Equity duration: a dividend yield approach...1 Equity duration: a dividend yield approach May, 23,...

OSSIAM RESEARCH TEAM

Equity duration: a dividend yield approach

May, 23, 2016

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Equity duration: a dividend yieldapproach

May, 23, 2016

Abstract

Carmine De Franco, PhDQuantitative [email protected]

Bruno Monnier, CFAQuantitative [email protected]

Ksenya Rulik, PhD, CFAHead of Quantitative [email protected]

We look at the exposure of stock portfolios - sorted by dividendyields - to interest rate risk and determine if this can explain differ-ences in risk and risk-adjusted performances between low and highdividend yield portfolios over a 25-year period for US equities. Asfor volatility sorted portfolios, we do find small but positive dura-tion for high dividend yield portfolios. Nevertheless, the additionof the interest rate factor brings little explanatory power to the4-Factor model and does not explain the alphas away. Becauseof the similarities in the results between volatility and dividendyield sorted portfolios with respect to interest rate risk, we try tohighlight any potential overlap between the two. More precisely,we build double sorted volatility portfolios in a way that neutral-izes the dividend yield difference between them. The model nowfits the portfolios’ returns better than the pure volatility sortedcase. The duration for lower (double sorted) volatility portfoliosis almost 38% lower than the pure case, although the alphas arenot explained away and remain significant. These findings shedlight on the existing link between low volatility and high dividendyield portfolios, for which there is a substantial overlap. As such,a significant portion of low volatility duration can be attributedto their high dividend yield characteristic.

JEL Classification: : C41, C52, G11, G12Key words: CAPM; Dividend investing; Equity duration; Fama-French equity model; Low volatility investing;


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1 Introduction

With the US interest rates at their lowestover the latest 50 years, the search for yieldhas oriented many investors towards stockswith high dividend yields. As a matter offact, several strategies focusing on dividendyields are now available to investors in anindex format, but not only. One possibil-ity for investors could be to gain exposureto dividend paying stocks in order to mone-tize a portion of their portfolio’s value whilekeeping their exposure to equity market.In this sense, investors actually keep theirexposure until the company pays its divi-dend and then decide to keep or remove itfrom their allocation. Different reasons canbe advocated to explain such investmentstrategies, among which tax-related issuesor the need for regular cash-flows. On theother hand, dividend yield has been usedin the literature as a forward-looking mea-sure of equity premium. This problem hasbeen extensively studied and goes beyondthe scope of this paper. We refer to theseminal works in Fama and French (1988),Fama and French (1988b) and referencestherein for the dividend yields predictivepower of the equity premium. Togetherwith default spread and term spread, it hasbeen one of the economic variables usedto explain variations in stocks expected re-turns. Campbell and Shiller (1988) insteadlook at the relationship between historicalearnings and real dividend, and as a con-sequence, to the relation between dividendyields and expected future returns. A sec-ond possibility for investors, following thisapproach, could then be to gain exposureto high dividend yield stocks in order toimprove their portfolio’s expected return.In this sense, they do not need to waituntil the company actually pays the divi-

dend before removing the stock from theirportfolio: provided that today’s dividendgives information about future prices, thistype of strategy mostly looks at the po-tential of upward price movements carriedby dividend figures. It seems that moderntheories have reached a sort of consensuson the fact that dividend yield is one ofthe quantitative measure to be looked atwhen it comes to set equity valuation mod-els1. However, as an indicator, the divi-dend yield is particularly business-cycle re-lated. Its forecasting power varies acrossthe business cycle (Rozeff, 1984): it tendsto correlate with the expected returns instrong economic conditions and worsen inrestrictive economic conditions (Jensen andJohnson, 1995). As a consequence, the re-lation between expected returns and div-idend yields weakens or strengthens, in-ter alia, according to the monetary pol-icy (Rozeff, 1974). More precisely, actualdividend yields can forecast expected re-turns conditionally to the monetary policyand interest rate movements (Jensen et al.,1996).

In this paper we focus on the empir-ical relationship between dividend yieldsand interest rates. Specifically we look atthe relationhip between expected returns ofportfolios based on different levels of divi-dend yields and interest rate movements.Although the literature on the dividendyield puzzle is an old and well documentedtopic, very little has been said over the rela-tion between interest rates and equity div-idend yields. Cohen (2003) studies the re-lationship between dividend yield, empiri-cal durations and forward-looking measures

1The position has changed since the seminalworks in Modigliani and Miller (1958), in whichdividends, and more generally capital structure,should not be accounted for when investors valueequities.


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of equity premium from the perspective ofequity valuation. According to his conclu-sions, the equity duration has an impact onfuture returns, but historical and forward-looking equity premium should never expectto converge as long as market and, sub-sequently, interest rates behave erratically.As pointed out in De Franco et al. (2015),measuring empirical equity duration for eq-uity is a complex operation. With respectto fixed income securities, duration, definedas the sensitivity of the security price tointerest rate movements, is not easily com-puted. The reason stands behind the riskassociated with expected cash flows linkedto the type of security. For fixed incomesecurities, cash-flows are known and thereis little risk that these cash-flows are im-pacted by macro-economic factors. So theonly risk investors carry when investingin fixed income securities is the time theyneed to recover the investment2. Mechani-cally, the longer the investor needs to wait,the more the security price is impacted bymovements in interest rates. On the otherside, for equities, the puzzle is complicatedby the fact that cash-flows (dividends) arenot known in advance and can change ac-cording to future macro-economic condi-tions. Company management can decideto reduce the dividend if economic condi-tions worsen, or can decide to pay a div-idend to maintain flows from investors orattract new investors. Dividend is also achoice of opportunity for a company, whomay decide to distribute to its investors ifthe management does not believe in theinvestment opportunities available to thecompany within some specific market con-ditions. These few examples show how dif-

