DIVIDEND POLICY

DIVIDEND POLICY

Dividends or Capital Gains?

The ultimate goal of financial managers should be the maximization of shareholder wealth.

Shareholder wealth can be maximized by maximizing the price of the stock.

As we know, the price of the stock is the expected present value of future cash flows.

Dividends or Capital Gains?

In the late 1950s, Myron Gordon proposed modeling price on a firm’s dividends and growth potential:

Optimal Dividend Policy:   To maximize price, an optimal balance must be found between current dividends (D₁) and the need for growth (g).

Dividend Irrelevance Theory

Miller and Modigliani showed algebraically that dividend policy didn’t matter:

n    They showed that as long as the firm was realizing the returns expected by the market, it didn’t matter whether that return came back to the shareholder as dividends now, or reinvested.

o     They would see it in dividend or price appreciation.

n    The shareholder can create their own dividend by selling the stock when cash is needed.

Dividend Policy and Stock Price

Dividend Irrelevance Theory:

n    Miller/Modigliani argued that dividend policy should be irrelevant to stock price.

n    If dividends don’t matter, this chapter is irrelevant as well (which is what most of you are thinking anyway).

n     

Dividend Irrelevance Theory

Dividend Irrelevance Theory

Dividends are not in the final equation!

Therefore, dividends are irrelevant to value!

Dividend Irrelevance Theory

But Miller and Modigliani made some unrealistic assumptions in developing their model:

n    Brokerage costs didn’t exist.

n    Taxes didn’t exist.

They made these assumptions to simplify the analysis.

Bird-in-the-Hand Theory

Gordon argued that a dividend-in-the-hand is worth more than the present value of a future dividend.

In essence, he said that the risk premium on the dividend yield is higher than on the growth rate.

Tax Preference Theory

There are three ways in which taxes affect the dividend preferences of shareholders.

n    For individual investors tax rates differ for capital gains and dividends.

n    Taxes on capital gains are not due until the stock is sold.

n    If the stock is held until the shareholder expires, no tax is due at all.

For years the capital gains rate was significantly below the dividend income rate, prompting many companies to retain more income, and declare smaller dividends.

With the Jobs and Growth Tax Relief Reconciliation Act of 2003, the dividend tax rate has fallen sharply.

Dividends or Capital Gains?

Summary:  Do shareholders prefer dividends or capital gains?

n    Dividend Irrelevance:  If the return on investment is what the market requires, then it doesn’t matter whether you get it in dividend or capital gains.

n    Bird in the Hand Theory:  Shareholders prefer dividends, and will require a higher discount rate for capital gains since they are riskier.

Dividends or Capital Gains?

n    Tax Preference Theory:  Under the old tax system, an unambiguous case could be made in favor of capital gains.  The shareholder would require the same after-tax return, meaning the required return on dividends used to be higher.

o     Today dividends and capital gains have virtually the same tax rate.

Signaling:

n  The theories thus far have assumed that investors and managers have the same information set.

n  When it comes to prospect for the company, managers may have better information than investors.

n  Therefore unexpected changes in dividends may relay information to the market that it didn’t know before.

n     Managers don’t cut dividends unless the firm is in financial distress.

n    It is therefore believed that firms do not increase dividends beyond Wall Street’s expectations unless managers anticipate stronger earnings than expectations.

n    Unexpected changes in dividends relay information to the market.

Clientele Effect Hypothesis

Tax-free foundations and retirees at lower marginal tax rates prefer cash now and on a predictable basis.

Investors at higher marginal tax rates might prefer capital gains to dividends.  With capital gains they can better time their tax liabilities.

Each firm, therefore, attracts the type of investor that likes its dividend policy.

Dividend Policy in Practice

Residual Dividend Policy:  Investors prefer to have the firm retain and reinvest earnings if they can earn a higher risk adjusted return than the investor can.

n  Residual Dividend Policy suggests that dividends should be that part of earnings which cannot be invested at a rate at least equal to the WACC.

Residual Dividend Policy Steps:

1.      Determine the optimal capital budget.

2.      Determine the retained earnings that can be used to finance the capital budget.

3.      Use retained earnings to supply as much of the equity investment in the capital budget as necessary.

4.      Pay dividends only if there are left-over earnings.

Stable, Predictable Dividend Policy: Due to the possibility of a negative signal to investors, many CFOs have set the policy of never reducing their dividends.

n    Dividends are only increased if management is certain future earnings will support such a high dividend.

Stable, Predictable Dividend Policy:

n    A variation of this policy is one in which dividends exhibit a stable, predictable growth rate.

n    In that instance the company has to set the policy in such a way that the growth rate can be sustained for the foreseeable future.

Stable, Predictable Dividend Policy Steps:

1.      Pay a predictable dividend every year.

2.      Base optimal capital budget on residual retained earnings (after dividend).

Constant Payout Ratio Policy:  It is possible that a company could set a policy to payout a certain percentage of earnings as dividends.

n    The problem is that such a policy would not fit the needs of the firms stockholders, since it would cause a great deal of volatility in dividends paid (see clientele effect spoken of earlier).

