Dividend Policy: Theory and Empirical Evidence Cheng-Few Lee Rutgers University

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5 Announcement for Handbook of Financial Econometrics and Statistics The purpose of this handbook is to publish original papers that apply either econometrics or statistics methods in important topics of empirical finance research. Chapters that update or expand upon well-known empirical papers are also acceptable. In this handbook, each paper should have appendices of 5 to 15 pages to demonstrate how empirical research has been executed. The tentative outline of this handbook is as follows: Part I. Introduction In this introduction, we will discuss overall application of econometrics and statistics in finance accounting research.

6 Part II. Overview of Financial Econometrics and Statistics A. Financial Econometrics B. Financial Statistics Part III. Financial Econometrics A. Asset Pricing Research B. Corporate Finance Research C. Financial Institution Research D. Investment and Portfolio Research E. Option Pricing Research F. Future and Hedging Research G. New Financial Products Research H. Mutual Fund Research I. Financial Accounting Research

7 Part IV. Financial Statistics A. Asset Pricing Research B. Investment and Portfolio Research C. Credit Risk Management Research D. Market Risk Research E. Operation Risk Research F. Option Pricing Research G. Mutual Fund Research H. Value at Risk Research We expect to include approximately 100 chapters in this handbook, which will published online and in three print volumes by Springer in Anybody who wishes to contribute a chapter to this handbook please send a proposal to Professor Cheng-Few Lee at the

Policy Framework of Finance Research Investment Policy Financing Policy Production Policy Dividend Policy (a) Forecasting Model (i) Partial Adjustment Model (Lintner, 1956 AER) (ii) Mixed Partial Adjustment and Adapted Expectation (Fama & Babiak, 1968 JASA) (iii) Generalized Dividend Forecasting Model (Lee et al., 1987, Journal of econometrics) then 8

Policy Framework of Finance Research (b) Theory (i)Dividend irrelevance (M&M, 1961) and corner solution (DeAngelo and DeAngelo, 2006) (ii)Dividend relevance (Gordon, 1962; and Lintner, 1964) - A bird in hand theory (Bhatacharya, 1979) - Signaling theory (John & Williams, 1985; Miller & Rock, 1985; and Lee et al., 1993) - Free cash flow theory (Eastbrook,1984; Jensen, 1986; and Lang and Lizenberger,1989) - Financial flexibility theory (Jagannathan et al. 2000, DeAngelo and DeAngelo, 2006; Blau and Fuller, 2008) 9

Abstract We develop a theoretical model of the optimal payout ratio under perfect markets and uncertainty. First, we theoretically derive the proposition of DeAngelo and DeAngelo's (2006) optimal payout policy when a partial payout is allowed. Second, we theoretically derive the impact of total risk, systematic risk, and growth rate on the optimal payout ratio. Taking the time varying growth rate, the imperfect market, and debt issuing into account, we further derive a dynamic model which jointly optimizes growth rate and payout ratio. We also derive a logistic equation which was first introduced by Pierre Verhulst (1845 and 1847) to obtain the optimal growth rate. Using the U.S. data during 1969 to 2008 to investigate the impact of total risk, systematic risk, and growth rate on the optimal payout ratio. We find that the relationship between the payout ratio and risk is negative (or positive) when the growth rate is higher (or lower) than the rate of return on assets. In addition, we also find that a company will generally reduce its payout when the growth rate increases. 10

11 Outline of Paper I 1. Introduction Policy Framework of Finance Research 2. The Model 3. Optimal Dividend Policy 4. Implications 4.1 Case I: Total Risk 4.2 Case II: Systematic Risk 4.3 Total Risk and Systematic Risk 4.4 No Change in Risk 5. Relationship between the Optimal Payout Ratio and the Growth Rate 6. Empirical Evidence 6.1 Sample Description 6.2 Multivariate Analysis 6.3 Fama-MacBeth Analysis 6.4 Fixed Effect Analysis 7. Summary and Concluding Remarks