2We do not consider here the credit risk associ-ated with fixed income securities, which of courseplays a role in the total risk investors carry

ficult can be to forecast the equity cash-flow streams since they strongly depend onthe economic conditions (Jensen and John-son, 1995). Both components (time andamount) of equity cash flows have then dif-ferent impacts on equity prices. For lowduration stocks, the equity risk is mainlyshort-term - as by definition they are sup-posed to repay the investors in the shortterm. As a consequence, the equity risk isdriven by market shocks on the cash-flows(expected or unexpected), such as profitwarning or dividend below market consen-sus. For these stocks, the interest rate riskis secondary as the total risk is captured bymarket risk and company’s specific idiosyn-cratic risk. For high duration stocks thepicture is somehow symmetric: short-termconditions should have relatively small im-pact as the expected cash flows are sched-uled in the long term. In this case, marketshocks have less impact on the stock pricesbut future movements in interest rates im-pact future cash-flows and, mechanically,today’s valuations. In distressed marketconditions, low duration stocks should ap-pear riskier than high duration ones, astoday’s cash flows are impacted. On theother side, in growing market conditionscoupled with increasing rates, high dura-tion stocks should appear riskier than lowduration stocks. This mechanism remainsvalid as long as the dividend stream is con-stant (or at least predictable). Since com-panies can manage their dividend policyand determine if, when and how to dis-tribute, the relation between market con-ditions, interest rates and dividend yieldsbecomes rapidly complicated. In this paperwe will not review or introduce new modelsthat may mimic the relationship betweeninterest rates, dividend yields and marketconditions. We will rather concentrate on


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two specific questions that can give an ideaof the type of relationship we may expectfrom the data:

Statement 1 Do high dividend yieldstocks carry a hidden interest raterisk?

Statement 2 Can the differences in div-idend yields across volatility-sortedportfolios explain the small but posi-tive duration for low volatility stocksfound in De Franco et al. (2015)?

Using US market data over the period1990-2014, we build ten portfolios basedon dividend yields and run classical regres-sion over a 4-Factor model (Market, Size,Value and Momentum) with the additionof an interest rate risk factor. We showthat when it comes to fit the historical data,the addition of the interest rate risk fac-tor does not bring significant explanatorypower to the 4-Factor model and fails to ex-plain the alphas away. In contrast, with thesame exercise with volatility (De Franco etal., 2015), we find here the 4-Factor modelgood enough to explain the cross-sectionalequity total variance. High dividend yieldsportfolios show significant positive alphasand a small but positive duration (around2). We recall it was between 1.5 and 1.8for low-volatility portfolios in De Franco etal. (2015). For the first statement then wedo not see from the data a significant inter-est rate risk for high dividend yields portfo-lios. Even if duration is found positive andsignificant, the majority of portfolios’ riskis explained by the 4-Factor model. Du-rations are similar to those found for lowvolatility portfolios, but we have here amodel with a sufficient explanatory power.In the second part of the paper we look intothe relationship between low volatility andhigh dividend yields portfolios. They both

show small but positive durations; mid-high dividend yields portfolios show lowervolatility compared to low dividend yieldsportfolios; similarly, low volatility portfo-lios show higher dividend yields comparedto high volatility ones. As pointed out inDe Franco et al. (2015), one of the reasonsfor the small but positive duration of lowvolatility portfolios is their historical highexposure to the Utility sector. Here we pro-pose a second approach by testing whetherthe low volatility portfolios inherit dura-tion because of their high dividend yields.More precisely we show that duration forlow volatility portfolios decreases from 1.8to 1.1 (38% circa in relative terms) when weneutralize the dividend yield components.In other words, a substantial proportionof the empirical duration of low volatilitystocks comes from the fact that, histori-cally, they have also been high dividendyields stocks.

2 Description of the invest-ment universe

The dataset is the same as defined inDe Franco et al. (2015). Portfolios arebuilt with US stocks belonging to the S&P500 Index from January 1990 to Decem-ber 2014. The 4-Factor time series (Market(MKT), Size (SMB), Value (HML) and Mo-mentum (UMD)) are taken from the Ken-neth French website. We refer to Famaand French (1993) and Carhart (1997) forfurther details on the construction andproperties of these factors. The InterestRate risk factor is proxied by the 10-yearUS Treasury bond yields, specifically theGeneric United States on-the-run govern-ment (annual) yield on 10Y maturity in-struments (Bloomberg ticker USGG10YRIndex ). Starting from the set of stocks in


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Annualized Annualized Max Sharpe CAPM CAPM DividendReturn Volatility Drawdown ratio Beta Alpha yield

Decile1 12.34% 23.97% -65.44% 0.38 1.36 -2.17% 0.12%Decile2 12.86% 20.88% -61.15% 0.46 1.26 -0.86% 0.30%Decile3 13.64% 18.67% -57.96% 0.55 1.12 1.08% 0.87%Decile4 12.92% 16.86% -51.23% 0.57 1.02 1.15% 1.34%Decile5 13.41% 16.49% -54.85% 0.61 0.97 2.12% 1.75%Decile6 13.47% 17.10% -59.28% 0.59 0.98 2.05% 2.04%Decile7 13.98% 15.84% -47.12% 0.67 0.91 3.11% 2.45%Decile8 13.97% 15.11% -39.13% 0.70 0.85 3.61% 2.92%Decile9 12.49% 16.42% -63.39% 0.56 0.92 1.54% 3.51%Decile10 12.50% 16.07% -62.47% 0.57 0.73 3.15% 4.88%

