options implied dividend yield and market returns

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Options Implied Dividend Yield and Market Returns

Version: September 2008

This paper proposes a new variable for the analysis of the stock market return predictability.

Recognizing that expected dividends are time-varying, I show that the variation in the expected

return can be captured by the expected dividend yield. Using options implied dividend yield

(IDY) to proxy for the expected dividend yield, I nd that the IDY serves as a strong predictor

for monthly and quarterly market excess returns. Indeed, the IDY predicts returns better than

the traditionally used realized dividend-price ratio, the earnings-price ratio, the consumption-to-

wealth ratio, the average implied correlation and the variance risk premium. To underpin theresults, I further show that the implied dividend growth (inferred from the IDY ) predicts the

future dividend growth.

Key Words: options implied dividend yield, dividend-price ratio, predictability

1. INTRODUCTION

Can the stock market return be predicted? This question has deep economic implica-

tions and has been the subject of much empirical and theoretical research. However, there

is still no consensus on whether market returns are predictable. While many studies claim

that returns can be predicted by variables such as the dividend-price ratio (DP) or the

earnings-price ratio (EP),1 a large body of the literature casts doubt on the documented

predictability.2 Generally, the evidence seems to suggest that the return predictability

is rather weak for short horizons and is the strongest for multi-year.3 In this study, I

re-examine the role of dividend ratios for predicting returns. Instead of relying on the

traditionally used realized DP, I employ an expected dividend yield extracted from index

options (implied dividend yield - IDY). I show that IDY serves as a strong predictorfor Dow Jones Industrial Average returns in the post 1997 period.4 Indeed, IDY predicts

monthly and quarterly returns better than a series of alternative predictor variables, such

as DP, EP, consumption-to-wealth ratio (CAY); variance risk premia and options implied

average correlation.5

1 See Keim and Stambaugh (1986), Fama and French (1988), Campbell and Shiller (1989), Lewellen(2004) and Cochrane (2006) among others.

2 See Goetzmann and Jorion (1995), Lanne (2002), Valkanov (2003), Boudoukh et al. (2007) amongothers.

3 One exception to this rule is variance risk premia recently analyzed by Bollerslev et al. (2008). Thevariance risk premia, dened as the dierence between the implied and the realized variance, is found to

have the strongest ability to predict returns at the intermediate (quarterly) horizon.4 The period under analysis is limited by data availability.5 Predictability of market returns with the realized average correlation was rst considered by Pollet and

Wilson (2007). This study is the rst to show that options implied correlation predicts returns.

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Predictability of market returns with the dividend-price ratio has been extensively stud-

ied.6 According to the standard view, if dividend growth is unpredictable, all the uctua-

tions in the DP come from the variations in the expected returns.7 However, recent evi-

dence suggests that the dividend growth is predictable and the expected dividend growth

is time-varying.8 As a result, the DP uctuates not only because of the variations in theexpected returns, but also because of the changes in the expected dividend growth.9 This

makes the DP a noisy proxy for the expected returns and diminishes its ability to predict

returns.10 To account for the variation in the expected dividend growth, van Binsbergen

and Koijen (2008) propose a linear regression of returns on the price-dividend ratio and

an estimate for the expected dividend growth. I demonstrate that the expected return is

a function of the product between the DP and the expected dividend growth. Therefore,

instead of relying on the predictive regression with the DP and the expected dividend

growth as two separate variables, we should consider predicting returns with the product

of both variables, an expected dividend yield. This approach alleviates the multicollinearity

problems and allows for the non-linear relation between the expected returns, the DP and

the expected dividend growth. Accordingly, it makes the prediction more precise.

Following this intuition, the main innovation of this paper lies in the estimation of the

expected dividend yield. Unlike the previous studies that estimate the expected dividends

from the past data,11 or they obtain them from the analyst forecasts,12 I use options

implied dividend yield (IDY) as a proxy for the expected dividend yield. The IDY is

extracted from the European index options by applying the put-call parity. 13 Thus, it

relies exclusively on the observed market prices and should therefore reveal the "true"markets expected dividend yield.

For a comparison with the IDY, I employ a series of alternative predictor variables. In

addition to the more traditional predictor variables (DP, EP and CAY), I also estimate

two options implied predictors, average implied correlation and variance risk premia. A

combination of the IDY and the alternative predictors provides a rich framework for the

empirical analysis, but poses certain data limitations. Construction of the average implied

correlation is rather cumbersome and possible only for indices with a small number of

stocks. Estimation of the IDY is limited to the indices with European options. As a

result, the analysis is restricted to Dow Jones Industrial Average (DJIA) between October1997 and December 2006.

The main empirical results are the following. In line with the previous studies, the DP

serves as a rather poor predictor for short-run returns. It explains 3 5% of the variation

6 First study dates back to 1920 (Dow) and the most inuential paper on dividend ratios by Fama andFrench (1988) has 325 ocial citations.

7 See Cochrane (2006) among others.8 See Lettau and Ludvingson (2005), Ribeiro (2004) and Van Binsbergen and Koijen (2008).9 See Campbell and Shiller (1988) and Van Binsbergen and Koijen (2008) among others.

10 See Fama and French, 1988; Kothari and Sanken, 1992; Goetzmann and Jorion, 1995; Menzly et al.,2004; Lettau and Ludvingson, 2005 and Rytchkov, 2006 among others.

11

See van Binsbergen and Koijen (2008) and Rytchkov (2006) among others.12 See Chen and Zhao (2008) among others.13 This is a frequently used approach for estimating expected dividend yield in the options literature. See

Ait-Sahalia and Lo (1998) and Buraschi and Jiltsov (2006) among others.

