On the Cross Section of Dividend Premiums

Transcription

1 On the Cross Section of Dividend Premiums Gang Li and Linti Zhang January, 2018 Both are from the Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong. Gang Li, Linti Zhang,

2 On the Cross Section of Dividend Premiums Abstract We use the exchange-traded options on individual stocks to replicate claims to shortterm dividends of the underlying stocks. The dividend premium is estimated by the average return to the claims. We find that the dividend premiums are 4.47% a quarter on average, vary substantially across stocks, and many of them are negative and statistically significant. The cross-sectional variations can largely be explained by the exposure of the claims to the risk of the aggregate consumption. The results indicate that the term structure of equity premium is downward sloping for the market, but varies across stocks.

3 1. Introduction How to value future cash flows is an important question in finance. Since a firm has an unlimited life presumably, the literature of equity valuation has mostly focused on valuing the sum of all the cash flows generated by the firm as a whole. In the recent years, in order to better understand how the stock price is determined, the literature has moved towards to examining the value of each individual cash flow over different horizons and to measuring the term structure of equity premium. van Binsbergen, Brandt, and Koijen (2012) show that a dividend strip which is synthetically created by index options and only pays dividends in the near-term future, has higher average return than the underlying market index. Since the return of the market index is the average return of the claims to all future dividends, this evidence suggests that the term structure of equity premium is downward sloping. The conclusion is supported by van Binsbergen, Hueskes, Koijen, and Vrugt (2013) using index dividend futures, and Cejnek and Randl (2016) using index dividend swaps. Weber (2017) reaches the same conclusion from the cross section of stocks. He creates a measure of cash flow duration at the firm level using balance sheet data, and shows that stocks with long cash flow duration earn lower average returns than short-duration stocks. Many early studies on the value premium in the cross section of stocks also provide indirect evidence, for example, Bansal, Dittmar and Lundblad (2005), Lettau and Wachter (2007) and Da (2009). The value premium refers to the empirical fact that stocks with low market-to-book ratios (value stocks) have higher average returns than stocks with high market-to-book ratios (growth stocks). If value stocks tend to have shorter cash flow durations than growth stocks, the value premium suggests that the term structure of equity premium is downward sloping. There are two issues in the existing literature. First, the indirect estimation approach based on individual stocks implicitly assumes that the slopes of the term structure of equity premium have limited variations across stocks, and they are more or less the same as the market index. Suppose that the term structure is on average flat, i.e., the term 1

4 structure of the market index is flat, but value stocks have a downward sloping term structure and growth stocks have an upward sloping term structure. The value premium exists as long as value stocks have shorter cash flow durations than growth stocks. This suggests that value premium may not be informative about the term structure of the market. Second, the results on the downward sloping market equity premium based on the direct estimation approach have been challenged recently. Boguth, Carlson, Fisher, and Simutin (2013) argue that the finding in van Binsbergen, Brandt, and Koijen (2012) may be due to market microstructure noise amplified by the leverage implicit in the derivative prices. Schulz (2016) attributes the outperformance of short-term assets to differential treatments of taxes on short and long term assets. This study attempts to use dividend strips replicated by the exchange-traded options on individual stocks to address these issues. We estimate the short-term equity premiums by the average returns to the synthetic dividend strips, and examine whether the shortterm equity premiums vary across stocks. The approach allows a direct measure of the term structure of equity premium across stocks rather than relying on an indirect measure from stock returns and balance sheet data. The aggregation of the short-term premiums across stocks would also be a good estimate for the short-term premium of the market, and serves as a robustness check by another sample. Our methodology to construct the dividend strip is as follows. One can replicate the payoff of a dividend strip by trading the underlying stock, options written on the stock and risk-free bonds. Specifically, a strategy of a short put option and a long call option plus a risk-free bond (with face value equal to the strike price of the options) replicates the ex-dividend payoff of the underlying stock at the maturity of the options. The difference between the actual stock and the above strategy is the future dividend to be paid by the stock during the life of the options. According to the put-call parity relation, the price of the future dividend, DI, is given by DI = S + P C Ke Rf T, (1) 2

