The dividend puzzle misspecification – Why the role of dividends is not what people think

Goyal, Shreyansh Article The dividend puzzle misspecification – Why the role of dividends is not what people think Cogent Economics & Finance Provided in Cooperation with: Taylor & Francis Group Suggested Citation: Goyal, Shreyansh (2019) : The dividend puzzle misspecification – Why the role of dividends is not what people think, Cogent Economics & Finance, ISSN 2332-2039, Taylor & Francis, Abingdon, Vol. 7, Iss. 1, pp. 1-55, https://doi.org/10.1080/23322039.2019.1649000 This Version is available at: https://hdl.handle.net/10419/270675 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may be saved and copied for your personal and scholarly purposes. You are not to copy documents for public or commercial purposes, to exhibit the documents publicly, to make them publicly available on the internet, or to distribute or otherwise use the documents in public. If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by/4.0/ Full Terms & Conditions of access and use can be found at https://www.tandfonline.com/action/journalInformation?journalCode=oaef20 Cogent Economics & Finance ISSN: (Print) 2332-2039 (Online) Journal homepage: https://www.tandfonline.com/loi/oaef20 The dividend puzzle misspecification – Why the role of dividends is not what people think Shreyansh Goyal | To cite this article: Shreyansh Goyal | (2019) The dividend puzzle misspecification – Why the role of dividends is not what people think, Cogent Economics & Finance, 7:1, 1649000, DOI: 10.1080/23322039.2019.1649000 To link to this article: https://doi.org/10.1080/23322039.2019.1649000 © 2019 The Author(s). This open access article is distributed under a Creative Commons Attribution (CC-BY) 4.0 license. Published online: 13 Aug 2019. Submit your article to this journal Article views: 3061 View related articles View Crossmark data Citing articles: 2 View citing articles FINANCIAL ECONOMICS | RESEARCH ARTICLE The dividend puzzle misspecification –Why the role of dividends is not what people think Shreyansh Goyal* Abstract: The dividend payout problem in literature has largely been misspecified. The roles of dividends as signals, agency cost reducers, fixed income providers or even the invariance of dividend payouts are all phenomenon that, based on market conditions, follow from the role of dividends as equalizers of firm value, discounted from a given point in time, across firm’s life. In this study, I discuss few problems with prevalent approaches towards solving dividend puzzle in academia, provide justification for the aforementioned hypothesis based on few assumptions, derive a model applicable under ideal conditions and then measure the deviations from the ideal model in two market indices—Nifty 500 (India) and S&P 500 (USA). The results obtained are then compared with the studies already done on these market and the reasons for deviation are discussed. Once the dividend model is derived, all roles of dividend flow automatically from the primary role of dividends and the extent of efficacy of each of the secondary role is based on numerous factors which vary, giving different results across different studies. The empirical investigation gives a view of these different factors at work in the markets. Subjects: Corporate Finance Keywords: dividend puzzle; agency costs; invariance; dividend preference; market efficiency; market cycles; harmonise; role of dividends; US; India 1. Introduction Dividend payout decisions have been a subject of debate for a long time in academia. Both, the effects of dividend payout on value of the firm, and the factors which affect the payout ratio, have been extensively studied in order to solve the puzzle, though no uniform consensus has been ABOUT THE AUTHOR Shreyansh Goyal has a Master of Business Administration degree in Financial Management from University of Delhi, India. The main areas of research for the author are in fields of Corporate Finance and how it relates to the world economy. This study is part of a larger ongoing research about opportunity costs arising in economy and how they affect the nature of financial transactions in the markets. PUBLIC INTEREST STATEMENT The dividend payout and its relation to firm value has an impact on how investors make decisions about their financial corpus. In this article, it is proposed that the payment of dividends performs the primary function of affecting a firm’s value (discounted appropriately) in such a way the value of the firm remains same across time. A model derived from the assumption is then tested on two different types of economies—India (Nifty 500) and USA (S&P 500) and the results are discussed. The findings show that generally assumed roles of dividend payouts are a reflection of market conditions and are not the primary factors in affecting the dividend payout decisions and its effects. The implications of the theory are discussed subsequently. Goyal, Cogent Economics & Finance (2019), 7: 1649000 https://doi.org/10.1080/23322039.2019.1649000 © 2019 The Author(s). This open access article is distributed under a Creative Commons Attribution (CC-BY) 4.0 license. Received: 19 April 2019 Accepted: 23 July 2019 First Published: 27 July 2019 *Corresponding author: Shreyansh Goyal Department of Financial Studies, University of Delhi, Delhi, India E-mail: [email protected] Reviewing editor: Zhaojun Yang, Finance, Southern University of Science and Technology, China Additional information is available at the end of the article Page 1 of 55 reached. While there have been few theoretical models that do outline the effects of dividends on firm value trying to hypothesize how investors and firms behave or how they should behave, Black (1976) argued that such models were inadequate. Even after several decades, it is still not clear which of these models best describes the reality in the world of corporate finance, because of mixed evidence, an emotion best captured by Allen, Bernardo, and Welch (2000) who stated that “dividends remain one of the thorniest puzzles in corporate finance”. Baker, Powell, and Veit (2002) also echoed similar sentiments, stating that it was still unclear why managers prefer one way of cash distribution over another. For example, Miller and Modigliani's (1961) dividend irrelevance model (henceforth M&M model) that argues that dividend policy is irrelevant to the value of the firm, under certain assumptions, has been supported by Fama (1978), Hakansson (1982), Berlingeri (2006a) and empirical findings of Naceur and Goaied (2002) but has been critiqued by Ross (1977) and DeAngelo and DeAngelo (2006). Similarly, Gordon’s hypothesis (1959) that investors prefer a high dividend payout policy has also been a subject of critique, for example, by Miller and Modigliani (1961), Bhattacharya (1979) and Easterbrook (1984), though it has been defended by Gordon (1963) and to some extent by Shefrin and Statman (1984), who argue that regret aversion would result in preference of cash dividends over capital earnings. Other hypotheses like Signalling Hypothesis and Tax Effect Hypothesis have met similar fate. While the empirical studies by Pettit (1972), Woolridge (1983) and Asquith and Mullins (1986) support the idea that dividend decisions generate positive signals, in a study by DeAngelo and DeAngelo and Skinner (1996), such was not found to be the case. The effect of taxes on dividend decisions is likewise unclear. Despite Brennan (1970) arguing for stocks with higher dividend yield to have higher before-tax returns (due to lower prices), a study by Black and Scholes (1974) found the evidence of the impact of taxes on stocks with different yields to be insignificant. Thus, it can be safely assumed that a verdict on the impact of dividend policy on value of the firm is not out due to contradicting pieces of evidence and arguments. Few reasons for this discrepancy have been pointed out. McCabe (1979) points out how choice of variables used in the model may have an effect on the results obtained. Similar has been pointed out by Watts (1976). Morgan (1982) mentions how results can be conflicting because of use of dissimilar methods. Watts (1973) mentioned how even choosing a different definition of dividends distributed in a particular year could affect the results and “fiscal definition of dividends”and “overlap definition of dividends”could not be assumed to yield similar results. Lease, John, Kalay, Loewenstein and Sarig (2000) argue that discrepancies arise in empirical testing because the quantitative methods used in studies are unable to measure both marketand firm-specific imperfections and that optimal dividend policy for each firm can be different than the other, owing to situation the firm uniquely finds itself in. Another reason for this discrepancy to be persistent in literature could be that the nature of the markets, managers and investors might not be a constant, over sectors, geographies, cultures and time and may have a significant contribution to the primacy of one dividend policy over another. The more recent studies point towards the same. The study by Zheng and Ashraf (2014) show significant relationship between cultural dimensions proposed by Hofstede, Hofstede, and Minkov (2010)and dividend payment. Similarly, a study by Shao, Kwok and Guedhami (2010) found out that Schwarts’(1994) national culture dimensions have a significant relationship to dividend payouts. Thus, the cultural factors cannot be distanced from the payout decisions and their implications. Recent studies on the issue of dividend payouts affecting share prices also offer contradictory results. An earlier study by Allen and Rachim (1996) found that contrary to indication of Baskin (1989), causal relations between dividend yields and stock price volatility are not clear. This is in contrast to the study by Qudah and Yusuf (2015) which suggests that higher payout ratios lead to low stock price volatility. A study by Zainudin, Mahdzan, and Yet (2018) found out that in case of industrial product firms in Malaysia, in pre and post crisis periods, the dividend payout ratio affects stock price volatility. Hussainey, Mgbame, and Mgbame (2011) found that for UK-based firms, a positive relationship exists between dividend yield and stock price volatility while a negative relationship exists between dividend payout ratio and stock price volatility. Profilet and Bacon Goyal, Cogent Economics & Finance (2019), 7: 1649000 https://doi.org/10.1080/23322039.2019.1649000 Page 2 of 55 (2013) found an exactly opposite relationship for US-based firms though it is worth pointing out that the observed positive relationship between dividend payout ratio and stock price volatility was not significant. The existence of negative relationship between dividend payouts and stock price volatility, is important factor for many dividend preference hypotheses to be correct. One may think of approaching the issue in a different manner and instead of studying the effects of dividend payouts, might study the factors that affect the dividend payout. However, the literature is not definite even on that aspect. In a recent study by Kumar and Sujit (2018), partial least square structural modelling (PLS SEM) was used to determine the determinants of dividend policy. PLS SEM is a technique wherein it is possible to study the effect of variables that cannot be observed directly (referred to as “latent variables”) on a dependent variable or the observable effects arising out of the particular value(s) of the dependent variable. The factors like liquidity, leverage and profitability were found to have an effect on the dividend payout. Considering these latent factors were themselves made up of several sub-factors, and significant combined loadings and cross loadings were present, the dividend payout decisions appears to be a lot more complex that their effects be captured by simple hypothesis that look at few variables. Frankfurter and Wood (2002) argue that current models of dividend policy do not incorporate behavioural factors and that models based solely on economic justification are inadequate in explaining dividend decisions. As pointed out by Black (1976), because firms lack knowledge of how many irrational investors there are, they cannot choose an optimum dividend policy. Similarly, investors, without a knowledge of how other investors would behave, are left at best to guess the movement of stock prices using proxy indicators. While study on the nature and responses of market participants forms an aspect of behavioural finance, the proxies for such behaviour may be used to form some idea about the market, investor and manager behaviour. The proxies, themselves would be inter-dependent on each other and not strictly independent and thus have to be studied collectively, in way that can be called a “paired analysis”, an aspect which has been missing in most of the previous studies, which assume only a few relatively independent factors at work in the dynamics of the market expectations. The proxy indicators that ultimately affect the value of the firm may be obtained from dividend discount model. One such proxy indicator is the expected rate of return. The aggregate of all investors favouring different amounts of risk-adjusted returns, can be assumed to be an aggregate measure of individual expectations and behaviours. The other proxy indicator is the rate of growth in net income, which can be assume to be the aggregate of firm’s payout and investment decisions. The aim of this study is to present a way to connect the proxies to the dividend payout using a suitable theory, and create a model that can be useful for testing applicability and efficacy of different dividend policy mechanisms. For this, the study proposes a theory, linking firm and investor expectations with dividend payouts, provides justification for it and then tests the model and hypotheses arising out of it on the Indian firms listed on the Nifty 500 Index, to see whether they are in line with the other dividend studies done on Indian markets. Then, the model is used on S&P 500 Index and the results are tabulated and contrasted with results obtained for Nifty 500 Index. A short commentary contrasting US markets with Indian markets follows next and subsequently the model’s efficacy is discussed. The rest of the paper is organized as follows. Section 2contains a review of literature on the dividend policy of the firms, Section 3sets the background for the hypotheses, Section 4presents initial assumptions required for the hypothesis and a defence of them, Section 5contains the construction of hypotheses, Section 6 discusses the significance of hypothesis, Section 7discusses how the empirical test is constructed, Section 8mentions how data are collected for the empirical test on Indian market and discusses research methodology, Section 9presents the results and the analysis of the test, Section 10 contains application of the model on US market and Section 11 contains a discussion of the theory while Section 12 concludes. Goyal, Cogent Economics & Finance (2019), 7: 1649000 https://doi.org/10.1080/23322039.2019.1649000 Page 3 of 55 2. Literature review The factors influencing share prices have been interest to academia for quite a long time, and the history up to the irrelevance hypotheses and history succeeding it are intricately linked. One of the very early papers on dividend policy by Tinbergen (1933) argued that in case of absolute certainty that dividends would stay constant, the price of the stock would be equal to dividends paid divided by yield of state bonds, which could be put in equation form as follows: P¼Dc Y(2:1) Where P¼Price of stock per shareðÞ Dc¼Constant dividend paid per shareðÞ Y¼Yield of state bonds However, when dividends change, the static theory is no longer applicable. The changes in dividends paid, Tinbergen (1933) found only produced about half as intensive change in worth of the stocks (given by price of stock multiplied by yield of state bonds). The expectance of abnormal dividend in the future was only half of the abnormal dividend paid in the last year. The importance of the expectations, thus, played a part in