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in the future quarterly excess returns. In comparison, IDY exhibits a R2 of 19%. This is

signicantly more than the R2 for the EP (R2 = 4%) and the CAY (R2 = 3%). Further,

IDY also outperforms the average implied correlation (R2 = 14%) and the variance risk

premia (R2 = 14%).

Results are robust to a battery of robustness checks and they are not driven by thespecic features of the DJIA. On the contrary, the S&P 500 implied dividend yield explains

22% of the variation in the quarterly S&P 500 returns. To underpin the return regression

results and to validate the initial motivation, I further show that the implied dividend

growth (inferred from the IDY) predicts DJIA quarterly dividend growth with a R2 of

31%.

The rest of the paper is organized as follows. Section 2 motivates the use of the expected

dividend yield for predicting market returns. Section 3 presents the data. Summary statis-

tics and predictive regressions with the dividend ratios are reported in Section 4. Section

5 compares predictive ability of the dividend ratios to the alternative predictor variables.

Section 6 concludes the paper.

2. PAST VS. EXPECTED DIVIDENDS

Motivating predictive regressions

The dividend-price ratio is one of the most frequently employed variables in the returnpredictability literature. It is dened as the ratio between the dividends accumulated over

the past period and the current price, Dt=Pt. Assuming prices are determined by the dis-

counted value of future dividends, Dt=Pt combines forward-looking prices and dividends

that are old relative to prices (Fama and French, 1988). As a result, uctuations in the

Dt=Pt can be interpreted in two ways. Firstly, Dt=Pt reects the rate at which future divi-

dends are discounted to the current price. When discount rates are high, prices are low and

the Dt=Pt is high. Therefore, the dividend-price ratio co-varies with the expected returns.

Secondly, a high ratio could be a signal of low future dividends. When investors expect

lower dividends in the future, the current price decreases and boosts the Dt=Pt. Takentogether, a high Dt=Pt is associated with either high expected returns, or low expected

dividends, or both.

This relationship was rst formalized by Campbell and Schiller (1989). Log-linearizing

the denition for the raw return, they show that the log dividend-price ratio can be ex-

pressed in terms of all the future one period expected returns adjusted for the expected

dividend growth rate. Just recently, van Binsbergen and Koijen (2008) develop a closed-

form present-value model in which they demonstrate that the price-dividend ratio is an

exact linear function of the expected return and the expected dividend growth.

I concentrate on the dividend-price ratio and present its relation to the expected return

and the expected dividend growth in a simplied setting. Consider the denition for the

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expected return, r;t

r;t = Et

Pt+1 + Dt+1

Pt

(1)

where Pt denotes the price at time t and Dt+1 stands for the dividends accumulated

between t and t + 1. As in Ang and Liu (2007), rewrite (1)

r;t =DtPt

Et

Dt+1

Dt

Et

"1

Dt+1Pt+1

+ 1

#!(2)

where Dt=Pt is the dividend-price ratio, Et [Dt+1=Dt] is the expected dividend growth

and Et [Dt+1=Pt+1] is the expected value of the next periods dividend-price ratio. To

simplify, assume that the next periods dividend-price ratio is equal to the long-term average

of the dividend-price ratio, Et

hDt+1Pt+1

i= DP.14 Hence, the third term in the equation (2)

becomes a constant and expected return can be expressed as

r;t =DtPt

Et

Dt+1

Dt

k (3)

where k = 1=DP + 1. Rewriting (3), we obtain an expression for the Dt=Pt:

DtPt

=r;t

Et [Dt+1=Dt] k(4)

Equation (4) says that Dt=Pt is positively related to the expected return and inversely

related to the expected dividend growth rate and k. Accordingly, high Dt=Pt should predict

either (i) high future return, or (ii) low future dividend growth rate, or (iii) both.

In line with this intuition, the standard approach in the empirical literature is to regress

returns, rt+1; and dividend growth rates, Dt+1; on the lagged Dt=Pt

Dt+1 = a0 + a1 (Dt=Pt) + "d;t+1 (5)

rt+1 = b0 + b1 (Dt=Pt) + "r;t+1 (6)

The typical nding from regression (5) is that Dt=Pt does not predict dividend growth(Cochrane, 1992, 2001, 2006). This is usually interpreted as the lack of time-variability in

the expected dividend growth and this suggests that most of the variaton in the Dt=Pt is

due to uctuations in the expected returns. As stated by Cochrane (2006), if Dt=Pt does

not predict dividend growth, it should predict returns. However, ndings from the return

predictive regression (6) are rather mixed. On the one side, many studies nd that the

Dt=Pt predicts returns, especially over the long-run (Fama and French, 1988; Campbell and

Shiller, 1988; Lewellen, 2004; Cochrane, 2006). On the other side, several academics argue

14 This assumption is used to avoid iterating forward the dividend-price ratio and to provide a simple

intuition for the predictive regressions. Even though the assumption is rather strict, it is not unrealistic.Investros have a better idea of the next periods expected returns and the next p eriods expected dividendgrowth rate than the next periods dividend-price ratio, which in turn depends on the expected returns andthe expected dividend growth rates of the even more distant future. Also, most studies in the predictabilityliterature assume some form of the mean-reversion for the dividend-price ratio.

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that the statistical evidence for the documented predictability is not reliable (Goetzman

and Jorion, 1995; Lanne, 2002; Valkanov, 2003; Boudoukh et al., 2007). Also, Goyal and

Welch (2005) show that the Dt=Pt does not predict returns out-of-sample.

