product of CLASS and lnAGE, on the right-hand side of the regression. In the table 5.3 you will find the coefficients of non-dual class firms and dual-class firms together with the difference and their t-statistics. In all specifications the lnAGE coefficients are negative and statistically significant but when having 10 future values for non-dual class companies. As for dual-class firms, the coefficient is statistically significant in three specifications and they are mostly positive.We can see that in all regression the effect is stronger (more negative) for non-dual class firms than for dual-class ones and this is also backed by the differences which are statistically significant in 3 occasions backing my hypothesis for weaker impact on dual-class firms. As an interpretation, consider the typical firm that doesn’t have a dual share class structure and is 2 years old. It’s M/B ratio is around 1.908. Taking the value of -0.054 of the lnAGE coefficient an otherwise identical firm that is only one year younger is expected to have a M/B of 2.01. Thus, a one-year difference in age tends to lead in a appraisal difference of 5,4%. A similar exercise for a typical 5-year old firm which has a M/B ratio of 1.479 shows that the valuation for a identical one-year old firm is higher by almost 27%.
The insight for my assertion is really interesting. Considering all these firms like Facebook, Alibaba, Yahoo etc. and how they seem to keep up with their initial good market valuations, the direction for future research for firms like the ones mentioned
28 5. Results is really interesting. High-tech companies seem to have an edge over the others and the fact that initial owners are still running those firms even with the minority of shares and still performing well is fascinating. Even though there are data about dual share structure firms only after 2007, and that is why my dataset about such firms was very limited, in future years there should be some direction in understanding the special nature of those firms and further research should be highly encouraged.
29
6
Robustness Checks
Following the results form my empirical investigation, it seems plausible to check other ways defining my methodology and variables in order to make sure that I didn’t define some variable in a wrong way and consequently have underestimated or overestimated results and even wrong directions for the coefficients.
First and foremost, share repurchase (or stock buyback) is defined as the re-acquisition by a company of its own stock. It serves a more flexible way (relative to dividends) of giving back cash to shareholders. Hence, a share repurchase is a broader definition for a dividend and it is important to redo the analysis defining dividend payers as firms that paid any dividend or repurchased any common stock in a given year. In order to save some space the results of the regression of table 5.1, but now with DD redefined, are not shown. What we get from the analysis is very similar to the initial results.
Next, what is going to be shown is table 6.1, in which I run a regression segre-gating into two sub-samples in order to find the effect for dividend paying firms and non-paying ones with the dividend dummy broadly defines as explained before. This is done by including a cross product of lnAGE and the dividend dummy DD, on the right-hand side of the equation. In the table 6.1 you will find the coefficients of
30 6. Robustness Checks
Table 6.1: The lnAGE coefficients for Dividend Payers versus Non-payers (Stock Repurchase counted as dividend)
For every year between 1962 and 2015, the log of the market-to-book ratio (M/B) is regressed cross-sectionally against the logarithm of the firm age (lnAGE), dividend dummy (DD), the interaction term lnAGE*DD, leverage (LEVER-AGE), the log of total assets (SIZE), the volatility of profitability (VOLP), the Class Share Structure (CLASS), return on equity (ROE), and future values of ROE and stock returns (RETURN), up to the number of leads listed in the column headings. The reported slope coefficients and their standard errors are computed from the time-series of the estimated cross-sectional slope coefficients. The t-statistics, adjusted for any significant serial correlation in the time series, are in parentheses. Also given are averages across these years of the R2’s and of the numbers of observations
from the cross-sectional regressions. The values in the first column are obtained from the regression of log M/B on lnAGE, lnAGE*DD and DD only. To obtain the t-statistics on the coefficients for non-dividend payers, the regression is rerun with DD redefined as its own complement.