5 where S is the price of the stock, P and C are prices of put and call options with strike price K and maturity T, and R f is the continuously compounding risk-free rate. DI is also termed as option-implied dividend since it is implied from option prices. 1 We measure the dividend premium by the average return of the dividend strips. Across stocks, the dividend premium is 8.51% a quarter on average with a 25th percentile of % and a 75th percentile of 14.01%. We aggregate the dividend strips across stocks, and construct a dividend strip for the market. The average quarterly return on the dividend strip of the aggregate market is 4.47%, higher than the average quarterly return on the S&P 500 index (2.39% during the sample period), which suggests a downward sloping of equity premium for the market. The result is consistent with the finding of van Binsbergen et al. (2012) from the S&P 500 index options. There are also large crosssectional variations in the dividend premiums among stocks, and near half of stocks have negative dividend premiums. Given that the majority of stocks have positive average returns, i.e., the long-term premium is positive, the variations in the dividend premiums suggest that the term structure of equity premium varies substantially across stocks. We further study what may explain the cross-sectional variations in dividend premiums. To mitigate the noises in the returns of dividend strips from individual stocks, we use a portfolio based approach. We sort dividend strips into five portfolios by the average normalized dividend premium in the previous four quarters, where the normalized dividend premium is calculated as the difference between the present value of future dividend and the option-implied dividend, divided by current stock price. The portfolio with the highest (lowest) historical dividend premium earns a quarterly value weighted return of 11.87% (-11.19%), and the spread between the return of two portfolios is 23.07%, with a t-statistic of 7.5. We aim to explain the cross-sectional variations in the dividend premiums by the risk exposure of the dividend strips. To this end, we use a rolling window of 1 The put-call parity holds for European-style options. Since we examine the prices of dividends implied by individual stock options, which are American-style, the relation does not hold exactly. When we adjust the early exercise premiums in the American options, the results are essentially the same. 3

6 five-year quarterly returns to estimate the beta coefficients with respective to the return of the market portfolio proxied by the S&P 500 index and the aggregate consumption growth rate. The portfolio with the highest historical dividend premium has an average market beta of 2.64 (t-stat = 2.9) and an average consumption beta of (t-stat = 2.9), while the two risk exposure measures for the portfolio with the lowest historical dividend premium are on average (t-stat = 1.9) and (t-stat = 2.3), respectively. The quarterly price of market risk and consumption growth risk are estimated to be 3.71% (t-stat = 4.4) and 0.44% (t-stat = 4.4) based on the Fama-Macbeth (1973) cross-sectional regression. The GRS test (Gibbons, Ross, and Shanken, 1989) fails to reject the consumption-based CAPM (CCAPM) to explain returns on dividend strips with a p-value of 0.094, while the CAPM is rejected by the GRS test. The results suggest that both the CAPM and the CCAPM explain considerable proportions of cross-sectional variations in dividend premiums, and that the CCAPM is better than the CAPM at describing returns on short-term dividend strips in the time series. If the stock is subject to short sale constraint, DI may be overestimated and the dividend premium may be underestimated since the actual stock price S is higher than the stock price replicated by options as in (1). To address the issue of short sale constraint, we do a double sorting analysis by first sorting stocks based on the percentage of institutional holding (PIH, which is a proxy for short sale constraint) and then sorting stocks based on historical dividend premium. After controlling for PIH, portfolio returns still increase with historical dividend premium. The finding indicates that the dividend premiums are not driven by the short sale constraint. The results of the cross-sectional regression and GRS test are similar to those for the univariate sorted portfolios. The remaining of the paper is organized as follows. In Section 2, we define the dividend premium and report the summary statistics of the dividend premium. In Section 3, we provides risk-based explanations for cross-sectional variations in dividend premiums. In Section 4, we conduct several robustness tests of our main results. Section 5 concludes 4

7 the paper. 2. Dividend Premium 2.1. Definition of Dividend Premium The price of dividend strips can be either calculated from futures or options on the underlying asset. We use options in this study since options market of individual stocks are much more well developed than their futures market in the US. Let D i q+1 be the cash dividend of stock i in quarter q + 1 and PV q (D i q+1) be the value of D i q+1 discounted at the risk free rate to the end of quarter q. We define the normalized dividend premium, DP i q, as DP i q = PV q(dq+1) i DI i q, (2) Sq i where DI i q is price of the dividend D i q+1 at the end of quarter q, implied by option prices, and S i q is the stock price. The normalization by S i q makes DP i q comparable across stocks. The detailed procedure to calculate option-implied dividend DI i q is discussed below. On a given date t, we use one pair of call and put options with strike price K and maturity T which is later than the ex-dividend date for quarter q+1, and the put-call parity relation to calculate the option-implied dividend as DI i q,t(t, K) = P i q,t(t, K) + S i q,t C i q,t(t, K) Ke Rf q,t (T t), (3) where Pq,t(T, i K) and Cq,t(T, i K) are average of closing bid and offer prices of put and call options written on stock i with maturity date of T and strike price of K on date t, Sq,t i is stock i s closing price on date t, R f q,t is the continuously compounding risk free rate on date t in quarter q. We require the option to expire after the ex-dividend date in quarter q + 1 but before the ex-dividend date in quarter q + 2, so that during the life of the option, there is only one dividend payment. We also require that date t is before the announcement date of dividend to be paid in quarter q + 1 so that the actual dividend 5