One of the reasons for the low ability of the Dt=Pt for predicting returns is related to the

time-variability of the expected dividend growth. Namely, recent literature shows that thelack of dividend growth predictability by the Dt=Pt does not imply that expected dividends

are constant. Lettau and Ludvingson (2005) nd that the dividend growth is predictable

by variables other than the Dt=Pt. Van Binsbergen and Koijen (2008) demonstrate that

regression (5) suers from the errors-in-variables problem that occurs when one does not

control for the expected returns. They nd that the adjusted R2 for the annual post-war

dividend growth rises from 2% to 15% once controlled for the expected returns ltered

from the past data15 . Thus, on the contrary to the standard belief, this evidence suggests

that the expected dividend growth varies over time. This makes the Dt=Pt a noisy proxy

for the expected return and diminishes its ability to predict returns (Fama and French,

1988; Lettau and Ludvingson, 2005). Specically, when expected dividend growth is time

varying, equation (4) shows that the Dt=Pt uctuates not only because of the variation

in the expected return, but also because of the changes in the expected dividend growth

(see also Campbell and Shiller, 1989 and van Binsbergen and Koijen, 2008). Hence, to

capture variation in the expected returns, we should take into account uctuations in both

the Dt=Pt and the expected dividend growth.

Motivated by the closed-form present value model, van Binsbergen and Koijen (2008)

account for the variation in the expected dividends by including an estimate for the expecteddividend growth as an additional regressor in the price-dividend return regression. Using

total payout ratio, they report that R2 for annual post-war returns increases from 15% to

17% once controlled for the expected dividend growth ltered from the past price-dividend

ratios and the past dividend growth rates.

Along similar lines of reasoning, we could augment predictive regression (6) by the

expected dividend growth:

rt+1 = c0 + c1 (Dt=Pt) + c2Et [Dt+1] + "t+1 (7)

Nevertheless, equation (3) shows that the expected return is a non-liner function of

the DP and the expected dividend growth. This suggests that the linear regression (7)

is misspecied and therefore, does not incorporate the full information contained in the

Dt=Pt and the Et [Dt+1] : To account for the non-linearity, equation (3) implies that we

should replace the Dt=Pt and the expected dividend growth by its product, an expected

dividend yield, Et [Dt+1=Pt] :

r;t =DtPt

Et

Dt+1

Dt

k = Et

Dt+1

Pt

k (8)

Hence, instead of relying on the predictive regression (7), we should consider predicting

15 Note: Van Binsbergen and Koijen (2008) concenrate on the price-dividend ratio instead of the dividend-price ratio.

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returns with the expected dividend yield:

rt+1 = d0 + d1Et [Dt+1=Pt] + "t+1 (9)

The appealing feature of the predictive regression (9) is that it relies on a single predictor

variable and therefore alleviates the multicollinearity problems. Also, it takes into account

the non-linear relationship between the expected returns, the DP and the expected dividend

growth. Consequently, it makes the prediction more precise.

Estimation of expected dividend yield

The remaining challenge is the estimation of the expected dividends (expected dividend

yield).16 Recent literature considers two ways for extracting expected dividends. Expected

dividends are estimated either from the observed history of past data (Rytchkov, 2006;

van Binsbergen and Koijen, 2008) or they are obtained directly from the analyst forecasts

(Chen and Zhou, 2008).

In this paper, I employ options implied dividend yield (IDY) as a proxy for the expected

dividend yield. The IDY is extracted from the index options by applying the put-call parity.

The put-call parity relates the price of a European call option (C) and a European put

option (P) to the current price of the underlying (S), the present value of the strike price

(P V(K)) and the present value of the future dividends P V(Div):

P + S = C+ P V(K) + P V(Div) (10)

Accordingly, we can infer implied dividends or the IDY from the observed market prices

(Ait-Sahalia and Lo, 1998; Buraschi and Jiltsov, 2006).

This approach has several advantages over alternative methods for estimating expected

dividends. Unlike extracting expected dividends from the observed history of past divi-

dends, the IDY is obtained without any assumptions about the dynamics of the dividends.

Specically, the put-call parity is independent of options pricing models and hence the

IDY is obtained in a model-free way. Further, because any violation of the put-call par-

ity gives rise to the arbitrage prots, the IDY is not likely to be subject to behavioralbiases that were found to inuence the analyst forecasts.17 Lastly, the IDY is based exclu-

sively on the observed stock and option prices. Since options have long been recognized as

forward-looking, the IDY should serve as a good proxy for the markets expected dividend

yield.18

16 Expected dividend growth is obtained from the dividend-price ratio and the expected dividend yield.17 Doukas et al. (2006), for example, nd that stock returns are positively related to the analysts

divergence of opinion.18 The forward-looking nature of options is also frequently exploited for predicting market volatility Poon

and Granger (2005) makes a survey of this literature and concludes that options implied volatility generally

predicts future volatility better than the volatility models based on the past data.

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3. DATA

The empirical analysis is based on Dow Jones Industrial Average (DJIA). This choice of

data is motivated by two considerations. Firstly, options on DJIA are European and hence

the put-call parity can be applied directly. Secondly, DJIA includes only 30 stocks and israrely subject to composition changes, so that the alternative predictor variables (average

implied correlation) can be constructed easily. Despite the small number of constituents, it

is by no means a negligible index. DJIA is the most widely cited index among practitioners

and accounts for about a fth of the whole market capitalization of all the U.S. stocks.19

The data comes from several sources. DJIA prices (with and without reinvested div-

idends) are obtained directly from the Dow Jones. Daily T-bill rates are extracted from

CRSP. All the information on options comes from OptionMetrics Ivy DB. Unfortunately,

the data on the DJIA options is not available before autumn 1997. This restricts the period

under analysis to the time between October 1997 and December 2006.The implied dividend yield, IDY, is downloaded directly from the Ivy DB Index Div-

idend Yields le.20 Under the put-call parity relationship and the assumption of a con-

tinuously compounded dividend yield, Ivy DB estimates the implied dividend yield from a

linear regression model:

C P = e0 + e1S+ e2ST + e3K+ e4KT + e5DBA (11)

where C P is the dierence between the price of a call and a put option with the

same strike price (K) and expiration (T) for a given underlying (S). To accommodatefor the bid ask spread, the bid price of a call is used with the ask price of the put, and

vice versa. DBA is a binary variable that equals 1 when the bid price for the call is used

and 0 otherwise. To estimate the model, Ivy DB uses 10 days of backward-looking data

for all strikes and expirations. The IDY is approximately equal to the negative value of

the estimated parameter be2:21 To guarantee comparability with other dividend ratios, Itransform continuously compounded dividend yield into a raw dividend yield.

