Risk and Return of Short-Duration Equity Investments∗ Georg Cejnek† WU Vienna University of Economics and Business Otto Randl‡ WU Vienna University of Economics and Business April 9, 2014
Abstract We implement a simple investment strategy using traded claims on index dividends. We show that equity investments with constant short-maturity outperform a systematic long position in the underlying equity index on a risk-adjusted basis and in absolute terms. Furthermore, we find higher international diversification benefits for this strategy as compared to traditional equity indices. We relate the attractive performance to market downside exposure. Alphas remain large and puzzling, though, in the light of the fact that dividends have historically been sticky in the short run. However, risk-adjusted outperformance diminishes if options-based risk factors are taken into account. We find evidence for time variation in expected returns from ex-ante risk premia, which we derive using Lintner-based dividend expectations. Implied risk premia are high on average and correlate with subsequent realized returns. Our results are consistent with recent asset pricing models that imply a downward-sloping term structure of equity risk premia.
Keywords: Dividend Derivatives, Short-Maturity Anomaly, Term Structure of Equity Risk Premia, Downside Risk, Investment Strategy
∗
We thank Christian Mueller-Glissmann at Goldman Sachs for providing us with data. We appreciate valuable comments
by Engelbert Dockner, Bart Lambrecht, Carolin Pflueger, and Neal Stoughton. † WU Vienna University of Economics and Business, Department of Finance, Accounting and Statistics, Welthandelsplatz 1, A-1020 Wien, Austria. E-mail:
[email protected], Phone +43 1 51818 934 ‡ WU Vienna University of Economics and Business, Department of Finance, Accounting and Statistics, Welthandelsplatz 1, A-1020 Wien, Austria. E-mail:
[email protected], Phone +43 1 31336 5076
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1
Introduction
Both academics and investors have recently indicated strong interest in the so-called term structure of equity risk premia, a term derived from the fixed income literature. There is evidence that the maturity of equity cash flows is related to expected risk premia, and consequently correlates with realized excess returns. Binsbergen, Brandt, and Koijen (2012) calibrate leading asset pricing models and derive the predictions those models provide for the shape of the term structure of risk premia. It turns out that traditional models such as consumption-based asset pricing models with habit formation, as in Campbell and Cochrane (1999), or long-run risk models, as in Bansal and Yaron (2004), imply risk premia that increase in maturity while more recent models, such as Lettau and Wachter (2007) explicitly predict a downward-sloping term structure of risk premia, as do variable rare disaster models like Gabaix (2012). Thus, it has become an interesting task to test these predictions by comparing the performance of short and long-duration equity investments. Binsbergen, Brandt, and Koijen (2012) use S&P 500 index options and implement an investment strategy that isolates the risk exposure to implied dividends. To formulate the appropriate strategy which exposes investors to short-term dividend claims, they rearrange the terms in the put-call parity. The authors find short-maturity dividend claims to outperform the underlying equity index on a risk-adjusted basis, thus providing support for equity risk premia that decrease in maturity. Using dividend swaps, Binsbergen, Hueskes, Koijen, and Vrugt (2013) construct equity yields similar to bond yields, where equity yields consist of discount rates, dividend expectations for a certain maturity and the corresponding risk premium. In addition to illustrating predictive power for important macroeconomic variables, such as consumption growth and dividend growth, their paper provides further evidence for a downward-sloping term structure of equity risk premia. Reconciling these empirical findings with traditional asset pricing theory, Belo, Goldstein, and CollinDufresne (2013) combine unlevered EBIT dynamics with a dynamic capital structure to conclude that dividends are riskier than EBIT in the short run. From an investment perspective, dividend derivatives have gained increasing attention, first among hedge fund managers, but also among large institutional investors. Traditionally those contracts were traded in the OTC markets. The introduction of listed dividend derivatives for three out of the four regions covered in this paper (Eurozone, UK, Japan, but not yet in the US) has increased the popularity of trading dividends even more. The market for dividends, as described in detail by Manley and MuellerGlissmann (2008), provides investment characteristics that are related to traditional equity investment vehicles but has additional features that make it an asset class in its own right. Most importantly, the final payoff of dividend derivatives depends only on the difference between the price at initiation and the amount of dividends accrued throughout the maturity year. This is in contrast to standard equity investments, where for any finite investment horizon there is not only uncertainty about cash flows but investors are also exposed to valuation risk at the time of divestment. In this paper we implement a simple investment strategy based on dividend swaps, which yields surprisingly good results. We construct portfolios that expose investors to a dividend cash flow of con2
stant duration by combining appropriate dividend swaps of two consecutive maturities. The strategy is implemented for four different markets, namely the Euro Stoxx 50, FTSE 100, S&P 500 and the Nikkei 225. Over our sample period we show that the strategy outperformed the underlying equity indices on a risk-adjusted and on an absolute basis. We attribute the results partly to high levels of downside risk; significant alphas remain after accounting for conditional betas, though. However, risk-adjusted outperformance diminishes if options based risk factors are taken into account. Furthermore, we find cross country correlations of the dividend strategies to be significantly lower than cross country correlations in the time series of traditional equity returns. Therefore we suggest a global constant maturity dividend strategy that benefits from a high degree of diversification. In addition to presenting an attractive investment strategy, our results can be interpreted as further support for asset pricing models that assign higher risk premia to short-maturity cash flows. In order to model implied ex-ante risk premia we build on the findings of Lintner (1956) that companies aim to smooth dividend payouts based on past dividends and current earnings. These findings are well established in the literature. We estimate coefficients of a Lintner-type model for all relevant markets to derive a structural model for dividend growth expectations based on consensus analysts’ forecasts for dividends and earnings. In combination with market prices for dividend swaps this enables us to compute implied risk premia appropriate for our strategy. We find that these risk premia are high on average and exhibit substantial time variation. Moreover, they are significantly related to subsequent holding period returns of our strategy. In addition to the literature highlighted so far, our work relates to the following papers: Brennan (1998) first introduced the idea to create distinct traded instruments that expose investors to dividend cash flows of a single year. He shows that this can increase efficiency in asset markets as different maturities of equity cash flows serve different investor clienteles. Shortly after publication of this paper, the market for dividend derivatives emerged. Manley and Mueller-Glissmann (2008) present the evolution of this market and elaborate in great detail on the mechanics of dividend derivatives. Boguth, Carlson, Fisher, and Simutin (2013) attribute the empirical results on the term structure of equity risk premia to leverage effects that arise when isolating the implied dividend stream from traded index derivatives. However, by implementing a successful short-maturity dividend strategy using direct claims to implied dividends only, we support the findings of Binsbergen, Brandt, and Koijen (2012) and Binsbergen, Hueskes, Koijen, and Vrugt (2013) in absence of leverage effects. In addition, the findings of this paper are similar to those derived by Duffee (2010) for the treasury bond market and by Derwall, Huij, and de Zwart (2009) for the corporate bond market. Our risk-based explanation relates to downside risk, an approach that has recently been applied comprehensively across asset classes by Lettau, Maggiori, and Weber (2014). Moreover, we find options-based risk factors to be important in capturing risk exposures of our strategies. Such nonlinear risk factors are usually used for hedge fund returns as shown for instance in Naik and Agarwal (2004). We extend the analyses on conditional correlations presented in Erb, Harvey, and Viskanta (1994). Finally, we relate to recent publications that employ
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structural Lintner-type models to explain aggregate dividends, such as Skinner (2008) and Lambrecht and Myers (2012).
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Short-Duration Equity Investments
In this section, we first elaborate on the dataset employed for empirical evidence. We define the investment strategy implemented, and present the results. Furthermore, we investigate the potential for international diversification benefits.
2.1
Data
We use a proprietary dataset on OTC dividend swaps from Goldman Sachs. Dividend swaps are available for several maturities. The underlying of index dividend swaps is dividends announced and paid by all member companies of a specific equity index accumulated within one calendar year. The investor who enters a long position pays a fixed amount, which is the current implied dividend level (the certainty equivalent of dividends of a given future calendar year), and receives at maturity the difference between the implied dividend level at initiation of the contract and the realized level at maturity. Thus, a dividend investor has zero exposure to market valuations of future dividend streams at maturity and consequently can trade purely upon his expectations with respect to dividends of the maturity year in question. Dividend swaps mature once every calender year in December, and traded contracts are available for maturities up to six years ahead. The sample covers dividend swaps on four major equity indices, S&P 500, FTSE 100, Nikkei as well as the Euro Stoxx 50 and reaches from 2006 to 2013. We use a weekly data frequency. The data sample is similar to that employed in Binsbergen, Hueskes, Koijen, and Vrugt (2013). As a robustness check we also employ exchange-listed dividend futures retrieved from Bloomberg for those markets and sub-periods where listed contracts are available; see appendix A. As benchmarks we use index futures for the underlying equity indices from Bloomberg with the same data range and frequency as for the dividend swaps. For the conditional correlations calculated in section 2.3 we gather monthly data on the ISM index for the economies corresponding to the equity indices in our sample, also from Bloomberg. Furthermore, we collect data to calculate options-based risk factors in section 3.2. To this end, we download time series of volatilities implied by one-month put options for all four indices and various levels of moneyness, as well as dividend yields, index levels and one-month libor rates (in EUR, GBP, USD and JPY) from Bloomberg. We employ Lintner models to model dividend policy in section 3.4, which requires us to use consensus analysts’ forecasts of aggregate dividends and earnings one and two years ahead. Those consensus estimates are also gathered at weekly frequency from Bloomberg.