determination of stock prices, even in as basic model as used by Tinbergen (1933). The model was as follows: W¼PY¼cþαD(2:2) Where W¼Worth of stock per shareðÞ D¼Dividends paid per shareðÞ The paper could be said one of the earlier attempts to implicitly demonstrate how effects of distribution of dividends may only produce a partial value increment to the value of the shares. Tinbergen (1939) added another factor to the equation aside from yield of state bonds and dividends paid. In the new model, called “the dynamic law of share price formation”, Tinbergen (1939) included rate of change in stock prices as another factor on which stock prices depend to account for speculation in the market. The stock prices were thus, dependent on dividends, interest rates and previous growth in stock prices, as follows: P¼α1Dþα2Yþα3_ P(2:3) Where _ P¼Rate of change in stock prices As such, the effect of speculation and herd instinct was included in the dynamics of share price formation. The price of a share was affected by the speculative interest in the share in the model, giving rise to yet another instance of value being dependent on investor expectations and not just raw yields received off the shares. The most direct affirmation of such expectations among these was arguably by Lintner (1956) who after studying corporate dividend policy suggested that corporations smoothed the dividend payout according to the following equation: ΔDi;t¼ciþαiD i;tDi;t1  (2:4) Goyal, Cogent Economics & Finance (2019), 7: 1649000 https://doi.org/10.1080/23322039.2019.1649000 Page 4 of 55 Where ΔDi;t¼Change in dividends paid for firm 0i0inyear 0t0 D i;t¼Target dividend ¼DPRT;iEi;t¼Target dividend payout Earnings in 0t0 Di;t1¼Dividend paid in year 0t10by firm 0i0 As such a view necessary entailed that dividend payouts moulded investor expectations, it is not surprising, thus, that one of the early views about impact of dividends was that companies that pay higher dividends would have higher stock prices. Graham and Dodd (1951) and Gordon (1959) argued for this view. Gordon (1959) also performed an empirical test on four types of industries and for two years, using data of prices, dividends and earnings and found that dividends had higher contribution to value of stocks than retained earnings. The equation Gordon used in his analysis was following: P¼α1Dþα2RE (2:5) Where P¼Year end equity value of the firm D¼Dividend paid in last year E¼Earnings retained in last year For only the earnings to be relevant in valuation of shares, Gordon (1959) argued that the expected rate of profit must be independent of the fraction of the income retained, which, according to him, was not the case. Gordon (1959) also proposed a refined model for the price of a stock which was as follows: P B¼β0þβ1  D Bþβ2 D D  Bþβ3 RE Bþβ4 RE RE  B(2:6) Where B¼Book value of the firm  D¼Average dividend paid RE ¼Average retained earnings The simple discount model when dividend payout ratio, expected rate of return and rate of growth in revenue is assumed to be constant could be put as follows: P0¼k ρgE0(2:7) Where P0¼Current total value of the firm E0¼Expected net earnings of the firm Goyal, Cogent Economics & Finance (2019), 7: 1649000 https://doi.org/10.1080/23322039.2019.1649000 Page 5 of 55 k¼Dividend Payout Ratio ρ¼Expected rate of return g¼Rate of growth in net income The present value of a stock could be represented thus by adding all incoming streams of dividends discounted appropriately, if the investors capitalized dividends over earnings and in such a case the retained earnings mattered only indirectly, as in a way they affected future dividends Such a view however came under criticism by Miller and Modigliani (1961) who argued that under certain assumptions, dividend policy would have no impact on value of the firm. The decreased retained earnings’effect on future dividends would, according to them, cause an equal but opposite change in value of the firm’s stock, under such assumptions, as caused by a present increase in dividend payout thus, in effect neutralizing the dividend policy effect on value of shares. VtðÞ¼ 1 ρtðÞþ1ðÞ EtðÞItðÞþVtþ1ðÞ½ (2:8) Where VtðÞ¼Total value of the firm at time 0t0 ρtðÞ¼Expected rate of return over the interval 0t0to 0tþ10 EtðÞ¼Firm0s total profit for period from 0t0to 0tþ10 ItðÞ¼Firm0s total investment in period from 0t0to 0tþ10 Vtþ1ðÞ¼Total value of the firm at time 0tþ10 That was because, Miller and Modigliani argued that in a “perfect market”, the company could raise money by selling its shares, if it pays the money required for investment in the next period as dividends and the cost of either of the option would be same. While the above equation by Miller and Modigliani (1961) was based on the assumptions of a perfect market, rational behaviour of investors and perfect certainty, even in case of uncertainty, granted assumptions of “imputed rationality”and “symmetric market rationality”, they argued, that dividend decisions would be irrelevant. Such a view was based on the idea that decisions like that of dividend payouts, or even corporate structuring decisions (Modigliani & Miller, 1958) were not by themselves value generating decisions mathematically and in a balanced equation, the effect on value of these decisions is impossible to factor in an ideal environment. Gordon (1963) critiqued Miller and Modigliani’s(1961) position and argued that such value generating proceeds from dividend payouts because delayed payments have higher uncertainty and investors are generally risk averse, thus making dividends preferable over retained earnings. It was an increase in the expected rate of return, he argued, that would increase if dividends were delayed, making share price go down and thus the dividend relevance was also a mathematical outcome and not just an empirical observation. Gordon argued that expected rate of return could be reasonably believed to be an increasing function of the rate of return from investment multiplied by fraction of earnings retained and the price equation thus could be restated as following: P0¼A0k ðÞ E0 ½ 1þ1k ðÞ r ½ α(2:9) WhereA0¼Factor depicting influence of all other variables except current dividend Goyal, Cogent Economics & Finance (2019), 7: 1649000 https://doi.org/10.1080/23322039.2019.1649000 Page 6 of 55 r¼The rate of return from investment Brennan (1971) argued against Gordon’s(1963) criticism of Miller and Modigliani’spositionby pointing that change in dividend payout does cause a change in firm value but only because such changes in payouts result in changes in investment levels. If the investment levels remain the same, as Miller and Modigliani (1961) assume, then dividend decisions would be irrelevant to the value of the firm. Yet, in such a case, Gordon’s main assumption of expected rate of return changing with the change in dividend payout would be violated. A change in investment amount, ΔItat time “t”, assuming the dividend payout ratio changes at time “t”equal to 0, would be given by following: ΔIt¼1k0 ðÞE0Y 1 τ¼1 1þgðÞ1k0 0  E0Y 1 τ¼1 1þg0 ðÞ (2:10) For the total effect of all change in investments, when appropriately discounted, on value of the firm, to be equal to zero, sum of appropriately discounted change in investment levels must equal to the appropriately discounted return accrued by them, from the point in time such changes are made, leading to the following: ∑ 1 t¼1 ΔIt 1þρt ðÞ t¼r∑ 1 t¼1 ΔIt 1þρt ðÞ t∑ 1 τ¼1 1 1þρtþτ  τ(2:11) Brennan argued that a general solution of the equation when r¼ρwhere ρis average discount rate is when ρtis constant. So, in general, ρtwill have to be invariant with respect to time, and dividend payout policy. And thus Gordon’s explanation for his relevance hypothesis was inconsistent with his hypothesis. Rubinstein (1976) mentioned two ways of proving dividend irrelevance, granted assumptions of Miller and Modigliani hold in the market in consideration. The first way, Rubinstein pointed, is to keep the investment levels constant. Then, a fair value transaction of shares for money would be used to compensate for dividends paid. This is the way used by Miller and Modigliani (1961), Rubinstein argues, evident in the use of following equation: Ptþ1ðÞNstþ1ðÞ¼ItðÞXtðÞDtðÞ½ (2:12) Where Ptþ1ðÞ¼Ex dividend price of shares at the start of time period 0tþ10 Nstþ1ðÞ¼Number of shares sold at price P t þ1ðÞ The increase in dividends of the firm by addition of investment will be matched by an equal increase in equity of the investors, thus, keeping the level of investment constant. This policy of “substitute financing”, Rubinstein points out, allows one to separate effects of dividend decisions from the effects of investment decisions. The second way is to allow investments to vary, but in such a way that the effect of any change in investment level on value of the firm is zero. Such will be the case, if the net present value of any change in investment level is zero, and could be called “neutral reinvestment”approach and was used by Brennan (1971) in his proof. Rubenstein then proceeded in his paper to generalize the neutral investment approach for conditions with uncertainty. These mathematical proofs by Brennan (1971)andRubinstein(1976) seemed to have turned the discussion at least partially away from the mathematical validity of the irrelevance hypothesis, for then the debate largely centred around empirical validity of the irrelevance hypothesis. Black (1976), for example, in an attempt to reconcile the theory with empirical observations, wondered why, in presence of taxes on dividend payout, firms continued to pay substantial amount of dividends, calling this seeming contradiction, a “dividend puzzle”. The proofs presented by the academia also seemed to be, in many studies, in contrast to intuitions of managers, and the empirical Goyal, Cogent Economics & Finance (2019), 7: 1649000 https://doi.org/10.1080/23322039.2019.1649000 Page 7 of 55 their monetary value or they can also be subsumed in expected rate of return. M&M model can be converted into Equation (2.7) under certain assumptions. The equation consists of all the value creators that are derived from the theoretical assessment of present value of cash flows to investors in form of dividends. Hence, the equation is of great value in solving the dividend puzzle. A simple dividend discount model defines value of a firm to be equal to the product of a constant dividend payout ratio in the next period multiplied by the net earnings accrued in the next year, divided by difference of a constant expected rate of return and a constant rate of growth in earnings. Hence, the value of the firm may be defined by only four variables, if assumptions behind the model hold. The price to earnings ratio of the firm, which indicates the premium at which the shares of a firm are selling, with respect to its earnings, is measurement of all relevant expectations about the firm. The expectations about the firm thus, is associated with three variables—dividend payout ratio, which is based on firm decision, rate of expected return, which is primarily based on investors perception of the surrounding economy and thus, the opportunity cost, and rate of growth in earnings, which is arguably, dependent on both firm decision and investors’perception of the surrounding economy. The three variables are related and to some extent, can act to counter effects of each other. When a firm raises payout, the value of the firm would increase (if growth and investors’expectation remain constant). However, on a higher payout, the retained earnings would be less. For a constant return on assets, the rate of growth in earnings would decrease. Which would offset the increase in value of the firm by a little amount. Also, if a higher payout exists within the whole economy, the expected rate of return would also increase as the opportunity costs increase. Similarly, the payouts may be decided by the current expected rate of return and growth rate in earnings of the firm. In fact, in order to decide the value of the cash that is retained and not paid out to investors in form of dividends, one must know the value at which to discount such cash (be it at the current or marginal opportunity cost) and the growth in earnings that such cash on investment in the firm itself, would produce. Without an analysis understanding cumulative and singular effects of each of the factor, in presence of complex workings of economy, the results of a study may lead to an observation of different results in different countries or at different time periods, or on different sets of companies, giving appearance of dominance of one dividend theory over another. To form a valuation hypothesis, few assumptions about the nature of the ecosystem for which the hypothesis is to be crafted need to be made. Firstly, the very basic assumption of “perfect capital markets”as used in Miller and Modigliani (1961) and a slightly modified assumption of “rational behaviour”, that is, the investors prefer more risk-adjusted returns to less, are taken. Hence, unlike as Miller and Modigliani assumed, the indifference of the investor towards cash payments or a corresponding increase in value of the firm is not assumed for this paper, because the risk factor of the two alternatives is not necessarily the same, as outlined by Gordon (1963). The assumption of “perfect certainty”is not necessary, however, assumptions of “imputed rationality”and “symmetric market rationality”are taken, in the similar vein as taken by Miller and Modigliani. It is also assumed, that the firm cannot raise any money from the market, in any form. This assumption is only required for an easier analysis and is not required for the applicability of the theory, as long as the firm raises money at fair value. In fact, if any such raising of money takes place, the same analysis can be done by just assuming the money raised as part of another corporation with a proportionate division of financial attributes. The equation derived from dividend discount model is not enough to test the presence or absence of dividend policy mechanisms because if for some reason for given values of payout ratio, expected rate of return and growth rate in earnings, the value of the firm does not match, one can easily argue that Goyal, Cogent Economics & Finance (2019), 7: 1649000 https://doi.org/10.1080/23322039.2019.1649000 Page 14 of 55 there is a difference in, for example actual long-term growth rate and growth rate taken in the model or actual long-term expected rate of return and expected rate of return taken in the model. This is because there is no way to reliably estimate the long-term values of these variables. Hence, two further constraints are required that are theoretically sound to get a reliable result. In M&M model, the constraint applied is that under certain assumptions, the expected rate of return for all firms in the market has to be equal (otherwise arbitrage would take place). However, that constraint is problematic because there is some evidence that dividend payout does impact expected rate of return or value of the firm. Another hypothesis that is consistent with Gordon’s(1959) view is proposed. The hypothesis that the paper proposes is that from any point in time “t”, the value of the firm at all points in time subsequent to “t”, should ideally be expected to be same as value of the firm at time “t”, appropriately discounted. This can be called the “Equal Value Equilibrium”hypothesis. Such a statement appears to be tautologically true. If discounted by the actual growth factor, it is expected that the value of the firm would appear to be the same. However, while being circular, the statement is informative because it allows one to form an epistemic criterion for figuring out active dividend policy workings in a market. In context of the hypothesis statement, the term “ideally”is of great importance. There are three assumptions inherent in this term. (1) No Response Friction/Delay—There is no delay in change of any variable in response to any change in other variable, that is there are no frictions in market which slow down the rate of change of any variable to anything less than immediate. (2) No Efficiency Change—There