The dividend-price ratio, DP, is estimated according to the standard procedure (Cochrane,

2006):

DPt = DtPt

= Pt + DtPt1

Pt1Pt

1 = RDt

RNDt 1 (12)

where RDt is the total return and the RNDt is the return without the reinvested divi-

dends.22 Since the focus of the study is on the predictability of the short run returns, I

primarily rely on the dividend-price ratio calculated on 91 days (one quarter) of backward-

looking data.23

19 Under robustness checks, I also consider predicting S&P 500 returns.20 I purposely rely on this data source to remedy data mining concerns and to enable easy replicability

of the presented results.21 Further details are provided in the Ivy DB Reference Manual.22 I calculate RDt and RNDt from the DJIA total prices and the DJIA prices without the reinvested

dividends, respectively.23 Under robustness checks, I also employ an annual DP ratio calculated on 365 days of backward-looking

data.

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The implied dividend growth, IDG, is calculated from the IDY and the DP:

IDGt = IDYt (Pt=Dt) = IDYt=DPt (13)

To test whether the implied dividend growth (implied dividend yield) predicts the future

realized dividend growth (future realized dividend yield), I also estimate the future realized

dividend yield, RDY; and the future realized dividend growth, RDG; on 91-days of forward-

looking data:

RDYt+1 =Dt+1

Pt=

Dt+1Pt+1

Pt+1Pt

=Dt+1Pt+1

RNDt (14)

RDGt+1 = RDYt+1 (Pt=Dt) (15)

In addition to the dividend ratios, I consider a set of alternative predictor variables,

such as the earnings-price ratio (Shiller, 1984), the consumption-to-wealth ratio (Lettau

and Ludvingson, 2001), the variance risk premia (Bollerslev et al., 2008)24 and the average

correlation (Pollet and Wilson, 2007).25

The earnings-price ratio, EP; is obtained from Datastream and the consumption-to-

wealth ratio, CAY, is downloaded directly from the Lettau and Ludvingsons website.

The average implied correlation, IM, is calculated as in Skintzi and Refenes (2003):

IMt =

2

P;tPNi=1 w2i;t2i;t

2PN1

i=1 wi;twj;ti;tj;t(16)

where 2P;t is the DJIA implied variance, 2i;t is the implied variance of the DJIA compo-

nents (N = 30) and wi;t is the price-weight of each DJIA constituent.26 ;27 Implied variance

for the DJIA and all its components is estimated on xed 30 days maturity options following

the estimation technique of Bakshi et al. (2003)28 .

The variance risk premia, V RP, is dened as the dierence between the DJIA annual-

ized 30 days implied variance and the DJIA annualized lagged realized variance estimated

over 91 days of backward-looking data.29 Realized DJIA variance is estimated as a sum-

mation of squared 30 minutes returns.

24 Bollerslev et al. (2008) show that the variance risk premia, den ed as the dierence b etween the optionsimplied variance and the lagged realized variance, forecasts returns because it captures uctuations in theeconomic uncertainty and the aggregate risk aversion.

25 Pollet and Wilson (2007) nd that average pair-wise correlations among stocks predict returns becausethey serve as a good proxy for the aggregate risk.

26 Unlike the majority of the U.S. indices, DJIA is a price-weighted index.27 In the period between October 1997 and December 2006, there was alltogether 7 DJIA index compo-

sition changes. In addition, 8 companies had their names changed.28 I extract the required data from the OptionMetics Ivy DB Volatility Surface le (for a similar approach

see Driessen et al., 2006).

29 Bollerslev et al. (2008) dene VRP as the dierence between the xed 30-days options implied varianceand the 30 days lagged realized variance. I use the 91-days lagged realized variance (instead of the 30-dayslagged realized variance) because I nd that the VRP constructed in this way possesses superior forecastingpower.

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4. PRELIMINARY RESULTS

The empirical analysis is divided in two sections. This section (Preliminary Results)

analyses predictability of market returns using the dividend ratios. The next section (Main

Results) compares the return-predictive ability of the dividend ratios with the alternativepredictor variables.

4.1. Summary statistics

Table 1 reports basic summary statistics for the employed variables. The annualized

mean DJIA log excess return is 1:86%.30 This low excess return is driven by a relatively

high risk-free rate and a big downward stock market correction at the beginning of the new

millennium.The dividend-price ratio (DP) is historically relatively low and amounts to 1:95. Since

the dividends exhibit positive growth (IDG = 1:03), the mean realized dividend yield

(RDY) is slightly higher than the DP and amounts to 2:00. The proxy for the expected

dividend growth (IDG) and the proxy for the expected dividend yield (IDY) are both

slightly higher than the RDG and the RDY. Nevertheless, the dierences are small (IDG

amounts to 1:06 and IDY is 2:07). The IDG and the IDY are also more volatile than

their realized counterparts. With respect to the higher moments, the employed variables

appear to be normally distributed. The only exception is the IDG, which is extremely

positively skewed and exhibits a high excess kurtosis.