8 amount is not known at t. 2 To ensure that options have relatively high liquidity and to mitigate data error issues, we restrict the sample to near the money options (0.8 K/S 1.2) with short to intermediate time to maturity (from 20 to 180 days). The mid closing bid-ask prices of options are required to be at least $0.5, and closing bid prices are required to be positive. Options are required to have positive open interests and implied volatility available. We also require options not to violate the put-call parity no-arbitrage bounds of Americanstyle options, C i q,t(t, K) + Ke Rf q,t (T t) P i q,t(t, K) + S i q,t C i q,t(t, K) + K + PV q,t (D i q+1). (4) The left inequality imposes that option-implied dividend is non-negative, and the right inequality imposes that option-implied dividend is bounded from above to avoid arbitrage opportunities. 3 In case of multiple pairs of options meeting all the above criteria, we take a simple average of option-implied dividend across pairs of options and get a daily average optionimplied dividend DI i q,t. Then, we calculate the daily normalized dividend premium at t, DP i q,t, as (2). For each quarter q, we average DP i q,t across t and multiply it by the annual frequency of dividend payments, and we have a quarterly observation of normalized dividend premium for each stock i and quarter q, DP i q. 4 2 We require date t to be 10 to 40 days before a dividend announcement date. The upper bound of 40 days ensures that date t is close enough to the announcement date so that the option market contains information about future dividend, and lower bound of 10 days ensures that the future dividend is not known date t so that DI i q reflects the premium due to the uncertainty of D i q+1. We also try other time windows from 5 days to 60 days before a dividend announcement date, and the results are similar. 3 Since D i q+1 is not known at time t, we simply use D i q as its estimate. Other approaches to estimating D i q+1 for calculating the no-arbitrage bound do not change our results. 4 During the sample period, 96.15% firms in our sample pay quarterly dividends, 0.19% firms pay monthly dividends, 1.75% firms pay semi-annual dividends, and 1.29% firms pay annual dividends. 6

9 2.2. Data Description and Summary Statistics Our sample includes common stocks (with shares code 10 or 11) traded on NYSE, Nasdaq or AMEX. We exclude stocks with prices lower than $5 at the end of last month. Stock price related data are obtained from CRSP. CRSP also provides data on cash dividends, including the amount of dividends paid, frequency of dividends, dividend announcement dates, ex-dividend dates, and earnings announcement dates. However, CRSP does not provide information if a firm does not pay a dividend. In that case, we use the earnings announcement date as the dividend announcement date. Accounting information is obtained from Compustat. We use PIH, the percentage of institutional holding, as the proxy for short sale constraint, which may contaminate DI as the measure of the price of dividend strips. PIH is calculated as the sum of stock holdings of all reporting institutions divided by the total shares outstanding for each stock at the end of each quarter. Stocks that cannot be matched with any institutional holdings are assumed to have zero institutional holdings. Data on institutional holdings are obtained from the Thomson Financial Institutional Holdings (13F) database. Data of exchange-traded options are obtained from OptionMetrics. The sample period is from January 1996 to December [ Insert TABLE 1 ] During the sample period, 6,173 unique individual stocks can be matched with exchangetraded options. On average, in each quarter we have 1,760 firms with exchange-traded options. Panel B provides summary statistics of stocks in our sample. We compute statistics across stocks in each quarter, and report the time-series average of the statistics. Firms in our sample have an average market capitalization (SIZE) of 7.72 $billion, which is larger than the average market capitalization of stocks listed on the three stock exchanges, since stocks with exchange-traded options tend to be large firms. The sample has an average book-to-market ratio (BM) of 0.49 and an average PIH of Panel C tabulates the characteristics of option contracts written on individual stocks. As we 7

10 restrict our sample to near the money and short to intermediate maturity options, the average moneyness ratio is 1.00, and the average time to maturity is 84 days. The implied volatility is 45% on average. The average open interest is 966 contracts, the average daily trading volume is 54 contracts, and both variables are right skewed. [ Insert TABLE 2 ] In Panel A of Table 2, we present the summary statistics of annual normalized dividend premium, DP, dividend yield DY (= D q+1 /S q ), option-implied dividend yield IDY (= DI q /S q ) and quarterly percentage return on dividend strips r (= D q+1 /DI q 1) of individual stocks. During the sample period, stocks in our sample have an average annual dividend yield of 1.00%. The average dividend premium is 0.05%, with an average standard deviation of 1.38%. Stocks in the 75th percentile earn a dividend premium of 0.27%, and stocks in the 25th percentile earn a dividend premium of -0.26%. The quarterly return on dividend strips is 8.51% on average, with a first quartile of % and a third quartile of 14.01%. The results indicate that the dividend premium is positive on average and there are large cross-sectional variations in dividend premium among stocks. One issue with dividends implied from put-call parity as in (3) is that options written on individual stocks are American-style, so option-implied dividends are contaminated by early exercise premium (EEP). To address this issue, we use a simple method to adjust for EEP. OptionMetrics uses Cox-Ross-Rubinstein (CRR, 1979) binomial tree model to compute implied volatility of American options. Since the binomial tree takes possibility of early exercise into account, the implied volatility computed by OptionMetrics has been adjusted for EEP. We substitute the implied volatility calculated by OptionMetrics into the Black-Scholes option pricing equation to calculate theoretical European option prices, and compute option-implied dividends based on these prices. 5 The summary statistics are 5 OptionMetrics use a proprietary algorithm to estimate the frequency, timing, and amount of dividends, and use these estimates to calculate option implied volatility. We follow the documentation from OptionMetrics, however, our estimates may not be exactly the same as theirs, which leads to an incorrect 8