is no change in efficiency of firm, in any capacity. (3) Epistemic Perpetual Existence—The firm(s) under consideration is(are) expected by investors and respective managers to last until perpetuity. None of these three assumptions is expected to be true. Their role is to merely allow for a possibility to derive an “ideal”value of the firm. 4. Analysis of assumptions (1) No Response Friction/Delay The first assumption is important to make any meaningful assertion. If there was any delay in change of variables and instead of immediately achieving their final value, the variables moved towards the value in accordance with a function dependent on time, then the lowest unit of period taken would be relevant as each change would have to be measured in terms of that small unit of time and the deviations from the required trend in that duration may produce over-arching effects even in the long-term data. However, in context to the perpetual existence of firm, any such aggregation of function response in case of a delay, if finite, can be reasonably assumed to amount to nothing significant. Assume for example that a payment, appropriately discounted, to investors by the firm was a function of time along with several other factors from a 1 to a n . Hence, Payf;t¼ft;a1;a2;...:; an ðÞ The value of the firm for each unit of time “t u ”under assumption of delay, using the function and the value of the firm for each unit of time under the “ideal”condition would be, in both the cases, just the sum of respective appropriately discounted payments, which the investors in the firm receive. Goyal, Cogent Economics & Finance (2019), 7: 1649000 https://doi.org/10.1080/23322039.2019.1649000 Page 15 of 55 Consider that before “t”, the actual value of firm and the value of the firm under ideal conditions are same. Further assume that a change takes place at time “t”causing a difference in the two values subsequently. The algebraic error in value of the firm at time “t”would simply be the sum of all deviations from the ideal value Videal f;t. error Vf;t  ¼ΔVf;tþi¼Videal f;tVf;t¼∑ 1 i¼1 ΔPayf;tþi Considering all deviations due to the change at time “t”settle to (approximately) zero, via some function, so as to become almost meaningless, in time “d”, error Vf;t  ¼ΔVf;t¼∑ d i¼1 ΔPf;tþi The relative error in estimating the value of the firm would be ΔVf;t Videal f;t ¼∑d i¼1ΔPf;tþi ∑1 i¼1Pideal f;tþi The relative error is what would be significantly worth of interest practically to the investors in the market as that would be responsible for wrongful estimation in returns that investors would receive. Considering, we have assumed that any deviation in valuing paymentswoulddecreasewithtime,thenumeratoris a finite and overall decreasing with time, and thus would have a finite value. The only way for relative error value to be not (close to) zero would be if the denominator itself converges to a finite value. Now, one could argue that it is to be expected that the denominator would converge, this is what enables us to derive finite value of a company’s stock and this is why a company’s shares have finite value, but such has little ground to stand on, granted a belief in firm’s perpetual existence. It is impossible to hold that a firm would have perpetual existence in any meaningful terms and simultaneously hold that its value converges. To understand the scenario, it would be appropriate to construct a simple thought experiment. Imagine an industry that produces a resource “X”. By owning a membership pass costing “W”of that industry, one could have a specific amount of that resource, let’s say “A”, delivered to his home, on the last day of every year. The worth “W”of the pass may be calculated as: W¼P1A 1þρðÞ 1þP2A 1þρ ðÞ 2þP3A 1þρ ðÞ 3þ... Or, alternatively as: W¼∑ 1 i¼0 PiA 1þρðÞ i The total quantity, “Q”, acquired would be Q¼∑ 1 i¼0 A So, technically, if “W”would converge, it would be possible to get an infinite amount of the resource, even if not at the same time, for a finite cost. This would mean that effective price of a unit of resource would be zero. However, such would not be the case if one buys the same quantity of resource in a - single day, and uses “A”amount of it, every year. In this case, the price of any unit of resource Goyal, Cogent Economics & Finance (2019), 7: 1649000 https://doi.org/10.1080/23322039.2019.1649000 Page 16 of 55 could be construed as either finite or infinite (depending on how price varies with quantity available, and whether the resource is available in finite quantity or has an infinite stock) but not zero. But should there be a difference as significant as this, between the two alternates of buying infinite amount of “X”at a given time and then consuming a specific amount of it, equal to “A” every year, and one buying and consuming quantity “A”at different times to a total amount of “X”? There seems to be no reason in support of such difference. One could similarly argue it for any other good, or any basket of products or for whole economy. But could one argue that for money? Money is merely a means of exchange of resources. If no resource singly, or jointly with any group of resources is free from the analysis, then inflation adjusted value of money would not be either, because it its value will be in terms of a specific amount of basket of goods it can buy. However, one, in theory, could construct a security, whose payments extend till perpetuity yet its value is convergent. A perpetual bond would be an example of that. The value “V b,t ”of the bond would be equal to Vb;t¼∑ 1 i¼tþ1 Cb;i 1þρðÞ i However, after elapse of some specific amount of time, let’s say “T”, it would be the case, in case the series converges, that the total value of the bond at time “t+T”, would be several orders magnitude less than the smallest unit of currency possible in the system. So, the bond, after “t+T” could be assumed to be worth practically nothing. This notion may be termed as “quantized nature of money”. One can see how this understanding applies to the firm’s equity, which is the main scope of discussion. Let us assume that someone buys x% of a company’s equity and receives dividend payments on it. The present value of any dividend payment received could be written as: Df;i¼kiEf;i 1þρ ðÞ i For the series involving addition of infinite payments of such dividends to converge, the payments received from the company should become smaller with time, tending to zero at infinity. Yet, as discussed in case of perpetual bonds, the value of all future dividends after a point in time would become insignificant in comparison to the lowest unit of currency available in system. Now, one may argue here that the receding value of the company’s discounted payments of dividends is because a receding share of the total initial value used to buy stock is behind these payments. Of course, the value of the firm could be summed up as mere summation of discounted payment values receding with time. If the investor would reinvest the dividend amount from the previous period back into the company, he could get similar value from each payment. However, doing that would increase the number of shares he has in the company. This would not increase the value that his existing shares provide him every year. If an investor really believes in the growth of the company he is investing in, why would he accept a receding payment from the company, provided that he knows the company’s future situation accurately and the company’s growth rate and his expected rate of return stays the same? Goyal, Cogent Economics & Finance (2019), 7: 1649000 https://doi.org/10.1080/23322039.2019.1649000 Page 17 of 55 If every investor of the firm chooses reinvestment, the firm would have to raise new shares every year so that the investors could buy them. But it can be known by mere casual observation that such is not the case. So, what is happening? A suggested answer to the question would be looked into later. Now, the first assumption put forward here is not fully justified. That is why it is an assumption but not an assertion. That is because information does not travel to all stakeholders instantaneously. There is always a delay in spread of information. Investors also need not be rational, and there may be no credibly estimated long-term expected rate of return or rate of growth of the company. The dividend payout ratio may change every year. The assumption, while justified under certain conditions, which are necessary to produce any useful model, is not true. Yet it is required to get the “ideal”value of the firm, deviations from which could be measured. One of the techniques employed to account for and reduce deviations from the assumption in empirical observation has been to use a five-year gap in analysis, rather than a gap of a single year, which will allow a time for the deviations originating from the previous event to settle to some extent. (2) No Efficiency Change The second assumption is merely an affirmation of the fact that this paper and the model described within do not account for differential managerial inefficiencies which can be mitigated or any growth in returns that could be realized by better investment made possible by higher or limited corpus of retained earnings. Such a model would be highly specialized to account for unique situation and operation of each firm, which is not required to support the hypothesis in its practical form. Yet a separate treatment, assuming there is such a change that is reflected in the return on equity of the firm is performed in the end. In accordance with the assumption, the return on equity or the return on investment of the firm is assumed to be constant in all respects. (3) Epistemic Perpetual Existence The third assumption is a rather simple assumption to prevent taking in account each investor’s beliefs about the longevity of the company they are investing in. The firm may or may not exist till perpetuity. The assumption is only about the belief of investors, and not about the actual life of the company. If the investors already believe that the company has some finite life expectancy, then they would already believe the value of the firm to be confined to some range independently, which makes theorization of any model irrelevant, for any such expectation might necessarily require that investors expect firm to cease any economic activity and liquidate (assuming opportunity to speculate does not exist), as that would ensure that they at least get the book value of equity back. Or, if the investors really have a reason to believe that the value of the firm will rise and then fall to zero, and thus, liquidating it later is a better option, the question is why would anyone invest in the company for long term? The only way to make short-term profits would be to either get it from other investors whom would make long-term investment decisions or from operations of the firm. Yet the latter cannot be the case, if return on equity remains a constant. And the former would not be an option for rational investors who believe that the firm would eventually liquidate and they would get only the nominal/book value of the capital invested. 5. The construction of hypothesis Aside from assumptions mentioned, there are two assertions, which form the core of the theory, to be made in regards to the role of management and behaviour of the market and investors that relate to the value of the firm. Goyal, Cogent Economics & Finance (2019), 7: 1649000 https://doi.org/10.1080/23322039.2019.1649000 Page 18 of 55 The management of a stable firm, under the assumptions taken, would always try to institute dividends in such a way so as the value of the firm before paying the dividend remains equal to the value of the firm after paying the dividend, appropriately discounted for the period passed. The value of the firm, obviously, after payment of dividend, cannot be greater than the value of the firm before paying of the dividend if the return on investment remains constant, as assumed, because of any increase in efficiency of the firm, because any such change in efficiency of the firm in cutting down costs, or increasing profits would reflect in the change in return on investment. There could be a possible increase in value of the firm for a short time, because of perceptions about the firm, which may change in case of change in amount of dividends received or any news about the company, that may not have an effect on return on investment. However, as none of these changes would be backed by any change in financial aspects that matter, but are merely reflective of ungrounded perceptions, in a longer period of time, the effects of such change would vanish. For example, even if an increase in prices is caused by an increase in dividends which by some form of signalling hypothesis in action, may give a false perception about an increase in future earnings, in subsequent periods, as the earnings are not revised to match investor expectation, the price of share will fall. Without any transaction costs in the market, as assumed, the rotation of money invested in the firm by primary or secondary transactions in capital markets, would not be non-recoverable. However, the value of the firm after payment of dividend, cannot be lesser than the value of the firm before paying of the dividend because then the managers would be literally giving a part of value of the corporate entity to the shareholders, thus, treating the firm as a bond. The management thus, would be left with a firm of lower value than what they possessed earlier and would be, in effect, destroying value of the firm. It should be noted that this assumes the corporate veil. Firms are separate entities than the shareholders. The earnings retained in the firm are not the same as earnings retained by its shareholders or vice versa, even if a transaction from one to other can take place at no transaction costs, because even if the value of the two options is assumed to the same, the state the money is in is different. Having money invested in firms, grants special privileges, that are not possible if the shareholder keeps the money with himself and does not invest. However, it should be noted that as we move from the limited liability public companies to proprietorship, the effect of the assumption decreases. The firms’perpetual existence is thus, an important consideration for the firm management. Yet, in the case of public limited liability companies, while such, may definitely occur in short term, without any change in return on investment and no transaction costs to lose money, along with the fact that such, if occurred in a long term would cast doubt an assumption of perpetual existence of the firm, there is a justification to hold that such process could not be a long-term process, of course on the assumptions held. To understand via an illustration, consider two firms “X”and “Y”which are very similar and have same initial value and initial value per share. Let us further assume that a person “P” invests an amount “A”in the firm “Y”, which pays no dividend, and gets the expected rate of return “E”inoneyear.Thus,afterayear,theassetsof“P”increase by “AE”. Consider, however, that firm “X”pays a dividend “D”on an investment of amount “A”. The value of the invested amount “A”in firm “X”after a year, considering the same expected rate of return “E”would be equal to “A(1 + E)-D”. While both the firms pay the same value to their investors considering both the dividends paid and capital gains, the value per share of firm “Y”becomes more than the value per share of firm “X”.If such a scenario continues for a long time, the value of firm “X”, provided number of shares remain the same, will be reduced to a small fraction of the value of the firm “Y”and for the same level of debt-equity ratio, the management of the firm “X”will be left in charge of controlling a relatively decreasing share of assets in the market. Such a position, even under assumptions of a constant return on equity, would not be what firm’s management could be assumed to desire, nor such a position is likely keep the rate of return on equity constant for a long time. Goyal, Cogent Economics & Finance (2019), 7: 1649000 