Dividend Policy and Dividend Payment Behavior:
Theory and Evidence
Cheng-Few Lee
Rutgers University
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
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In this introduction, we will discuss overall application of
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2
• Part II. Overview of Financial Econometrics and Statistics
A. Financial Econometrics
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A. Asset Pricing Research
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I. Financial Accounting Research
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• Part IV. Financial Statistics
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4
Flow Chart of Dividend Policy and Dividend Behavior
Dividend
Policy
Time-Series
Dividend
Behavior
Partial Adjustment
Process
Dividend
Relevance Theory
with Tax Effect
Dividend
Relevance Theory
without Tax Effect
Dividend
Irrelevance Theory
Information
Content or
Adaptive
Expectations
Cross-Sectional
Signaling
Hypothesis
Myopic Dividend
Policy
CAPM
Approach
Free Cash Flow
Hypothesis
Flexibility
Hypothesis
Non-CAPM
Approach
Life-Cycle
Theory
Residual Dividend
Policy
5
Empirical Analyses in Dividend Policy Research
Descriptive Data
Analysis
Time Series
Cross-Sectional
Regression
Analysis
Time Series
Probit / Logit
Cross-Sectional
Fama-MacBeth
Procedure
Panel Data
Analysis
Seemly
Uncorrelated
Regression
(SUR)
Fixed Effect
Model
6
Dividend Policy and Dividend Payment Behavior
A. 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)
- Life-cycle theory (DeAngelo et al., 2006)
7
Dividend Policy and Dividend Payment Behavior
B. Dividend Behavior Models
(i) Partial Adjustment Model (Lintner, 1956 AER)
Dt  a0  a1 Dt 1  a2 Et  et
(1)
(ii) Mixed Partial Adjustment and Adapted Expectation (Fama & Babiak, 1968
JASA)
(iii) Generalized Dividend Forecasting Model (Lee et al., 1987, Journal of
Econometrics)
Dt  a1  a2 Dt 1  a3 Dt  2  a4 Et  vt
(2)
where a1   , a2   2      , a3  1   1    , a4  r  , and vt  ut  1    ut 1.
8
Dividend Policy and Dividend Payment Behavior
C. Cross-Section Relationship between Stock Prices, Dividends, and
Retained Earnings
(i) Friend and Puckett (1964 AER) have proposed the relationship between
stock prices, dividends, and retained earnings as follows:
Pti  A  BDti  CRti
i  1,
,N
t  1,
,T 
(3)
where
Pti , Dti , and Rti represtne price per share, dividend per share and retained earnings
per share, respectively.
Based upon Eq. (1) and discount cash flow model in terms of optimal
forecasting, Granger (1975 JF) has shown that B and C can be written in
terms of discount rate, ,a1and aof
Eq. (1). Therefore, it can be concluded
2
that Eq. (3) is a theoretical derived model instead of an ad-hoc model.
9
Dividend Policy and Dividend Payment Behavior
D. Integration of Dividend Policy and CAPM
(Litzenberger and Ramaswamy 1982 JF)
10
Summary of Our Research
1. We propose a dynamic framework and show the existence of an optimal
payout ratio under a perfect market.
2. The relationship between firm’s optimal payout ratio and its growth rate is
negative in general.
3. The relationship between firm’s optimal payout ratio and its risks.
- depends on its growth rate relative to its ROA
- separate the considerations of free cash flow problem and flexibility
4. We develop a fully dynamic model for determining the time optimal
growth and dividend policy under stochastic conditions.
- A convergence process in the optimal growth rate.
5. Empirical evidence on the optimal payout ratio. (Supports our model)
11
Outline
1. Introduction
2. The Model for Optimal Dividend Policy
3. Comparative Static Analysis of Dividend Payout Policy
3.1 Case I: Total Risk
3.2 Case II: Systematic Risk
3.3 Total Risk and Systematic Risk
3.4 No Change in Risk
3.5 Relationship between the Optimal Payout Ratio and the Growth Rate
4. Joint Optimization of Growth Rate and Payout Ratio
4.1 Optimal Growth Rate v.s. Time Horizon
4.2 Optimal Growth Rate v.s. Degree of Market Perfection
4.3 Optimal Growth Rate v.s. ROE
4.4 Optimal Growth Rate v.s. Initial Growth Rate
4.5 Optimal Dividend Policy v.s. Optimal Growth Rate
12
Outline
5. Dividend Behavior Model
5.1 Partial Adjustment Model (Lintner, 1956 AER)
5.2 Mixed Partial Adjustment and Adapted Expectation (Fama & Babiak, 1968
JASA)
5.3 Generalized Dividend Forecasting Model (Lee et al., 1987, Journal of
Econometrics)
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
7.1 Limitations of cross-sectional approach to investigate dividend policy
7.2 We need to use dividend behavior model to supplement cross-sectional
approach to obtain more meaningful conclusion for decision making.
13
Introduction
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.
14
Introduction
•
•
•
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.
15
[Blau and Fuller (2008)]
Introduction
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.
16
The Model for Optimal Dividend Policy
- Let r (t ) represent the initial assets of the firm and h(t )
represent the growth rate. Then, the earnings of this firm are
given by Eq. (1), which is
x(t )  r (t ) A(o)eht
(1)
- The retained earnings of the firm, y  t  , can be expressed as
y (t )  x(t )  m(t )d (t )
(2)
where m(t ) is the number of shares outstanding, and
d (t ) is dividend per share at time t.
17
The Model for Optimal Dividend Policy
The new equity raised by the firm at time t can be defined as
e(t )   p(t )m(t )
(3)
where  = degree of market perfection, 0 <   1.
Therefore, the investment in period t can be written as:
hA(o)eht  x(t )  m(t )d (t )   m(t ) p(t )
(4)
Rearranging Eq.(4), we can get