Table 1: Performance statistics of dividend yields portfolios.Source S&P, Datastream. Data from Jan, 31,1990 to Dec, 31,2014. The Sharpe Ratio is computed with a risk-free rate over the period of 3.34%.

the S&P 500 Index, we build ten equally-weighted portfolios based on stock dividendyields. To avoid jumps in yields when thedividend is paid, we adjust dividend yieldson a daily basis, as if the company wouldpay a (small) amount of dividend each day.More in details, for a given stock, let Pt bethe stock price at time t, and define (tk, Dk)the sequence of all dividends amounts Dk

paid by the company at time tk. We definethen the daily dividend yield as follows

dYt :=Dk

Ptk

1

nk

where tk is chosen to verify tk ≤ t < tk+1

and nk is the number of business days be-tween tk and tk+1. Even if this measuredepends on tk+1, i.e. the next dividenddate, it is not completely forward-looking:for the majority of companies, next divi-dend dates are known in advance. Shouldthis not be the case, using nk = constantcould be an alternative, if we assume that,for the US large cap stocks, quarterly divi-dend payments is the standard. The annualdividend yield is then computed as the sum

of the past 250 daily yields:

DYt =t∑

u=t−249

dYu

Under this measure, the stock’s dividendyield is smoothed over time. Stocks thathave not yet paid any dividends are as-signed dYt = 0. The first portfolio (Decile1) contains those stocks that have not paidregular dividends or have done so only asspecial dividends (those for which DYt =0). Decile 2 contains stocks with the low-est dividend yields and Decile 10 with thehighest dividend yields. Portfolios are re-balanced monthly, each third Friday of themonth. Net dividends are invested in eachportfolio following S&P methodology. Ta-ble 1 collects basic portfolios’ statistics overthe last 25 years. We do not notice anyclear pattern in the ex-post returns whensorting stocks by dividend yields, even ifmid-high dividend yields portfolios (Decile6, 7, and 8) show higher returns thanlow dividend yields or no paying portfo-lios (Decile 1 or 2). Deciles 7 and 8 showthe lowest volatility, although volatility lev-els are quite stable from Decile 4 to 10.


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Figure 1: Performance statistics of dividend yields deciles.Source S&P, Datastream. Data from Jan, 31,1990 to Dec, 31,2014. The Sharpe Ratio is com-puted with a risk-free rate over the period of3.34%.

Sharpe ratio is almost monotonically in-creasing from Decile 1 to Decile 8 whereit peaks and then decreases. The fact thatSharpe ratio is at its highest in the mid-high deciles (Figure 1) is partially expected.In general low dividend paying companiesare more of growth stocks with high volatil-ity. On the other side, in higher decileswe potentially include troubled companies,showing high dividend yields because ofsevere drops in their prices. This is be-cause in our calculation we do not includeforward looking dividend yield. As a re-sult, the deciles at both ends shows lowerSharpe ratios. By sorting stocks accord-ing to their past volatility, De Franco etal. (2015) found a decreasing relationshipbetween volatility and dividend yields: lowvolatility portfolios showed 2.71% annualdividend yield compared to only 0.39% forthe high volatility one. To a lesser extent,this is confirmed in Table 1, where volatilitydecreases (even if not monotonically) whiledividend yields increase.

MKT SMB HML UMD

SMB 0.25***HML -0.25*** -0.33***UMD -0.25*** 0.05*** -0.14***

IR -0.10** -0.20*** 0.04*** 0.19***

Table 2: Correlation matrix of the factors in theregression model (3.1). Significance:*** = 1% ** = 5% * = 10%. Nostars = correlation not significant

3 Multi-factor model de-scription

To assess potential relationship betweendividends and interest rate risk, we usethe 4-Factor Fama-French-Carhart (FFC)model completed with the interest rate fac-tor:

rDecileit =α+ βMKT MKTt (3.1)

+βSMB SMBt + βHMLHMLt

+βUMD UMDt + βIR IRt + εt

The portfolio returns rDecilei together withthe FFC factors are observed monthly atthe last business day. IR is the monthlytime series of 10-Year US Treasury bondyields variations.Since we want to interpret the loadingβIR as an empirical equity duration, wemultiply yield changes by -1:

IRt = US10Yt−1 − US10Yt;

Consequently positive loading means thatthe portfolio return decreases when inter-est rates increase.The correlation matrix of our explanatoryfactors is given in Table 2. Note that thefactors show significant correlation duringthe time period of our analysis. In particu-lar, the SMB and HML factors, designed to


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be weakly correlated, show significant neg-ative correlation. Moreover, our proxy forthe interest rate factor has significant neg-ative correlation of -0.20 to the SMB fac-tor, significant positive correlation of 0.19with the UMD factor and significant, evenif with less precision, negative correlationof -0.10 with the market factor.Thus, the model can potentially suffer frommulticollinearity, which can result into ar-tificially high loadings for some factors. Wewill address these issues in the followingsections.