Table 1 also reports rst-order autocorrelation coecients for the employed variables.

Consistent with the previous studies, the DP is very persistent and exhibits an autocor-

relation coecient of 0:92. In comparison, the rst order autcorrelation coecient for the

IDY is slightly lower and amounts to 0:88.

4.2. Predicting dividend growth and dividend yield

Section II shows that the DP is a function of the expected returns and the expected

dividend growth rate. This implies that the return predictability depends not only on the

observable DP, but also on a proxy for the expected dividend growth. The better the

proxy for the expected dividend growth, the better we can predict returns. Therefore, I

rst test how well the proposed proxy for the expected dividend growth (implied dividend

growth) predicts the future realized dividend growth.

Figure 1.a plots the realized dividend growth together with the implied dividend growth.

RDG uctuates between 0:8 and 1:3 throughout the analyzed period. IDG is more volatile

than the RDG and exhibits several spikes and troughs. Nevertheless, the IDG seems to30 Even though Section II motivates predictive regressions for raw returns, I instead base the empirical

part on the log excess returns. This is done merely because most of the studies in the predictablity literatureanalyse forecastability of the log excess returns.

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capture variations in the RDG reasonably well. This is also conrmed by the regression in

which the realized dividend growth is regressed on the lagged implied dividend growth:

RDGt+1 = f0 + f1(IDGt) + "t+1 (17)

Table 2 (Panel A) reports results for quarterly non-overlapping observations. The esti-

mated parameter is 0:41 and the R2 amounts to 31%.31 Thus, the implied dividend growth

indeed predicts the future dividend growth. This result is in stark contrast to the conven-

tional wisdom - that the dividend growth is unpredictable - and clearly indicates that the

expected dividend growth is time-varying. Therefore, adding the IDG as an additional

regressor in the standard DP predictive regression should signicantly improve the return

predictability.

Section II further implies that the DP and the proxy for the expected dividend growth(implied dividend growth) can be replaced by a proxy for the expected dividend yield

(implied dividend yield). Therefore, I additionally consider how well the IDY predicts the

future realized dividend yield. Since IDG predicts the future dividend growth and the IDY

is a simple product of the IDG and the DP; the IDY should serve as a strong predictor

for the future dividend yield.

Figure 1.b plots the time series of the future realized dividend yield (RDY) together

with the implied dividend yield (IDY). RDY uctuates between 1% and 3% throughout

the analyzed period. It exhibits the lowest values at the time of the market boom at the

turn of the millennium and a signicant rise in the subsequent years of a downward marketcorrection. As expected, the IDY exhibits several spikes and troughs, but seems to track

uctuations in the RGY well. To underpin the visual interpretation, I regress the realized

dividend yield on the lagged implied dividend yield:

RDYt+1 = g0 + g1(IDYt) + "t+1 (18)

Table 2 (Panel B) presents results for quarterly non-overlapping observations. The

estimated parameter is 0:64 and the R2 amounts to 65%.32 Hence, the IDY indeed strongly

predicts the future realized dividend yield and should therefore also serve as a good predictorfor the future returns.

4.3. Predicting DJIA returns

To test for the predictability of market returns, I consider three specications for the

return predictive regressions. The rst is the standard DP predictive regression:

rt+1 = b0 + b1(DPt) + "t+1 (19)31 In comparison, the lagged dividend growth rate is negatively related to the future dividend growth

rate.32 In comparison, the lagged dividend yield predicts only 28% of the variation in the future dividend yield.

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This return regression does not take into account that the DP is a function of both

the expected returns and the expected dividend growth. Therefore, the second regression

augments the rst by the proxy for the expected dividend growth (implied dividend growth):

rt+1 = c0 + c1(DPt) + c2(IDGt) + "t+1 (20)

To account for the nonlinear relationship between the DPt and the IDGt and to remedy

the multicollinearity problems, the third return regression replaces the dividend-price ratio

and the proxy for the expected dividend growth with the proxy for the expected dividend

yield (implied dividend yield):

rt+1 = d0 + d1(IDYt) + "t+1 (21)

Table 3 reports regression results for quarterly (91 days) non-overlapping excess returns.

All the predictors have positive signs. The DP explains 5% of the variation in the quarterly

returns. By including the IDG in the DP regression, R2 triples and jumps to 14%. This

conrms that the expected return depends not only on the DP; but also on the expected

dividend growth. Moreover, the expected dividend growth seems to be at least as important

predictor as the DP33 . Results from the third regression further revel that the IDY predicts

returns even better than the DP and IDG separately. Specically, IDY explains as much

as 19% of the variation in the quarterly excess returns. This result is in line with the the

initial conjecture and conrms that the non-linear structure among the return, the expected

dividend growth and the DP indeed plays an important role for predicting returns

34

.Additionally, I evaluate the results from predicting monthly (30 days) excess returns.

Table 4 details results. As expected, the degree of predictability is signicantly lower.

Nevertheless, the main conclusions remain the same and the IDY stands out again. It

explains around 5% of the variation in the monthly returns. In comparison, the joint

regression of the DP and the IDG exhibits a R2 of 3%. The DP explains only 1% of the

variation in the monthly returns.

5. MAIN RESULTS

In order to assess the predictive power of the implied dividend yield, we have to compare

it with the alternative predictor variables. The recent literature has proposed several

variables that predict returns. In addition to the dividend-price ratio, the most frequently

33 In comparison, van Binsbergen and Koijen (2008) report that the expected dividend growth only hasa m oderate inuence on the predictability of the future returns. The dierence between their results andmy results is most probably driven by the dierent methods for estimating expected dividend growth.