11 presented in Panel B of Table 2. After adjusting for EEP, the average dividend premium is 0.07%, and average quarterly return of individual dividend strips is 9.20%, both are slightly higher than those without adjusting for EEP. We also compute the distribution of difference between option-implied dividend yield with and without adjusting for EEP. On average, option-implied dividend yield decreases by 0.02% after adjusted for EEP, which is consistent with prior literature s finding that put options generally have greater EEPs than call options. The difference between option-implied dividend yield with and without adjusting for EEP is small. The results indicate that whether adjusting for EEP or not does not significantly affect the estimates of option-implied dividend yield and the dividend premium. In the main empirical analysis, we do not adjust for EEP and report the results with EEP-adjusted dividend premium in a robustness check in Section 4. Since the option-implied dividend has to be non-negative, the dividend premiums of stocks which do not pay dividends are at most zero. In Panel C of Table 2, we also how the results for the dividend payer stocks only, which have ever paid a cash dividend in the last 5 years. On average, there are 816 dividend payers in each quarter. For the sample of dividend payer, the average normalized dividend premium is 0.20% and the average return on dividend strips is 11.33%, both higher than those of the full sample Aggregate Dividend Premium From the dividend strips of individual stocks, we can calculate the dividend strip of the aggregate market. Let DI A q be the price of the aggregate dividend strip in quarter q, calculated as the sum of each firm s number of shares outstanding multiplied by the optionimplied dividend per share at the end of quarter q. The payoff of the aggregate dividend strip in quarter q + 1, Dq+1, A is calculated as the sum of cash dividends paid by all firms in our sample. The quarterly return on aggregate dividend strip is rq+1 A = Dq+1/DI A A q 1. EEP adjustment. We drop about 2% of the observations that the EEP adjusted option price is less than half of the market price, or the estimated EEP is negative with a magnitude greater than 5% of the market price. 9

12 [ Insert TABLE 3 ] Panel A of Table 3 reports summary statistics of return on the aggregate dividend strip during the sample period from 1996 to On average, aggregate dividend strip earns a quarterly return of 4.47% with a standard deviation of 15.79%. During our sample period, mean and standard deviation of quarterly return on the S&P 500 index are 2.39% and 8.44%, respectively. The results that the short-term dividend strip has higher average return and higher volatility than the long-term asset are consistent with the finding of van Binsbergen et al. (2012). They find that during the sample period from 1996 to 2010, index dividend strip with one year maturity constructed using S&P 500 index options earns an average monthly return of 1.16% (3.48% a quarter) with a standard deviation of 7.8% (13.51% a quarter). During their sample period, mean and standard deviation of quarterly return on the S&P 500 index are 1.68% and 8.10%, respectively. We further examine whether the dividend premium can be explained by standard asset price models. We consider the CAPM, and the consumption-based capital asset pricing model (CCAPM). For the CAPM, we use the return on the S&P 500 index as a proxy for return on wealth portfolio, r m. Data on the S&P 500 index are obtained from CRSP. For the CCAPM, we follow the approach in Breeden et al. (1989) and Jagannathan and Wang (2007) to construct a consumption mimicking portfolio (CMP). Specifically, we regress quarterly consumption growth rate on excess returns of the six Fama-French (1993) benchmark portfolio sorted by firm size and BM ratio for the full sample, and use the estimated coefficients as portfolio weights. Data on aggregate consumption, measured as the seasonally adjusted real per capita consumption of nondurables plus service, is from the website of Federal Reserve of St. Louis. Real consumption growth rate is converted to nominal using the PCE deflator. 6 The aggregate consumption growth rate, g c, is the quarterly percentage change in aggregate consumption. During our sample period, mean and standard deviation of quarterly consumption growth rate are 0.34% and 0.39%, 6 We also do analysis using real returns and real consumption growth rate and find very similar results. 10

13 respectively. In panel B of Table 3, βm A (βcmp A ) is slope coefficient of regressing aggregate dividend strip s quarterly excess return on index quarterly excess return (quarterly excess return on CMP), while αm A and αcmp A are the estimated intersects. The aggregate dividend strip has a market beta, β A m, of 0.36 (t-stat = 1.72), and the CAPM alpha, α A m, is 3.50% (t-stat = 1.93). For the CCAPM, β A CMP is estimated as 0.41 with t-stat of 1.96, and αa CMP is estimated as 2.33% with t-stat of The results suggest that it is difficult for the CAPM to explain the return on aggregate dividend strips, consistent with the finding in the literature, for example, van Binsbergen, Brandt, and Koijen (2012). We also find that the CCAPM is better at describing the return than the CAPM, as evidenced by smaller alpha, and higher R 2 for the time-series regression. 3. Pricing of Dividend Strips in the Cross Section 3.1. Sorting Portfolios To mitigate the noises in the returns on dividend strips from individual stocks, we use a portfolio based approach. We need portfolios of stocks with different levels of dividend premium to examine the portfolios risk and return properties. If the dividend premium is due to risk, it is likely that the dividend premium is persistent, i.e., the stocks with high dividend premium in the past, tend to have high dividend premium in the future. Therefore, we sort dividend strips into five portfolios by the average normalized dividend premium in the previous four quarters. To be specific, at the end of each quarter q for each firm i, we average quarterly dividend premium in the last one year to get a long term dividend premium, DP i q = 3 j=0 DP i q j. (5) 4 By taking the average across last four quarters, we smooth out the unexpected components of the return on dividend strips to better estimate the premium. We sort stocks based 11