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Moreover, we want to analyze dividend growth historically and calibrate a Lintner model to empirical data. Thus, we retrieve data on realized annual dividends and earnings in the US from Prof. Shiller’s website1 . To create a corresponding sample for the other regions we use total return indices and price indices as well as time series of price-earnings ratios and dividend yields for the Eurozone, UK and Japan from Global Financial Data. Based on those ratios and index levels we are able to back out historical index dividends and index earnings for all regions on an annual basis. For the US and the UK the resulting sample starts in 1946, for Japan in 1957 and for the Eurozone in 1972.
2.2
2
Investment Strategy
We create investable indices that go long the dividend swap that matures next (in December of the current fiscal year) and roll into the subsequent swap contract shortly before the maturity date. In a similar fashion we implement indices that systematically roll the second, third, fourth, fifth and sixth dividend contracts. At the roll date we adjust the number of contracts held to account for gains or losses due to the roll yield. Thus if we denote the fair dividend swap strike at time t for a swap maturing in December of the current fiscal year by Ft ,F Y (t ) , while Ft ,F Y (t +1) is the corresponding strike at time t for a swap maturing in December of the following fiscal year, we increase the number of contracts that we go long (or equivalently we increase the notional of the swap) if Ft ,F Y (t ) > Ft ,F Y (t +1) at t = roll date, and we decrease the number of long contracts if Ft ,F Y (t ) < Ft ,F Y (t +1) at t = roll date, so that all available funds are invested. Note that investors would have a variable remaining maturity as we roll only once a year. Since we are interested in relating our results to recent studies on the term structure of realized risk premia, our goal is to create investable constant maturity dividend profiles. To this end we introduce the following simple strategy. On the third Friday in December (contract settlement date), buy 52 contracts of the dividend swap maturing in exactly n years time. One week later sell one contract of maturity n and buy one contract of maturity December of year n +1 etc. Put differently, we interpolate linearly between two subsequent maturities by adjusting the amount of contracts held once a week. As a result we are left with strategies that have a constant remaining maturity. Formally, the price of the replicating portfolio of the strategy reads as: w t Ft ,F Y (t ) + (1 − w t )Ft ,F Y (t +1) , where w t determines the weights of the two contracts involved. At the roll date in December each year wt =
52 52 .
The numerator declines by one contract every week up to the next roll date in December of
the subsequent year, so that the weight (1 − w t ) of the second year contract increases gradually. 1 2
http://aida.wss.yale.edu/ shiller/data.htm We use France and Germany as proxies for the Eurozone for the empirical calibration of the Lintner model.
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100% weight 2011 0% weight 2012
0% weight 2011 100% weight 2012
1 year constant maturity dividend strategy (for 2011)
maturity/roll date dividend swaps
2010
January 2011
December 2011 2012
1s t maturity/roll date index futures
2nd maturity/roll date index futures
Figure 1: Illustration of the Constant Maturity Dividend Strategy - This figure illustrates the mechanics of the constant maturity dividend strategy. For the purpose of illustration we consider the year 2011. Dividend swaps are rolled over into the subsequent contract in December of 2010 and then again in December 2011 (as indicated in the chart). The benchmark strategy consisting of index futures are rolled twice a year in March and December, as they have a maximum available maturity of 9 months. For the constant maturity dividend strategy, we put 100% weight (or 52 of 52 contracts) on the dividend swap maturing in December 2011 at the roll date in December 2010. This weight decreases linearly to 0% (0 of 52 contracts) at the subsequent roll date in December of 2011, where the weight of the dividend swap maturing in December of 2012 has increased to 100%. The resulting portfolio has a constant exposure to a risky dividend cashflow in exactly one year’s time.
As a benchmark we invest in index futures of the underlying equity indices. Exchange-listed index futures are only available with maturities up to nine months, consequently we roll these index futures into the subsequent futures contract twice a year. In accordance with the systematics of the dividend investments we vary the number of contracts conditional on the futures curve. We compare the investment performance of a systematic long strategy in the constant maturity dividend swaps (with maturities of one and five years) and a systematic long position in the equity index itself (via futures). This is done for each of the four markets in our sample. We compute weekly excess returns of our strategies (R t +1 ) as follows: R t +1 =
Ft +1 − Ft , Ft
where Ft is the fair dividend swap strike at initiation, or the current index futures price in case of the benchmark strategies. In order to interpret R t +1 directly as excess returns, we need to assume that investors enter a fully collateralized position (the margin placed with the broker equals the notional of the derivatives contract). This can be proved as follows: If we denote the amount of funds placed as margin at initiation as M t , then the market value of the investment strategy one week later is given by M t (1 + r f ) + Ft +1 − Ft and the one week total return per unit of capital is given by which can be simplified to of capital
Ft +1 −Ft Mt
Ft +1 −Ft Mt
M t (1+r f )+Ft +1 −Ft −M t Mt
,
+ r f . Subtracting the risk-free rate r f yields the excess return per unit
. Assuming a fully collateralized position equates M t and Ft , which shows that our
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return R t +1 is the appropriate measure for excess returns.3 Moreover we analyze the correlation across the four markets of our dividend strategies as compared to the correlation across traditional equity markets. This highlights whether dividend markets provide investors with more or less diversification benefits than traditional equity markets. Subsequently, we implement global strategies, where the four markets are equally weighted and rebalanced weekly.
2.3
Investment Performance
Figure 2 illustrates the results of the strategies implemented for all four regions. The blue lines depict the results for the constant one-year dividend strategy, the green line is the equivalent for a maturity of five years and the purple line is the benchmark, which is a systematic long investment in the underlying equity index via index futures. The surprising result to note is that the one-year maturity strategy outperforms in three out of the four markets over the sample horizon of close to eight years. This strategy does not only outperform on a risk-adjusted basis but also in absolute terms. The dividend strategy exposing investors to realized dividends in five years’ time does much worse than the short-maturity strategy and also underperformed the benchmark index in most regions. 3
A similar interpretation can be found in Koijen, Moskowitz, Pedersen, and Vrugt (2013).
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Figure 2: Short-Maturity Equity Strategy and Benchmark - This figure illustrates the performance of the investment strategies described above. The blue lines represent the performance of a systematic dividend strategy with constant maturity of one year, the green line is the corresponding strategy with a five-year maturity and the purple line is the benchmark strategy, which is a systematic investment in the underlying equity index via index futures. The four panels show results for the four regions in our sample. The performance indices are set to 100 in January 2006. Note that the indices represent total excess returns.
The result is even more puzzling in the light of the fact that a substantial amount of dividends that are to be paid in one year’s time are announced the year before. So there is very good visibility in terms of the expected level of realized dividends. Since most dividends for the next year have already been announced, the gradual increase in dividend swap strikes is similar to the pull to par effect of a bond, despite the fact that equity investors only have residual claims on company profits. It seems that the moderate dividend risk of the one-year maturity strategy offers investors a disproportional realized risk
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premium. Remember that our strategy results are excess returns by construction. Hence, from a theoretical perspective our results support the predictions of those asset pricing models that imply a downwardsloping term structure of risk premia. Furthermore, the results support earlier empirical findings on short-maturity dividend strategies using index options, such as Binsbergen, Hueskes, Koijen, and Vrugt (2013). Tables 1 to 4 provide annualized mean returns, standard deviations and Sharpe ratios for the one and five-year constant maturity dividend strategies as well as for the benchmark strategy. These tables reveal that the short-maturity dividend strategies produced very attractive Sharpe ratios as compared to the benchmark strategies over our sample and within most sub-periods. International Diversification Benefits:
Apart from investigating the performance of our strategies
within regions it is very relevant to analyze whether the short-maturity strategies provide international diversification benefits beyond those of the benchmark strategies. Tables 5, 6 and 7 contain correlations across the four regions in the sample for the one and five-year dividend strategies and the benchmark strategy. It can be seen that the correlation of returns across markets is substantially lower for the dividend strategies. We conduct Jennrich tests for the statistical significance of the difference in the correlation matrices, which yield p-values of below 0.001. Thus, we conclude that the dividend strategies have higher potential for international diversification than the benchmark strategies. As a result we implement globally diversified strategies. We assign all markets equal weights and rebalance weekly. Figure 3 illustrates the performance of the global strategies and table 8 provides performance statistics. Due to the high diversification benefits the global one-year constant maturity dividend strategy yields a very attractive Sharpe ratio.