4 Empirical results

We start by testing the explanatory powerof the FFC model. Table 3 collects the re-sults of a classical linear regression for thedividend-deciles monthly returns over theFFC model without the addition of the in-terest rate risk factor (i.e. model (3.1) withβIR = 0) over the last 25 years.Compared with volatility portfolios in DeFranco et al. (2015), we notice that the 4-Factor model is able to explain the major-ity of the risks and the performances of ourten portfolios based on dividend yields. Asa matter of fact, R2 is above 80% for alldeciles except for Decile 10 (74.84%). Lowdividend yields deciles are characterized bymarket beta higher than 1 and tend to beSmall (positive exposure to SMB). Highdividend yields deciles instead have mar-ket beta lower than 1, they are negativelyexposed to Size and positively exposed toValue. They tend to be large and valuecompanies with stable dividend yields. Aswe already explained, Decile 10 may con-tain distressed companies that show abnor-mal high dividend yields. For these compa-nies, the idiosyncratic risk is quite signifi-cant and this can partially explain why the

R2 is lower than the other deciles. We thenadd the interest rate risk factor to the 4-Factor model and regress monthly returnsof the ten portfolios according to (3.1). Ta-ble 4 shows the first set of results. We firstnotice that, as in De Franco et al. (2015),there is no significant increase in the good-ness of fit. R2 slightly increases for Deciles2, 9 and 10, and remains almost unchangedfor the other deciles. Moreover, the ad-dition of the interest rate factor fails toexplain the alphas away. Deciles 7 to 10still show residual alphas of similar mag-nitude with or without the interest ratefactor. Finally, high dividend yields port-folios exhibit significant positive duration,while the lowest dividend decile has nega-tive duration.3 Positive duration for highdividend yields stocks may be explained bythe fact that these stocks are usually seenas substitutes for fixed income products ina low rate environment. Previous research(Stone, 1974; Chance and Lane, 1980) al-ready showed that negative duration is ex-pected for growth stocks and a more bond-like duration for dividend paying stocks.We notice that the interest rate sensitiv-ity structure is very similar to what wasfound in De Franco et al. (2015), that wereport for the sake of clarity in Table 5. Onthe one hand we do not find any increase inthe explanatory power of the model whenadding interest rate factor; on the otherhand, high dividend yields deciles (like lowvolatility deciles) show small but positiveduration (between 1 and 2.6 for dividendyields Deciles 8, 9 and 10 and between 1.5to 1.8 for low volatility-sorted Deciles 1 and2). Similarly Decile 2, with the lowest divi-dend yield, shows negative duration of -1.3as the high volatility-sorted Decile 9 which

3We recall that Decile 1 contains all non payingstocks.


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Bucket Alpha MKT SMB HML UMD R2

Decile 1 0.002*** 1.22*** 0.336*** -0.369*** -0.282*** 88.15%Decile 2 0.001*** 1.2*** 0.136*** 0.118*** -0.209*** 86.03%Decile 3 0.001*** 1.138*** 0.035*** 0.236*** -0.07*** 83.84%Decile 4 0.002*** 1.044*** 0.009*** 0.34*** -0.066*** 85.33%Decile 5 0.003**** 1.005*** -0.045*** 0.447*** -0.08*** 83.48%Decile 6 0.003**** 1.028*** -0.034*** 0.505*** -0.112*** 84.27%Decile 7 0.004*** 0.957*** -0.08*** 0.48*** -0.109*** 85.08%Decile 8 0.003*** 0.883*** -0.09*** 0.472*** -0.135*** 83.40%Decile 9 0.003*** 0.959*** -0.101*** 0.55*** -0.166*** 85.96%Decile 10 0.002*** 0.788*** 0.034*** 0.778*** -0.166*** 74.84%

Table 3: 4-Factor model regression of dividend yields deciles. Source S&P, Datastream,Kenneth French website. Data from Jan, 31, 1990 to Dec, 31,2014. Signifi-cance: *** = 1% ** = 5% * = 10%. No stars = loading not significant

Bucket Alpha MKT SMB HML UMD IR R2

Decile 1 0.003*** 1.22*** 0.331*** -0.369*** -0.279*** -0.267*** 88.15%Decile 2 0.002*** 1.2*** 0.114*** 0.117*** -0.194*** -1.3*** 86.34%Decile 3 0.001*** 1.138*** 0.028*** 0.235*** -0.066*** -0.407*** 83.88%Decile 4 0.002*** 1.044*** 0.013*** 0.34*** -0.069*** 0.251*** 85.35%Decile 5 0.003**** 1.005*** -0.043*** 0.447*** -0.081*** 0.068*** 83.48%Decile 6 0.003**** 1.028*** -0.035*** 0.505*** -0.112*** -0.02*** 84.27%Decile 7 0.004*** 0.957*** -0.08*** 0.48*** -0.109*** 0.008*** 85.08%Decile 8 0.003*** 0.884*** -0.072*** 0.472*** -0.146*** 1.049*** 83.79%Decile 9 0.002**** 0.96*** -0.067*** 0.551*** -0.189*** 2.012*** 87.15%Decile 10 0.003**** 0.789*** 0.077**** 0.779*** -0.194*** 2.562*** 76.86%

Table 4: 5-Factor model regression of dividend yields deciles. Source S&P, Bloomberg, Datas-tream, Kenneth French website. Data from Jan, 31, 1990 to Dec, 31,2014. Significance:*** = 1% ** = 5% * = 10%. No stars = loading not significant


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Bucket (Volatility) Alpha MKT SMB HML UMD IR R2

Decile 1 0.004*** 0.559*** -0.194*** 0.433*** 0.039*** 1.824*** 55.23%Decile 2 0.003*** 0.783*** -0.193*** 0.321*** -0.025*** 1.598*** 74.51%Decile 3 0.003*** 0.818*** -0.171*** 0.351*** -0.057*** 0.697**** 79.28%Decile 4 0.002*** 0.958*** -0.111*** 0.406*** -0.088*** 0.321*** 82.93%Decile 5 0.003*** 0.984*** -0.019*** 0.425*** -0.115*** 0.03*** 84.94%Decile 6 0.001*** 1.06*** 0.004*** 0.497*** -0.135*** 0.161*** 88.56%Decile 7 0.003*** 1.079*** 0.05*** 0.39*** -0.19*** -0.323*** 87.67%Decile 8 0.001*** 1.17*** 0.148*** 0.314*** -0.173*** -0.553*** 89.46%Decile 9 -0.001*** 1.364*** 0.243*** 0.103*** -0.336*** -1.445*** 89.20%Decile 10 0.002*** 1.613*** 0.654*** -0.275*** -0.587*** -0.369*** 85.84%

Table 5: Source: De Franco et al. (2015). 5-Factor model regression of volatility-sorted deciles, from low tohigh. Significance: *** = 1% ** = 5% * = 10%. No stars = loading not significant

has significant duration of -1.445.