Number of future ROE and RETURN included
0 1 5 10 15 Non-payers -0.147 -0.187 -0.183 -0.233 -0.175 -0.918 (8.68)*** (5.78)*** (6.15)*** (5.62)*** (2.72)** (3.85)*** Payers -0.129 -0.016 -0.025 -0.028 -0.010 -0.122 (5.87)*** (0.91) (1.64) (2.04)** (0.54) (1.48) Difference 0.018 0.171 0.158 0.205 0.165 0.796 (0.64) (4.64)*** (4.72)*** (4.69)*** (2.46)** (3.15)*** Average R2 0.06 0.25 0.42 0.59 0.70 0.83 N : Non-payers 111,120 38,230 29,167 12,014 4,371 1,629 N : Payers 87,046 29,948 22,917 9,441 3,435 1,281 Observations 198,166 68,178 52,084 21,455 7,806 2,910 Years 54 45 44 40 35 30 * p < 0.1; ** p < 0.05; *** p < 0.01
non-payers and payers along with the difference and their t-statistics. In all specifica-tions the lnAGE coefficients are negative and statistically significant for non-payers. As for payers, the coefficient is only statistically significant in the first specification and the fourth one and they are always negative in contrast to table 5.2, which has in two specifications 2 positive ones. We can see that in all regressions the effect is stronger (more negative) for non-dividend paying firms than for paying ones and this is also backed by the differences which are all statistically significant. The differences
6. Robustness Checks 31
Table 6.2: Determinants of the 1st difference of the M/B ratio
For every year between 1962 and 2015, the change of log of the market-to-book ratio (M/B) over 1 year is regressed cross-sectionally against the logarithm of the firm age (lnAGE), dividend dummy (DD) which is broader defined considering share repurchase as a dividend ,leverage (LEVERAGE), the log of total assets (SIZE), the volatility of profitability (VOLP), the Class Share Structure (CLASS), return on equity (ROE), and future values of ROE and stock returns (RET), up to the number of leads listed in the column headings. The reported slope coefficients and their standard errors are computed from the time-series of the estimated cross-sectional slope coefficients. The t-statistics, adjusted for any significant serial correlation in the time series, are in parentheses. Also given are averages across these years of the R2’s and of the numbers of observations from the cross-sectional regressions. The values in the first
column are obtained from the regression of the 1-year difference of log M/B on lnAGE only. Only the coefficients of lnAGE are reported.
Number of future ROE and RETURN included
0 1 5 10 15 lnAGE 0.044 0.041 0.030 0.023 0.018 -0.003 (3.06)*** (5.32)*** (4.31)*** (2.91)*** (1.85)* (0.20) Average R2 0.02 0.44 0.51 0.62 0.68 0.82 Observations 174,658 68,178 52,084 21,455 7,806 2,910 Years 50 45 44 40 35 30 * p < 0.1; ** p < 0.05; *** p < 0.01
are all statistically significant except in the first specification, which is really impor-tant because it also backs my hypothesis in the statistical significance level. As an interpretation, consider the typical firm that doesn’t pay dividend and is 2 years old. It’s M/B ratio is around 2.2. Taking the value of -0.175 of the lnAGE coefficient an otherwise identical firm that is only one year younger is expected to have a M/B of 2.585. Thus, a one-year difference in age tends to lead in a valuation difference of 15.5%. A similar task for a typical 5-year old firm which has a M/B ratio of 1.66 shows that the valuation for a identical one-year old firm is higher by almost 87.5%. Overall, even with dividends defined more broadly, we can see that our results don’t change and non-dividend payers have stronger effects on their valuations due to learning than dividend paying firms have.
32 6. Robustness Checks
Table 6.3: Determinants of the 3rd difference of the M/B ratio
For every year between 1962 and 2015, the change of log of the market-to-book ratio (M/B) over 3 years is regressed cross-sectionally against the logarithm of the firm age (lnAGE), dividend dummy (DD) which is broader defined considering share repurchase as a dividend ,leverage (LEVERAGE), the log of total assets (SIZE), the volatility of profitability (VOLP), the Class Share Structure (CLASS), return on equity (ROE), and future values of ROE and stock returns (RETURN), up to the number of leads listed in the column headings. The reported slope coefficients and their standard errors are computed from the time-series of the estimated cross-sectional slope coefficients. The t-statistics, adjusted for any significant serial correlation in the time series, are in parentheses. Also given are averages across these years of the R2’s and of the numbers of observations from the cross-sectional regressions. The values in the first column are obtained from the regression of the 3-year difference of log M/B on lnAGE only. Only the coefficients of lnAGE are reported.
Number of future ROE and RETURN included
0 1 5 10 15 lnAGE 0.091 0.153 0.140 0.090 0.068 0.033 (1.79)* (8.74)*** (7.73)*** (5.89)*** (4.13)*** (0.98) Average R2 0.03 0.18 0.24 0.33 0.45 0.65 Observations 140,808 66,887 51,112 21,048 7,646 2,863 Years 50 45 44 40 35 30 * p < 0.1; ** p < 0.05; *** p < 0.01
ratio over time for a given stock. As was shown in my descriptive statistics and in figure 4.1 the decline in M/B ratios seems to be steeper in the first years of a firms life and thus younger firms should have higher decreases in their M/B. I first consider a 1-year and then a 3-year difference in M/B ratio. This is done by running again the main model in my thesis but now having as dependent variable the change in M/B.
In table 6.2, we can see the determinants of the 1st difference of the M/B ratio. Only the lnAGE coefficients are shown in order to save some space. The prediction I previously maid is firmly backed by the results. In all specifications except the last one, the coefficients are positive and statistically significant. This means that changes in M/B ratios are more negative for younger firms.