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Figure 3: Short-Maturity Equity Strategy and Benchmark - Global - This figure illustrates the performance of the global investment strategies. The blue lines represent the performance of a systematic dividend strategy with constant maturity of one year, the green line is the corresponding strategy with a five-year maturity and the purple line is the benchmark strategy, which is a systematic investment in the underlying equity index via index futures. The performance indices are set to 100 in January 2006. Note that the indices represent total excess returns.
Following Erb, Harvey, and Viskanta (1994), we analyze conditional correlations to detect whether diversification benefits disappear during times of market distress. To this end, we partition returns into three states. We analyze correlations for a subsample where both returns of two markets in question are positive, where both returns are negative, and for times where returns are out of phase. Tables 10, 11 and 12 show that correlations tend to increase if returns are negative. However, international correlations remain lower for the short-maturity strategies as compared to the benchmark strategies even during phases of negative returns. As an alternative stress test we use macro data as a conditioning variable. We observe pairwise correlations if the ISM index in both regions is above 50 (indicating expansion), if it is below 50 in both regions and if it is out of phase. Results are shown in tables 13, 14 and 15. Again the potential for international diversification remains superior in the domain of the short-maturity dividend strategies as compared to the benchmark strategy. Summarizing our findings, figure 4 relates mean returns (weekly) and standard deviations for constant maturity dividend strategies with maturities of 1 to 5 years as well as benchmark strategies. It is striking that the shortest maturity strategies tend to be in the top left, indicating that those strategies 10
exhibit less risk than longer maturity strategies and at the same time generate higher excess returns.
Figure 4: Risk Return Characteristics of Various Strategies - This figure relates weekly mean returns and standard deviation for constant maturity dividend strategies with maturities of 1 to 5 years as well as benchmark strategies.
Transaction Costs:
So far, our analyses are based on mid-market prices, for both dividend derivatives
and equity index futures. To properly account for transaction costs, we adjust returns in the following way: To implement the constant maturity dividend strategy in practice, one needs to roll
1 52
of the
overall exposure into the subsequent contract each week. Thus, we adjust returns according to R tD i v,n,T C = R tD i v,n −
T CD , 52
where R tD i v,n,T C are returns after transaction costs T CD . For the benchmark strategy, we need to roll the whole exposure twice a year. Therefore, we adjust returns for transaction costs T C b m only at these roll dates:
R tb m ,T C =
R b m t
ift 6= roll date
R b m − T C b m t
ift = roll date
We set T CD equal to 20 basis points per round trip and T C b m equal to 5 basis points per round trip. The latter number is consistent with recent literature, e.g. Herold, Maurer, and Purschaker (2005). To account for lower levels of liquidity in OTC dividend derivatives, we use four times that magnitude for T CD . Table 9 provides performance statistics after accounting for transaction costs. Despite imposing 11
higher percentage costs for short-duration dividend strategies, their outperformance relative to the benchmark index is robust.
3
Time-Varying Risk and Risk Premia
In this section, we relate the performance to downside risk as well as options-based risk factors. To gain further insight into the economic significance of dividend downside risk, we analyze the empirical variability of cash dividends. Moreover, we calibrate a Lintner model of dividend payouts and estimate ex-ante risk premia implied by dividend swap prices.
3.1
Beta Regressions
After having elaborated on the realized returns of our strategy we are interested in the risk exposures. Hence, we relate excess returns of the strategies to the excess returns of the benchmark strategy. To account for the possibility of increased downside risk of the strategy we analyze state-dependent market risk. We implement the following set of time series regressions: R tD i v,n = α + β R tb m + β d o w n R t D + εt ,
(1)
where R tD i v,n is the excess return of a dividend strategy with n years of maturity, R tb m is the excess return on the benchmark strategy and D is a dummy variable that has a value of 1 if the market excess return is smaller than µ − σ and 0 otherwise. Thus, the term β d o w n R t D is an interaction term that changes the slope of the regression line if the regressor is less than the mean minus one standard deviation. In economic terms it states how much the systematic market risk of the dividend strategy increases in phases of bad capital market returns. Since we use a proprietary data set on dividend swaps we want to ensure that we properly account for the possibility of stale prices. Thus we regress the dividend returns on contemporaneous as well as on lagged benchmark returns and aggregate the beta coefficients. We follow the widely used procedure suggested by Dimson (1979). For the constant one-year maturity strategy, table 16 shows that the systematic co-movement with the benchmark strategy is substantially below one, but significantly different from zero in most markets. Alphas are statistically significant and economically large, ranging from 14 to 48 basis points per week. However, market betas increase significantly when the benchmark strategy performs poorly, as indicated by the downside betas. Betas roughly double in bad times (or even triple in Japan), which attributes the attractive empirical performance of the dividend strategy partly to downside risk. Table 17 provides corresponding results for the five-year constant maturity strategy. Interestingly, betas are much higher than for the one-year strategy. The beta in bad states (the sum of beta and down beta) is above one for some markets, showing that this strategy is exposed to huge systematic market risk especially for negative returns. Tables for other constant maturity strategies are provided in the
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appendix.
3.2
Options-Based Downside Risk Measure
The constant maturity dividend strategies presented in this paper are related to hedge fund strategies for two reasons. First, the strategies yield stable returns as compared to the benchmark indices (i.e. lower volatility), while exhibiting increasing overall market exposure in down states. This nonlinearity is a typical feature of hedge fund returns as shown by Mitchell and Pulvino (2001) and Fung and Hsieh (2001). Second, hedge funds have been among the most active investors in the market for traded dividend claims as reported by Manley and Mueller-Glissmann (2008). Thus, we extend our analysis to include an options-based risk factor to account for downside risk in dividend strategies. Naik and Agarwal (2004) find that hedge fund returns have significant exposure to systematic outof-the money put writing strategies. We create a similar risk factor and relate it to the returns of the constant maturity dividend strategies as follows: For all four equity indices relevant for this paper we collect volatilities implied by put options with one-month to maturity (from Bloomberg). We gather the appropriate times series of implied volatility for various levels of moneyness: 80%, 90%, 95%, 97.5%, 100%, 102.5%, 105% and 110%. Then we interpolate to get a continuum of implied volatility levels for all four markets. Using one-month libor rates (in EUR, GBP, USD and JPY) as the relevant risk-free rate, the spot price of the equity indices and dividend yields for the equity indices we are able to determine prices of European put options with any given moneyness using the Black-Scholes formula with continuous dividends. W
Now we implement systematic put writing strategies: Each week we sell an amount equal to S t r i k et 0.95% of 5% out-of-the money put options and collect the premium; where Wt denotes wealth at each point in time t . We hold the short put position for one week, then we buy back the put and write a new put again with one-month maturity and 5% out-of-the money. Note that we assume a rather conservative strategy, since we cannot lose more than our initial wealth. Weekly returns of this strategy can be derived by calculating the percentage changes of the resulting time series of wealth (Wt ), which consists of the initial wealth level, put premia collected, negative market values of the short put positions in the portfolio and interest earned on the cash. We deduct the risk-free rate to get excess returns. Finally we construct an equally weighted put writing portfolio using all four markets. Using the excess returns on the option strategy as a risk factor which is nonlinear in nature, we analyze the following regression setup as an alternative way to capture downside risk in dividend strategies. We regress excess returns of the one-year constant maturity dividend strategies on excess returns of the underlying equity index and on excess returns of the put strategies. The regression reads as: put
R tD i v,n = α + β R tb m + β p u t R t 13
+ εt ,
(2)
where R tD i v,n is the excess return of a dividend strategy with n years of maturity, R tb m is the excess reput
turn on the benchmark strategy and R t
is the put-options-based risk factor for nonlinear returns.
Consistent with our downside beta analysis we regress the dividend returns on contemporaneous and on lagged benchmark returns as well as on contemporaneous and on lagged put option returns to account for the possibility of stale prices. We aggregate the coefficients and use Wald tests to test for the joint significance of the contemporaneous and the lagged coefficients. Again we follow the widely used procedure suggested by Dimson (1979). The results are provided in table 18 for all four markets and the global portfolio. It is striking that the coefficients on the put option risk factor are significant for all markets except the UK (Note, however, that we have fewer observations for the UK since implied volatilities for the FTSE 100 Index are only available on Bloomberg starting in 2007). Market betas decrease as compared to the downside beta analysis and alphas disappear except for Japan. Hence, returns of the short-maturity dividend strategies seem to exhibit significant nonlinearities which dominate traditional market risk. Even though dividends are sticky and to a certain extent predictable in the short run, options-based risk factors usually applied to hedge fund returns are necessary to account for risk in traded dividend claims properly.