5 Interest rate exposure ofdividend yields deciles:different model specifica-tions

In this section we test different specifica-tions of the model in 3.1 to see if the factorcolinearity in Table 2 may have affected thedeciles’ loadings on the 4-Factor with inter-est rate model. We will focus on Deciles8, 9 and 10, for which we found signif-icant positive duration. The first modelspecification is given by the Market fac-tor together with the interest rate factor(i.e. βSMB = βHML = βUMD = 0).This model specification gives significantlylower R2 statistics for high dividend yieldsdeciles. For Decile 10, the R2 dramaticallydrops from 76.86% to 44.29%. Durationfor Decile 8 is no longer significant, whileit was 1.049 within the 5-Factor model. Asthe duration appears only when we add theSMB, HML and UMD factors, we can arguethat the duration for Decile 8 is likely theproduct of factors’ colinearity rather than

a significant and distinguishable measure ofinterest rate exposure. For Deciles 9 and 10(Tables 7–8), the empirical duration coef-ficients are always significant, even if mag-nitudes and estimation errors strongly de-pend on the model specifications. We no-tice that the inclusion of the Momentumfactor (UMD), whose loading always ap-pears significant and negative, automati-cally increases the magnitude of the empiri-cal duration, for both Deciles 9 and 10. Ta-ble 7 extends our analysis on Decile 9. Eachrow contains the loading of the model (3.1)where only some factors are included. Firstrow, for example, tests the model whereβSMB = βHML = βUMD = 0; second rowthe model where βHML = βUMD = 0 andso on.

6 Interest rate expo-sure: dividend yieldand volatility

According to De Franco et al. (2015), lowvolatility deciles show small but signifi-cant positive duration when monthly port-folio returns are regressed over the 4-Factor


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Bucket Alpha MKT IR R2

Decile 1 -0.001*** 1.416*** -1.891*** 80.52%Decile 2 0.001*** 1.25*** -2.13*** 83.42%Decile 3 0.002*** 1.118*** -0.64*** 81.58%Decile 4 0.002**** 1.004*** 0.055*** 79.89%Decile 5 0.003*** 0.939*** -0.025*** 73.11%Decile 6 0.003*** 0.962*** -0.221*** 71.56%Decile 7 0.005*** 0.886*** -0.089*** 70.62%Decile 8 0.004*** 0.826*** 0.817*** 66.72%Decile 9 0.002*** 0.9*** 1.65*** 66.98%Decile 10 0.005*** 0.715*** 1.902*** 44.29%

Table 6: 2-Factor model regression of dividend yields deciles.Source S&P, Bloomberg, Datastream, Kenneth Frenchwebsite. Data from Jan, 31, 1990 to Dec, 31,2014.Significance: *** = 1% ** = 5% * = 10%. No stars= loading not significant

Decile9: Model Alpha MKT SMB HML UMD IR R2

IR-MKT 0.003*** 0.901*** -*** -*** -*** 1.651*** 66.98%IR-MKT-SMB 0.003*** 0.946*** -0.263*** -*** -*** 1.088*** 70.03%IR-MKT-HML 0.001*** 1.013*** -*** 0.637*** -*** 1.563*** 83.47%IR-MKT-UMD 0.005*** 0.829*** -*** -*** -0.275*** 2.497*** 74.37%IR-MKT-SMB-HML 0.001*** 1.025*** -0.097*** 0.608*** -*** 1.36*** 83.85%IR-SMB-HML-UMD 0.013*** -*** 0.168*** 0.25*** -0.433*** 1.956*** 23.44%IR-MKT no intercept -*** 0.913*** -*** -*** -*** 1.741*** 84.50%

Table 7: Interest rate loadings across various regression models. Source S&P, Bloomberg, Datastream, KennethFrench website. Data from Jan, 31, 1990 to Dec, 31,2014. Significance: *** = 1% ** = 5% * =10%. No stars = loading not significant

Decile10: Model Alpha MKT SMB HML UMD IR R2

IR-MKT 0.005*** 0.716*** -*** -*** -*** 1.903*** 44.29%IR-MKT-SMB 0.005*** 0.747*** -0.182*** -*** -*** 1.515*** 45.81%IR-MKT-HML 0.001*** 0.861*** -*** 0.823*** -*** 1.789*** 73.10%IR-MKT-UMD 0.007*** 0.638*** -*** -*** -0.298*** 2.82*** 53.34%IR-MKT-SMB-HML 0.001*** 0.856*** 0.049*** 0.838*** -*** 1.89*** 73.20%IR-SMB-HML-UMD 0.011*** -*** 0.272*** 0.532*** -0.396*** 2.516*** 31.97%IR-MKT no intercept -*** 0.735*** -*** -*** -*** 2.049*** 74.94%

Table 8: Interest rate loadings across various regression models. Source S&P, Bloomberg, Datastream, KennethFrench website. Data from Jan, 31, 1990 to Dec, 31,2014. Significance: *** = 1% ** = 5% * =10%. No stars = loading not significant


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Figure 2: Annualized volatility and dividendyield for volatility-sorted portfolios.Source De Franco et al. (2015)

model completed with interest rates as in3.1. Moreover, according to their ex-postperformances (Table 1 in De Franco et al.(2015)), the low volatility portfolios showhigher dividend yields than high volatilityportfolios (Figure 2)

On the other hand, according to Table 1,high dividend yields portfolios show lowervolatility than low dividend yields portfo-lios. Finally, both low volatility and highdividend yields portfolios show small butsignificant positive duration. The goal ofthis section is to see if a link appears be-tween low volatility-sorted and high divi-dend yields-sorted portfolios (Figure 3).