https://doi.org/10.1080/23322039.2019.1649000 Page 19 of 55 The second assertion is that the investors in the market would always try to price the firm in such a way, that the value of the firm, under the assumptions taken, before paying the dividend remains equal to the value of the firm after paying the dividend. This in addition to the workings of the management, producing a “double effect”on firm pricing, but for similar reasons, as investors would perceive the firm to remain a going concern till perpetuity. Thus, when a firm pays out more dividend, the investors, instead of changing the future value of the firm, as would be in the case of Miller and Modigliani’s assumptions, would change their discount rate. That makes sense, as the investors really cannot control the value or the price of the firm as easily, but they can alter their expectation rates in response to a piece of information or an event easily. This not only allows theoretical preference of expected rate of return over value of the firm as variable expected to be the more directly under control of the investors but also allows the less risky nature of cash in hand, obtained via payment of dividends, to be accommodated in the equation. The hypothesis rests on the idea that the expected value of dividends paid by the company must be dependent on and adjust itself to the dividends actually paid. If investors find that there is any change in dividend, their expectation of rate of return changes in response to that. Thus, instead of causing a change in the value of the firm, the payment of dividend can be assumed to change the expected rate of return. That seems more reasonable because the most significant difference between equal amount of dividends and capital gains is not primarily of value, but of risk, and any change in risk adjusted value is subsequent of the change in risk and opportunity cost. The above statement is what harmonises the central premises of Miller and Modigliani’s model with the Gordon model. Miller and Modigliani’s model attempts to show that in presence of its central assumptions, the value of both options should be same, and if it were not, it would become so by arbitrage. And the Gordon model still proposes investor’s preference of dividends over capital gains and thus such preference must come from the lowered risk posed by the dividends, if not by the value of the two options. The only way to accommodate a functioning arbitrage with differential risk adjusted value of dividends and capital gains is by the hypothesis in the paper. Imagine a firm “f”in a perfect market “M”(as defined by Miller & Modigliani, 1961) with a relatively stable dividend payout ratio “k f,t ”, net profit at time “t”equalling to E f,t and an annual growth in net profit “g”, which is expected to continue till perpetuity. Assume that investors in this firm expect a long-term annual rate of return “ρ”. The value of the firm V f,t at time “t”,as discounted to time “t”, is calculated from simple dividend discount model and would be Vf;t;t¼kf;tEf;t ρf;tgf;t (5:1) Let us assume that for some reason, there is change in dividend payout ratio, at time “t+T”. Such a change might reflect and persist in growth rate, and expected rate of return from the firm. In this case, the value of the firm V f,t+T at time “t+T”, would be Vf;t;tþT¼kf;tþTEf;tþT ρ0 f;tþTg0 f;tþT (5:2) Where - ρ0 f;tþT¼Long term constant expected rate of return after change in payout of the firm 0f0at time 0t þT0 g0 f;tþT¼Long term constant expected growth rate in profits after change in payout of the firm 0f0at time 0t þT0 Let it be that the growth rate in earnings at time “t+T”from earnings a time “t”be equal to “g f,t,t+T ” and new dividend payout ratio at “t+T”be k f,t+T. Goyal, Cogent Economics & Finance (2019), 7: 1649000 https://doi.org/10.1080/23322039.2019.1649000 Page 20 of 55 Thus the above equation can be stated as: Vf;t;tþT¼kf;tþT  Ef;t1þgf;t;tþT  ρ0 f;tþTg0 f;tþT (5:3) gf;t;tþT¼Growth rate in earnings for firm 0f0from time 0t0to0tþT0 The value of the firm at time “t+T”, as discounted to time “t”, would be Vf;t;tþT¼kf;tþTEf;t1þgf;t;tþT  ρ0 f;tþTg0 f;tþT  1þρf;t;tþT  (5:4) Where ρf;t;tþT¼Expected rate of return for firm 0f0from time 0t0to 0tþT0 The value of the firm, in both cases, should be the same, according to the hypothesis. Hence, - Vf;t;tþT¼Vf;t;t(5:5) Putting value of Vf;t;tþTand Vf;t;tin Equation (5.5) from Equation (5.4) and (5.2) respectively, we get the following: kf;tþTEf;t1þgf;t;tþT  ρ0 f;tþTg0 f;tþT  1þρf;t;tþT  ¼kf;tEf;t ρf;tgf;t (5:6) Now, let us assume that ρf;tgf;t¼r(5:7) Where r¼a rate of return Multiplying both sides by D ρf;tDgf;tD¼rD (5:8) Where gD represents the amount lost on growth of earnings that could have been achieved had no dividend been given ρD represents the amount gained on dividend by investor taking the dividend and investing it in the next best option Because the two options are not exact substitutes of each other, it is possible that some rate of return be accrued by choosing one over the other. However, the difference in the two rates must be a constant across securities and time, because if such were not the case, arbitrage would take place. This arbitrage that can be called “pair arbitrage”is different than the normal arbitrage that is assumed to take place on a normal rate of return. The difference between the two is that a normal arbitrage procedure would result in prices of same type of asset in two differing markets to be absolutely same, while a pair arbitrage would result in merely price of same type of asset in two differing markets to be relatively same, that is Goyal, Cogent Economics & Finance (2019), 7: 1649000 https://doi.org/10.1080/23322039.2019.1649000 Page 21 of 55 that there might be a fixed difference between the two prices. Owing to more relaxed assumptions and consistency with the actual world, the pair arbitrage assumption is better to understand the price functioning of securities in the market. The pair arbitrage, in effect, is however significant for one more reason. Instead of assuming that any rate of return of an asset could be compared to any other rate of return of a similar but not the same asset, it is better to base the analysis on the assumption that the difference in the best and the second best alternative for a particular security could be compared to such differences over different securities and over time and over different amounts of investment. That is because, a higher return for a security for a particular option may be generating at the expense of other options available with the security, while such cannot be the case in case the securities or the time (not duration) or the amount invested is different, unless by design, because there is no direct causal relationship that exists naturally over such difference. By design, one can transfer the losses and gains, to different security, by means of, for example, swaps, to different time, by means of, for example, futures, and to different amounts invested, by means of, for example, progressive taxation. Any such measures that occur thus, need separate treatment, but their effects occur by chain of wilful contractual obligations and not primarily by natural mechanisms. A good example, for illustration of working of the above principle, wherein a higher return can be generated on a security at the expense of a lower return for the second option exercised on the same asset, is financial bubbles, wherein the short-term investors in an asset make abnormal gains off the backs of long-term investors. This situation may be completely natural and driven by sentiments and expectations, instead of a formal contract in which long-term investors may agree to give up their potential gains to provide gains to short-term investors. Thus, in line with the above discussion, the following is held to be the case ρ0 f;tþTg0 f;tþT¼r However, the assumption can be relaxed and belief about value of “r”allowed to vary with time. Thus, the equation can be instead stated as the following: ρ0 f;tþTg0 f;tþT¼λtþT;tr(5:9) And the equation becomes the following: kf;tþT1þgf;t;tþT  1þρf;t;tþT  ¼λtþT;tkf;t(5:10) Because kf;tþT¼kf;tþΔkf;t;tþT(5:11) Where Δkf;t;tþT¼Change in dividend payout ratio of firm 0f0from time 0t0to 0tþT0 Hence, the equation becomes kf;tþΔkf;t;tþT  1þgf;t;tþT  ¼λtþT;tkf;t1þρf;t;tþT  (5:12) Simplifying, we get Δkf;t;tþT¼λtþT;tkf;t 1þρf;t;tþT  1þgf;t;tþT  kf;t(5:13) Goyal, Cogent Economics & Finance (2019), 7: 1649000 https://doi.org/10.1080/23322039.2019.1649000 Page 22 of 55 Or, - Δkf;t;tþT¼λtþT;tkf;tφf;t;tþTkf;t(5:14) Where φf;t;tþT¼1þρf;t;tþT 1þgf;t;tþT  ¼Dividend Increment Factor Alternatively, the equation can be written as: λtþT;tkf;tφf;t;tþT¼Δkf;t;tþTþkf;t(5:15) Δkf;t;tþTand kf;tare under the control of management. kf;tφf;t;tþTdenotes a combination of all factors that emanate from a combination of investor and management decisions. The “paired analysis”of the factors such as expected rate of return and growth rate of firm’s profits, allows us to ignore any complex feedback effects going on between the variables in the equation and the financial and physical counterparts to them, because such is irrelevant to the theory being proposed in the paper. Here, it is to be noted that λtþT;tkf;tφf;t;tþT¼Δkf;t;tþTkf;tand Δkf;t;tþT¼kf;tþλtþT;tkf;tφf;t;tþTare different syntactically and the latter is expected to be less valid than the former generally when verified empirically, because in case of the former, kf;tφf;t;tþTis the dependent variable, while in the latter case Δkf;t;tþTis the dependent variable. While ideally, both could be said to equally be dependent on the other, practically, the management decisions may have less ability to capture the movement of these variables than the market, especially in cases where the market is efficient. So, in general, it is more useful to hold a view that the market adjusts to the firm’s decisions, but that does not mean that the management decisions are not taken considering the market perceptions, it is just that the latter is less efficient. Granted all assumptions mentioned in the paper to be valid in the real world, the coefficients of Δkf;t;tþTand kf;tin the equation λtþT;tkf;tφf;t;tþT¼Δkf;t;tþTþkf;tmust both be significant and equal to 1. Thus, an empirical test, in which such coefficients are found to be not significant or close to 1 may serve as an evidence against the theory, provided that the assumptions approximate the actual scenario, surrounding the cases used in the test. In this paper, the hypothesis is tested on Indian markets and results are discussed subsequently. (1) Hypothesis significance The hypothesis, under ideal market conditions, should fit with the data completely. However, owing to many violations of the assumptions in the real world, the hypothesis will most often, just represent a trend line. The firm value may, thus, be above the theoretical value derived from the model or below it, but is expected to stick close to the trend line, unless of course, the firm changes its efficiency. In that case, the firm value is expected to settle to another value in long term. The significance of hypothesis, is thus, not in conveying that it is impossible to increase firm value without increasing its operational, or investment efficiency, though that appears to be the case, but in forming an epistemic empirical model through which several dividend policy mechanisms can be tested for relevancy in a particular market for a period. The factors mentioned in the model are by no means the only ones the dividend decisions by managers or investors will depend on. However, all other factors will only violate the equation as much as they violate the assumptions taken in the model. For example, a firm may decide to hold back an amount of dividend to be paid out to invest in a project it can gain a higher return on. Such an investment will surely lead to a change in return on equity and a departure from the assumptions and thus the theory will be Goyal, Cogent Economics & Finance (2019), 7: 1649000 https://doi.org/10.1080/23322039.2019.1649000 Page 23 of 55 Calcbench and the data for the index is taken from Yahoo Finance. A three-year gap is taken, instead of the five-year gap, in case of Indians markets. The rest of the procedure is same, except that the financial year is taken from January to December and not April to March. The descriptive statistics for the data from the S&P 500 Index are shown in Table 12. The regression results for both the equations are presented in Table 13 and Table 14. The standardized coefficient values are shown in Table 15 and Table 16. EQUATION 1 Δkf;t;tþT¼a1kf;tφf;t;tþTþa2kf;tþc EQUATION 2 kf;tφf;t¼a1Δkf;t;tþTþa2kf;tþc The value of coefficients after standardization are EQUATION 1 EQUATION 2 It is evident that in US markets, there is a strong model oriented approach. Managers do not base their decisions as much on investors’perceptions directly, unlike in case of Indian markets, as on the need of the company or their own personal decisions. Similarly, investors’ base their decisions on models and thus the attitude towards appreciation of the modeloriented approach is mutual which is necessary otherwise the management would be in error of basing their policy on something which is completely foreign to attitude of the investors. The results of the study are consistent with the findings of Pruitt and Gitman (1991), Baker and Powell (2000) and Baker, Veit, and Powell (2001). Pruitt and Gitman (1991) Table 9. White test results for the second equation for Indian data P-Value—F Test 0.000 Table 10. Regression test results for the second equation for Indian data Variable Coefficient Standard Error PValue c−0.0341 0.0480 0.477 Δkf;t;tþT1.0689 0.1711 5.00E-10 kf;t0.9863 0.1273 1.36E-14 R Squared 0.492 Table 11. Standardized coefficients for the first equation for Indian data Variable Standardized Coefficient Value c−0.0345 Δkf;t;tþT1.0837 kf;t1.0000 Goyal, Cogent Economics & Finance (2019), 7: 1649000 https://doi.org/10.1080/23322039.2019.1649000 Page 30 of 55 conducted a survey of highest-ranking financial officers of around 1000 largest US firms in 1988 and found from the 144 responses that they received that managers believed “projected net earnings„,“recently enacted dividend changes„,“current dividend payout ratio„and “level of cash flows„as the four most explanatory factors in their dividend decisions, with previous earnings levels and capital investment requirements jointly ranking fifth. Baker and Powell (2000) conducted a similar study on firms listed on New York Stock Exchange and found that “level of current and expected future earnings„,“pattern or continuity of past dividends„, “concern about maintaining or increasing stock price„and“concern that dividend change Table 12. Descriptive statistics for S&P 500 data Δkf;t;tþTkf;tkf;tφf;t;tþT Mean −0.029 0.409 0.175 Median 0.001 0.236 0.264 Standard Deviation 4.826 4.332 12.935 Skewness −30.979 43.212 −54.426 Kurtosis 1545.268 2280.337 3184.118 Number of observations 3752 3752 3752 Table 13. Regression results for the first equation for US data Variable Coefficient Standard Error PValue c0.3529 0.0351 1.82E-23 kf;t−0.9445 0.0324 1.88E-168 kf;tφf;t;tþT0.0241 0.0114 0.0345 R Squared 0.810 Table 14. Regression results for the second equation for US data Variable Coefficient Standard Error PValue c1.0182 0.2526 0.0001 Δkf;t;tþT −2.0338 0.7458 0.0064 kf;t0.3353 0.1534 0.0289 R Squared 0.633 Table 15. Standardized coefficients for the first equation for US data Variable Standardized Coefficient Value c0.3736 kf;t−1.0000 kf;tφf;t;tþT0.0255 Table 16. Standardized coefficients for the second equation for US data Variable Standardized Coefficient Value c3.0366 Δkf;t;tþT −6.0656 kf;t1.0000 Goyal, Cogent Economics & Finance (2019), 7: 1649000 https://doi.org/10.1080/23322039.2019.1649000 Page 31 of 55 may provide a false signal to investors„were the four most important factors for the mangers while deciding dividend policy. Baker, Veit and Powell (2001) conducted a survey of managers of firms with stocks trading on Nasdaq and which paid dividends for every quarter of 1996 and 1997. Their finding was that concern about dividend policy affecting stock price was significantly less than concerns about creation of payout policy in line with the “pattern of past dividends„,“stability of earnings„,“level of current earnings„and “level of expected future earnings„in managers’decisions about dividend payouts. None of the four most important factors has anything to do with the investor perception directly. Interestingly, Baker and Kapoor (2015) found in their study of National Stock Exchange listed firms, that managers of these firms believe that investors in their firms prefer a certain dividend stream to uncertain stock price appreciation, though in even that study the concern about dividend changes affecting stock price or consideration of needs of shareholders as a reason for a particular payout decision were overshadowed by similar factors as found in Baker and Powell’s(2000) study on firms listed in the United States. However, Baker and Kapoor also found that 73.5% of the managers agreed to the proposition that a firm’s stock price usually increases when it unexpectedly increases its dividend or pays a dividend for the first time. It also seems to be the case that dividend payouts above a fixed value are strongly disliked, which is different than what is the case in Indian market. That is not surprising considering around 80% of the constituents of S&P 500 index based on market value are owned by institutional investors (as in April 2017) and payment of dividends above the value as may seem fit to these investors may signal these investors that there is a difference between their and management’s view about future prospects of the firm. The observation also falls in line with the general idea of agency costs being reduced by presence of institutional investors and hence the role of dividends as tools in decreasing such costs has reduced importance. This is in line with Fama and French (2001) study in which it was found that firms in US markets were less likely to pay dividends in 1999 than in 1978. Also, the study shows that US markets are relatively more efficient than Indian markets. 