34 For a comparison, I estimate the return regression with the DP, IDG and their product (IDY):

rt+1 = g0 + g1(DPt) + g2(IDGt) + g3(IDYt)"t+1 (22)

Results are outlined in Table 3 (Panel D). The R2

jum ps to 26%, therby conming that the expectedreturn is indeed a non-linear function of the DP and the expected dividend growth. Nevetheless, thisregression may be subject to the multicolinearity problems (e.g. g1 and g2 are negative). Therefore, R2

may also be exaggerated.

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employed predictors are the earnings-price ratio, EP, (Shiller, 1984) and the consumption-

to-wealth ratio, CAY, (Lettau and Ludvingson, 2001). Just recently, the menu of predictors

has been extended by the variance risk premia (Bollerslev et al., 2008) and the average

correlation (Pollet and Wilson, 2007). The average pair-wise correlation among stocks, ;

is found to predict returns because it is a good proxy for the aggregate risk. The variancerisk premia, V RP, dened as the dierence between the options implied variance and

the lagged realized variance, serves as a good predictor for returns because it captures

uctuations in the economic uncertainty and the aggregate risk aversion.

The and the V RP are of special interest for this study. They are both extracted from

the options data and therefore present the most relevant comparison for the IDY.

Summary statistics

Table 5 reports the basic summary statistics and the unconditional correlation structurefor all the predictors (since the CAY is available only on the quarterly frequency, summary

statistics are based on the end-of-quarter observations). The numbers are all in line with

the previous studies. Except for the variance risk premia, all the predictors are relatively

highly persistent.

Predictive Regressions

I begin by reporting in Table 6 the results for quarterly return regressions. Not sur-

prisingly and in line with the previous research, the traditional predictor variables serveas rather poor predictors for future returns. CAY and EP explain approximately 3% and

4% of the variation in the quarterly excess returns, respectively. Unlike the traditional pre-

dictor variables, the implied correlation and the variance risk premia are both statistically

signicant predictors and exhibit R20s of approximately 14%.35 Despite this seemingly high

predictive ability, neither of them outperforms the adjusted R2 of 19% for the IDY.

Similar results are obtained for monthly return regressions. As outlined in Table 7, only

the options-related predictors surpass the usual test of statistical signicance. Nonetheless,

their predictive power is well below the one of the IDY.

35 Results for the variance risk premia are directly in line with Bollerslev et al. (2008) who report thatthe spread between the implied and the past variance explains 15% of the variation in quarterly S&P500 returns in the time span b etween 1990 and 2005. The high predictive power of the average impliedcorrelation is new. Pollet and Wilson (2007) test predictive power of average correlations using past dailydata and report an R2 of 5% for 30 years of quarterly observations. Driessen et al. (2006) calculate averageimplied correlations for S&P 100 for 8 years of data, but report no predictive power for monthly returns.However, they do not consider forecasting returns over longer horizons.

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6. ROBUSTNESS CHECKS

In order to address concerns regarding the validity of the presented results, I consider

a battery of robustness checks.

Predicting excess returns (without the reinvested dividends)Initially, I based predictive regressions on the total returns. Nevertheless, a similar

relation can be also derived for the returns without the reinvested dividends:

ndr;t = Et

Pt+1

Pt

=

DtPt

Et

Dt+1

Dt

k = Et

Dt+1

Pt

k (23)

where k = Et

h1= Pt+1

Dt+1

i= 1=DP: Therefore, for the rst robustness check, I re-run

the predictive regressions for the excess returns without the reinvested dividends. Table

8 reports results for quarterly non-overlapping observations. The predictive ability of the

dividend ratios remains largely unaected when the total excess returns are replaced bythe excess returns without the reinvested dividends. The predictive power decreases only

marginally and the IDY still explains 18% of the variation in the quarterly excess returns.

Annualized dividend-price ratio

The main empirical analysis is based on the DP calculated over 91 days of data (one

quarter). However, the dividend payments exhibit within-year variations and hence the

DP may be aected by the seasonal uctuations. Therefore, for the second robustness

check, I re-run the predictive regressions with the dividend-price ratio calculated over one

year (365 days) of backward-looking data (DPAnn:). Table 9 outlines results for quarterlynon-overlapping observations. The DPAnn: exhibits R2 of approximately 3%. This is

around 2 percentage points less than the R2 for the DP. Thus, replacing the DP with

the DPAnn: only widens the dierence in the return predictive ability between the realized

dividend-price ratio and the implied dividend yield.

Predicting S&P 500 returns

For the last robustness check, I address the concern that the results may be driven by

the unique features of the Dow Jones Index. DJIA is the only price-weighted U.S. market

index and includes only 30 most prominent stocks. Therefore, it is necessary to test whetherIDY also predicts returns of a broader S&P 500 index.36 Following the procedures of the

previous section, I extract the S&P 500 IDY and total excess returns for the matching time

period between October 1997 and December 2006. Figure 2 plots the IDY for the S&P

500 along with the IDY for the DJIA. The S&P 500 implied dividend yield is somewhat

lower than the DJIA implied dividend yield. Also, it exhibits less pronounced spikes and

troughs. However, both IDY0s behave similarly and exhibit an unconditional pair-wise

correlation of 65%.

S&P 500 implied dividend yield also serves as a good predictor for the S&P 500 returns.

For the quarterly horizon, it explains as much as 22% of the variation in the future excess

returns. The R2 for the monthly returns amounts to 5%.

36 Options on S&P 500 are European.

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7. CONCLUSION

I propose a new variable for the analysis of the stock market return predictability.

Recognizing that the expected dividends are time-varying, I show that the variation in

the expected return can be captured by the product of the dividend-price ratio and theexpected dividend growth, an expected dividend yield.