For this, we build ten portfolios, sortedby volatility, but in a way that they all showsimilar dividend yields, so as to neutralizethis component when it comes to regresstheir monthly returns on our model in(3.1). We start by considering the ten port-folios built by sorting the stocks in S&P500 Universe according to their dividendyields as explained in section 2. Withineach decile4, we rank the stocks accord-

4We recall that Decile 1 contains non payingstocks, Decile 2 the stocks with the lowest divi-

Figure 3: Relation between low volatility-sorted and high dividend yields-sorted portfolios

ing to their volatility and we build tenvolatility-based sub-portfolios within eachdecile. The double sorted decile i will thenbe the union, across dividend deciles, ofsub-portfolios i in each decile (Figure 4).

Stocks in double-sorted portfolios (DSDeciles) are equally weighted and are re-balanced each third Friday of the month.Volatility is computed over 500 businessdays ending 3 days before the Rebalanc-ing date. Net dividends are reinvested ineach double sorted portfolio according tothe S&P methodology.Two different double-sorted deciles arethen union of ten sub-portfolios - horizon-tally in Figure 4 - such that

• Pairwise, sub-portfolios in the samedividend yields decile have differentvolatilities - vertical sorting in Figure4

• Pairwise, sub-portfolios in the samedividend yields decile have similar div-idend yields - vertical sorting in Figure4

dend yield and Decile 10 the ones with the highestdividend yield.


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Figure 4: The construction of double sorted portfolios at each rebalanc-ing. Within each dividend yields decile (boxes in blue) we considerten sub-portfolios by ranking stocks according to their volatilities(boxes in green - vertical sorting). The Double sorted deciles arethe union of similar volatility sub-portfolios (horizontal aggrega-tion).

• Sub-portfolios in the same line havethe same rank in volatility - horizontalsorting in Figure 4

The dividend yield for this ten doublesorted deciles is expected to be the same,as Figure 5 confirms.

By using double-sorted deciles instead ofvolatility deciles, we neutralize the divi-dend component effect when it comes toassess the relation between volatility andinterest rates. Table 9 collects basic per-formance statistics for our double sorteddeciles over the period January 1990 - De-cember 2012. From Figure 6 we noticehow the double sorting technique still al-lows us to distinguish between low and highvolatility stocks. When comparing withthe volatility results in De Franco et al.(2015), we only notice a minor increase inthe volatility for DS Decile 1 versus the

Figure 5: Dividend yields for double sorteddeciles. Source S&P, Datastream.Data from Jan, 31, 1990 to Dec,31,2014.


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Double Annualized Annualized Max Sharpe CAPM CAPM DividendSorted Return Volatility Drawdown ratio Beta Alpha yield

DS Decile1 14.35% 12.19% -37.08% 0.90 0.28 8.56% 2.05%DS Decile2 12.90% 13.06% -38.81% 0.73 0.34 6.54% 1.96%DS Decile3 14.10% 13.93% -43.81% 0.77 0.39 7.28% 2.02%DS Decile4 13.74% 15.17% -48.90% 0.69 0.44 6.52% 2.00%DS Decile5 11.09% 16.13% -52.99% 0.48 0.50 3.33% 1.95%DS Decile6 11.93% 17.16% -58.35% 0.50 0.55 3.72% 1.93%DS Decile7 13.57% 19.16% -56.13% 0.53 0.63 4.67% 1.98%DS Decile8 11.57% 21.48% -63.93% 0.38 0.72 1.85% 1.93%DS Decile9 13.01% 23.17% -66.34% 0.42 0.78 2.74% 1.84%DS Decile10 12.21% 27.26% -76.23% 0.33 1.00 0.00% 1.76%

Table 9: Performance statistics of double sorted.Source S&P, Datastream. Data from Jan, 31, 1990 to Dec, 31,2014.The Sharpe Ratio is computed with a risk-free rate over the period of 3.34%.

pure (low) volatility Decile 1 (12.19% vs.11.64%, see Figure 2) and a significant re-duction in the volatility of the DS Decile 10versus the pure (high) volatility Decile 10(27.26% vs. 34.10%, see Figure 2). For therest, the differences in annualized volatil-ities between volatility-sorted and doublesorted deciles are really small. We do notnotice any clear pattern in the ex-post re-turns of double sorted deciles, while theSharpe Ratio declines as the volatility in-creases, and, by construction, the dividendyield is stable across double sorted deciles.We start by testing the explanatory powerof the classical 4-Factor model without in-terest rate factor for the set of doublesorted deciles. Table 10 collects regressionsloadings of double sorted monthly returnsover the model (3.1) without interest rates(βIR = 0) over the period January 1990 toDecember 2014.

Compared to the pure volatility decilesin De Franco et al. (2015), the 4-Factormodel has a better explanatory power forthe double sorted deciles, especially for theDS Decile 1, for which the R2 is 67.84% (vs.53.27% for the pure (low) volatility decile),

Figure 6: Performance statistics of dividend yieldsdeciles. Source S&P, Datastream. Datafrom Jan, 31, 1990 to Dec, 31,2014. TheSharpe Ratio is computed with a risk-freerate over the period of 3.34%.