12 Introduction & Motivation of Paper I Dividend Policy Miller and Modigliani (1961) - Firm Value is independent of dividend policy. - Assumptions of M&M theory 1)no tax. 2)no capital market frictions (i.e., no transaction cost, asset trade restriction, or bankruptcy cost) 3)firms and investors can borrow or lend at the same rate. 4)firm financial policy reveals no information. 5)only consider no payout and payout all cash flow. DeAngelo and DeAngelo (2006) > M&M (1961) irrelevance result is “irrelevant” because it only considers payout policies that pay out all free cash flow. > Payout policy matters when partial payouts are allowed.

13 Introduction & Motivation of Paper I Signaling Hypothesis - The signaling hypothesis suggests managers with better information than the market will signal this private information using dividends. - A company announcements of an increase in dividend payouts act as an indicator of the firm possessing strong future prospects. [Bhatacharya (1979), John and Williams (1985), Miller and Rock (1985), and Nissam and Ziv (2001)] Free Cash Flow Hypothesis (Agency Cost) - Dividend payment can reduce potential agency problem. [Eastbrook (1984), Jensen (1986), Lang and Lizenberger(1989), Lie (2000), and Grullon et al. (2002)] Financial Flexibility - Management trades off two aspects of Dividends. One is financial flexibility by not paying dividends. Another is deterioration on stock price if not paying dividends. [Blau and Fuller (2008)]

Introduction & Motivation of Paper I 1.Based on the DeAngelo & DeAngelo (2006) static analysis, we derive a theoratical dynamic model and show that there exists an optimal payout ratio under perfect market. 2.We derive the relationship between firm’s optimal payout ratio and its risks. 3.We derive the relationship between firm’s optimal payout ratio and its growth. 4.We further develop a fully dynamic model for determining the time optimal growth and dividend policy under the imperfect market, the uncertainty of the investment, and the dynamic growth rate. 5.We study the effects of the time-varying horizons, the degree of market perfection, and stochastic initial conditions in determining an optimal growth and dividend policy for the firm. 6.When the stochastic growth rate is introduced, the expected return may suffer a model specification. 7.Empirical evidence of the determination of the optimal payout policy. 14

Introduction & Motivation of Paper I Paper I: 1.We derive a theoratical dynamic model and show that there exists an optimal payout ratio under perfect market. 2. We derive the relationship between firm’s optimal payout ratio and its risks. (depends on its growth rate relative to its ROA) 3. We derive the relationship between firm’s optimal payout ratio and its growth. (Negative) 4. Empirical evidence on the optimal payout ratio. (support our theoretical results)

Paper I -Let represent the initial assets of the firm and represent the growth rate. Then, the earnings of this firm are given by Eq. (1), which is -The retained earnings of the firm,, can be expressed as where is the number of shares outstanding, and is dividend per share at time t.

Paper I The new equity raised by the firm at time t can be defined as where = degree of market perfection, 0 <  1. Therefore, the investment in period t can be written as: Rearranging Eq.(4), we can get

Paper I Because, Postulate a exponential utility function, We can get a certainly equivalent dividend stream

Paper I Under CAPM,. is the market index, and is the correlation coefficient between and. : nondiversifiable risk; : diversifiable risk. The unsystematic risk usually can be diversified away by the investors. Therefore, Eq.(9) can be revised as

Optimal Dividend Policy -The stock price should equal the present value of this certainty equivalent dividend stream discounted at the cost of capital (k) of the firm. -Eq.(14) can be formulated a differential Equation: where

Optimal Dividend Policy -Solve the differential equation -Optimization=>max p(0) =>

Optimal Dividend Policy Optimal Payout Ratio when : If, the optimal payout ratio still exists.