Following this motivation, I use the options implied dividend yield (IDY) as a proxy for

the expected dividend yield. I nd that the IDY serves as a strong predictor for monthly

and quarterly excess returns. Indeed, IDY predicts returns better than the traditionally

used realized dividend-price ratio. Moreover, IDY also outperforms earnings-price ratio,

consumption-to-wealth ratio, average implied correlation and variance risk premium. To

underpin the return regression results and to validate the initial motivation, I further show

that the implied dividend growth (inferred from the IDY) predicts the future dividend

growth.

To my knowledge, this is the rst study to employ the options implied dividend yield

for predicting market returns. Results are promising, but a lot is left for my future work.

Do the same results hold for the implied dividend yield extracted from the index futures?

How does the IDY t in the traditional risk-return relation? Additionally, I also consider

extending the analysis to the cross-section of stock returns.

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[17] Goetzmann, W., Jorion P., 1995. A longer look at dividend yields. Journal of Business

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[22] Lettau, M. and S. Ludvigson, 2001. Consumption, aggregate wealth and expectedstock returns, Journal of Finance 56, 815 - 849.

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approach. Working paper.

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Table 1: Summary Statistics

Rm;t+1 Rf;t+1 DPt RDGt RDYt IDGt IDYt

Mean 0.0186 1.9508 1.0301 2.0017 1.0619 2.0769

Std. Dev. 0.1586 0.3524 0.1331 0.4058 0.2369 0.5677

Skewness -0.4002 0.0074 0.4404 0.1211 1.0879 -0.1776

Kurtosis 3.4087 2.0524 3.4994 2.2025 7.0140 3.1602

Autocorrelation -0.0240 0.9265 0.4881 0.8839 0 .7505 0.8803

Table presents summary statistics for 110 end-of-month observations between October 1997

and December 2006. Rm;t+1 Rf;t+1 is the annualized 30 days log return in excess of the T-bill

rate. DPt is the dividend-price ratio calculated on 91 days of backward-looking data. RDGt and

RDYt are the future realized dividend growth and the future realized dividend yield, respectively.

They are both calculated on 91 days of forward-looking data. IDGt and IDYt are the implied

dividend growth and the implied dividend yield, respectively. All the dividend ratios are multiplied

by 100.

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Table 2: Predictive regressions for DJIA Realized Dividend Growth andRealized Dividend Yield

Panel A: Predicting dividend growth

Intercept IDGt adj:R2

0.5972 0.4106 0.3106

(4.85) (3.52)

Panel B: Predicting dividend yield

Intercept IDYt adj:R2

0.6576 0.6442 0.6507

(4.98) (7.71)

Table presents predictive regressions for the DJIA dividend growth and the dividend yield.

Panel A outlines results obtained by regressing 91 days future realized dividend growth (RDGt+1)

on the lagged implied dividend growth (IDGt). Panel B presents results obtained by regressing 91

days future realized dividend yield (RDYt+1) on the lagged implied dividend yield (IDYt). All

the results are based on OLS regressions with 36 end-of-quarter observations from December 1997

until October 2006. Statistical signicance of parameters is measured with Newey-West t-statistics

with 4 lags.

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Table 3: Predictive Regressions for Quarterly DJIA Total Excess Returns

Intercept DPt IDGt IDYt adj:R2

Panel A: Standard predictive regression-0.1161 0.0624 0.0497

(-2.37) (2.63)

Panel B: Std. predictive regression + expected dividend growth

-0.2405 0.0578 0.1237 0.1363

(-2.51) (2.40) (2.04)

Panel C: Predictive regressions with the expected dividend yield

-0.1361 0.0673 0.1876

(-2.40) (2.96)

Panel D: Multivariate regression

0.9135 -0.5798 -1.0374 0.6366 0.2568

(3.46) (-3.78) (-3.83) (4.09)

Table presents results obtained by regressing quarterly DJIA total excess returns between

October 1997 and December 2006 on the lagged predictor variables. Risk-free rate is 90 days T-

bill rate. DPt is the dividend-price ratio calculated on 91 days of backward-looking data, IDGt

is the implied dividend growth and IDYt is the implied dividend yield. All the results are based

on OLS regression with 36 non-overlapping observations extracted on the last day of each quarter.

Statistical signicance of the parameters is measured with Newey-West t-statistics with 4 lags.

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Table 4: Predictive Regressions for Monthly DJIA Total Excess Returns


Panel A: Standard predictive regression-0.0334 0.0179 0.0102

(-2.47) (2.67)


-0.0631 0.0165 0.0304 0.0265

(-2.52) (2.15) (1.70)


-0.0376 0.0188 0.0469

(-2.46) (2.94)

Panel D: Multivariate regression

0.3080 -0.1972 -0.3391 0.2111 0.0887

(4.88) (-5.31) (-5.69) (6.05)

Table presents results obtained by regressing monthly DJIA total excess returns between Oc-

tober 1997 and December 2006 on the lagged predictor variables. Risk-free rate is 90 days T-bill

rate. DPt is the dividend-price ratio calculated on 91 days of backward-looking data, IDGt is

the implied dividend growth and IDYt is the implied dividend yield. All the results are based on

OLS regression with 110 non-overlapping observations extracted on the last day of each month.