10. Discussion The main motive of the paper was to develop an equilibrium theory or an ideal case theory, and then using that theory to arrive at an equation, which can be used to identify different dividend policy mechanisms working in a market and their efficacy. Any distortion in the equilibrium creates an opportunity for specific theories of dividend policy to spring into action, as the results suggest. However, the very reason the equal value equilibrium equation is applicable in deciphering any distortion is because the equilibrium theory is correct. One of the interesting things to note is that studying results of the first equation, we find that while one coefficient is higher than 1, the other is less than 1. In the ideal case, both should have been equal to 1. There seems to a deviation, which is expected because many of the ideal case assumptions are not completely in line with the actual mechanisms of the market, however there seems to be an accompanied balancing effect towards the ideal scenario. In Finance, one may not just look at the empirical factors associated with a security as they exist, like risk and return, but the very nature of the security itself, something which may be called “Financial Essentialism”. While investing in a security, people also look at what the security looks like and not just how much risk adjusted return it can provide. Temporal but non-perpetual securities (like non-perpetual bonds) must be distinguished from non-temporal securities (like stocks), which may be distinguished from temporal but perpetual securities (like perpetual bonds). The very nature of the security would define any a priori considerations and perceptions about the security upon which empirical measures of the performance of the security would be built on. Deriving key postulates for a security and supplanting them with performance indicators might serve as a better measure to value a security. Goyal, Cogent Economics & Finance (2019), 7: 1649000 https://doi.org/10.1080/23322039.2019.1649000 Page 32 of 55 The value of a share, for example, among other things is determined by management decisions and investors’perceptions. While the management and investors (excluding manipulators and speculators) may adopt different mechanisms, their goal is a lot similar, at least in an ideal case. Instead of merely value maximization, which is done by removing inefficiencies in the business and market information, they would supplant it with desire for the perpetual existence of the company. The different dividend policy mechanisms interact with each other and keep the value of the company on a nominal trend line. While it is possible that value of a fully efficient company may increase for short amount of time, because of investor perception, the principle of arbitrage, would in ideal case, keep the value growth in check. It will be impossible for any firm to generate or lose significant amount of extra inflow of money consistently without any change in its efficiency. However, that is not the only thing that is important. Moving from realm of principles to the methodology, because of interdependent nature of variables associated with company financials, it is also better to study the effect of the variables cumulatively and divide the different contributing factors based on the dynamics affecting them, rather than their type or source. It is quite possible that multiple dividend theory mechanisms are in action simultaneously and any frame of time or segment of the market from which the data is captured may show overbearing effect of one over the other, which may not be the case for any other period of time or market segment. That is not to say that techniques for isolation of one effect over another are not important, but in presence of theoretical justifications on all sides, the issue is rather left unsolved by consideration of such effects independently of each other. The main thesis behind the model is that dividends are not primary management selection criterion. The payment of dividends is dependent on a more fundamental aspect of equalizing firm value across time for firms expecting to last till perpetuity. That aspect forms the ground for all different roles of dividends discussed in literature like use as signals, or tools to reduce agency costs. Thus, while dividends can alter the value of the firm (contrary to what Miller and Modigliani (1961) suggest), the equalization of firm value (across time) is the goal behind payment of dividends. That is how the Gordon’s(1959,1963)viewisharmonized with the view of Miller and Modigliani. It is to be noted that the claim is not that payment of any amount of dividend will lead to equalization of firm value. The equalization of firm value, as a motive, is the determinant of dividend policy and the dividends are instituted in such a way so that the firm value is equalized. The issue with the M&M model is that it assumes that value of the firm is contingent on the expected rate of return and the arbitrage affects the rate of return instead of value of the firm.Thisviewisproblematicbecausevalueisthe precursor to expected rate of return and not the other way around. A rational investor will set his investment goals based on his consumption pattern, such that he is able to consume a set quantity of products every year, no matter the price of products. There will be deviations from it based on the stage of life the investor is in and the circumstances and events in his life. However, over a large population with characteristics that do not change drastically (e.g. percentage of youth, mortality rate, life expectancy), these deviations will tend to minimum. For a uniform consumption to occur, the value of the products appropriately discounted must remain constant, no matter the expected rate of return or interest rate or inflation rate. Similarly, assuming that value of all the products is in equilibrium (the values of different products may be unequal), the products are expected to show an increase in value in a constant proportion in an ideal situation where supply and demand curves do not change and the efficiency of extraction and sale of products remains also the same. The same is true for the firm value. The arbitrage is present, however it is just acting in a different way. The results of the paper, point out interesting facts about Indian markets. Not only the management of the Indian firms seem to accept the importance of signalling power of dividends, the preference of dividends among investors’is also quite present. This makes sense, because in earlier Goyal, Cogent Economics & Finance (2019), 7: 1649000 https://doi.org/10.1080/23322039.2019.1649000 Page 33 of 55 studies Indian markets have been found to be inefficient (Gupta & Parikshit, 2007; Harper & Jin, 2012; Mehla & Goyal, 2012). Thus, dividend payouts become an important way of predicting future prices of shares. Similarly, the comparison of US markets with India using the methodology points out interesting results that are intuitive. The magnitude of the coefficients, in both cases, seem to point out respective efficacy of the mechanisms in action, which can be compared to markets in other countries, to get an estimate of differential effects of the theoretical mechanisms in different types of markets. 11. Conclusions An “Equal Value Equilibrium model”for the dual benefits of testing of empirically observable effects of dividend theories in markets and also presenting general outline of the behaviour of stock markets in an idealized situation, is derived with theoretical justification. The model relies on its simplicity and potency to present effects of different theoretical mechanisms in such a manner that they can be studied easily, while attempting to harmonise different theories of dividend policy. What investors value is neither dividends or earnings per se, but what they value is their stake in company and any abnormal gains associated with that stake. In contrast, what the management cares about is that firm remains working till perpetuity because that is related to their job security. Management does not care about abnormal gains to the extent investors do because they do not get same amount of benefits for any abnormal gains, unless they either own a stake in the company (in which case they are investors in the company) or there is some incentive structure for abnormal gains. However, considering management has better knowledge of which gains are abnormal and won’t be persistently acquirable in future, the value of any such incentive is short lived. The actions of the investors thus, to squeeze out any abnormal gains by use of arbitrage from the firm and the actions of management to not go for risk-based approaches threatening their job security, mean that the value of the company, barring any efficiency change, is expected to remain constant over the years. Unlike as previous studies on the subject and prevalent theories on the dividend payout decisions point out, it is not the case that dividends perform some rigid primary function as academic literature points out. The theories that point out a specific primary function of the dividends at the exclusion of other functions are severely deficient in explaining many empirical tests in favour of the other functions. Stressing on making better models for validation of these theories has not solved the puzzle but has complicated it even more as nowfewmodelsthatmakeuseofquiteafewvariableshavecomeup.Itwouldbesurprising if as these studies suggest, the management really uses an extensive modelling based on firm’s financial parameters and sets the dividend payout based on extensive regression involving coefficients that alter with time and economic conditions. And if that is really the case, then the surveys seem to be a better way of figuring the dividend determinants rather than model based regressions. The actual role of dividends is to just equalize firm value to an ideal value for a given level of efficiency and firm and market conditions, which can be assumed to be close to a stable value with similar parameters. Even if such equalization is not done by use of dividends, it is expected to happen on its own as investors will eventually price the firm to its fair value, however the inefficiencies and delay in that process is what gives rise to inconsistent instances of verification of prevalent dividend theories in empirical studies. The actual mechanism behind the applicability of prevalent theories in different markets is the process of firm value equalization. The theory of “Equal Value Equilibrium”also leads to two pragmatic conclusions. Firstly, for the investors, the best method of investing in absence of any knowledge of future efficiency change of the firm is selecting those firms whose value in current period has changed significantly from their Goyal, Cogent Economics & Finance (2019), 7: 1649000 https://doi.org/10.1080/23322039.2019.1649000 Page 34 of 55 expected value without any observable change in efficiency. Secondly, for the managers more importantly, the best way of setting dividend payout is to set the value of dividend equal to a value which will equalize their firm value to a past stable value, of course, in the case, when the money that is paid off as dividend cannot be used to increase operational or financial efficiency. Thus, the dividend decision is a residual decision, after meeting operational, investing and capital budgeting costs and the management needs to keep a track of expected rate of return for the market in deciding the optimal dividend payout. Funding The author received no funding for this research. Author details Shreyansh Goyal E-mail: [email protected] Department of Financial Studies, University of Delhi, Delhi, India. Limitations of the Study and Future Recommendations The study is only as good as its assumptions. Also, it is only conducted in two markets and may show different results in markets of other countries. Yearly data prevents studying causal direction in more detail. The validity of the model derived from the proposed theory need to be studied in other countries and markets with different features than the Indian and US markets. Also, a better way of deriving more stable variables for the study needs to be discussed to get more stabilized results. A study of causality would also be beneficiary. Taking quarterly data and arranging it in a manner to study which effect precedes what would clarify how the application of theory in real world must be undertaken. One of the other interesting points of research would be to see how much the theory is actually applicable in the real world markets in terms of firm value and to which extent the value of the firms might increase or decrease in real terms, accounting for the opportunity cost. Further, the study of ways to incorporate effects of other dividend policy theories in the model and pronouncing the isolation of effects of such theories also seems to be a good future projects. Citation information Cite this article as: The dividend puzzle misspecification – Why the role of dividends is not what people think, Shreyansh Goyal, Cogent Economics & Finance (2019), 7: 1649000. References Aharony, J., & Swary, I. (1980). Quarterly dividend and earnings announcements and stockholders’returns: An Empirical analysis. Journal of Finance,35,1–12. doi:10.1111/j.1540-6261.1980.tb03466.x Al-Deehani, T. (2003). Determinants of dividend policy: The case of Kuwait. Journal of Economic and Administrative Sciences,19,59–76. doi:10.1108/ 10264116200300006 Allen, D. E., & Rachim Veronica, S. (1996). Dividend policy and stock price volatility: Australian evidence. Applied Financial Economics,6(2), 175–188. doi:10.1080/096031096334402 Allen, F., Bernardo, A. E., & Welch, I. (2000). A theory of dividends based on tax clienteles. The Journal of Finance,55(6), 2499–2536. doi:10.1111/00221082.00298 Al-Najjar, B., & Kilincarslan, E. (2016). The effect of ownership structure on dividend policy: Evidence from Turkey. Corporate Governance,16(1), 135–161. doi:10.1108/CG-09-2015-0129 Amihud, Y., & Murgia, M. (1997). Dividends, taxes, and