23 Implications: Optimal Payout Ratio vs. Total Risk -High growth firms : negative relationship between optimal payout ratio and total risk. -Low growth firms : positive relationship between optimal payout ratio and total risk. 23

24 Implications: Optimal Payout Ratio vs. Systematic Risk -High growth firms : negative relationship between optimal payout ratio and total risk. -Low growth firms : positive relationship between optimal payout ratio and total risk. -Financial Flexibility: Firm’s risks are related to its financial risk from financial leverage. When a firm faces higher financial risk, it will decrease its payout ratio to obtain more cash for the preparation for the interest payment in the future. [Jagannathan et al. (2000), DeAngelo and DeAngelo (2006), and Blau and Fuller (2008)]

25 Implications: Optimal Payout Ratio vs. Total Risk and Systematic Risk where -Relative effect on the optimal dividend payout ratio 25

Implications: Optimal Payout Ratio When No Change in Risk When there is no change in risk, the optimal payout ratio is identical to the optimal payout ratio of Wallingford (1972). 26

27 Relationship between the Optimal Payout Ratio and the Growth Rate -The sign is not only affected by the growth rate (h), but is also affected by the expected rate of return on assets ( ), the duration of future dividend payments (T-t), and the cost of capital (k). -Sensitivity analysis shows that the relationship between the optimal payout ratio and the growth rate is generally negative. =>a firm with a higher rate of return on assets tends to payout less when its growth opportunities increase.

28 Relationship between the Optimal Payout Ratio and the Growth Rate -When, there is a negative relationship between the optimal payout ratio and the growth rate. =>when a firm with a high growth rate or a low rate of return on assets faces a growth opportunity, it will decrease its dividend payout to generate more cash to meet such a new investment.

Sample Stock price, stock returns, share codes, and exchange codes are CRPS. Firm information, such as total asset, sales, net income, and dividends payout, etc., is collected from COMPUSTAT. The sample period is from 1969 to Only common stocks (SHRCD = 10, 11) and firms listed in NYSE, AMEX, or NASDAQ (EXCE = 1, 2, 3, 31, 32, 33) are included. Utility firms and financial institutions (SICCD = , ) are excluded. For the purpose of estimating their betas to obtain systematic risks, firm years in our sample should have at least 60 consecutively previous monthly returns. 29

Summary Statistics of Sample Firm Characteristics 30

31 Summary Statistics of Sample Firm Characteristics

32 Multivariate Regression – Fama MacBeth Model

33 Multivariate Regression (with Growth Dummy)

34 Multivariate Regression – Fixed Effect Model 34

35 Outline of Paper II Introduction and Motivation Model Optimal Growth Rate - Optimal Growth Rate v.s. Time Horizon - Optimal Growth Rate v.s. Degree of market Perfection - Optimal Growth Rate v.s. ROE - Optimal Growth Rate v.s. Initial Growth Rate Optimal Dividend Policy - Optimal Dvidend Policy v.s. Optimal Growth Rate Stochastic Growth Rate Conclusion

36 Introduction & Motivation of Paper II Dividend Policy and Growth Rate Gordon (1962), Lintner (1964), Lerner and Carleton (1966), Modigliani and Miller (1961), Miller and Modigliani (1966) - Relationships between optimal dividend policy and rate of return under no growth and under both internally and externally, financed growth assumptions. Higgins (1977, 1981, and 2008) - Sustainable growth rate: assuming that a firm can use retained earnings and issue new debt to finance the growth opportunity of the firm. DeAngelo and DeAngelo (2006) - M&M (1961) irrelevance result is “irrelevant” because it only considers payout policies that pay out all free cash flow. -Payout policy matters when partial payouts are allowed.

37 Introduction & Motivation of Paper II Rozeff (1982) - The optimal dividend payout is related to the fraction of insider holdings, the growth of the firm, and the firm’s beta coefficient. DeAngelo et al. (1996 and 2006) Grullon et al. (2002) -Increases in dividends convey information about changes in a firm’s life cycle from a higher growth phase to a lower growth phase. Is there an optimal dividend policy for a firm under the imperfect market, the uncertainty of the investment, and the dynamic growth rate?