6. Robustness Checks 33 order to check the differences in even greater distance in time. In table 6.3, we can see the determinants of the 3rd difference of the M/B ratio. Again only the lnAGE coefficients are shown in order to save some space. The prediction I previously maid is firmly backed by the results again, now even in differences across more years. In all specifications except the last one, the coefficients are positive and statistically significant. This again means that changes in M/B ratios are more negative for younger firms.
34
7
Conclusion
In this thesis, an empirical analysis is conducted in order to develop a framework for valuing stocks whose average future profitability is unknown. The main empirical strategy is based on a multiple cross-sectional regression having as dependent variable the M/B ratio and as main independent variable the firm age, which is the proxy for learning following Paśtor and Veronesi (2003). The other proxy for learning, which could be a more interesting one is the dispersion of the forecast of the analysts’ reports but it wasn’t used because it is biased towards big and established stocks. Moreover, many known determinants of M/B are used for controls such as leverage, asset size, volatility of profitability, current return on equity value and future ROE and future stock returns, which are the proxies for future profitability and return predictability respectively. All the coefficients are time series averages of the cross-sectional regressions following the Fama MacBeth approach.
My model predicts that with ageing comes a decline in the Market-to-Book ratio of a firm and this effect is even stronger for non-dividend paying companies which is also supported by the model of Paśtor and Veronesi (2003). Even when redefining as dividend paying firms those which also repurchased any shares whatsoever the results are similar. In the paper of Fereira et al(2007), in one of their regressions they find
7. Conclusion 35 similar results about ageing even though they use informational measures. They also find similar signs for the coefficients of leverage and assets size, which are negative and positive respectively. The current ROE and the future values of it are positively related to the M/B ratio confirming Paśtor and Veronesi (2003). The future stock returns are negatively associated with the M/B, which is also found by Paśtor and Veronesi (2003) and of course by Fama and French (1993) in their famous three factor CAMP model. It is also interesting to stress out that the future values are used in hindsight and are not predictions of them.
The also interesting assertion that the Market-to-Book ratio has a steeper decline when considering younger firms is also backed by my analysis. This is proved when regressing the difference of the M/B ratio across years against all of the previously mentioned variables. In any year difference used, a significant and positive coefficient for firm age is found. Thus, the model is also endorsed by the prediction that the decline in the M/B ratios is faster for younger firms.
A new element added to the current literature is how learning affects companies that have dual class share structure. The outcome of the analysis is that learning has a weaker effect on dual class firms than on other regular companies. Even though there is a relatively low but sufficient sample, the result is significant. Of course, the number of observations is a limitation to my analysis and a wider sample could be more interesting to use. Therefore, there is a large space for future research on those kind of firms.
The other important factor in my analysis is the variable capturing uncertainty, which is the volatility of profitability. The results supports my prediction that un-certainty raises relative valuations. The coefficient of V OLP (volatility) is positive and significant supporting my assertion. This is also shown by Paśtor and Veronesi (2003, 2006) and also backed by Leipold et al (2007) and Fereira et al (2007). The
36 7. Conclusion implications of this outcome for investors are very important. Knowing that newly listed firms are most likely to have overestimated values due to uncertainty can lead investors and entrepreneurs to invest in those firms in order to exploit this situation and reap the benefits.
37
8
Appendix
8.1
Autoregressive Integrated Moving Average
Model (ARIMA)
An ARIMA(p,d,q) model, where p the order of the AR process, d is the difference and q is the order of the MA process, is shown in the following way:
(1 − p X i=1 aiLi)Xt= (1 + q X i=1 θiLi)t
where X is the variable, L is the lag operator, the αi are the parameters of the
autoregressive part of the model, the θi are the parameters of the moving average
part and the t are error terms. The error terms t are generally assumed to be
independent, identically distributed variables sampled from a normal distribution with zero mean.
Depending on what path the autocorrelations and partial autocorrelation follow on a plot we can detect what order is the AR and the MA model. Depending on the stationarity of the model we choose the difference order. If our variable is not
38 8. Appendix stationary then we take the first difference of that variable in order to have a stationary process. We keep on up-scaling the order until we have stationarity.
In this thesis the ARIMA model is used to calculate the volatility of the stock return. Based on my calculations I found that the stock returns follow on average an AR(2)process because the autocorrelations fade out exponentially and only the first two partial autocorrelations are different than zero and a first difference was needed to have a stationary process. Therefore, an ARIMA(2,1,0) model was needed and the standard deviation of the predict returns of the model was used a the volatility of profitability (V OLP ).
39
9
References
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40 9. References [7] Ľuboš Paśtor and Pietro Veronesi, 2006, Was there a Nasdaq bubble in the late
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