3.3
Empirical Evidence on Cash Dividend Variability
Even though we show that market risk of the dividend strategies increases in times of market distress, alphas remain economically large. To further investigate the level of downside risk of the shortduration strategies we use a long time series of annual dividends and equity prices from Global Financial Data (and cross check the US analysis with data from Prof. Shiller’s website). In table 19 we illustrate one-year changes in nominal dividends paid in the US, one-year equity index returns and one-year changes in the payout ratio for those years in the post World War II sample where either the price return or the dividend change was below the 10% quantile. Tables 20 to 23 provide corresponding information for the other regions relevant for this paper (excluding payout ratios). Figure 5 depicts historical changes in nominal dividends over one year (left panel) and changes in nominal equity prices over one year (right panel) for all relevant regions (we use France and Germany to proxy for the Eurozone). In accordance with the notion in the literature that dividends are sticky in the short run, we show that usually substantial drawdowns in nominal dividends can be observed together with even more severe drawdowns in equity prices. This makes the attractive relative performance of the very short-maturity dividend strategies even more puzzling.
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Figure 5: Boxplot of 1 Year Nominal Dividend Changes and Index Changes - This figure compares historical one-year nominal dividend changes (left panel) and one-year nominal equity index changes (right panel). We use France and Germany to proxy for the Eurozone. The data was retrieved from Global Financial Data. To cross check the data set we use US data from Prof. Shiller’s website: http://aida.wss.yale.edu/ shiller/data.htm and compare the results of our US analysis using both data sets.
Campbell and Vuolteenaho (2004) show that market betas can be split into bad beta, representing sensitivity to cash flow news, and good beta, related to the sensitivity with respect to discount rate news. While lower stock valuations can result from both, decreased future cash flows and increased discount rates, only discount rate shocks lead to improved investment opportunities. Therefore, the risk premium associated with bad beta should be higher, resulting in lower prices for value stocks. In this respect one can argue that traded claims on near term dividends constitute an extreme form of value stocks, exhibiting much more sensitivity to cash flow news than to changes in discount rates. Our finding of low prices (i.e. high average excess returns) of short-term dividend claims, which can only partially be explained by high overall or downside betas, appears consistent with dividend strip prices being driven by bad beta.
3.4
Ex Ante Risk Premia
A dividend swap or dividend futures price for year n can be interpreted as the risk-adjusted expectation of the dividends that will be paid during year n . An alternative view is to perform the risk adjustment by applying an appropriate discount factor to the expected dividends (where the expectation is based on real-world probabilities). A position in the analyzed dividend derivatives does not require a cash outlay (apart from typically interest-bearing margin requirements). Therefore, the risk-free interest rate does not enter the equation and the dividend futures curve depends only on dividend growth expectation and risk premia. If the expected nominal growth in dividends exceeds the risk premium for this dividend stream, the curve is upward-sloping; if dividend growth is below risk premia, the dividend futures curve is downward-sloping. In their decomposition of equity yields, Binsbergen, Hueskes, Koijen, and
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Vrugt (2013) use a VAR model to predict dividend growth, which then allows to infer risk premiums. An alternative is to use a structural model for dividend growth. Lintner (1956) was able to explain the apparent stickiness in dividends by modeling current dividend payouts as a function of profitability and previous dividends, a methodology that is still widely and successfully used to model dividends on an aggregate basis (see for instance Skinner (2008) as well as Lambrecht and Myers (2012)). We implement a structural model for dividends to back out implied ex-ante risk premia of our dividend strategies. Thus, we gather data on historical dividends and earnings for all four regions (France and Germany are used as a proxy for the Eurozone) to estimate the following model for dividends: ∆DY (t ) = λ · DY (t −1) + β · E Y (t ) + εt ,
4
(3)
where DY (t ) are dividends of year t , E Y (t ) are earnings of year t and ∆DY (t ) = DY (t ) − DY (t −1) . For the US we use data from Professor Robert Shiller’s website, whereas we use price-to-earnings ratios, price-to-dividend ratios and price indices from Global Financial Data to construct the corresponding dataset for the other three regions. The annual sample starts in 1946 for the US and UK, in 1957 for Japan and in 1972 for France and runs through to the end of 2005 for all regions.5 Table 24 shows the regression results. To capture the short-term dynamics in the dividend growth rate gˆtD,Y (t −1),Y (t ) , we transform equaˆ and βˆ from table 24 to obtain predicted dividend growth from tion 3 and use estimated coefficients λ year Y (t − 1) to Y (t ): gˆtD,Y (t −1),Y (t )
ˆ + βˆ · =λ
E E Y (t )
DY (t −1)
(4)
Note that earnings that accumulate over year t are not yet known at the beginning of the year; thus we have to use expectations instead of realized numbers. Here we use consensus analysts’ estimates from Bloomberg as inputs. Similarly estimates for the following year’s dividend growth gˆtD,Y (t ),Y (t +1) can be calculated as E E Y (t +1) ˆ + βˆ · , gˆtD,Y (t ),Y (t +1) = λ E DY (t )
(5)
where we use consensus analysts’ estimates for index dividends of the current fiscal year as well as consensus analysts’ estimates for second-year earnings as the appropriate expectations. To estimate ˆ t ,Y (t ) inherent in the price of the first available dividend swap Ft ,Y (t ) note that the risk premium µ 4 This corresponds to the approach in Skinner (2008). However, we estimate the regression without intercept to avoid level dependence in dividend growth rates. 5 We estimate the Lintner regressions on a sample up to 2005, as our dividend swap data start in 2006. This way we ensure that we estimate ex-ante risk premia out of sample.
16
Ft ,Y (t ) =
E DY (t )
ˆ t ,Y (t ) 1+µ
,
(6)
which is equal to
Ft ,Y (t ) =
DY (t −1) · 1 + gˆtD,Y (t −1),Y (t ) ˆ t ,F Y (t ) 1+µ
,
(7)
and by rearranging terms the risk premium implied by the first year dividend swap reads as ˆ t ,Y (t −1),Y (t ) = µ
DY (t −1) · 1 + gˆtD,F Y (t −1),F Y (t ) − 1, Ft ,Y (t )
(8)
with gˆtD,F Y (t −1),F Y (t ) from equation 4. Similarly, it is possible to obtain estimates for the risk premium for dividends of year Y (t + 1), observed at t : ˆ t ,Y (t ),Y (t +1) = µ
Ft ,F Y (t ) Ft ,F Y (t +1)
· 1 + gˆtD,Y (t ),Y (t +1) − 1.
(9)
After having established our approach to estimate implied risk premia for single dividend swaps of given maturities we need to adapt the estimation to fit our constant maturity dividend strategy. Hence, we use a method similar to the calculation of bond yields to back out the appropriate risk premia. Recall that our strategy is implemented by combining current year and next year dividend swaps; w t Ft ,F Y (t ) + (1 − w t )Ft ,F Y (t +1) ; to achieve a constant maturity of dividend cash flows. The price of the replicating portfolio has to be (approximately) equal to the weighted average of current and next year dividend expectations discounted by the risk premium of the constant maturity portfolio µt ,t +1Y : w t DˆY (t ) (1 + µt ,t +1Y )(Y (t )−t )
+
(1 − w t )DˆY (t +1) (1 + µt ,t +1Y )(Y (t +1)−t )
= w t Ft ,F Y (t ) + (1 − w t )Ft ,F Y (t +1) .
(10)
As discussed before, dividend swaps are unfunded investments. Thus expected dividends must be discounted with risk premia, i.e. excess returns, as opposed to returns including both risk premia and the risk-free rate. Using our dataset of dividend swap prices and expected dividends from the Lintner model presented above we can back out the risk premium of the constant maturity dividend portfolio every week by calculating roots in equation 10. Figure 6 shows the dynamics of the short-duration equity risk premiums implied by dividend swap prices and Lintner-type dividend expectations. It is interesting to see that implied risk premia were low (even negative in the Eurozone) up to 2007. Coinciding with the emerging financial crisis they spiked tremendously to values near or above 100% p.a. While they have come down in the US and Japan, risk premia are still elevated in the Eurozone and the UK compared to the pre-crisis levels. Table 25 displays summary statistics of the risk premia for all markets. Median risk premia are fairly high and lie between 5.5% and 18.5%, while average values range between 12.8% and 21.6%. Ex-ante risk premia are lowest for the S&P 500 and highest for the FTSE. Standard deviations between 16.6% and 25% indicate that
17
risk premia (expected returns) vary substantially over time.
Figure 6: Risk Premia - This figure illustrates ex-ante risk premia implied by our one-year constant maturity dividend strategy. Expected dividends are extracted from a Lintner model and risk premia are backed out by calculating roots of equation 10. The risk premia presented are p.a. To calculate risk premia of the Euro Stoxx strategy we use the coefficients from the Lintner model for France.