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Bucket Alpha MKT SMB HML UMD R2

DS Decile 1 0.003*** 0.703*** -0.195*** 0.271*** 0.028*** 67.84%DS Decile 2 0.002**** 0.777*** -0.141*** 0.272*** -0.028*** 75.53%DS Decile 3 0.002*** 0.874*** -0.129*** 0.326*** -0.025*** 83.67%DS Decile 4 0.002*** 0.943*** -0.07*** 0.291*** -0.046*** 83.96%DS Decile 5 -0.001*** 0.998*** -0.088*** 0.309*** -0.116*** 87.95%DS Decile 6 0.001*** 1.029*** 0.072*** 0.258*** -0.171*** 89.69%DS Decile 7 0.002*** 1.114*** 0.124*** 0.307*** -0.247*** 90.11%DS Decile 8 -0.001*** 1.249*** 0.16*** 0.311*** -0.288*** 91.32%DS Decile 9 -0.001*** 1.313*** 0.262*** 0.351*** -0.32*** 90.45%DS Decile 10 -0.001*** 1.422*** 0.409*** 0.274*** -0.474*** 87.47%

Table 10: 4-Factor model regression for double sorted deciles. Source S&P, Datastream,Kenneth French website. Data from Jan, 31, 1990 to Dec, 31,2014. Significance:*** = 1% ** = 5% * = 10%. No stars = loading not significant

Bucket Alpha MKT SMB HML UMD IR R2

DS Decile 1 0.004*** 0.703*** -0.175*** 0.271*** 0.015*** 1.13*** 68.53%DS Decile 2 0.001**** 0.778*** -0.121*** 0.272*** -0.041**** 1.176*** 76.18%DS Decile 3 0.002*** 0.874*** -0.122*** 0.326*** -0.03*** 0.404*** 83.73%DS Decile 4 0.002*** 0.943*** -0.052*** 0.292*** -0.058*** 1.084*** 84.37%DS Decile 5 -0.001*** 0.998*** -0.085*** 0.309*** -0.118*** 0.219*** 87.97%DS Decile 6 0.001*** 1.028*** 0.066*** 0.257*** -0.168*** -0.327*** 89.72%DS Decile 7 0.002*** 1.114*** 0.12*** 0.307*** -0.244*** -0.268*** 90.13%DS Decile 8 0*** 1.248*** 0.145*** 0.311*** -0.279*** -0.861*** 91.45%DS Decile 9 -0.001*** 1.313*** 0.255*** 0.351*** -0.315*** -0.429*** 90.48%DS Decile 10 -0.001*** 1.422*** 0.406*** 0.273*** -0.472*** -0.172*** 87.48%

Table 11: 5-Factor model regression for double sorted deciles. Source S&P, Bloomberg, Datastream, Ken-neth French website. Data from Jan, 31, 1990 to Dec, 31,2014. Significance: *** = 1% ** =5% * = 10%. No stars = loading not significant


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as showed in Table 10. We notice how themarket beta for the DS Decile 1 is signifi-cantly higher than the one for the pure lowvolatility decile (0.703 vs. 0.559).We can now add the interest rate factorand perform the same type of regressionto assess the differences in the empiricalduration between the double sorted andthe volatility sorted deciles. Table 11 col-lects regressions loadings of double sortedmonthly returns over the model (3.1) com-pleted with the interest rate factor. Wealso report the results in De Franco et al.(2015) relative to the regressions of volatil-ity sorted deciles to make comparisons eas-ier (Table 12). We remark that the doublesorted Deciles 1 and 2 have a significantpositive duration (resp. 1.13 and 1.176), aswas the case for pure volatility sorted port-folios. But the magnitude is significantlylower, as showed in Table 12: the (low)volatility Decile 1 showed duration of 1.824while the double sorted Decile 1 has 1.13duration ( 38% reduction). Similarly, thevolatility Decile 2 has 1.598 empirical dura-tion while double sorted Decile 2 only 1.176( 26% reduction). Interestingly, DS Decile2 has higher duration than DS Decile 1:when neutralizing the dividend yield com-ponent, the relation between volatility andempirical duration is not monotone any-more. Going down with the deciles, we no-tice how DS Decile 3 has no longer signifi-cant duration - it was 0.697 for the volatil-ity sorted Decile 3, although with 10% sig-nificance. On the other side, DS Decile 4has significant duration of 1.084 while thecorresponding volatility sorted Decile 4 hasno significant duration. Again, DS Decile4 duration is higher than DS Decile 3 as itwas the case for the couple DS Decile 1/DSDecile 2. For the high volatility deciles, wenotice how DS Decile 9 has no significant

IR R2

VS DS VS DS

Decile 1 1.824*** 1.13*** 55.23% 68.53%Decile 2 1.598*** 1.176*** 74.51% 76.18%Decile 3 0.697**** 0.404*** 79.28% 83.73%Decile 4 0.321*** 1.084*** 82.93% 84.37%Decile 5 0.03*** 0.219*** 84.94% 87.97%Decile 6 0.161*** -0.327*** 88.56% 89.72%Decile 7 -0.323*** -0.268*** 87.67% 90.13%Decile 8 -0.553*** -0.861*** 89.46% 91.45%Decile 9 -1.445*** -0.429*** 89.20% 90.48%Decile 10 -0.369*** -0.172*** 85.84% 87.48%

Table 12: 5-Factor model regression for volatility sorted (VS)versus double sorted (DS) deciles. Source S&P,Bloomberg, Datastream, Kenneth French websiteand De Franco et al. (2015). Data from Jan, 31,1990 to Dec, 31,2014. Significance: *** = 1% **= 5% * = 10%. No stars = loading not significant

duration, unlike is the case for its volatilitysorted counterpart.