14 on DP i q into five portfolios. Stocks in portfolio 1 (5) have the highest (lowest) historical dividend premium. 7 One concern of using put-call parity relation to calculate optionimplied dividend is that the put-call parity relation can be violated due to the cost and difficulty of short selling, for example, Ofek et al. (2004). To address the concern that the dividend premium may be contaminated by the short-sale constraint, we conduct a double-sorting portfolio analysis. We first sort stocks by short-sale constraint, proxied by PIH, defined as a stock s shares held by institutional investors divided by total shares outstanding at the end of a quarter. 8 Then, within each group sorted by PIH, we sort stocks by the historical dividend premium, DP. [ Insert TABLE 4 ] The characteristics of sorted portfolios are reported in Table 4. Stocks with the higher DP tends to be larger firms, and have higher BM and lower implied volatility. DP does not seem to be correlated with PIH. We also calculate portfolio retaining rate, RR, which is defined as the proportion of stocks in the portfolio in quarter q 1 that remains in the portfolio in quarter q. Average RR of portfolio with the highest and the lowest DP are 92.68% and 92.74%, while for the rest three portfolios, average RR is at least 80%. The high average RRs indicate that the dividend premium is persistent. Panel B of Table 4 tabulates characteristics of 25 portfolios sorted by PIH and DP. For each of the five portfolios sorted by PIH, SIZE and BM ratio tend to decrease from the subportfolio with the highest DP to the subportfolio with the lowest DP, while the subportoflios with different DP have similar PIH and implied volatility. All the 25 portfolios have average retaining ratios of at least 60%, and subportfolios with the highest and the lowest DP tend to have higher RR than other subportfolios. 7 The option-implied dividend can be overstated and dividend premium can be understated due to short sale constraint. The short sale constraint is most serious during the financial crisis in late 2008 and early To mitigate the effect of the short sale constraint on portfolio sorting, the portfolios from the third quarter of 2008 to the first quarter of 2009 are sorted by DP at the second quarter of 2008, and do not change during the period. 8 Nagel (2005) argues that institutional ownership is a good proxy for short-sale constraint. 12

15 For each portfolio, we construct a trading strategy of dividend strips that is easy to implement. At the end of each quarter q, for each stock i, we long the dividend strip replicated by the underlying stock, the risk-free bond, and the pair of call and put options with K/S ratio closest 1. We choose the most at-the-money option because they have high liquidity and the difference in EEP between put and call options is small. In each portfolio, individual dividend strips are weighted by total market capitalization of the stock. 9 Portfolios are re-balanced on a quarterly basis. Thus, we have a quarterly time series of portfolio returns rq+1. p [ Insert TABLE 5 ] Panel A of Table 5 reports the average returns of quintile portfolios sorted by DP. Portfolio returns decrease monotonically from high DP to low DP. Portfolio 1 earns a quarterly average return of 11.87% (t-stat = 3.1), and the return of Portfolio 5 is % (t-stat = 2.7). The return spread between Portfolios 1 and 5 is 23.07%, with a t-statistic of 7.5. [ Insert TABLE 6 ] Returns of the 25 double sorted portfolios are reported in Panel A of Table 6. For all five groups of stocks with different levels of PIH, the portfolio returns decrease monotonically from high DP to low DP, and the spreads in returns are all statistically significant. For each DP groups, we aggregate the dividend strips across the five PIH portfolios, and report the results in the last row. These five portfolios are DP quintile portfolios controlled for short sale constraints because they have similar level of PIH. The high DP portfolio still earn higher return than the low DP after controlling for PIH. The spread in return is 27.64% with t-statistics of 8.4. The results suggest that the dividend premium is not simply driven by the short-sale constraint. 9 We also compute equal weighted and dividend value weighted portfolio returns and get similar results. 13