After having presented our approach towards calculating ex-ante risk premia implied by dividend swap strategies, we investigate whether these implied risk premia are significantly related to realized excess returns of the constant maturity dividend strategies. Thus we perform the following regression: v,1 R tD,ti+1Y = α + β µt ,t +1Y + εt ,
18
(11)
v,1 where R tD,ti+1Y is the holding period (excess) return of the one-year constant maturity dividend strategy
from t to t plus one year, and µt ,t +1Y is the appropriate ex-ante risk premium. Put differently, at every point in time we calculate implied risk premia for the one-year constant maturity strategy and relate it to the realized (excess) return of the strategy over the following year. In order to perform the regression analysis at a weekly frequency we compute rolling annual returns. As this induces serial correlation in the residuals, we use p-values derived from Newey-West standard errors for statistical inference. Table 26 presents the regression results. Whereas intercepts are indistinguishable from zero, betas are economically large and significantly different form zero. The systematic relation between ex-ante risk premia and subsequent dividend holding period returns is smallest in magnitude for the US market, which is not surprising since the strategy performs worst compared to the benchmark in this market. For the other markets betas range between 0.5 and 0.6. On the basis of the reported values of R 2 implied risk premia explain realized returns reasonably well in our sample.
4
Conclusions
Drawing on recent evidence in the literature that the term structure of equity risk premia might slope downwards, we utilize a proprietary dataset on dividend swaps in four regions to implement a simple investment strategy. We create systematic long positions in the dividend swap market and rebalance the portfolio in such a way that investors have a constant remaining maturity to a risky dividend payoff. We construct this strategy for each of the four regions, both for a one and a five-year constant maturity and compare it to a benchmark strategy, which is a systematic long position in the underlying index via index futures. It turns out that the very short-maturity strategy outperforms the benchmark strategy in most regions on a risk-adjusted basis and in absolute terms. Moreover, we show that international correlations across regions are significantly lower for the short-maturity equity strategies than for the equity indices itself. Thus, we exploit the increased diversification benefits to construct an equally weighted global portfolio, which outperforms a traditional global equity portfolio in terms of the Sharpe ratio. To analyze whether international correlations increase in times of market distress we calculate conditional correlations, either conditioned on market returns or on a proxy for the macroeconomic environment. Correlations also increase for the shortmaturity equity strategies; they remain substantially lower than for the benchmark strategies even in times of market stress, though. To account for the possibility that observed excess returns of the dividend strategies are a pure risk premium for downside risk, we conduct regression analyses allowing for state-dependent market betas. We find that the systematic risk exposure to the underlying equity indices increases significantly if market returns are very negative. However, the short-maturity strategies generate significant alphas for most regions and also for the global portfolio. As an alternative way to capture nonlinear risk ex-
19
posures, we relate the returns of the short-maturity dividend strategies to risk factors derived from systematic put writing strategies, an approach usually applied for hedge fund returns. Risk loadings on the options-based risk factors seem to capture a substantial amount of the risk-adjusted outperformance of our strategies. Drawing on historical dividend data, we show that severe drawdowns in nominal dividends usually are associated with even more severe equity market drawdowns, mitigating the downside risk of short (constant) maturity equity strategies. We present an approach to estimate implied risk premia corresponding to the short-maturity dividend strategies using a Lintner model for dividend policy and consensus analysts’ forecasts for aggregate dividends and earnings. Those ex-ante risk premia spiked tremendously during the recent financial crisis. While they have come down in some markets, risk premia are still elevated in other markets. Over our sample implied risk premia are high, with median values between 5.5% and 18% and even higher magnitudes on average. Ex-ante risk premia also exhibit high volatility, indicating substantial time variation in expected returns of our strategies. Furthermore, we show that implied risk premia are significantly related to subsequently realized holding period returns of our strategies. Our results support recent asset pricing models that imply a downward-sloping term structure of equity risk premia. Moreover, the results extend the empirical evidence gained from implementing investment strategies exposing investors to short-maturity dividend claims by trading in index options. We motivate future steps in our analysis by potential risk-based explanations from asset pricing theory, in particular the separation of betas into cash flow and discount rate sensitivity. Moreover we are about to implement further investment strategies using traded dividend claims that are related to well established findings in the fixed income literature.
20
5
Tables
Mean
CMDS 1 St.dev. Sharpe
Mean
CMDS 5 St.dev. Sharpe
Mean
Benchmark St.dev. Sharpe
2006 2007 2008 2009
0.145 0.032 -0.285 0.465
0.054 0.065 0.285 0.137
2.665 0.496 -0.999 3.404
0.221 0.022 -0.758 0.453
0.150 0.125 0.360 0.321
1.476 0.172 -2.104 1.410
0.135 0.064 -0.469 0.283
0.144 0.147 0.399 0.296
0.939 0.437 -1.175 0.957
2010 2011 2012 2013
0.086 -0.004 0.107 0.154
0.086 0.108 0.096 0.027
1.001 -0.041 1.115 5.627
-0.068 -0.178 0.184 0.141
0.258 0.330 0.185 0.106
-0.263 -0.541 0.992 1.337
-0.000 -0.116 0.185 0.209
0.220 0.293 0.178 0.161
-0.001 -0.397 1.038 1.298
0.082
0.137
0.598
-0.010
0.259
-0.038
0.022
0.251
0.089
Overall
Table 1: Performance Statistics Euro Stoxx 50 - This table provides annualized mean returns, standard deviations and Sharpe ratios for the one and five-year constant maturity dividend strategies as well as for the benchmark strategy for every year in the sample and overall.
CMDS 1 Mean St.dev. Sharpe
CMDS 5 Mean St.dev. Sharpe
Benchmark Mean St.dev. Sharpe
2006 2007 2008 2009
0.114 -0.052 -0.168 0.415
0.061 0.077 0.207 0.151
1.856 -0.670 -0.811 2.758
0.241 -0.028 -0.634 0.444
0.135 0.147 0.353 0.292
1.782 -0.193 -1.794 1.518
0.076 0.032 -0.329 0.305
0.115 0.145 0.361 0.239
0.661 0.222 -0.911 1.277
2010 2011 2012 2013
0.041 0.056 0.115 0.186
0.093 0.057 0.034 0.041
0.437 0.994 3.428 4.482
0.110 -0.143 0.154 0.564
0.187 0.131 0.091 0.099
0.588 -1.090 1.684 5.700
0.138 -0.020 0.098 0.328
0.177 0.199 0.124 0.101
0.781 -0.100 0.789 3.251
Overall
0.080
0.111
0.722
0.050
0.210
0.237
0.059
0.205
0.286
Table 2: Performance Statistics FTSE - This table provides annualized mean returns, standard deviations and Sharpe ratios for the one and five-year constant maturity dividend strategies as well as for the benchmark strategy for every year in the sample and overall.
21
Mean
CMDS 1 St.dev. Sharpe
CMDS 5 St.dev. Sharpe
Mean
Mean
Benchmark St.dev. Sharpe
2006 2007 2008 2009
0.049 0.032 -0.234 0.168
0.101 0.075 0.207 0.115
0.482 0.431 -1.129 1.463
0.021 -0.024 -0.445 0.220
0.146 0.107 0.218 0.256
0.143 -0.225 -2.039 0.861
0.075 0.015 -0.423 0.305
0.097 0.142 0.349 0.258
0.768 0.108 -1.213 1.181
2010 2011 2012 2013
0.011 0.045 0.072 0.091
0.045 0.034 0.026 0.041
0.256 1.329 2.705 2.195
0.189 -0.022 0.110 0.358
0.134 0.150 0.081 0.089
1.417 -0.150 1.357 4.005
0.140 0.041 0.126 0.456
0.176 0.219 0.121 0.110
0.796 0.186 1.042 4.131
Overall
0.024
0.102
0.238
0.027
0.164
0.163
0.063
0.207
0.302
Table 3: Performance Statistics S&P 500 - This table provides annualized mean returns, standard deviations and Sharpe ratios for the one and five-year constant maturity dividend strategies as well as for the benchmark strategy for every year in the sample and overall.
CMDS 1 Mean St.dev. Sharpe
CMDS 5 Mean St.dev. Sharpe
Benchmark Mean St.dev. Sharpe
2006 2007 2008 2009
0.292 0.059 -0.366 0.326
0.176 0.067 0.167 0.186
1.652 0.870 -2.195 1.750
0.260 0.069 -0.961 0.286
0.228 0.119 0.272 0.332
1.142 0.582 -3.526 0.859
0.074 -0.104 -0.416 0.229
0.171 0.196 0.404 0.276
0.433 -0.534 -1.029 0.828
2010 2011 2012 2013
0.211 0.066 0.175 0.211
0.103 0.163 0.055 0.054
2.044 0.404 3.188 3.878
0.133 -0.060 0.399 0.924
0.212 0.252 0.158 0.128
0.628 -0.239 2.522 7.200
-0.005 -0.151 0.241 0.886
0.181 0.205 0.172 0.195
-0.028 -0.736 1.399 4.551
Overall
0.114
0.139
0.822
0.067
0.236
0.284
0.030
0.241
0.125
Table 4: Performance Statistics Nikkei - This table provides annualized mean returns, standard deviations and Sharpe ratios for the one and five-year constant maturity dividend strategies as well as for the benchmark strategy for every year in the sample and overall.