7 Conclusions

We estimated the empirical duration ofportfolios with different levels of dividendyields, using a linear 4-factor model com-pleted with 10-year nominal rates thatproxy the interest rate risk factor. Despitethe potential issues with model specifica-tion using interest rate factor together withFama-French-Carhart factors (market, size,value and momentum), we find several ro-bust results. It turns out that portfolioswith low dividend yields tend to have smallbut significant negative duration, meaningthat they tend to respond positively wheninterest rates rise. On the other hand,higher dividend yields deciles have a pos-itive duration meaning that they have aninverse relation with interest rates, morein line with bonds. However, the inclusion


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of the interest rate factor does not bringany significant explanatory power, neitherexplains away the alphas of high dividendyields portfolios, even when controlling forFama-French risk factors. These resultsmatch the conclusions for volatility sortedportfolios in De Franco et al. (2015). Wefind several striking similarities betweenthe two distinct datasets:

• Both volatility and dividend yieldssorted portfolios’ R2 show almost noimprovement when we add the interestrate factor, although the model does abetter job in the dividend sorted port-folios.

• The alphas remain significant

• Both low volatility and high dividendsyield portfolios have small but positiveduration.

• Low volatility portfolios show highdividend yields, while high dividendyields are generally associated withlow volatility.

To see if any potential links underliesthese similarities, we build a dataset of tenvolatility-sorted portfolios while controllingfor dividend yields. This double sortingmethod is very standard when it comesto neutralize some specific characteristics,similar to the one used by Kenneth Frenchto build his factors. This should allowus to see if the relation between interestrate sensitivity and volatility still holdsunder equal dividend yields condition. Wecompare our results with the ones obtainedby De Franco et al. (2015) in the case ofpure volatility sorted portfolios. We findthat the 4-Factor model does a better jobfor the double-sorted volatility portfolios,at least for the lowest deciles. But the

addition of the interest rate in the modeldoes not explain the alphas for the low-est (double-sorted) deciles. And finally,although the lowest double-sorted decilestill has small but significant duration,its magnitude is reduced by almost 38%.Furthermore, the monotonic relationbetween volatility and duration does nothold anymore. In other words, it seemsthat part of the duration of low volatilityportfolios comes from their overlap withhigh dividend paying portfolios.

We thank Pouya Azimi for his assistance.

EndnoteThe S&P 500 composition data is a courtesy ofS&P. The S&P 500 Index (”Index”) is a prod-uct of S&P Dow Jones Indices LLC and/or itsaffiliates and has been licensed for use by Os-siam. Copyright c©2014 by S&P Dow JonesIndices LLC, a subsidiary of the McGraw-HillCompanies, Inc., and/or its affiliates. All rightsreserved. Redistribution, reproduction and/orphotocopying in whole or in part are prohib-ited without written permission of S&P DowJones Indices LLC. For more information onany of S&P Dow Jones Indices LLC’s indicesplease visit www.spdji.com. S&P R©is a reg-istered trademark of Standard & Poor’s Fi-nancial Services LLC and Dow Jones R©is aregistered trademark of Dow Jones TrademarkHoldings LLC. Neither S&P Dow Jones IndicesLLC, Dow Jones Trademark Holdings LLC,their affiliates nor their third party licensorsmake any representation or warranty, expressor implied, as to the ability of any index toaccurately represent the asset class or marketsector that it purports to represent and nei-


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ther S&P Dow Jones Indices LLC, Dow JonesTrademark Holdings LLC, their affiliates northeir third party licensors shall have any liabil-ity for any errors, omissions, or interruptions ofany index or the data included therein.


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References

Campbell, J.Y. and Shiller, R.J. (1988) Stock prices, earnings, and expected dividendsThe Journal of Finance, vol. 43 N. 3, 661–676 .

Carhart, M.M. (1997) On persistence in mutual fund performance The Journal ofFinance, vol. 52 N. 1, 57-82 .

Chance, D.M. and Lane, W.R. (1980) A re-examination of interest rate sensitivity in thecommon stocks of financial institutions The Journal of Finance, vol. 3 N. 1, 49–55 .

Cohen, R.D. (2003) The Relationship Between the Equity Risk Premium, Duration,and Dividend Yield Corporate Finance Structured Products, Citigroup. Available atSSRN Id = 392030 .

De Franco, C., Monnier, B. and Rulik, K. (2015) Interest rate exposure for low volatilityportfolios Ossiam research paper 2015

Fama, E. and French, K. (1988) Dividend yields and expected stock returns Journal offinancial economics, vol. 22 N. 1, 3–25 .

Fama, E. and French, K. (1988) Permanent and temporary components of stock pricesThe Journal of Political Economy, JSTOR, 246–273 .

Fama, Eugene and French, Kenneth (1993) Common risk factors in the returns on stocksand bonds Journal of financial economics, vol. 33 N. 1, 3-56 .

Jensen, G.R. and Johnson, R.R. (1995) Discount rate changes and security returns inthe US, 1962–1991 Journal of Banking & Finance, vol. 19 N. 1, 79–95 .

Jensen, G.R. and Mercer, J.M. and Johnson, R.R. (1996) Business conditions, monetarypolicy, and expected security returns Journal of financial economics, vol. 40 N. 2,2013–237 .

Modigliani, F. and Miller, M.H. (1958) The cost of capital, corporation finance and thetheory of investment The American economic review, 261–297 .

Rozeff, M.S. (1974) Money and stock prices: Market efficiency and the lag in effect ofmonetary policy Journal of financial economics, vol. 1 N. 3, 245–302 .

Rozeff, M.S. (1984) Dividend yields are equity risk premiums Journal of Portfoliomanagement, 68–75 .

Stone, B.K. (1974) Systematic interest-rate risk in a two-index model of returns Journalof Financial and Quantitative Analysis, vol. 9 N.5 709–721 .


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