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Table 5: Summary Statistics and Unconditional Correlation StructureFor Final Comparison

EPt CAYt IM

t V RPt IDYt

Panel A: Summary statistics

Mean 0.0464 -0.0107 0.3120 0.0193 2.0971

Std. Dev. 0.0061 0.0106 0.1275 0.0190 0.5619

Skewness 0.0094 -0.1858 0.8440 1.3981 -0.3874

Kurtosis 2.2102 2.6175 3.2295 5.3122 2.2287

Autocorrelation 0.5765 0.6409 0.6061 0.1053 0.5964

Panel B: Unconditional correlation structure

EPt 1.0000 0.2154 -0.2503 -0.1411 0.2309

CAYt . 1.0000 0.2886 0.1786 0.6966

IMt . . 1.0000 0.7764 0.3079

V RPt . . . 1.0000 0.2440

IDYt . . . . 1.0000

Table presents summary statistics and unconditional correlation structure for end-of-quarter

observations between October 1997 and December 2006. EPt is the earnings-price ratios, CAYt

is the consumption-to-wealth ratio, IMt is the average implied correlation, V RPt is the variancerisk premia and IDYt is the implied dividend yield.

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Table 6: Predictive Regressions for Quarterly DJIA Total Excess Returns

Intercept EPt CAYt IMt V RPt IDYt adj:R

2

-0.1532 3.4115 0.0361(-1.65) (1.75)

0.0242 1.7950 0.0265

(1.48) (2.84)

-0.0774 0.2641 0.1427

(-2.12) (2.82)

-0.0284 1.7324 0.1350

(-1.37) (2.88)

-0.1361 0.0673 0.1876

(-2.40) (2.96)-0.1527 0.0897 0.8765 0.0538 0.2411

(-3.84) (0.67) (1.01) (2.55)


October 1997 and December 2006 on the lagged predictor variables. Risk-free rate is 90 days

T-bill rate. EPt is the earnings-price ratios, CAYt is the consumption-to-wealth ratio, IMt is the

average implied correlation, V RPt is the variance risk premia and IDYt is the implied dividend

yield. All the results are based on OLS regression with 36 non-overlapping observations extracted

on the last day of each quarter. Statistical signicance of the parameters is measured with Newey-West t-statistics with 4 lags.

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Table 7: Predictive Regressions for Monthly DJIA Total Excess Returns

Intercept EPt IMt V RPt IDYt adj:R

2

-0.0369 0.8305 0.0035(-1.31) (1.48)

-0.0181 0.0613 0.0186

(-1.98) (2.24)

-0.0039 0.3144 0.0067

(-0.75) (2.02)

-0.0376 0.0188 0.0469

(-2.46) (2.94)

-0.0481 0.0170 0.2888 0.0188 0.0516

(-3.47) (0.33) (1.00) (2.82)

Table presents results obtained by regressing monthly DJIA total excess returns between Oc-

tober 1997 and December 2006 on the lagged predictor variables. Risk-free rate is 90 days T-bill

rate. EPt is the earnings-price ratios, CAYt is the consumption-to-wealth ratio, IMt is the aver-

age implied correlation, V RPt is the variance risk premia and IDYt is the implied dividend yield.

All the results are based on OLS regression with 110 non-overlapping observations extracted on

the last day of each month. Statistical signicance of the parameters is measured with Newey-West

t-statistics with 12 lags.

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Table 8: First Robustness Check:

Predictive Regressions for Quarterly DJIA Excess Returns(w/o. Reinvested Dividends)


Panel A: Standard predictive regression

-0.1173 0.2428 0.0451

(-2.39) (2.54)


-0.2404 0.2243 0.1223 0.1296

(-2.50) (2.31) (2.01)


-0.1384 0.0660 0.1803

(-2.43) (2.89)


October 1997 and December 2006 on the lagged predictor variables. Risk-free rate is 90 days T-

bill rate. DPt is the dividend-price ratio calculated on 91 days of backward-looking data, IDGt

is the implied dividend growth and IDYt is the implied dividend yield. All the results are based

on OLS regression with 36 non-overlapping observations extracted on the last day of each quarter.


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Table 9: Second Robustness Check

Predictive Regressions for Quarterly DJIA Excess Returns(Annual Dividend-Price Ratio)

Intercept DPAnn::t IDGt IDYt adj:R2

Panel A: Standard predictive regression

-0.1154 0.0622 0.0327

(-2.53) (2.88)


-0.2389 0.0568 0.1242 0.1198

(-2.29) (2.35) (2.01)


-0.1361 0.0673 0.1876

(-2.40) (2.96)


October 1997 and December 2006 on the lagged predictor variables. Risk-free rate is 90 days

T-bill rate. DPAnn:t is the dividend-price ratio calculated on 365 days of backward-looking data,

IDGt is the implied dividend growth and IDYt is the implied dividend yield. All the results are

based on OLS regression with 36 non-overlapping observations extracted on the last day of each

quarter. Statistical signicance of the parameters is measured with Newey-West t-statistics with

4 lags.

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Figure 1: Dividend Yield and Dividend Growth

Figure 1.a: Realized and implied dividend growth

30.6.1998 29.12.2000 30.6.2003 30.12.2005

0.5

1

1.5

2

Realized dividend growth

Implied dividend growth

Figure 1.a: Realized and implied dividend yield

30.6.1998 29.12.2000 30.6.2003 30.12.20050.5

1

1.5

2

2.5

3

3.5

4

Realized dividend yield

Implied dividend yield

Figure A plots monthly observations of the 91 days realized dividend growth together with the

implied dividend growth. Figure B plots monthly observations of the 91 days realized dividend

yield together with the implied dividend yield. The data is based on the Dow Jones Industrial

Average in the period between October 1997 and December 2006.

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Figure 2: S&P 500 and DJIA Implied Dividend Yield

30.6.1998 29.12.2000 30.6.2003 30.12.20050.5

1

1.5

2

2.5

3

3.5

4

4.5Implied dividend yield

S&P 500

DJIA

The gure plots monthly observations of the implied dividend yield for the S&P 500 and the

DJIA between October 1997 and December 2006.

options implied dividend yield and market returns

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