Euro Stoxx FTSE S&P Nikkei
Euro Stoxx
FTSE
S&P
Nikkei
1.00 0.64 0.33 0.14
0.64 1.00 0.28 0.18
0.33 0.28 1.00 0.32
0.14 0.18 0.32 1.00
Table 5: Correlations CMDS 1 Year - This table provides correlation across the four regions in our sample for the one-year constant maturity dividend stategy.
22
Euro Stoxx
FTSE
S&P
Nikkei
1.00 0.61 0.43 0.28
0.61 1.00 0.45 0.34
0.43 0.45 1.00 0.43
0.28 0.34 0.43 1.00
Euro Stoxx FTSE S&P Nikkei
Table 6: Correlations CMDS 5 Year - This table provides correlation across the four regions in our sample for the five-year constant maturity dividend stategy.
Euro Stoxx
FTSE
S&P
Nikkei
1.00 0.91 0.87 0.70
0.91 1.00 0.88 0.69
0.87 0.88 1.00 0.69
0.70 0.69 0.69 1.00
Euro Stoxx FTSE S&P Nikkei
Table 7: Correlations Benchmark - This table provides correlation across the four regions in our sample for the benchmark stategy.
CMDS 1 Mean St.dev. Sharpe
CMDS 5 Mean St.dev. Sharpe
Benchmark Mean St.dev. Sharpe
2006 2007 2008 2009
0.150 0.018 -0.263 0.344
0.059 0.046 0.163 0.098
2.547 0.389 -1.610 3.519
0.1856 0.0097 -0.6993 0.3506
0.108 0.100 0.220 0.218
1.712 0.097 -3.175 1.606
0.0900 0.0019 -0.4092 0.2803
0.115 0.141 0.360 0.243
0.784 0.013 -1.136 1.151
2010 2011 2012 2013
0.087 0.041 0.117 0.160
0.056 0.062 0.039 0.021
1.558 0.660 2.971 7.573
0.0912 -0.1010 0.2118 0.4969
0.164 0.168 0.102 0.069
0.557 -0.600 2.077 7.150
0.0681 -0.0615 0.1625 0.4699
0.170 0.209 0.126 0.120
0.400 -0.295 1.285 3.931
Overall
0.075
0.085
0.885
0.033
0.163
0.204
0.043
0.207
0.209
Table 8: Performance Statistics Global - This table provides annualized mean returns, standard deviations and Sharpe ratios for the one and five-year constant maturity dividend strategies as well as for the benchmark strategy for every year in the sample and overall.
Euro Stoxx FTSE S&P 500 Nikkei Global
Mean
CMDS 1 St.dev. Sharpe
Mean
CMDS 5 St.dev. Sharpe
Mean
Mean 0.080 0.078 0.022 0.112 0.073
St.Dev. 0.137 0.111 0.102 0.139 0.085
Mean -0.012 0.048 0.025 0.065 0.031
St.Dev. 0.259 0.210 0.164 0.236 0.163
Mean 0.021 0.058 0.062 0.029 0.042
Sharpe 0.584 0.704 0.218 0.807 0.861
Sharpe -0.046 0.228 0.150 0.275 0.192
Benchmark St.dev. Sharpe St.Dev. 0.251 0.205 0.207 0.242 0.207
Sharpe 0.085 0.281 0.297 0.121 0.205
Table 9: Performance Statistics with Transaction Costs - This table provides annualized mean returns, standard deviations and Sharpe ratios for the one and five-year constant maturity dividend strategies as well as for the benchmark strategy for the overall sample.
23
Euro Stoxx / FTSE Euro Stoxx / S&P Euro Stoxx / Nikkei FTSE / S&P FTSE / Nikkei S&P / Nikkei
Up
Down
Out-of-Phase
0.68 0.19 0.01 0.27 0.24 0.30
0.82 0.69 0.40 0.66 0.36 0.59
-0.36 -0.41 -0.61 -0.59 -0.61 -0.43
Table 10: Conditional Correlations CMDS 1 Year - This table provides conditional pairwise correlations for the one-year constant maturity strategy
Euro Stoxx / FTSE Euro Stoxx / S&P Euro Stoxx / Nikkei FTSE / S&P FTSE / Nikkei S&P / Nikkei
Up
Down
Out-of-Phase
0.40 0.10 0.05 0.31 0.16 0.33
0.77 0.61 0.38 0.58 0.42 0.35
-0.50 -0.61 -0.35 -0.48 -0.33 -0.39
Table 11: Conditional Correlations CMDS 5 Year - This table provides conditional pairwise correlations for the five-year constant maturity strategy
Euro Stoxx / FTSE Euro Stoxx / S&P Euro Stoxx / Nikkei FTSE / S&P FTSE / Nikkei S&P / Nikkei
Up
Down
Out-of-Phase
0.82 0.78 0.42 0.82 0.37 0.44
0.89 0.80 0.69 0.84 0.75 0.70
-0.67 -0.52 -0.59 -0.60 -0.57 -0.60
Table 12: Conditional Correlations Benchmark - This table provides conditional pairwise correlations for the benchmark strategy
Euro Stoxx / FTSE Euro Stoxx / S&P Euro Stoxx / Nikkei FTSE / S&P FTSE / Nikkei S&P / Nikkei
Up
Down
Out-of-Phase
0.47 0.21 0.17 0.14 0.08 0.20
0.71 0.41 0.11 0.38 0.24 0.46
0.58 0.21 0.29 0.17 0.33 0.22
Table 13: Correlations Conditional on ISM - CMDS 1 - This table provides conditional pairwise correlations for the one-year constant maturity strategy using ISM data as conditioning variable.
24
Euro Stoxx / FTSE Euro Stoxx / S&P Euro Stoxx / Nikkei FTSE / S&P FTSE / Nikkei S&P / Nikkei
Up
Down
Out-of-Phase
0.61 0.34 0.35 0.40 0.37 0.40
0.61 0.44 0.19 0.43 0.28 0.47
0.65 0.56 0.41 0.60 0.51 0.46
Table 14: Correlations Conditional on ISM - CMDS 5 - This table provides conditional pairwise correlations for the five-year constant maturity strategy using ISM data as conditioning variable.
Euro Stoxx / FTSE Euro Stoxx / S&P Euro Stoxx / Nikkei FTSE / S&P FTSE / Nikkei S&P / Nikkei
Up
Down
Out-of-Phase
0.88 0.84 0.60 0.87 0.56 0.61
0.94 0.91 0.81 0.91 0.79 0.80
0.87 0.81 0.50 0.85 0.59 0.53
Table 15: Correlations Conditional on ISM - Benchmark - This table provides conditional pairwise correlations for the benchmark strategy using ISM data as conditioning variable.
CMDS 1yr
Euro Stoxx
FTSE
S&P 500
Nikkei
Global
Alpha
0.0032*** 0.00097***
0.0019*** 8e-04***
0.0014*** 0.00078***
0.0048*** 0.0011***
0.0022*** 0.00056***
Beta
0.2809*** 0.0515***
0.2613*** 0.0512***
0.1282*** 0.0503***
0.0918*** 0.0582***
0.2673*** 0.0361***
Down-Beta
0.2271*** 0.0681***
0.1726*** 0.0755***
0.2153*** 0.0673***
0.3534*** 0.0787***
0.1772*** 0.0483***
No. obs Adj. R 2
384*** 0.3248***
384*** 0.1799***
384*** 0.1372***
384*** 0.1469***
384*** 0.3673***
Table 16: Beta Regressions 1 Year Constant Maturity - This table provides summary statistics for the beta regressions for four regions as well as for a global strategy. Asterisks denote significance at the 1%,5%,and 10 % level derived from a p-value of a Wald test for joint significance of the coefficient on the contemporaneous and the lagged return. Standard errors are presented below the coefficients in italics. Number of observations and R 2 are provided at the bottom.
25
CMDS 5yr
Euro Stoxx
FTSE
S&P 500
Nikkei
Global
Alpha
0.0033*** 0.0016***
0.0029*** 0.0014***
0.00057*** 0.0012***
0.0040*** 0.0018***
0.0018*** 0.00098***
Beta
0.6993*** 0.0826***
0.5378*** 0.0879***
0.4693*** 0.0787***
0.3869*** 0.0961***
0.6294*** 0.0634***
Down-Beta
0.4918*** 0.1093***
0.6175*** 0.1297***
0.1170*** 0.1054***
0.4152*** 0.1300***
0.3175*** 0.0847***
No. obs Adj. R 2
384*** 0.5113***
384*** 0.3168***
384*** 0.2026***
384*** 0.1939***
384*** 0.4744***
Table 17: Beta Regressions 5 Year Constant Maturity - This table provides summary statistics for the beta regressions for four regions as well as for a global strategy. Asterisks denote significance at the 1%,5%,and 10 % level derived from a p-value of a Wald test for joint significance of the coefficient on the contemporaneous and the lagged return. Standard errors are presented below the coefficients in italics. Number of observations and R 2 are provided at the bottom.