Introduction & Motivation of Paper II Paper II We develop a fully dynamic model for determining the time optimal growth and dividend policy under stochastic conditions. - Given the uncertainty of ROE, the theoretical model shows the existence of an optimal payout ratio and an optimal growth rate by maximizing firm value. 2. We study the effects of the time-varying horizons, the degree of market perfection, and stochastic initial conditions in determining an optimal growth and dividend policy for the firm. - A convergence process in the optimal growth rate. - A negative relationship between optimal dividend payout and optimal growth rate. 3. When the stochastic growth rate is introduced, the expected return may suffer a model specification. 38

39 Paper II The total asset of a firm at time t where

Paper II The earnings at time t is a stochastic variable. where 40

41 Paper II The new investment at time t is where Retained Earnings New Equity New Debt

Paper II The model defined in the equation (3) is for the convenience purpose. If we want the company’s leverage ratio unchanged after the expansion of assets then we need to modify equation (3) as we can obtain the growth rate as which is the generalized version of Higgins’ (1977) sustainable growth rate model. Our model shows that Higgins’ (1997) sustainable growth rate is under-estimated due to the omission of the source of the growth related to new equity issue which is the second term of our model. 42 Our Model Higgins’ sustainable g

Paper II The dividend per share is Concerning the risk of ROE, 43 Risk Adj.

Paper II Discount cash flow The price per share can be expressed as PV of future dividends with a risk adjustment. => maximize p(o) by jointly determine g(t) and n(t). 44 Future Dividends Risk Adj.

Optimal Growth Rate Logistic Equation – Verhulst (1845) => a convergence process 45

Case I: Optimal Growth Rate v.s. Time Horizon 46

47 Case I: Optimal Growth Rate v.s. Time Horizon Convergence Process - Firms with different initial growth rates all tend to converge to their target rates (ROE).

Case II: Optimal Growth Rate v.s. Degree of Market Perfection 48

Case II: Optimal Growth Rate v.s. Degree of Market Perfection 49

Case III: Optimal Growth Rate v.s. ROE When initial growth rate is lower than the target rate (ROE), eq. (22) is positive. => If the target rate (ROE) is higher, the adjustment process will be faster. 50

Case IV: Optimal Growth Rate v.s. Initial Growth Rate Eq. (23) is always positive. => The higher initial growth rate is, the higher optimal growth rate at each time. 51

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Optimal Dividend Payout Ratio where Assuming, - Wallingford (1972), Lee et al. (2010) 53

Optimal Dividend Payout Ratio v.s. Growth Rate 54 The relationship between optimal dividend payout and growth rate is negative in general cases.

Stochastic Growth Rate and Specification Error 55 Retained Earnings New Equity New Debt When a stochastic growth rate is introduced,

Stochastic Growth Rate and Specification Error 56

Conclusion Paper I We derive a stochastic dynamic dividend policy model under perfect market and uncertainty. Different from M&M model, our model considers 1) partial payout; 2)uncertainty (risks); 3) stochastic earnings. The theoretical model shows that the relationship between firm's optimal payout ratio and its risks depends on its growth rate relative to its ROA. The theoretical model shows that the relationship between firm's optimal payout ratio and its risks is generally negative. The empirical results are consistent to the implications of our model.

Conclusion Paper II Based upon Model (I), we derive a dynamic model of optimal growth rate and payout ratio which allows a firm to finance its new assets by retained earnings, new debt, and new equity. The theoretical model shows the existence of an optimal payout ratio jointly determined by the number of shares outstanding and the growth rate. The optimal growth rate follows a convergence processes, and the target rate is firm’s expected ROE. The relationship between the optimal dividend payout and the optimal growth rate is negative in general. 58

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