d (t )   r (t )  h  A(o)e ht   m(t ) p(t ) m(t )
(5)
18
The Model for 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.
p(o)   dˆ (t )e kt dt
T
0
( A  bI  h) A(o)eth   m(t ) p(t )   A(o) 2  (t ) 2  (t ) 2 e 2th  kt
 [

]e dt
2
0
m(t )
m(t )
T
(14)
- Eq.(14) can be formulated a differential Equation:
 m(t )
p(t )  [
 k ] p(t )  G(t )
(17)
m(t )
(a  bI  h) A(o)eth   A(o)2  (t )2  (t ) 2 e2th
where G(t ) 

m(t )
m(t )2
(18)
19
Optimal Dividend Policy
Optimal Payout Ratio when 
 1:
D(t ) (a  bI  h)  (h  (t ) 2  (t ) 2   (t ) 2  (t ) 2   (t ) 2  (t ) 2 )[e( h  k )(T t )  1] 

1 

x (t )
(a  bI ) 
 (t ) 2  (t ) 2 (h  k )

(a  bI  h)  [e( h  k )(T t )  1] 
 (t ) 2  (t ) 2  
=

1 
h

2
(a  bI ) 
(h  k ) 
 (t )  (t ) 2  
(26)
20
Relationship between the Optimal Payout Ratio
and the Growth Rate
[ D(t ) / x (t )]
h
  k   h  h  k  (T  t )  e( h k )(T t )  k 
1
k  he( h k )(T t )
h
 (
)[
]  (1 
)

2
a  bI
hk
a  bI 

h  k 

(32)
- The sign is not only affected by the growth rate (h), but is also
affected by the expected rate of return on assets (a  bI ), 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.
21
22
Relationship between the Optimal Payout Ratio
and the Growth Rate
[ D(t ) / x (t )]  (a  bI )  h  (T  t )  h(T  t )  1 




h
a  bI


(34)
1
1 
When h  (a  bI ) 
, there is a negative

2
(T  t ) 
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.
23
Implications
Hypothesis 1: firms generally reduce their dividend payouts when
their growth rates increase.
The negative relationship between the payout ratio and the growth ratio
in our theoretical model implies that high growth firms need to
reduce the payout ratio and retain more earnings to build up
“precautionary reserves,” while low growth firms are likely to be
more mature and already build up their reserves for flexibility
concerns.
[Rozeff (1982), Fama and French (2001), Blau and Fuller (2008), etc.]
24
Optimal Payout Ratio vs. Total Risk
  D(t ) / x (t ) 
  (t ) 

2

(
t
)