CMDS 1yr
Euro Stoxx
FTSE
S&P 500
Nikkei
Global
Alpha
3e-04*** 0.00077***
0.0012*** 0.00092***
-0.00033*** 0.00066***
0.0018*** 0.00094***
0.00064*** 0.00048***
Beta
-0.0962*** 0.0746***
0.2728*** 0.0884***
0.0446*** 0.0723***
0.1577*** 0.0741***
0.1352*** 0.0533***
Option-Beta
1.4168*** 0.1855***
0.2224*** 0.2126***
0.6108*** 0.1929***
0.3464*** 0.1794***
0.6239*** 0.1303***
No. obs Adj. R 2
384*** 0.3976***
294*** 0.1901***
384*** 0.1866***
384*** 0.1093***
384*** 0.3924***
Table 18: Sensitivity to Option Strategies - This table provides regression results in which we relate the returns of the one-year constant maturity dividend strategies to the return of the benchmark indices and the returns to systematic out-of-the money put writing strategies on the corresponding equity indices. The option strategies sell each week 5% out-of-the money puts on the equity index with one-month maturity and hold it for one week. In the following week the put is bought back and a new 5% out-of-the money put is sold. Implied volatilities are taken from Bloomberg and put prices are calculated using the Black-Scholes formula with continuous dividends. Asterisks denote significance at the 1%,5%,and 10 % level derived from a p-value of a Wald test for joint significance of the coefficient on the contemporaneous and the lagged return. Standard errors are presented below the coefficients in italics. Number of observations and R 2 are provided at the bottom.
26
Dividend Change
Index Change
Payout Change
0.183 -0.041 -0.022 -0.006 -0.022 0.065 0.022 0.086 -0.025 -0.033 0.021 0.082 -0.211
-0.156 0.257 -0.095 -0.115 0.035 -0.188 -0.245 -0.131 0.142 -0.063 -0.146 -0.214 -0.372
-0.148 0.060 0.074 0.065 -0.073 -0.009 0.057 -0.018 -0.021 0.312 -0.055 -0.226 -0.646
1947 1951 1958 1970 1971 1974 1975 1978 2000 2001 2002 2003 2009
Table 19: Historical Price and Dividend Changes US - This table illustrates one-year changes in nominal dividends paid in the US, one-year equity index returns and one-year changes in the payout ratio for those years in the post World War II sample where either the price return or the dividend change was below the 10% quantile. The sample is based on data from Prof. Shiller’s website: http://aida.wss.yale.edu/ shiller/data.htm.
1947 1949 1958 1969 1974 1976 1987 1990 2001 2002 2005 2008 2009 2010
Dividend Change
Index Change
-0.176 1.388 -0.090 -0.151 0.084 -0.081 0.101 0.105 0.018 -0.060 -0.185 0.024 -0.151 -0.077
-0.027 -0.206 -0.141 0.266 -0.308 -0.170 -0.294 -0.254 -0.209 -0.311 0.253 -0.431 0.239 0.004
Table 20: Historical Price and Dividend Changes France - This table illustrates one-year changes in nominal dividends paid in France and one-year equity index returns in France for those years in the post World War II sample where either the price return or the dividend change was below the 10% quantile. The data source is Global Financial Data.
27
1962 1970 1972 1973 1983 1987 1995 2002 2003 2008 2009 2010
Dividend Change
Index Change
0.049 0.153 -0.124 -0.028 -0.071 0.013 -0.166 -0.385 -0.096 0.192 -0.171 -0.072
-0.241 -0.246 0.132 -0.195 0.360 -0.372 0.026 -0.410 0.340 -0.444 0.203 0.151
Table 21: Historical Price and Dividend Changes Germany - This table illustrates one-year changes in nominal dividends paid in Germany and one-year equity index returns in Germany for those years in the post World War II sample where either the price return or the dividend change was below the 10% quantile. The data source is Global Financial Data.
1962 1963 1967 1969 1973 1974 1990 1993 1999 2000 2001 2002 2008 2009
Dividend Change
Index Change
-0.100 -0.125 -0.052 0.035 0.093 0.086 0.083 -0.037 -0.120 -0.032 -0.002 0.013 -0.001 -0.109
-0.018 0.106 0.290 -0.152 -0.314 -0.553 -0.143 0.233 0.212 -0.080 -0.154 -0.250 -0.328 0.250
Table 22: Historical Price and Dividend Changes UK - This table illustrates one-year changes in nominal dividends paid in the UK and one-year equity index returns in the UK for those years in the post World War II sample where either the price return or the dividend change was below the 10% quantile. The data source is Global Financial Data.
28
Dividend Change
Index Change
-0.235 0.037 -0.100 -0.154 0.131 -0.091 0.284 -0.109 0.005 -0.108 0.005 -0.141 0.109
-0.024 -0.237 0.235 0.109 -0.398 -0.011 -0.237 -0.255 -0.196 -0.183 -0.418 0.056 -0.189
1964 1973 1978 1987 1990 1991 1992 2000 2001 2002 2008 2009 2011
Table 23: Historical Price and Dividend Changes Japan - This table illustrates one-year changes in nominal dividends paid in Japan and one-year equity index returns in Japan for those years in the post World War II sample where either the price return or the dividend change was below the 10% quantile. The data source is Global Financial Data.
ˆ λ βˆ No. obs Adj. R 2
France
Germany
UK
US
Japan
-0.1563*** 0.0991***
-0.1416*** 0.0699***
-0.1859*** 0.1285***
-0.0674*** 0.0485***
-0.0960*** 0.0466***
34*** 0.1240***
34*** 0.0529***
60*** 0.5232***
60*** 0.7045***
49*** 0.1688***
Table 24: Lintner Model - This table provides the OLS estimation output of a Lintner dividend model on annual data for the relevant regions through the end of 2005 as in equation 3. Asterisks denote significance at the 1%,5%,and 10% level. Number of observations and R 2 are provided at the bottom.
Euro Stoxx
FTSE
S&P 500
Nikkei
Mean Median
0.1660 0.1125
0.2168 0.1842
0.1285 0.0554
0.1557 0.0750
St.Dev.
0.2451
0.1936
0.1662
0.2501
-0.1270 1.4745
-0.0453 1.2804
-0.0280 0.8581
-0.1071 1.0721
Min Max
Table 25: Ex-Ante Risk Premia - This table provides summary statistics for ex-ante risk premia of the constant one-year dividend strategies for all four markets. Expected dividends are derived from a Lintner model as elaborated on in section 3.4 and risk premia are calculated as roots in equation 10. Figures are displayed as decimal numbers, so median risk premia lie between 5.5% and 18% p.a.
29
Euro Stoxx
FTSE
S&P 500
Nikkei
-0.0014*** 0.0721***
-0.0689 *** 0.0404***
-0.0216*** 0.0734***
0.0125*** 0.1327***
Beta RP
0.5015*** 0.0957***
0.6545*** 0.0949***
0.2800 *** 0.1181***
0.5972*** 0.1934***
Adj. R 2 No. Obs.
0.5098 *** 332 ***
0.6233*** 332***
0.1967*** 332***
0.4523 *** 332 ***
Intercept
Table 26: Ex-Ante Risk Premia vs. Ex-Post Returns - This table reports results from regressing rolling annual realized (excess) returns of the one-year constant maturity dividend strategy on implied ex-ante risk premia. Realized returns are lagged by one-year so that for every (weekly) observation implied risk premia correspond to the realized annual return of the year subsequent to the observation. Since rolling returns induce serial correlation in the residuals Newey-West standard errors are reported below the coefficients. Asterisks denote significance at the 1%,5%,and 10 % level derived from standard errors based on a covariance matrix robust to serial correlation and heteroscedasticity (Newey-West).