16 3.2. Risk Exposures and Price of Risk The standard asset pricing theory suggests that differences in asset returns should be explained by differences in risk exposures. In the absence of arbitrage opportunities, there exists a stochastic discount factor M which prices all future cash flows. The value of the portfolio p, DI p q+1, which pays an aggregate dividend in quarter q + 1, Dq+1, p can be calculated by DI p q = E q (M q+1 Dq+1) p (6) where Rq f is the continuously compounding risk-free rate, and E q ( ) denotes expectation conditional on information set at quarter q. Using the definition of covariance and E q (M q+1 ) = e Rf q, we get, DI p q = E q (M q+1 )E q (D p q+1) + Cov q (M q+1, D p q+1) = E q (D p q+1)e Rf q + Cov q (M q+1, D p q+1), (7) where Cov q (M q+1, D p q+1) is the q conditional covariance between M q+1 and D p q+1, and it represents a risk adjustment term. A dividend strip whose payoff covaries positively with the discount factor has its price raised, and vice versa. Dividing both sides of (7) by DI p q, we have, E q (Dq+1)e p Rf q DI p ( q DI p = Cov q M q+1, Dp q+1 DI p ) q q DI p q E q ( r q+1) p = β q (rq+1, p M q+1 )λ M q, (8) where E q ( r q+1) p = [E q (Dq+1)e p Rf q DI p q]/di p q is the excess return to the portfolio of dividend strips, r p q+1 = Dq+1/DI p p q 1, β q (rq+1, p M q+1 ) is the slope coefficient from a regression of r p q+1 on M q+1, and λ M q = Var q (M q+1 ), is the price of risk and is the same for all assets, where Var q ( ) is the q conditional variance. We consider two asset pricing models: the CAPM, in which the stochastic discount factor is approximated by the negative return of the wealth portfolio, rq+1, m and the CCAPM, 14

17 in which the stochastic discount factor is approximated by the negative aggregate consumption growth rate, gq+1. c As such, we have the following pricing relations, E q ( r q+1) p = β q (rq+1, p rq+1)λ m m q, (9) E q ( r q+1) p = β q (rq+1, p gq+1)λ c c q (10) where β q (rq+1, p rq+1) m and β q (rq+1, p gq+1) c are portfolios risk exposures to market risk and consumption growth risk, respectively, and λ m q of consumption growth risk, respectively. and λ c q are price of market risk and price We run time-series regressions in rolling windows to estimate the two risk exposures β q (r p q+1, r m q+1) and β q (r p q+1, g c q+1) for each quarter q and portfolio p. There is a tradeoff for the choice of rolling window. On one hand, a long rolling window provides more historical data to run the time-series regressions, and thus enables us to estimate regression coefficients more precisely. On the other hand, a short rolling window contains more recent and more relevant information, so a short rolling window may be more suitable for a conditional asset pricing model. To balance the robustness and instantaneousness of the estimates, we use a rolling window of 20 quarters with at least 12 quarters. 10 Since r p q+1 is a quarterly percentage return, we regress it on quarterly index return and quarterly consumption growth rate. 11 Panel B of Table 5 and 6 tabulate average estimated market betas and consumption betas for 5 univariate sorted and the 25 double sorted portfolios, and the Newey and West (1987) t-statistics. For the quintile portfolios sorted by DP, both risk measures decrease monotonically from the high DP portfolio to the low DP portfolio. The highest DP portfolio has an average exposure to market risk β q (r p, r m ) of 2.64 (t-stat = 3.9) and an average exposure to consumption risk β q (r p, g c ) of (t-stat = 2.9), and the two risk exposures for the lowest DP portfolio are (t-stat = 1.9) and (t-stat 10 We also use rolling windows from 8 quarters to 20 quarters, and the main results do not change. 11 Since firms has different ex-dividend dates in a quarter, the return on a portfolio is earned during the entire quarter rather than on a particular date. This creates an issue that the timing of the portfolio returns and pricing factors does not match exactly and a bias of the estimate of the risk exposures towards zero. 15

18 = 2.3). The results of double sorted portfolios shows that risk exposures increasing with DP is robust after controlling for short-sale constraint. We run quarter-by-quarter Fama-Macbeth (1973) cross-sectional regressions to estimate the price of risks. Specifically, in each quarter we regress portfolios ex-post quarterly excess returns on conditional betas as, r p q+1 = λ m 0 + λ m 1 β p q (r p, r m ) + ε p,m q+1 (11) r p q+1 = λ c 0 + λ c 1β p q (r p, g c ) + ε p,c q+1 (12) The parameters of interests are λ m 1 and λ c 1, the price of market risk and consumption risk. [ Insert TABLE 7 ] Panel A and B of Table 7 report the parameter estimates in the cross-sectional regressions, Newey and West (1987) t-statistic and time-series mean of adjusted R 2 estimated from the five portfolios sorted by DP or from the 25 portfolios first sorted by PIH and then by DP. For the case of five portfolios, the (quarterly) price of market risk λ m 1 is estimated to be 3.71% (t-stat = 4.4), and the (quarterly) price of consumption growth rate risk λ c 1 is estimated to be 0.44% (t-stat = 4.4). Both pricing models explain a considerable portion of the cross-sectional variations in dividend premiums. For the CAPM, the mean adjusted R 2 is 46.8%, and for the CCAPM, the mean adjusted R 2 is 48.9%. Results are similar for the 25 double-sorted portfolios. Price of market risk λ m 1 and price of consumption growth risk λ c 1 are estimated to be 4.18% and 0.46%, respectively, and they are highly significant, with a Newey and West (1987) t-statistics of 4.3 and 6.5, respectively. Exposures to consumption risk and market risk explain 30.9% and 37.4% of cross-sectional variations in 25 double-sorted portfolio returns. [ Insert FIGURE 1 ] Figure 1 shows the scatter plot of average quarterly excess return of portfolios, r p q+1, against expected quarterly excess returns according to the CAPM and the CCAPM, 16