signaling: Evidence from Germany. The Journal of Finance,52(1), 397–408. doi:10.1111/j.15406261.1997.tb03822.x Anand, M. (2004). Factors influencing dividend policy decisions of corporate India. ICFAI Journal of Applied Finance,10(2), 5–16. Asquith, P., & Mullins, D. W., Jr. (1983). The impact of initiating dividend payments on shareholders’ wealth. Journal of Business,56,77–96. doi:10.1086/ 296187 Asquith, P., & Mullins, D. W., Jr. (1986). Signalling with, dividends, stock repurchases, and equity issues. Financial Management,15,27–44. doi:10.2307/ 3664842 Attig, N., Boubakri, N., Ghoul, S. E., & Guedhami, O. (2015). The global financial crisis, family control, and dividend policy. Financial Management,45(2), 291–313. doi:10.1111/fima.12115 Azhagaiah, R., & Sabaripriya, N. (2008). The impact of dividend policy on shareholders’wealth. International Research Journal of Finance and Economics,20, 180–187. Baker, H. K., Farrelly, G. E., & Edelman, R. B. (1985). A survey of management views on dividend policy. Financial Management,14,78–84. doi:10.2307/ 3665062 Baker, H. K., & Kapoor, S. (2015). Dividend policy in India: New survey evidence. Managerial Finance,41(2), 182–204. doi:10.1108/MF-01-2014-0024 Baker, H. K., & Powell, G. E. (1999). How corporate managers view dividend policy. Quarterly Journal of Business and Economics,38,17–35. Baker, H. K., & Powell, G. E. (2000). Determinants of corporate dividend policy: A survey of NYSE firms. Financial Practice and Education,10,29–40. Baker, H. K., Powell, G. E., &Veit, E. T. (2002). Revisiting the dividend puzzle: Do all of the pieces now fit? Review of Financial Economics,11, 241–261. doi:10.1016/ S1058-3300(02)00044-7 Baker, H. K.,Veit, E. T., & Powell, G. E. (2001). Factors influencing dividend policy decisions of Nasdaq Firms. The Financial Review,38,19–37. doi:10.1111/ j.1540-6288.2001.tb00018.x Ball, R., Brown, P., Finn, F. J., & Officer, R. R. (1979). Dividend and the value of the firm: Evidence from the Australian equity market. Australian Journal of Management,4,13–26. doi:10.1177/ 031289627900400102 Banerjee, P., & Banerjee, P. S. (2012). Signalling hypothesis and clientele shifts: Evidence from Indian stock splits. Global Business Review,13(2), 297–309. doi:10.1177/097215091201300208 Bar-Yosef, S., & Kolodny, R. (1976). Dividend policy and capital market theory. The Review of Economics and Statistics,58(2), 181–190. doi:10.2307/1924024 Baskin, J. (1989). Dividend policy and the volatility of common stock. Journal of Portfolio Management,15 (3), 19–25. doi:10.3905/jpm.1989.409203 Berlingeri, H. O. (2006a). Yes, after all, in an MM World, dividends are irrelevant. SSRN Electronic Journal. doi:10.2139/ssrn.905045 Goyal, Cogent Economics & Finance (2019), 7: 1649000 https://doi.org/10.1080/23322039.2019.1649000 Page 35 of 55 Berlingeri, H. O. (2006b). U-Shaped cost of equity function? Digging into Modigliani-Miller (1958) Mistake. SSRN Electronic Journal. doi:10.2139/ssrn.934550 Bernheim, B., & Wantz, A. (1995). A tax-based test of the dividend signaling hypothesis. The American Economic Review,85(3), 532–551. Bezawada, B., & Kumar Tati, R. (2017). Dividend policy and firm valuation—A study of Indian electrical equipment manufacturing industry. Theoretical Economics Letters,07, 1233–1243. doi:10.4236/tel.2017.75083 Bhattacharya, S. (1979). Imperfect information, dividend policy, and “the Bird in the Hand”Fallacy. Bell Journal of Economics,10, 259–270. doi:10.2307/3003330 Black, F. (1976). The dividend puzzle. Journal of Portfolio Management,2,5–8. doi:10.3905/jpm.1976.408558 Black, F., Jensen, M. C., & Scholes, M. (1972). The capital asset pricing model: Some empirical tests. In M. C. Jensen, (Ed.), Studies in the Theory of Capital Markets. New York: Praeger Publishers Inc. Black, F., & Scholes, M. S. (1974). The effects of dividend yield and dividend policy on common stock prices and returns. Journal of Financial Economics,1,1–22. doi:10.1016/0304-405X(74)90006-3 Blume, M. E. (1980). Stock returns and dividend yields: Some more evidence. The Review of Economics and Statistics,62(4), 567. doi:10.2307/1924781 Brennan, M. (1971). A note on dividend irrelevance and the Gordon valuation model*. The Journal of Finance, 26(5), 1115–1121. Brennan, M. J. (1970). Taxes, market valuation and corporate financial policy. National Tax Journal,23, 417–427. Cao, L., Du, Y., &Hansen, J. Ø. (2017). Foreign institutional investors and dividend policy: Evidence from China. International Business Review,26(5), 816–827. doi:10.1016/j.ibusrev.2017.02.001 Chen, C., & Wu, C. (1999). The dynamics of dividends, earnings and prices: Evidence and implications for dividend smoothing and signaling. Journal of Empirical Finance,6(1), 29–58. doi:10.1016/S09275398(98)00008-5 De Bondt, W. F. M., & Thaler, R. (1985). Does the stock market overreact? The Journal of Finance,40(3), 793–805. doi:10.1111/j.1540-6261.1985.tb05004.x DeAngelo, H., & DeAngelo, L. (2006). The irrelevance of the MM dividend irrelevance theorem. Journal of Financial Economics, Elsevier,79(2), 293–315. doi:10.1016/j.jfineco.2005.03.003 DeAngelo, H., & DeAngelo, L. (2008). Reply to: Dividend policy: Reconciling DD with MM☆.Journal of Financial Economics,87(2), 532–533. doi:10.1016/j. jfineco.2007.10.001 DeAngelo, H., DeAngelo, L., & Skinner, D. J. (1996). Reversal of fortune: Dividend signalling and the disappearance of sustained earnings growth. Journal of Financial Economics,40, 341–371. doi:10.1016/0304405X(95)00850-E Dempsey, S. J., & Laber, G. (1992). Effects of agency and transaction costs on dividend payout ratios: Further evidence of the agency-transaction cost hypothesis. Journal of Financial Research,15(4), 317–321. doi:10.1111/jfir.1992.15.issue-4 Duqi, A., Jaafar, A., & Warsame, M. H. (2019). Payout policy and ownership structure: The case of Islamic and conventional banks. The British Accounting Review. doi:10.1016/j.bar.2019.03.001 Easterbrook, F. H. (1984). Two agency costs explanations of dividends. American Economic Review,74, 650–659. Fama, E. (1970). Efficient capital markets: A Review of theory and empirical work. The Journal of Finance,25 (2), 383–417. doi:10.2307/2325486 Fama, E. (1978). The effects of a firm’s investment and financing decisions on the welfare of its security holders. The American Economic Review,68, 272–284. Fama, E. F., & French, K. R. (2001). Disappearing dividends: Changing firm characteristics or lower propensity to pay? Journal of Financial Economics,60,3–43. doi:10.1016/S0304-405X(01)00038-1 Farrukh, K., Irshad, S., Shams, K. M., Ishaque, S., Ansari, N. Y., & McMillan, D. (2017). Impact of dividend policy on shareholders wealth and firm performance in Pakistan. Cogent Business & Management, 4, 1. doi:10.1080/23311975.2017.1408208 Frankfurter, G. M., & Wood, B. G., Jr. (2002). Dividend policy theories and their empirical tests. International Review of Financial Analysis,11, 111–138. doi:10.1016/S1057-5219(02)00071-6 Gonzalez, L, Powell, J. G, Shi, J, & Wilson, A. (2005). Two centuries of bull and bear market cycles. International Review Of Economics & Finance,14(4), 469–486. doi: 10.1016/j.iref.2004.02.003 Gordon, M. J. (1959). Dividends, earnings, and stock prices. Review of Economics and Statistics,41, 99–105. doi:10.2307/1927792 Gordon, M. J. (1963). Optimal investment and financing policy. Journal of Finance,18, 264–272. Graham, B., & Dodd, D. L. (1951). Security analysis. New York, NY: McGraw-Hill. Gupta, R., & Parikshit, K. B. (2007). Weak Form Efficiency In Indian Stock Markets. Journal of International Business Studies,6,57–64. Gupta, S., Dogra, B., & Vashisht, A. K. (2013). Examining validity of known dividend models in Indian companies. International Journal of Management Excellence,1, 26. doi:10.17722/ijme.v1i2.6 Hakansson, N. H. (1982). To Pay or Not to Pay Dividend. The Journal of Finance,37, 415–428. Handley, J. (2008). Dividend policy: Reconciling DD with MM☆.Journal of Financial Economics,87(2), 528–531. doi:10.1016/j.jfineco.2007.02.002 Harper, A., & Jin, Z. (2012). Examining market efficiency in India: An empirical analysis of the random walk hypothesis. Journal of Finance and Accountancy,10, 68–73. Hoang, E. C., & Hoxha, I. (2016). Corporate payout smoothing: A variance decomposition approach. Journal of Empirical Finance,35,1–13. doi:10.1016/j. jempfin.2015.10.011 Hofstede, G., Hofstede, G. J., & Minkov, M. (2010). Cultures and Organizations: Software of the Mind (Rev. 3rd ed.). New York: McGraw-Hill. Hunjra, A. I. (2018). Mediating role of dividend policy among its determinants and organizational financial performance. Cogent Economics & Finance,6(1), 1558714. doi:10.1080/23322039.2018.1558714 Hussainey, K., Mgbame, C. O., & Mgbame, A. M. C. (2011). Dividend policy and share price volatility: UK evidence. Journal of Risk Finance,12(1), 57–68. doi:10.1108/15265941111100076 Jabbouri, I. (2016). Determinants of corporate dividend policy in emerging markets: Evidence from MENA stock markets. Research in International Business and Finance,37, 283–298. doi:10.1016/j.ribaf.2016.01.018 Jensen, M. C. (1986). Agency Costs of Free Cash Flow, Corporate Finance, and Takeovers. American Economic Review,76, 323–329. Jensen, M. C., & Meckling, W. H. (1976). Theory of the Firm: Managerial behavior, agency costs and Goyal, Cogent Economics & Finance (2019), 7: 1649000 https://doi.org/10.1080/23322039.2019.1649000 Page 36 of 55 ownership structure. Journal of Financial Economics, 3, 305–360. doi:10.1016/0304-405X(76)90026-X Lease, R. C., John, K., Kalay, A., Loewenstein, U., & Sarig, O. H. (2000). Dividend Policy: Its Impact on Firm Value. Boston, Massachusetts: Harvard Business School Press. Lee, C., & Forbes, S. (1980). Dividend policy, equity value, and cost of capital estimates for the property and liability insurance industry. The Journal of Risk and Insurance,47(2), 205–222. doi:10.2307/252328 Lintner, J. (1956). Distribution of Incomes of corporations among dividends, retained earnings, and taxes. American Economic Review,46,97–113. Litzenberger, R. H., & Ramaswamy, K. (1979). The effect of personal taxes and dividends on capital asset Prices. Journal of Financial Economics,7, 163–195. doi:10.1016/0304-405X(79)90012-6 Litzenberger, R. H., & Ramaswamy, K. (1982). The effects of dividends on common stock prices: Tax effects or information effects? Journal of Finance,37, 429–443. doi:10.1111/j.1540-6261.1982.tb03565.x McCabe, G. (1979). The empirical relationship between investment and financing: A new look. Journal of Financial and Quantitative Analysis,14(1), 119–135. doi:10.2307/2330658 Mehla, S., & Goyal, S. K. (2012). Empirical Evidence on Weak Form of Efficiency in Indian Stock Market. AsiaPacific Journal of Management Research and Innovation,8(1), 59–68. doi:10.1177/ 2319510X1200800107 Miller, M. H., & Modigliani, F. (1961). Dividend policy, growth, and the valuation of shares. Journal of Business,34, 411–433. doi:10.1086/294442 Miller, M. H., & Scholes, M. S. (1982). Dividend and taxes: Some empirical evidence. Journal of Political Economy,90, 1118–1141. doi:10.1086/261114 Modigliani, F., & Miller, M. H. (1958). The Cost of Capital, Corporation Finance and the Theory of Investment. American Economic Review,48, 261–297. Morgan, I. G. (1982). Dividends and Capital Asset Prices. Journal of Finance,37, 1071–1086. doi:10.1111/ j.1540-6261.1982.tb03599.x Naceur, S. B., & Goaied, M. (2002). The relationship between dividend policy, financial structure, profitability and firm value. Applied Financial Economics, 12(12), 843–849. doi:10.1080/09603100110049457 Partington, G. H. (1985). Dividend policy and its relationship to investment and financing Policies: Empirical evidence. Journal of Business Finance and Accounting,12, 531–542. doi:10.1111/j.14685957.1985.tb00792.x Profilet, K. A., & Bacon, F. W. (2013). Dividend Policy and Stock Price Volatility in the U.S. Equity Capital Market. Journal of Business and Behavior Sciences, 25(2), 63. Pruitt, S. W., & Gitman, L. J. (1991). The Interactions between the investment, financing, and dividend decisions of Major U.S. Firms. The Financial Review,26 (3), 409–430. doi:10.1111/fire.1991.26.issue-3 Qudah, A. A., & Aziz, Y. (2015). Stock price volatility and dividend policy in Jordanian Firms. Research Journal of Finance and Accounting,6(22), 2015. Rajesh, K. B., Sujit, K. S., & Vivian, A., (Reviewing Editor). (2018). Determinants of dividends among Indian firms—An empirical study. Cogent Economics & Finance,6,1. Rajverma, A. K., Arrawatia, R., Misra, A. K., Chandra, A., & McMillan, D. (2019). Ownership structure influencing the joint determination of dividend, leverage, and cost of capital. Cogent Economics & Finance,7(1), 1600462. doi:10.1080/ 23322039.2019.1600462 Randall, W. J. (1983). Dividend changes and security prices. Journal of Finance,38, 1607–1615. doi:10.1111/j.1540-6261.1983.tb03844.x Pettit, R. R. (1972). Dividend announcements, security performance, and capital market efficiency. Journal of Finance,27, 993–1007. doi:10.1111/j.15406261.1972.tb03018.x Ross, S. (1977). The Determination of Financial Structure: The Incentive-Signalling Approach. The Bell Journal of Economics,8(1), 23–40. doi:10.2307/ 3003485 Rozeff, M. S. (1982). Growth, beta and agency costs as determinants of dividend payout ratios. The Journal of Financial Research,5, 249–259. doi:10.1111/ j.1475-6803.1982.tb00299.x Rubinstein, M. (1976). The Irrelevancy of dividend policy in an arrow-debreu economy. The Journal of Finance, 31(4), 1229–1230. doi:10.1111/j.1540-6261.1976. tb01972.x Schwartz, S. H. (1994). Beyond individualism/collectivism: New cultural dimensions of values. Thousand Oaks, CA: Sage. Shao, L., Chuck, C. Y. K., & Guedhami, O. (2010). National Culture and Dividend Policy. Journal of International Business Studies,41, 1391–1414. doi:10.1057/ jibs.2009.74 Sharpe, W. F. (1964). Capital asset prices: A theory of market equilibrium under conditions of risk*. The Journal of Finance,19(3), 425–442. Shefrin, H., & Statman, M. (1984). Explaining Investor Preference for Cash Dividends. Journal of Financial Economics,13, 253–282. doi:10.1016/0304-405X(84) 90025-4 Stacescu, B. (2006). Dividend Policy in Switzerland. Financial Markets and Portfolio Management,20(2), 153–183. doi:10.1007/s11408-006-0013-7 Thirumagal, P. G., & Vasantha, S. (2016). Dividend policy on shareholders wealth –evidences from Indian Pharmaceutical Industry. Indian Journal of Science and Technology,9(15). doi:10.17485/ijst/2016/v9i15/ 90568 Tinbergen, J. (1933). The notions of horizon and expectancy in dynamic economics. Econometrica,1, 247. doi:10.2307/1907039 Tinbergen, J. (1939). The dynamics of share-price formation. The Review of Economics and Statistics, 21, 153. doi:10.2307/1926601 Watts, R. (1973). The Information Content of Dividends. Journal of Business,46,191–211. doi:10.1086/ 295525 Watts, R. (1976). Comments on the impact of dividend and earnings announcements: A reconciliation. The Journal of Business, University of Chicago Press,49(1), 97–106. Zainudin, R., Mahdzan, N. S., & Yet, C. H. (2018). Dividend policy and stock price volatility of industrial products firms in Malaysia. International Journal of Emerging Markets,13(1), 203–217. doi:10.1108/IJoEM-092016-0250 Zheng, C., & Ashraf, B. N. (2014). National culture and dividend policy: International evidence from banking. Journal of Behavioral and Experimental Finance,3, 22–40. doi:10.1016/j.jbef.2014.07.002 Goyal, Cogent Economics & Finance (2019), 7: 1649000 https://doi.org/10.1080/23322039.2019.1649000 Page 37 of 55 Appendix 1 The value of a firm, stated by Miller and Modigliani (1961) is, as follows: VtðÞ¼ 1 ρtðÞþ1ðÞ DtðÞþVtþ1ðÞmtþ1ðÞptþ1ðÞ½ WhereVtðÞ¼Value of the firm at 0t0 ρtðÞ¼Expected rate of return DtðÞ¼Dividends paid by the firm during the period 0t0 Vtþ1ðÞ¼Value of the firm at0tþ10 mtþ1ðÞ¼The number of shares sold during 0t0at the ex dividend closing price 0ptþ1ðÞ 0 Any change in payment of dividends, Miller and Modigliani (1961) argued would be absorbed in either future value of the firm or the value at which the new shares are sold, leaving the effect of dividends paid on the current value of the firm to be zero. If the expected rate of return remains constant, no matter the