2
h
 (1 
a  bI
 e( h k )(T t )  1 
)

h

k


(27)
 High growth firms  h  a  bI  :
negative relationship between optimal payout ratio and total
risk.
 Low growth firms  h  a  bI  :
positive relationship between optimal payout ratio and total risk
25
Optimal Payout Ratio vs. Systematic Risk
  D(t ) / x (t ) 
  (t ) 

2

(
t
)


2
h
 (1 
a  bI
 e( h k )(T t )  1 
)

h

k


(28)
 High growth firms  h  a  bI  :
negative relationship between optimal payout ratio and
systematic risk.
 Low growth firms  h  a  bI  :
positive relationship between optimal payout ratio and
systematic risk
26
Implications
• Hypothesis 2: the relationship between the firms’ dividend payouts
and their risks is negative when their growth rates are higher than
their rates of return on asset.
- Flexibility Hypothesis
High growth firms need to reduce the payout ratio and retain more
earnings to build up “precautionary reserves.” These reserves
become more important for a firm with volatile earnings over time.
=> For flexibility concerns, high growth firms tend to retain more
earnings when they face higher risk.
27
Implications
• Hypothesis 3: the relationship between the firms’ dividend payouts
and their risks is positive when their growth rates are lower than
their rates of return on asset.
- Free Cash Flow Hypothesis
1. Low growth firms are likely to be more mature and most likely
already built such reserves over time.
2. They probably do not need more earnings to maintain their low
growth perspective and can afford to increase the payout [see
Grullon et al. (2002)].
3. The higher risk may involve higher cost of capital and make free
cash flow problem worse for low growth firms.
=> For free cash flow concerns, low growth firms tend to pay more
dividends when they face higher risk
28
Optimal Payout Ratio vs. Total Risk and
Systematic Risk
 (t )2
 (t )2
d [ D(t ) / x (t )]   d (
)   d(
)
2
2
 (t )
 (t )
where
(29)
h
e ( hk )(T t )  1
  (1 
)[
]
a  bI
hk
• Relative effect on the optimal dividend payout ratio
 (t )2
 (t )2
d[
]  d [
]
2
2
 (t )
 (t )
(30)
29
Optimal Payout Ratio when No Change in Risk
h
k  he( h k )(T t )
[ D(t ) / x (t )]  (1 
)[
]
a  bI
hk
(30)
When there is no change in risk, the optimal payout ratio is identical to
the optimal payout ratio of Wallingford (1972).
30
Joint Optimization of Growth Rate and Payout Ratio
• The new investment at time t is
dA  t 
 A t 
dt
t
g  s  ds

o
 g t  A  o  e
(3)
 Y t   D t   n t  p(t )  LA t 
Retained Earnings New Equity
where
New Debt
D  t   the total dollar dividend at time t;
p t   price per share at time t;
  degree of market perfections, 0 <   l;
n  t  P t   the proceeds of new equity issued at time t;
L = the debt to total assets ratio
31
Joint Optimization of Growth Rate and Payout Ratio
• 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
t
g  s ds

o
A t   g t  A  o  e
 Y  t   D t   n t  p(t )  1  D / E  Y t   D t   n t  p (t ) 
we can obtain the growth rate as
g (t ) 
Our Model
ROE 1  d 
1  ROE 1  d 

 n t  p t  / E
1  ROE 1  d 
Higgins’ sustainable g
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.
32
Joint Optimization of Growth Rate and Payout Ratio
Discount cash flow
p  o    dˆ  t  e kt dt
T
(8)
0
The price per share can be expressed as PV of future dividends with a
risk adjustment.
p o 
1

n o

T
0
g  s  ds

 1
2
  2 2 0 g  s  ds   kt

2
0



r t   g t  A  o  e
 a A  o   t  n t  e
n t 
 e dt




Future Dividends
t
t
Risk Adj.
=> maximize p(o) by jointly determine g(t) and n(t).
33
Optimal Growth Rate
g t  
*

r

r   rt    2
1  1   e
 go 
go r
go   r  go  e
(19)
 rt    2 
Logistic Equation – Verhulst (1845) => a convergence process
34
Case I: Optimal Growth Rate v.s. Time Horizon

r   r   r t    2
r  1   
 e
*
g  t 
 go      2  
*
g t  

2
t
 

r  r t    2
1

1

 

e
  go 

(20)
When g0  r , g*  t   0.
When g0  r , g*  t   0.
When g0  r , g*  t   0.
35
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).
36
Case II: Optimal Growth Rate v.s. Degree of Market
Perfection
g *  t 