19 E q [ r q+1]. p E q [ r q+1] p is computed as β p (r p, r m )λ m 1 in case of the CAPM and as β p (r p, g c )λ c 1 in case of the CCAPM, where β p (r p, r m ) and β p (r p, g c ) are time-series averages of market beta and consumption beta, respectively. Returns on both univariate sorted and doublesorted portfolios fit close to the 45 degree line, indicating the expected return based on the two asset pricing models well explain the future realized returns of dividend strips. Overall, we find that the exposures of the dividend strips to the consumption growth risk and market risk explain a considerable proportion of the cross-sectional variations in returns on dividend strips. [ Insert TABLE 8 ] Finally, we evaluate the ability of the CAPM and the CCAPM to describe returns on dividend strips using the multivariate test proposed by Gibbons, Ross, and Shanken (1989). We run full sample time-series regressions of portfolios excess returns on the pricing factors. For the CAPM, the pricing factor is simply the excess return of the S&P 500 index, r m. For the CCAPM, the pricing factor is excess return of CMP, r CMP. Table 8 reports the estimated intercepts (alphas) and full period post-ranking betas and t- statistics of the estimated parameters. For the CAPM, the ex post factor loading increases with DP. For the univariate sorted portfolios, the portfolio with the highest DP has an ex-post market beta of 2.29 (t-stat = 5.9), and the portfolio with the lowest DP has an ex-post market beta of (t-stat = 4.5). However, these portfolios have significant alphas, and the GRS test rejects the CAPM with a p-value of The CCAPM seems to perform better at explaining time-series variations in these portfolio returns. For the univariate sorted portfolios, Portfolio 1 has an ex-post CMP beta of 1.97 (t-stat=5.6), and Portfolio 5 has an ex-post CMP beta of (t-stat=-5.0). The GRS test fails to reject CCAPM to describe returns on dividend strips with a p-value of Results are similar for the 25 sorted portfolios. 17

20 4. Robustness Tests In this section, we address several concerns with the main empirical analysis. First, we show that option-implied dividends are informative about future dividends beyond historical dividends. This evidence would suggest that option-implied dividends are good estimates of the prices of dividend strips, and our empirical results are not driven by the errors in option-implied dividends due to, for example, short sale constraint and liquidity issues. Second, we restrict the sample to dividend payers to address possible differences between dividend payers and non-payers. Finally, we examine the effects of early exercise premiums on the results Predictability of Option-Implied Dividend Prior studies argue that option prices contain information about options traders expectations on future dividends, and many papers find that option-implied dividends can predict realized dividends. For example, using options written on 69 firms on 226 dividend announcement dates from 1984 to 1985, Bae-Yosef and Sarig (1992) find that option-implied dividend surprises are significantly related to stock markets reactions to dividend announcements. Golez (2014) find that dividend growth implied by options and futures on the S&P 500 index reliably predict future dividend growth rate of the index. Fodor et al. (2017) examine option-implied dividends of 67 firms which cut dividends during the financial crisis from 2008 to 2009, and find that option-implied dividends are effective in predicting dividend omissions compared to some equity market and accounting variables. Kragt (2017) uses options written on individual stocks in the US market and the putcall parity relation to calculate option-implied dividends, and finds that option-implied dividend growth rate is able to predict realized dividend growth rate in the cross section. We present complementary evidences that option-implied dividends can predict future dividends beyond historical dividends based on the univariate and double sorted portfolios. 18

21 Specifically, we run the following time-series regression for each of the five portfolios sorted by DP and the 25 portfolios sorted by PIH and DP, D p q+1 Dq p = β 1 + β 2 (DI p q Dq) p + ε p q+1 (13) where Dq p is aggregate dividends of portfolio p in quarter q, and DIq p is the aggregate option-implied dividend estimated at the end of quarter q. β 2 measures the amount of change in dividends predicted by option-implied change in dividend. If option-implied dividends provide incremental information about future dividends, coefficient β 2 should be significantly positive. [ Insert TABLE 9 ] As shown in Panel A of Table 9, for each of the five portfolios sorted by DP, β 2 s are positive and statistically significant. For example, for the portfolio with the highest DP, β 2 is estimated to be (t-stat = 2.72). Panel B reports estimated regression coefficients of the 25 double sorted portfolios. The estimated coefficients on option-implied change in dividends are positive for all portfolios, among which most are statistically significant. The results indicate that option-implied dividends do contain information about future dividends beyond historical dividends Analysis on Dividend Payers Prior studies find that investors may perceive dividend payers to be different from nonpayers, and paying dividends or not may affect firm value and expected return on equity. To address the issues that dividend payers are systematically different from non-payers in some way and that the results are not driven by the difference between dividend payers and non-payers, we restrict the sample to dividend payers and examine whether the main results change significantly. [ Insert TABLE 10 ] 19