dividend payout, then the value of the firm in the next period would be dependent on the dividends paid and value of the new shares sold, in addition to the value of the firm in the current period. On a per share basis, however, the value of the firm in the next period would be dependent only on value of the firm and dividends paid in the current period. For a higher dividend paid, the future value of the firm will be lower. The value of a corpus of shares, thus, on any payment of dividend, would increasingly become smaller (when appropriately discounted), as viewed from a particular point in time, and thus would necessarily reach a value of termination, in terms of what was earlier described as “quantized nature of money”. V0tþ1ðÞ¼ρtðÞþ1 fg VtðÞDtðÞ½ WhereV0tþ1ðÞ¼The value of the initial corpus at time 0tþ10 As viewed from time period “t”, the value of the corpus of shares at time ‘t+1ʹwould be Vttþ1ðÞ¼ V0tþ1ðÞ ρtðÞþ1¼VtðÞ DtðÞ ρtðÞþ1 The equity stock would thus, behave exactly like a perpetual bond, wherein payment of dividends is akin to payment of coupon on dividends and the value of the stock would reduce each time, the dividend is paid, assuming the discount rate remains constant. Yet unlike, in case of a perpetual bond, it is not expected that the limiting value of the firm at infinity would be zero, for unlike bond which is basically an extended payment of a fixed value of money, the equity stock represents ownership over profits of the company, which, if the firm never ceases to exist, would not become zero, and with the growth in firm’s business, might actually remain stable. However, Gordon (1963) argued that change in payment of dividends would reduce the opportunity cost of the investor for the firm as the dividends represent cash in hand which is certain over Goyal, Cogent Economics & Finance (2019), 7: 1649000 https://doi.org/10.1080/23322039.2019.1649000 Page 38 of 55 any changes in price of the stock, which is by nature, riskier. Let us assume that the firm decided to revise the amount of dividend it pays. Hence V0 ttþ1ðÞ¼ V00 tþ1ðÞρtðÞþ1 fg ρ0tðÞþ1¼VtðÞρtðÞþ1 fg ρ0tðÞþ1D0tðÞ ρ0tðÞþ1 Where V00 tþ1ðÞ¼The value of the initial corpus at time 0tþ10after revision D0tðÞ¼Revised amount of dividends paid ρ0tðÞ¼Revised rate of return dependent on payment of dividends Now, one can apply the reasoning of Miller and Modigliani, with a slight modification. The values of firm, whether the dividend is paid or not, as estimated with respect to a fixed point in time, would be equal, and hence such value of the firm would be independent of the amount of dividend paid, as pointed out in Miller and Modigliani Model. Hence, Vttþ1ðÞ¼V0 ttþ1ðÞ Or, VtðÞ DtðÞ ρtðÞþ1¼VtðÞρtðÞþ1 fg ρ0tðÞþ1D0tðÞ ρ0tðÞþ1 Rearranging terms, we get VtðÞρtðÞρ0tðÞ fg ρ0tðÞþ1¼D0tðÞ ρtðÞþ1 fg DtðÞρ0tðÞþ1 fg ρ0tðÞþ1 fg ρtðÞþ1 fg Simplifying further VtðÞρtðÞρ0tðÞ fg ¼D0tðÞρtðÞþ1 fg DtðÞρ0tðÞþ1 fg ρtðÞþ1 Assuming that initially, the dividend paid was zero VtðÞ¼ D0tðÞ ρtðÞρ0tðÞ Now, ρ0tðÞrepresents the expected rate of return when the dividend D0tðÞis paid, while ρtðÞis the expected rate of return when no dividend is paid. When no dividend is being paid, the opportunity cost entails both a fixed interest rate, to account for all passage of time, and inflation, and an added component for risk. However, when a stable and static amount of dividend is being paid, the opportunity cost only entails the component of risk, as the fixed rate is already being paid in form of dividends. If Rfis fixed component of the opportunity cost and Rvis the risk-based variable component, at a time “t”, then VtðÞ¼ D0tðÞ RftðÞþRvtðÞRvtðÞ Goyal, Cogent Economics & Finance (2019), 7: 1649000 https://doi.org/10.1080/23322039.2019.1649000 Page 39 of 55 Assuming that kf;tÞ0, we get - a1 ρs;f;t;tþT 1þroef;t;tþT ¼a2þ1ðÞ a1ρs;f;t;tþT¼a2roef;t;tþTroef;t;tþTa21 Putting ρs;f;t;tþT¼0, for speculation to not exist, we get a2¼1 Similarly, instead of putting ρs;f;t;tþT¼0, putting a2¼1, we get a1ρs;f;t;tþT¼0 Hence, speculation in the market can be avoided by either there being no speculative tendencies existent among investors or coefficient of kf;tφf;tbeing zero. The latter makes sense because in a market not driven by investor expectations, but by a model-oriented approach, the chances of speculation are low. For example, De Bondt and Thaler (1985) found that portfolios that lost money previously outperformed portfolios that gained money previously. This finding suggests that investors and the market might have a tendency to over react to good and bad news. The authors suggest this to be a violation of weak form of efficiency in the market. In markets that have weak form of efficiency, the only way to get abnormal returns consistently is by fundamental analysis of stocks. Hence, in such markets, it is expected that dependence on kf;tφf;t;tþTas an indicator of value of a stock would be low. However, the importance of standardization and how the concept relates to market cycles is the main reason for adopting the approach as main value of setting a2to −1 lies in its ability to standardize the equation. In a regression equation when expected the dependent variable is completely explained by the equation if error term is included in the analysis. Δkf;t;tþT¼a1kf;tφf;t;tþTþa2kf;tþcþf;t;tþT The error term could be expected to include firm and time specific effects outside reach of the model, while the constant value reflects the effects that are same for all the firms and for the time period under consideration. We know that we can rewrite the equation as: Δkf;t;tþT¼a2 a1 a2 kf;tφf;t;tþTkf;tþc a2 þf;t;tþT a2  Taking a2to the other side, we get Δkf;t;tþT a2 ¼a1 a2 kf;tφf;t;tþTkf;tþc a2 þf;t;tþT a2 As once error term is included, there can be no doubt about the value of Δkf;t;tþTobtained, Δkf;t;tþT=a2 suggests a degree to which the dividend gap is matched, thus giving an indication of difference between theoretical dividend change and actual dividend change. The formation of cycles is thus, when there is agapbetweendividendthatshouldbepaidanddividend that is actually paid, which could be construed as one of the cause of generation of false signals of financial health of the company. Appendix 4 The signalling power of dividends is contingent mostly on two factors. Firstly, the expected rate of return, that is, the power of dividends to change the expectation of investors, which the management can potentially use to alter stock prices. Secondly, the rate of growth in earnings, which acts Goyal, Cogent Economics & Finance (2019), 7: 1649000 https://doi.org/10.1080/23322039.2019.1649000 Page 46 of 55 as a constraint in setting up payout policy as a future decrease in dividend payout because of lower earnings can send undesired signals to investors, thus affecting the management’s plans. Taking Equation (6.1), for example Δkf;t;tþT¼a1kf;tφf;t;tþTþa2kf;tþc The value of the coefficient of kf;tφf;t;tþTcan inform us about the managerial and investor expectations at play in the market. If the value of a1is significant, and so is the value of a2, then the value of a1 a2gives the extent of such expectations. We can rewrite the Equation (6.1) as follows: Δkf;t;tþT¼a2 a1 a2 kf;t 1þρf;t;tþT 1þgf;t;tþT  kf;tþc a2  (A4:1) Let the actual expected rate of return and rate of growth in earnings be ρ0 f;t;tþTand g0 f;t;tþT respectively such that 1þρf;t;tþT¼γρ;f;t;tþT1þρ0 f;t;tþT  (A4:2) 1þgf;t;tþT¼γg;f;t;tþT1þg0 f;t;tþT  (A4:3) Combining A4.2 and A4.3 with A4.1, we get Δkf;t;tþT¼a2 a1 a2 γρ;f;t;tþT γg;f;t;tþT kf;t 1þρ0 f;t;tþT 1þg0 f;t;tþT "# kf;tþc a2 ! (A4:4) If the equation holds, in the ideal case, the coefficient of kf;t 1þρ0 f;t;tþT 1þg0 f;t;tþT  would be equal to 1. Hence a1 a2 γρ;f;t;tþT γg;f;t;tþT ¼1 (A4:5) Or— a1γρ;f;t;tþTþa2γg;f;t;tþT¼0 (A4:6) If the management is underestimating the growth rate in earnings, then γg;f;t;tþT<1, and thus a1=a2<1, if γρ;f;t;tþT¼1. Such underestimation might be due to error or due to a cautious approach adopted by the management to prevent cutting down dividend payout in times of economic downturn or whenever firm performs poorly. If the management is overestimating the expected rate of return, then γp;f;t;tþT>1, and thus a1=a2<1, if γg;f;t;tþT¼1. Such overestimation might be due to error or because of management being cautious and factoring in more risk and thus volatility, or more premium than what is actually required. One of the interesting point worth mentioning here is the relation of the equation with the Capital Asset Pricing Model. Capital Asset Pricing model, as put by Sharpe (1964) could be used to write expected rate of return for a firm as follows: ρf;t;tþT¼ρrf;t;tþTþβf;t;tþTρmr;t;tþTρrf;t;tþT  (A4:7) Goyal, Cogent Economics & Finance (2019), 7: 1649000 https://doi.org/10.1080/23322039.2019.1649000 Page 47 of 55 Where— ρmr;t;tþT¼Market rate of return for aperiod from 0t0to 0tþT0 ρrf;t;tþT¼Risk free rate of return for aperiod from 0t0to 0tþT0 βf;t;tþT¼Beta of firm 0f0with respect to the market for aperiod from 0t0to 0tþT0 The Capital Asset Pricing Model puts the expected rate of return from a security as a sum of risk free rate and a premium for the risk involved with the security, which is measured, most often, by volatility in price of security with respect to the volatility in the market. However, the volatility in the market price of a security is based on the information that is available to investors in the market and may not fully reflect the risk associated with the security. Assume that there is another component of risk that involves information which is with managers and not available for to investors (this assumes that the markets are not fully efficient). So, Equation (4.7) can be written as follows: ρ0 f;t;tþT¼ρrf;t;tþTþβf;t;tþTρmr;t;tþTρrf;t;tþT  þRf;t;tþTYf;t;tþT(A4:8) Where Rf;t;tþT¼Added risk ratio for the firm 0f0from period 0t0to 0tþT0 Yf;t;tþT¼Rate of return for risk ratio Rf;t;tþTfor the firm 0f0from period 0t0to 0tþT0 The above equation can be rewritten as: ρ0 f;t;tþT¼ρf;t;tþTþRf;t;tþTYf;t;tþT(A4:9) Or ρ0 f;t;tþTρf;t;tþT¼Rf;t;tþTYf;t;tþT(A4:10) The gap in the risk may be signalled to some extent by management decisions of formulating certain payouts, or the dividend payouts might actually alter risk as Gordon (1963) opined. In either case, the difference in expected rate of return can be modelled in similar terms as in case of premium in a normal Capital Asset Pricing Model equation. ρ0 f;t;tþT¼ρrf;t;tþTþβf;t;tþTρmr;t;tþTρrf;t;tþT  þβd;f;t;tþTρmd;f;t;tþT  (A4:11) Here ρmr;t;tþTdoes not include dividend yield on the market. ρmd;f;t;tþTcan be equated to total dividend yield of the index and βf;t;tþTand βd;f;t;tþTcould be assumed to be beta derived by factoring out dividend yields and only in dividend yields respectively. There is no risk free rate subtracted from dividend yield because cash dividends are assumed to be risk free by nature, however the treatment of cash dividends with respect to risk free rate may require a deeper analysis. If βf;t;tþT¼βd;f;t;tþT, then the model would resemble the Capital Asset Pricing Model. However, if βf;t;tþT>βd;f;t;tþTthen dividend paying stocks will be associated with lower rate of expected return for the same total yield. It is crucial to note that the risk decreasing effect of dividend payout in this case will not be just the result of payment of dividends, but the effect of payment of a consistent dividend. An irregularity in other firms’payment of dividend, and yet consistency in Goyal, Cogent Economics & Finance (2019), 7: 1649000 https://doi.org/10.1080/23322039.2019.1649000 Page 48 of 55 payment of dividends by the firm under consideration would send signals about an internal firm specific stability of the firm, in a period of systematic volatility. From Equations (A4.10) and (A4.2), the following equation is obtained: 1γp;f;t;tþT  1þρ0 f;t;tþT  ¼Rf;t;tþTYf;t;tþT(A4:12) The above could be written as: 1γp;f;t;tþTþρ0 f;t;tþTγp;f;t;tþTρ0 f;t;tþT¼Rf;t;tþTYf;t;tþT From Equation (A4.5), assuming value of γg;f;t;tþT¼1, the following equation is obtained: 1þa2 a1 þρ0 f;t;tþTþa2 a1 ρ0 f;t;tþT¼Rf;t;tþTYf;t;tþT On simplification, we get following: a1 a2 ¼1þρ0 f;t;tþT 1þρ0 f;t;tþTRf;t;tþTYf;t;tþT (A4:13) If a1¼1 and a2¼1, then 1þρ0 f;t;tþT¼1þρ0 f;t;tþTRf;t;tþTYf;t;tþT Hence, in such a case, Rf;t;tþTYf;t;tþT¼0. Thus, there would be no risk perceived by management that is not being priced by the market. If only a2¼1, then 1þρ0 f;t;tþT¼a1þa1ρ0 f;t;tþTa1Rf;t;tþTYf;t;tþT On rearranging terms, we get the following: 1a1 ðÞ1þρ0 f;t;tþT  ¼a1Rf;t;tþTYf;t;tþT Taking all terms involving a1to one side, we get the following: 11 a1  1þρ0 f;t;tþT  ¼Rf;t;tþTYf;t;tþT(A4:14) If a1>0, which will usually be the case, more the signalling power (a1Þ, more there will be risk gap in perception of management and investors. Or in other words, higher the risk gap in perception of management and investors, more the signalling power of dividends, which is expected. It is also interesting to note that λtþT;tin Equation (5.14) is very similar to a1=a2in Equation (A4.1). That is because the risk aversion in Lintner model or the signalling under Signalling Hypothesis serve as a way in which management prepares for any trend in future that may turn out to be different than the current trend, for example, a higher rate of growth in earnings observed currently might not persist in the future. If investors also lower their expected rate of return in response to a lower growth rate in earnings, then there would be no need for change in dividends. However, the expected rate of return may change only partially in response to a downturn in the market or lag a little bit. Thus a part of the signalling and risk aversion, that comes from the difference of the two opportunity costs not being a constant is what is signified by Goyal, Cogent Economics & Finance (2019), 7: 1649000 https://doi.org/10.1080/23322039.2019.1649000 Page 49 of 55 λtþT;t. However, there may also be a firm specific effect, which is not considered here. That is because the firm specific effect might arise out of inefficiencies in the functioning of a particular firm with respect to other firms in the same industry. If such inefficiencies persist, the firm cannot be expected to last till perpetuity as it will be outcompeted by other firms in the industry, which would violate the assumption taken before. It might be the case that such inefficiencies do not persist, however knowledge of when that would happen is out of bounds of a theory like this and hence such limitation in scope of theory is pragmatically unavoidable. Hence, while the firm specific effect will show in the regression results, they are not considered in the theory. It is expected though that taking a large number of firms in the sample will decrease the extent of firm specific effect. It is to be noted here that the effects subsumed in λtþT;twould be long term because the terms used to get its value are long term. One way in which the difference in expected rate of return between the option of realizing capital gains and the option of taking dividends would change permanently for perpetuity would be because of a permanent change in tax rates on the options. Of course, a lot of it is dependent on the extent of tax change, presence of tax clienteles, and whether the investors and managers believe that such tax changes would never be revoked or mitigated in future. As transaction costs are not being considered in the study, the effect of taxes is also ignored, though if such is present, it would be subsumed in λtþT;t. Appendix 5 The preference of dividend over capital gains in general could be defined in a practical sense as a greater placement of value on a particular amount of dividend over the same amount of capital gain. The preference of capital gains, on the other hand, would be defined by a lesser placement of value on a particular amount of dividend in comparison with the same amount of capital gains. Gordon (1959) proposed the following model for studying preference for dividend: P B¼β0þβ1  D Bþβ2 D D  Bþβ3 RE Bþβ4 RE RE  B Multiplying both sides of the equation by book value by earnings of the firm, B= Ewe get the following: P E¼β0 B  Eþβ1  D  Eþβ2 D D   Eþβ3 RE  Eþβ4 RE RE   E(A5:1) The above equation can