Constant Payout Ratio Policy Steps:

1.      Pay a constant proportion of earnings (if positive).

2.      Base optimal capital budget on residual retained earnings.

Low Regular Dividend Plus Extras:  This policy is a hybrid of the last two policies.  It is meant to keep expectations low for dividends, and supplement those dividends with bonuses in good years.

n    The problem is the potential for negative signaling.

Low Regular Dividend Plus Extras Steps:

1. Pay a predictable dividend every year.
2. In years with good earnings pay a bonus dividend.
3. Base optimal capital budget on residual of regular dividend and compromising with bonus for capital budgeting projects.

General Motors – Dividends

General Motors – Dividends

General Motors – Dividend History

Caterpillar – Dividend History

Internally Generated Growth

Dividend Payout Ratio:

n    The company can only pay for its own growth if it retains earnings.

n    The stockholder is more certain of earnings if the firm pay out part of “earnings” as dividends.

Retention Ratio:

n    The retention ratio depends on what proportion of earnings is paid-out as dividends.

n    Everything else is retained.

The Internal Growth Rate

The internal growth rate tells us how much the firm can grow assets using retained earnings as the only source of financing.

b = Retention Ratio

The Sustainable Growth Rate

The sustainable growth rate tells us how much the firm can grow by using internally generated funds and issuing debt to  maintain a constant debt ratio.

b = Retention Ratio

Dividend Policy

A company’s dividend policy depends on:

n    The shareholders of the company.

n    Market signaling.

o     The more understandable the better.

o     The more stable the better.

n    The growth potential of the company.

INTEREST RATE MODELS

INTEREST RATE MODELS

Classifications of Interest Rate Models

·         Discrete vs. Continuous

·         Single Factor vs. Multiple Factors

·         General Equilbrium vs. Arbitrage Free

Discrete Models

·         Discrete models have interest rates change only at specified intervals

·         Typical interval is monthly,daily, quarterly or annually also feasible

·         Discrete models can be illustrated by a lattice approach

Continuous Models

Interest rates change continuously and smoothly (no jumps or discontinuities)

Mathematically tractable

Accumulated value = e^rt

Example

            $1 million invested for 1 year at r = 5%

            Accumulated value = 1 million x e^.05 = 1,051,271

Single Factor Models

Single factor is the short term interest rate for discrete models

Single factor is the instantaneous short term rate for continuous time models

Entire term structure is based on the short term rate

For every short term interest rate there is one, and only one, corresponding term structure

Multiple Factor Models

Variety of alternative choices for additional factors

Short term real interest rate and inflation (CIR)

Short term rate and long term rate (Brennan-Schwartz)

Short term rate and volatility parameter (Longstaff-Schwartz)

Short term rate and mean reverting drift (Hull-White)

General Equilibrium Models

Start with assumptions about economic variables

Derive a process for the short term interest rate

Based on expectations of investors in the economy

Term structure of interest rates is an output of model

Does not generate the current term structure

Limited usefulness for pricing interest rate contingent securities

More useful for capturing time series variation in interest rates

Often provides closed form solutions for interest rate movements and prices of securities

Arbitrage Free Models

Designed to be exactly consistent with current term structure of interest rates

Current term structure is an input

Useful for valuing interest rate contingent securities

Requires frequent recalibration to use model over any length of time

Difficult to use for time series modeling

Which Type of Model is Best?

There is no single ideal term structure model useful for all purposes

Single factor models are simpler to use, but may not be as accurate as multiple factor models

General equilibrium models are useful for modeling term structure behavior over time

Arbitrage free models are useful for pricing interest rate contingent securities

How the model will be used determines which interest rate model would be most appropriate

Term Structure Shapes

Normal upward sloping

Inverted

Level

Humped

Litterman and Scheinkmann (1991) investigated the factors that affect yield movements

Over 95% of yield changes are explained by a combination of three different factors

• Level
• Steepness
• Curvature

Level Shifts

Rates of maturities shift by approximately the same amount

Also called a parallel shift

Steepness Shifts

Short rates move more (or less) than longer term interest rates

Changes the slope of the yield curve

Curvature Shifts

Shape of curve is altered

Short and long rates move in one direction, intermediate rates move in the other

ARCH AND GARCH MODELS

ARCH and GARCH Models

Background

Most of the statistical tools are designed to model the conditional mean of a random variable.

ARMA and ARIMA time series model assume that there lies stationarity in the data.

Now there are some situations where variance of error terms varies with time, so in this situation we can not apply these models.

Autoregressive Conditional Heteroskedasticity (ARCH) models are specifically designed to model and forecast conditional variances.

ARCH models were introduced by Engle (1982) and generalized as GARCH (Generalized ARCH) by Bollerslev (1986).

The variance of the dependent variable is modeled as a function of past values of the dependent variable and independent, or exogenous variables.

These models are widely used in various branches of econometrics, especially in financial time series analysis.

WHY ARCH/GRACH MODELS?

There are several reasons that you may want to model and forecast volatility.

First, you may need to analyze the risk of holding an asset or the value of an option.