30
References Bansal, Ravi, and Amir Yaron, 2004, Risks for the Long Run: A Potential Resolution of Asset Pricing Puzzles, Journal of Finance 59, 1481–1509. Belo, Frederico, Robert Goldstein, and Pierre Collin-Dufresne, 2013, Dividend Dynamics and the Term Structure of Dividend Strips, Journal of Finance forthcoming. Binsbergen, Jules, Michael W. Brandt, and Ralph S.J. Koijen, 2012, On the Timing and Pricing of Dividends, American Economic Review 102, 1596–1618. Binsbergen, Jules, Wouter Hueskes, Ralph Koijen, and Evert B. Vrugt, 2013, Equity Yields, Journal of Financial Economics 110, 503–519. Boguth, Oliver, Murray Carlson, Adlai Fisher, and Mikhail Simutin, 2013, Leverage and the Limits of Arbitrage Pricing: Implications for Dividend Strips and the Term Structure of Equity Risk Premia, Working Paper. Brennan, Michael, 1998, Stripping the S&P 500 Index, Financial Analysts Journal 54, 12–22. Campbell, John, and John Cochrane, 1999, By Force of Habit: A Consumption-Based Explanation of Aggregate Stock Market Behavior, The Journal of Political Economy 107, 205–251. Campbell, John, and Tuomo Vuolteenaho, 2004, Bad Beta, Good Beta, American Economic Review 94, 1249–1275. Derwall, Jeroen, Joop Huij, and Gerben de Zwart, 2009, The Short-Term Corporate Bond Anomaly, Working Paper. Dimson, Elroy, 1979, Risk measurement when shares are subject to infrequent trading, Journal of Financial Economics 7, 197–226. Duffee, Gregory, 2010, Sharpe ratios in term structure models, Working Paper. Erb, Claude, Campbell Harvey, and Tadas Viskanta, 1994, Forecasting International Equity Correlations, Financial Analysts Journal 50, 32–45. Fung, William, and David Hsieh, 2001, The Risk in Hedge Fund Strategies: Theory and Evidence from Trend Followers, Review of Financial Studies 14, 313–341. Gabaix, Xavier, 2012, Variable Rare Disasters: An Exactly Solved Framework for Ten Puzzles in MacroFinance, Quarterly Journal of Economics 127, 645–700. Herold, Ulf, Raimond Maurer, and Nader Purschaker, 2005, Total return fixed-income portfolio management., Journal of Portfolio Management 31, 32 – 43. Koijen, Ralph, Tobias Moskowitz, Lasse Pedersen, and Evert Vrugt, 2013, Carry, Working Paper. 31
Lambrecht, Bart M., and Stewart C. Myers, 2012, A lintner model of payout and managerial rents., Journal of Finance 67, 1761 – 1810. Lettau, Martin, Matteo Maggiori, and Michael Weber, 2014, Conditional Risk Premia in Currency Markets and other Asset Classes, Journal of Financial Economics forthcoming. Lettau, Martin, and Jessica Wachter, 2007, Why is Long-Horizon Equity Less Risky? A Duration-Based Explanation of the Value Premium, Journal of Finance 62, 55–92. Lintner, John, 1956, Distribution of incomes of corporations among dividends, retained earnings, and taxes, The American Economic Review 46, 97–113. Manley, Richard, and Christian Mueller-Glissmann, 2008, The Market for Dividends and Related Investment Strategies, Financial Anaylsts Journal 64, 17–29. Mitchell, Mark, and Todd Pulvino, 2001, Characteristics of Risk in Risk Arbitrage, Journal of Finance 56, 2135–2175. Naik, Narayan, and Vikas Agarwal, 2004, Risk and Portfolio Decisions Involving Hedge Funds, Review of Financial Studies 17, 63–98. Skinner, Douglas, 2008, The evolving relation between earnings, dividends, and stock repurchases, Journal of Financial Economics 87, 582–609.
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A
OTC Dividend Swaps versus Listed Dividend Futures
Figure 7: OTC Dividend Swaps vs. Listed Dividend Futures - This figure compares the performance of the one-year constant maturity dividend strategy using two different investment vehicles. The solid line is implemented using OTC dividend swaps, which are the basis of all the analyses in this paper. As a robustness check we implement the equivalent strategy using listed dividend futures (dashed lines). Note that currently there aren’t any dividend futures listed for the S&P 500. Listed dividend futures for the Euro Stoxx 50 are available starting mid 2008; for the FTSE starting mid 2009 and for the Nikkei starting mid 2010. The total excess return indices for the listed dividend futures have been rebased so that they match the index value of the OTC index at the date when listed contracts were first available for the respective market. The "listed" strategies run through April 2014, while our OTC sample ends mid 2013.
Our sample of dividend swap prices is a proprietary data set, however, there are also listed dividend futures available for some markets. Thus, we implement the one-year constant maturity dividend strategy also using listed dividend futures as a robustness check. At the time of writing, listed dividend 33
futures are only available for three out of four markets considered in this paper (not yet in the US). Figure 7 illustrates the comparison of the strategies using both OTC dividend swaps and listed dividend futures. Note that listed dividend futures are available for the Euro Stoxx 50 starting mid 20086 , for the FTSE starting mid 2009 and for the Nikkei starting mid 2010. As revealed by figure 7 the difference between the two investment vehicles is negligible for the Euro Stoxx 50 and the FTSE. For the Nikkei the listed strategy performs worse than the OTC strategy by a small margin. However, Nikkei dividend futures are less liquid in terms of trading volume than either Euro Stoxx 50 or FTSE dividend futures. So we consider the OTC data to be more reliable for the Nikkei. Moreover, the listed Nikkei strategy still outperforms the benchmark strategy substantially. In conclusion, the limited data on listed dividend futures confirms the findings of this paper, which we derived by employing a proprietary sample of OTC dividend swaps.
B
Beta Regressions for Other Maturities
The following tables provide results on the beta regressions for 2,3 and 4 year constant maturity dividend strategies. CMDS 2yr
Euro Stoxx
FTSE
S&P 500
Nikkei
Global
Alpha
0.0045*** 0.0014***
0.0029*** 0.0012***
0.00074*** 0.0011***
0.0051*** 0.0017***
0.0026*** 0.00086***
Beta
0.5130*** 0.0729***
0.4305*** 0.0761***
0.3230*** 0.0691***
0.2037*** 0.0890***
0.4541*** 0.0555***
Down-Beta
0.5034*** 0.0963***
0.5203*** 0.1123***
0.1731*** 0.0925***
0.4982*** 0.1204***
0.3739*** 0.0742***
No. obs Adj. R 2
384*** 0.4588***
384*** 0.2953***
384*** 0.1669***
384*** 0.1595***
384*** 0.4522***
Table 27: Beta Regressions 2 Year Constant Maturity - This table provides summary statistics for the beta regressions for four regions as well as for a global strategy. Asterisks denote significance at the 1%,5%,and 10% level derived from a p-value of a Wald test for joint significance of the coefficient on the contemporaneous and the lagged return. Standard errors are presented below the coefficients in italics. Number of observations and R 2 are provided at the bottom. 6
For the Euro Stoxx 50 BofA Merrill Lynch launched a one-year constant maturity dividend index in 2013, which can be tracked using its Bloomberg ticker MLEIDVD1.
34
CMDS 3yr
Euro Stoxx
FTSE
S&P 500
Nikkei
Global
Alpha
0.0041*** 0.0015***
0.0030*** 0.0013***
0.00069*** 0.0011***
0.0044*** 0.0018***
0.0023*** 0.00092***
Beta
0.6108*** 0.0788***
0.4854*** 0.0809***
0.4073*** 0.0708***
0.3338*** 0.0958***
0.5602*** 0.0590***
Down-Beta
0.5388*** 0.1041***
0.6092*** 0.1193***
0.1587*** 0.0948***
0.4262*** 0.1296***
0.3609*** 0.0788***
No. obs Adj. R 2
384*** 0.4921***
384*** 0.3236***
384*** 0.2086***
384*** 0.1722***
384*** 0.4846***
Table 28: Beta Regressions 3 Year Constant Maturity - This table provides summary statistics for the beta regressions for four regions as well as for a global strategy. Asterisks denote significance at the 1%,5%,and 10% level derived from a p-value of a Wald test for joint significance of the coefficient on the contemporaneous and the lagged return. Standard errors are presented below the coefficients in italics. Number of observations and R 2 are provided at the bottom.
CMDS 4yr
Euro Stoxx
FTSE
S&P 500
Nikkei
Global
Alpha
0.0036*** 0.0016***
0.0031*** 0.0013***
0.00064*** 0.0011***
0.0042*** 0.0018***
0.0021*** 0.00095***
Beta
0.6654*** 0.0827***
0.5018*** 0.0847***
0.4278*** 0.0738***
0.3852*** 0.0961***
0.5963*** 0.0613***
Down-Beta
0.5142*** 0.1093***
0.6445*** 0.1250***
0.1437*** 0.0988***
0.4256*** 0.1300***
0.3566*** 0.0819***
No. obs Adj. R 2
384*** 0.4979***
384*** 0.3244***
384*** 0.2043***
384*** 0.1946***
384*** 0.4879***
Table 29: Beta Regressions 4 Year Constant Maturity - This table provides summary statistics for the beta regressions for four regions as well as for a global strategy. Asterisks denote significance at the 1%,5%,and 10% level derived from a p-value of a Wald test for joint significance of the coefficient on the contemporaneous and the lagged return. Standard errors are presented below the coefficients in italics. Number of observations and R 2 are provided at the bottom.
35