22 We first define the sample of dividend payers. At the end of each quarter, we define dividend payers to be firms that have ever paid a cash dividend in the last 5 years, which is consistent with the rolling window to estimate conditional betas. On average, dividend payers account for about one half of the whole sample. We repeat the univariate and double sorting analysis on the dividend payer sample. Table 10 shows that both returns and risk exposures increase with DP for the dividend payer sample. Dividend-paying stocks with the highest (lowest) DP earn a mean quarterly return of 14.57% (-13.68%), and the spread in return is significant at 1% level (t-stat=4.0). Average market beta and consumption beta of Portfolio 1 are 2.80 (t-stat=4.6) and (t-stat=3.7), respectively, and the two risk exposures of Portfolio 5 are (t-stat=-1.9) and (t-stat=-2.6), respectively. Portfolios risk exposures to market index return and consumption growth rate as measured by β q (r p, r m ) and β)q(r p, g c ) explain 40.3% and 46.6% and of crosssectional variations in portfolio returns. The estimated quarterly price of market risk λ m 1 is 3.75% (t-stat = 3.1) and the estimated quarterly price of consumption growth risk λ c 1 is 0.43% (t-stat = 3.1), which are similar to the those estimated from the full sample. The GRS test rejects the CAPM but fails to reject the CCAPM at the conventional significance level. 12 Results are similar for the double sorting analysis. Overall, our results are robust when we restrict the sample to dividend payers Early Exercise Premium Options written on individual stocks in the US market are American-style. Optionimplied dividends from the put-call parity relation as (3) are contaminated by difference between EEP of put and call options. To examine the effects of EEP, we repeat the univariate and double sorting analysis using option-implied dividend adjusted for EEP, and report the results in Table 11. For quintile portfolios sorted by EEP adjusted DP, the portfolio return also increases monotonically with DP. Portfolio 1 has an average quarterly return of 12.26% (t-stat = 2.8), and the average return of Portfolio 5 is -8.66% 12 We do not report the results to save space. 20

23 (t-stat = 2.2), with a statistically significant (t-stat=4.5) spread in return of 20.92%. Average conditional consumption growth beta and market beta decrease monotonically from 2.94 (t-stat = 2.8) and (t-stat = 3.6) for Portfolio 1 to (t-stat = 2.0) and (t-stat = 2.9) for Portfolio 5, respectively. Average adjusted R 2 of crosssectional regressions are 41.1% and 44.3% for the CAPM and the CCAPM. The prices of market risk and consumption growth risk are positive and significant (3.73% with t- stat of 3.9 and 0.48% with t-stat of 5.7, respectively). Thus, after adjusting for EEP, risk exposures to market portfolio return and consumption growth rate still explain a considerable proportion of cross-sectional variations in short-term dividend premiums. For the GRS test, consistent with the results of the full sample, the CAPM is rejected and the CCAPM cannot be rejected at the conventional significance level. Results are similar for the 25 portfolios sorted by PIH and DP. [ Insert TABLE 11 ] 5. Conclusion In this paper, we construct the dividend strips synthetically from options on individual stocks, and examine the risk and return properties of the dividend strips. We find that the return to the dividend strips, i.e., dividend premium, aggregated across stocks, is very high, with 4.47% a quarter, for the sample period from 1996 to The results provide additional support for the downward sloping equity premium at the market level. We also find substantial variations in the dividend premiums across stocks. Near half of the dividend strip portfolios have average negative returns, and many of them are statistically significantly. Given that the majority of stocks have positive average returns, i.e., the longterm premium is positive, the large variations in the short-term dividend premium indicate large cross-sectional variations in the term structure of equity premium. In particular, the stocks with high dividend premium are likely to have a downward sloping term structure, whereas the stocks with negative dividend premium are likely to have an upward sloping 21

24 term structure. We also find that the dividend strips with high (low) average returns load positively (negatively) on the market risk and the aggregate consumption risk and that the CAPM and CCAPM explain a considerable proportion of cross-sectional differences in dividend premiums. The GRS test favours the CCAPM over the CAPM in explaining dividend premiums. 22

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28 Table 1 Summary Statistics: Stock and Option Characteristics Panel A presents equity characteristics of all stocks in the sample. SIZE is total market capitalization in billion dollars, BM is the book-to-market ratio, and PIH is the percentage of institutional holdings. Panel B presents characteristics of option contracts written on individual stocks. KS is the ratio of strike price to price of the underlying stock, T is the number of day until option maturity date, IV is option-implied volatility, OI is the open interests, and V is the daily trading volumes of options in contracts. Mean, standard deviation (std), first quartile (p25), median (p50) and third quartile (p75) are reported. We first calculate cross-sectional statistics in each quarter and report time-series average of the statistics. The sample period is from January 1996 to December A. Stock Characteristics mean std p25 p50 p75 SIZE BM PIH B. Option Characteristics mean std p25 p50 p75 KS T IV OI V