Second, forecast confidence intervals may be time-varying, so that more accurate intervals can be obtained by modeling the variance of the errors.

Third, more efficient estimators can be obtained if heteroskedasticity in the errors is handled properly.

Basic Assumptions

The basic version of the least squares model assumes that the expected value of all error terms, when squared, is the same at any given point. This assumption is called homoskedasticity, and it is this assumption that is the focus of ARCH/ GARCH models.

Data in which the variances of the error terms are not equal, in which the error terms may reasonably be expected to be larger for some points or ranges of the data than for others, are said to suffer from heteroskedasticity.

Instead of considering this as a problem to be corrected, ARCH and GARCH models treat heteroskedasticity as a variance to be modeled.

How To Start Modeling

Stationarity of time series

·         Unit Root Test

The Box - Jenkins ARIMA Methodology

·         Identification

·         Estimation

·         Diagnostic Checking

·         Forecasting

Stationarity Checks

The ARCH specification

In developing an ARCH model, you will have to provide two distinct specifications-one for the conditional mean and one for the conditional variance.

The ARCH(1) Model

GARCH (1,1) Model

NOTE:An ordinary ARCH model is a special case of a GARCH specification in which there are no lagged forecast variances in the conditional variance equation.

GARCH (p, q) Model

Higher order GARCH models, denoted GARCH (p, q), can be estimated by choosing either p or q, both are greater than 1. The representation of the GARCH(p, q) variance is

where p is the order of the GARCH terms and q is the order of the ARCH term.

Model Checking

1.      The Ljung-Box Q Statistic

2.      Jarque-Bera Statistic

3.      Histogram Normality test

4.      ARCH–LM Test

5.      Correlogram of Standardized Residuals and Correlogram of squared residuals

A Value-at-Risk Example

·         Applications of the ARCH/GARCH approach are widespread in situations where the volatility of returns is a central issue. Many banks and other financial institutions use the concept of “value at risk” as a way to measure the risks faced by their portfolios.

·         The 1 percent value at risk is defined as the number of dollars that one can be 99 percent certain exceeds any losses for the next day. Statisticians call this a 1 percent quantile, because 1 percent of the outcomes are worse and 99 percent are better.

·         Let’s use the GARCH(1,1) tools to estimate the 1 percent value at risk of a $1,000,000 portfolio on March 23, 2000. This portfolio consists of 50 percent Nasdaq, 30 percent Dow Jones and 20 percent long bonds. The long bond is a ten-year constant maturity Treasury bond.1 This date is chosen to be just before the big market slide at the end of March and April. It is a time of high volatility and great anxiety.

Hypothetical Portfolio Example

ARCH – LM Test

Descriptive

Table 2

Results from table 2

The portfolio shows substantial evidence of ARCH effects as judged by the autocorrelations of the squared residuals in Table 2.

The first order autocorrelation is .210, and they gradually decline to .083 after 15 lags. These autocorrelations are not large, but they are very significant. They are also all positive, which is uncommon in most economic time series and yet is an implication of the GARCH(1,1) model.

Table 3 showing GARCH (1,1)

Results from table 3

The basic GARCH(1,1) results are given in Table 3.

Under this table it lists the dependent variable, PORT, and the sample period, indicates that it took the algorithm 16 iterations to maximize the likelihood function and computed standard errors using the robust method of Bollerslev-Wooldridge.

The three coefficients in the variance equation are listed as C, the intercept; ARCH(1), the first lag of the squared return; and GARCH(1), the first lag of the conditional variance. Notice that the coefficients sum up to a number less than one, which is required to have a mean reverting variance process.

Normality of Residuals

Residuals Generated from the Model  

Plots the value at risk estimated each day using this methodology within the sample period and the losses that occurred the next day. There are about 1 percent of times the value at risk is exceeded, as is expected, since this is in-sample.

Conclusion

ARCH and GARCH models have been applied to a wide range of time series analyses, but applications in finance have been particularly successful and have been the focus of this introduction.

Financial decisions are generally based upon the tradeoff between risk and return; the econometric analysis of risk is therefore an integral part of asset pricing, portfolio optimization, option pricing and risk management.

The analysis of ARCH and GARCH models and their many extensions provides a statistical stage on which many theories of asset pricing and portfolio analysis can be exhibited and tested.

Reference

Bollerslev, Tim. 1986. “Generalized Autoregressive Conditional Heteroskedasticity.” Journal of Econometrics. April, 31:3, pp. 307–27.

Bollerslev, Tim and Jeffrey M. Wooldridge. 1992. “Quasi-Maximum Likelihood Estimation and Inference in Dynamic Models with Time- Varying Covariances.” Econometric Reviews. 11:2, pp. 143–72.

Engle, Robert F. 1982. “Autoregressive Conditional Heteroskedasticity with Estimates of the Variance of United Kingdom Inflation.” Econometrica. 50:4, pp. 987–1007.

 Engle, Robert and Gary G. J. Lee. 1999. “A Permanent and Transitory Component Model of Stock Return Volatility,” in Cointegration, Causality, and Forecasting: A Festschrift in Honour of Clive W. J. Granger. Robert F. Engle and Halbert