 r
 r t    2 2rt
  1 e
2
g


2


 o 
 
r  r t    2 
1  1   e

  go 

2
(21)
If the market is more perfect   is larger  , the speed of convergence is faster.
37
Case II: Optimal Growth Rate v.s. Degree of Market
Perfection
38
Case III: Optimal Growth Rate v.s. ROE
g *  t 
r



t
 rt    2  
 rt    2   

go  go 1  e
  g o  r 
re





2



 




 go   r  go  e

 rt    2 


2
(22)
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.
39
Case IV: Optimal Growth Rate v.s. Initial
Growth Rate
2
g *  t 
g o

 r   rt    2
  e
 go 
 
r   rt    2 
1   1   e

g
o 
 

2
(23)
Eq. (23) is always positive.
=> The higher initial growth rate is, the higher optimal growth rate at
each time.
40
41
Optimal Dividend Payout Ratio
D t 
 g* t  
 1 

Y  t  
r  t  
2
*
*
2
*
t

 2
 
kt    g *  s  ds     t     t  g  t    r  g  t      t  g  t  

0
1  e
W


3



2
*
 


2



t
r

g




t 



T
where W  
t
s
(29)
2
g  u  du  ks 2
 1
e 0
  s   r  g *  s   ds

*
• Assuming   1 and g *  t   g * ,


( g *  k )(T t )

2 
e
1 
D t  

g 

(
t
)
*
 1 
1

g




Y  t   r  t   
(g*  k ) 
 (t ) 2  


*
- Wallingford (1972), Lee et al. (2010)
42
Optimal Dividend Payout Ratio v.s. Growth Rate
[ D(t ) / Y (t )]
g *
 (
* ( g *  k )(T t )
1 k  g e
)[
r t 
g*  k
  k   g *  g *  k  (T  t )  e( g *  k )(T t )  k 
g 


]  (1 
)
2
*

r t  
g

k




*
  r (t )  g *  (T  t )  g * (T  t )  1 



*


r (t )  g


(31)
(33)
The relationship between optimal dividend payout and growth rate is
negative in general cases.
43
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 2008.
• 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 = 4900-4999, 60006999) 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.
44
Summary Statistics of Sample Firm Characteristics
45
45
Summary Statistics of Sample Firm Characteristics
46
Multivariate Regression – Fama MacBeth Model
 payout ratioi 
ln 
   1BetaRiski   2Growth _ Optioni  3 ln( Sizei )  ei
 1   payout ratioi  


47
47
Multivariate Regression (with Growth Dummy)
 payout ratioi 
ln 
   1BetaRiski  2 D  g  ROA  Riski  3Growth _ Optioni  4 ln(Sizei )  ei
 1   payout ratioi  


48
48
Multivariate Regression – Fixed Effect Model
 payout ratio
i ,t
ln 
 1  payout ratioi ,t




    1 Riski ,t   2 Di,t  g  ROA  Riski ,t  3Growth _ Optioni,t   4 ln( Size)i,t  Fixed Effect Dummies  ei


49
49
Conclusion
• We derive an optimal payout ratio using an exponential utility
function to derive the stochastic dynamic dividend policy
model.
- Different from M&M model, our model considers 1) partial
payout; 2)uncertainty (risks); 3) stochastic earnings.
• A negative relationship between the optimal dividend payout
ratio and the growth rate.
• The relationship between firm’s optimal payout ratio and its
risks depends on its growth rate relative to its ROA.
- high growth firms pay dividends due to the consideration of
flexibility and low growth firms pay dividends due to the
50
consideration of free cash flow problem.
Conclusion
• 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 optimal growth rate follows a convergence processes, and
the target rate is firm’s expected ROE.
51
Potential Future Research
1. Time-series v.s. cross-sectional research
2. Relationship among discount cash flow, dividend partial
adjustment model, and price multiplier model
3. Tax effect on dividend policy in terms of CAPM with
dividend Effect
4. Limitations of cross-sectional approach to investigate
dividend policy
5. We need to use dividend behavior model to supplement crosssectional approach to obtain more meaningful conclusion for
decision making.
6. The impacts of Integrated Tax System enacted in Taiwan on
Dec 26, 1997 can be explored.
52