be modified to be following: P  E¼β0 B  Eþβ1β3 ðÞ  D  Eþβ2β4 ðÞ D D   Eþβ3 E  Eþβ4 E E   E(A5:2) The average dividend paid over years can be approximately represented as kf;t E. The above equation then can be approximated as following: P  E¼β0 B  Eþβ1β3 ðÞkf;tþβ2β4 ðÞΔkf;t;tþTþβ3β4 ðÞþβ4 E  E(A5:3) The price to average earnings ratio of the firm seems to be dependent on five factors in the model, namely, the book value to average earnings ratio, the average dividend payout ratio, change in dividend payout ratio, a constant and growth rate in earnings of the firm. If β1¼β3and β2¼β4, then dividend payout will be irrelevant as Miller and Modigliani (1961) propose, and the price of the a firm would be a function of its book value and earnings growth rate, with the latter being decided by the investment policy which is assumed to be fixed under M&M model. While the book value gives afirm’s base value (i.e., value if firm is liquidated immediately and assets and liabilities are priced in the market at their value as written in books), the earnings give the subsequent additions to the value of the firm, forming the complete value of the firm’s share. If β1>β3and β2¼β4,thenitmust Goyal, Cogent Economics & Finance (2019), 7: 1649000 https://doi.org/10.1080/23322039.2019.1649000 Page 50 of 55 be assumed that while investors prefer dividend over capital gains, they do not trust changes in dividend (both expected and unexpected) to base their decisions on it and their adjustment to dividend is with a lag. If both β1>β3and β2>β4, then it must be assumed that while investors prefer dividend over capital gains, in all forms, whether the dividend is stable or not. If the use of dividend as only a signal is valuable, then β1¼β3and β2>β4would be expected, because the unexpected change in dividend will be what will produce observable value in the market but only because of availability of new information in the market by proxy of a change in dividend or a confirmation of existing expectations. When this new change would be accommodated, the increased or decreased dividend would have no further contribution towards value of the firm. Here, the paper’s assertion becomes a bit clearer. If dividend is more preferable than capital gains, then there would be extensive opportunities for arbitrage and as Miller and Modigliani (1961) suggest, both the options would become equally preferable by workings of the market, assuming no differential tax effect. However, Miller and Modigliani (1961) allow signalling function of the dividend to alter value of the firm if there is information asymmetry between the managers and investors. In such a case, an unexpected change in dividend would cause a change in the value of the firm, but not the payout that is stable over a long period of time. However, that would violate Gordon’s(1963) idea of dividend possessing, whether they are stable or not, a lower risk than capital gains, which also seems to be a reasonable position. One way to harmonise the two positions is to allow a value differential because of differential dividend payout to be partially covered by arbitrage. If β1β3Þ0, or in other words, coefficient of kf;tis not zero, then a cycle in the market could be assumed, which would be eventually fixed by arbitrage. However, if β2β4Þ0 that might be suggestive of investors’preference for dividend or capital gains, while controlling for a cyclical effect in the market, giving us a hint of whether there is a rational preference for dividend. The extent of this preference can be known by computing the value of β2β4 ðÞ=β1β3 ðÞ,ifβ1β3>0 which would generally be the case. This preference would be a result of signalling effect, however the signalling effect itself would be based on the lower risk that dividends carry. The price to earnings ratio of a firm could be thought in the following way. If an amount of stock is sold in a period, for a particular amount of earnings, it allows one to get a specific amount of capital gain accrued in that period. If an amount of stock is not sold, it will accrue dividend for one more period, after which the investor can again make a decision whether to sell the stock or retain it. If arbitrage is possible under the market, the value realized by a capital gain for a period for a firm, must be (approximately) same as the value realized by the dividend paid for the period for the same firm. Assuming two alternate scenarios, one in which the firm decides to increase the dividend paid by Δkf;t;tþTand in the other scenario, the firm decided to keep the dividend payout the same as the previous period. Using Equation (5.3), the change in price to average earnings ratio could be represented as the following: P0  EP  E¼β0 B0  EB  E  þβ2β4 ðÞΔkf;t;tþT(A5:4) The appreciation in price of stock with respect to earnings can be assumed to be equal to decrease in amount of capital gained by the decision, which can be approximately equated to change in dividend payouts. The dividend payout at time “t”is kf;t. The expected payout at time “t+T”by rational investors could be derived to be the following: Next Period Payout ¼kf;t 1þρ0 f;t;tþT 1þg0 f;t;tþT "# Goyal, Cogent Economics & Finance (2019), 7: 1649000 https://doi.org/10.1080/23322039.2019.1649000 Page 51 of 55 This is because the value of payout must increase to the same extent as the capital gains accrued by holding the firm’s stock. However, as earnings in the current period grow by a rate of g0 f;t;tþT, the payout ratio is divided by 1 þg0 f;t;tþTto get the value of the payout ratio that must be set to get the same gain as an increment in capital. All of this assumes no differential taxation. Now, Equation (A5.4) can be written as following: kf;t 1þρ0 f;t;tþT 1þg0 f;t;tþT "# kf;t¼β0 B0 E0B E  þβ2β4 ðÞΔkf;t;tþT(A5:5) The dividend payout at time “t+T”would be based on the change in book value with respect to earnings of the firm, change in dividend payout and a change in dividend payout. If there is no change book value of the firm (which would generally be the case, as the book value used in the model refers to the book value before addition of current earnings), then that component can be discarded and the Equation (A5.6) can be written as the following: kf;t 1þρ0 f;t;tþT 1þg0 f;t;tþT "# kf;t¼β2β4 ðÞΔkf;t;tþT(A5:6) As the next period payout as calculated is an expected payout, the value of Δkf;t;tþTcould be assumed to approximate only the expected change in dividend and hence the coefficient of Δkf;t;tþTdoes not denote comprise of signalling effect of dividend policy, and consists of only the dividend preference effect, because of other reasons. The Equation (A5.6) is similar to the Equation (5.15), except that the coefficient of Δkf;t;tþTis β2β4 ðÞ, instead of 1. If Miller and Modigliani’s hypothesis stands true, then value of β2β4would be equal to zero. In such a case, there would be no effect of change in dividend. The expected dividend payout ratio could be assumed to be same as prior dividend payout ratio because there would be no reason to expect a different dividend payout as such is irrelevant. One of the other things to notice is that the magnitude of the coefficient of kf;tis 1 in Equation (A5.6). The coefficient will not be 1 if either β1β3Þ0, or in the two alternate scenarios, the way for calculating kf;twould not be same. In both cases, there will be formation of cycles, and in such a case, the method to get the usable coefficient of Δkf;t;tþTwould be by division of its coefficient by the coefficient of kf;twhich has already been discussed previously. It is important to note that forcing the different approximations on Gordon’s(1959) equation are not a major problem because the equation is not an actual equation derived by a theory but merely an equation used in regression and the point of using it is not to derive the proposed model but to link it to the proposed model. Appendix 6 Fama (1970) discussed the efficient market hypothesis in detail. In weak form of efficiency tests of the market, it is studied whether prices at particular point in time fully include information about the past prices, or in other words, whether it is possible for an investor to use only the information about past share prices in the market to earn an abnormal return consistently. Fama (1970) talks about fair game model, sub-martingale model and random walk model. Fair game model is what is of most importance here and it forms the base of other models. According to the model, for the stock market investment to be a fair game with respect to an information set Savailable at the time, the expected price of the stock as observed should be such that gain and loss from the stock over its actual value is equalized and thus the net return is zero. EP f;t  ¼FwPf;t1;Pf;t2;Pf;t3;......  (A6:1) Goyal, Cogent Economics & Finance (2019), 7: 1649000 https://doi.org/10.1080/23322039.2019.1649000 Page 52 of 55 Where EP f;t  ¼Expected price of share for afirm 0f0at time 0t0 Fw¼Pricing function involving only historical prices of the stock being employed by the market Thus, it is impossible to earn a consistent return that is abnormal in such markets using a pricing function that only includes historical prices because probability weighted value of gain over a price thus calculated is equal to the probability weighted value of loss. If the markets do not have even weak form of efficiency, then it means that the expected price of the stock would be different than the price calculated by using past prices by a value that itself is a function of past prices of the stock. This can be represented as the following: EP f;t  ¼FwPf;t1;Pf;t2;Pf;t3;......  þFuPf;t1;Pf;t2;Pf;t3;......  (A6:2) Where Fu¼Pricing function involving only historical prices of the stock not being employed by the market In such a case, an investor who knows about the function Fucan have an edge over other investors in the market and gain a consistent abnormal rate of return, by trading with the investors in the market who do not know the exact value of the function, given the historical prices in the market. Now if the hypothesis in the paper is correct and dividend payout changes are important in aligning the value of the firm’s stock to its actual value, then it follows that when there is not even a weak form of efficiency in the market then the following would hold in case of existence of market equilibrium: Δkf;t;tþT¼DuFuPf;t1;Pf;t2;Pf;t3;......  (A6:3) Where Du¼Dividend function to convert pricing function output to aparticular dividend output Dumay be a function involving many other inputs and not just historical stock prices. If there is no gap between the actual (or rather expected) pricing of the stock and the pricing as being done by the market, no dividend change would be required and Miller and Modigliani (1961) hypothesis would prevail. Note that the situation when the dividend payout change would be relevant is not exactly the same as in case of signalling hypothesis in which the investors’perceptions about a firm’s value change by change in payout because they perceive the change in payout as an indication of change in management’s beliefs future growth prospects of the firm. In the latter case, the investors lay more trust in management’s views about the firm because of lack of some information. However, even if both the management and the investors lack information about Fu, they might not share similar views about the actual value of the firm. And thus a particular change in payout may not be enough to align the value of the firm to its true value and it becomes a long process involving a series of adjustments. In contrast, when a market has a strong form of efficiency, it is impossible to beat the market consistently because stock prices at a particular point in time already reflect all the available information materially relevant to the price of the stock and thus it is impossible for anyone to predict the future movement of the stock with a greater accuracy than anyone else consistently. Jensen uses the Capital Asset Pricing Model to develop an equation of expected returns, and Goyal, Cogent Economics & Finance (2019), 7: 1649000 https://doi.org/10.1080/23322039.2019.1649000 Page 53 of 55 converts the ex ante equation into an ex post equation by replacing the expected market rate of return with the realized market rate of return. E~ rf;tþ1jϕt;rmr;tþ1  ¼rfr;tþ1þβfϕt ðÞrmr;tþ1rfr;tþ1  (A6:4) Where ϕt¼All information available at time 0t0 βfϕt ðÞ¼Beta of the firm 0f0estimated based on information ϕt It can be assumed that a firm’s return has no considerable effect on either the market (portfolio) return or risk free rate of return because there are many firms in the market and economy and the effect of each individual firm on the economy is marginal compared to the market or economy as a whole. Thus, rfr;tþ1and rmr;tþ1can be assumed to be constant with respect to the firm. However, rfr;tþ1and rmr;tþ1would not necessarily be constant with time. Yet a part of the risk free rate of return and market rate of return can be assumed to be constant even with respect to time. Assume that based on current information set ϕt, investors in the market have an expectation value for all future rate of returns till infinity (based on the assumption that firms exist until perpetuity). While the expected value of return may differ from the actual value because of availability of new information, generally it could be assumed that over a moderate time period, there won’tbeany significant deviations from the expected value because generally all information at a particular point in time would also contain information about the long-term capital budgeting and capital structuring decisions. The collective of these individual strategies and the overall outlook towards economy can be expected to provide a foundation for a reasonable value of expected returns from the market and government bonds. In any case, if there is still a difference in the expected and the observed value of a stock in the market, whatever the cause of the difference is, it must be constant of the firm specific effects to a considerable degree (some of the difference might also be attributable to same information but different valuing mechanism, different time horizons and so on). The change in payout ratio would then be an attempt to mitigate the difference in actual risk and expected risk and the payout thus could be written as the following: Δkf;t;tþT¼c(A6:5) Where c¼aconstant with respect to firm;time;and all information available at time 0t0 Thus from complete inefficiency to a complete efficiency, the dividend payout is expected to range from a high dependence on firm specific factors to a high dependence on a constant value (which would depend on several factors like economic conditions). Goyal, Cogent Economics & Finance (2019), 7: 1649000 https://doi.org/10.1080/23322039.2019.1649000 Page 54 of 55 © 2019 The Author(s). This open access article is distributed undera Creative Commons Attribution (CC-BY) 4.0 license. You are free to: Share —copy and redistribute the material in any medium or format. Adapt —remix, transform, and build upon the material for any purpose, even commercially. The licensor cannot revoke these freedoms as long as you follow the license terms. Under the following terms: Attribution —You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use. No additional restrictions You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits. Cogent Economics & Finance (ISSN: 2332-2039) is published by Cogent OA, part of Taylor & Francis Group. Publishing with Cogent OA ensures: •Immediate, universal access to your article on publication •High visibility and discoverability via the Cogent OA website as well as Taylor & Francis Online •Download and citation statistics for your article •Rapid online publication •Input from, and dialog with, expert editors and editorial boards •Retention of full copyright of your article •Guaranteed legacy preservation of your article •Discounts and waivers for authors in developing regions Submit your manuscript to a Cogent OA journal at www.CogentOA.com Goyal, Cogent Economics & Finance (2019), 7: 1649000 https://doi.org/10.1080/23322039.2019.1649000 Page 55 of 55