The Pedictive Powe of Dividend Yields fo Stock Retuns: Risk Picing o Mispicing? Glenn Boyle Depatment of Economics and Finance Univesity of Cantebuy Yanhui Li Depatment of Economics and Finance Univesity of Cantebuy Novembe 20, 2013 PRELIMINARY AND INCOMPLETE. PLEASE DO NOT QUOTE Inspiation fo this study came fom John Cochane s 2012 JB Condliffe Memoial Lectue at the Univesity of Cantebuy. We ae gateful to Matin Lally fo poviding us with essential data. Coesponding autho: Pivate Bag 4800, Chistchuch 8140, New Zealand. Phone: 64-3-364-3479. Email: glenn.boyle@cantebuy.ac.nz
The Pedictive Powe of Dividend Yields fo Stock Retuns: Risk Picing o Mispicing? Abstact If obseved pedictability is pimaily due to maket mispicing, then the elationship between dividend yields and futue stock etuns should be stongest in maket envionments that face the geatest limits to abitage. Howeve, using 1931-2012 data fom New Zealand, we find that the popotion of dividend yield volatility attibutable to expected etun vaiation is geate in the post-libealisation peiod, when thee should be less scope fo mispicing. Although othe factos could also be at wok, this esult poses a challenge to mispicing explanations of stock etun pedictability. JEL classification: G12, G14 Keywods: etun pedictability; discount ates; limits to abitage
The Pedictive Powe of Dividend Yields fo Stock Retuns: Risk Picing o Mispicing? 1 Intoduction Thee is much evidence to suggest that the dividend-pice atio has stong pedictive powe fo futue stock etuns see, fo example, Cochane (2008, 2011). Less clea, howeve, is the pope intepetation of this elationship. On the one hand, a low dividend-pice atio may indicate that peceived futue isk is low, causing investos to set pices so that isk pemia, and hence expected etuns, ae low. Subsequent aveage etuns then tun out to be low, as pedicted by the ealie dividend-pice atio. On the othe hand, a low dividend-pice atio may simply eflect excessive optimism on the pat of investos who ove-pice stocks elative to thei intinsic value. As the mispicing dissipates, subsequent etuns ae low. Eithe stoy is consistent with the obseved powe of dividend-pice atios to foecast futue etuns. 1 In this pape, we popose a simple appoach fo distinguishing between these two hypotheses. If obseved pedictability is pimaily due to mispicing, then the elationship between dividend yields and futue stock etuns should be stongest in maket envionments most conducive to mispicing, i.e., makets in which fictions, egulations, illiquidity, and financing constaints impose limits to abitage and so inhibit the incopoation of infomation in pices. Makets in which infomation is moe easily incopoated in pices, esulting in fewe mispicing oppotunities, should, ceteis paibus, see weake etun pedictability. If, on the othe hand, obseved pedictability is pimaily due to time vaying isk pemia, then the elationship between dividend yields and futue stock etuns should be unaffected by any change in the potential fo mispicing. We implement this idea using 1931 2012 stock maket data fom New Zealand (NZ). Pio to July 1984, New Zealand had limited and highly egulated financial makets. Shotselling was pohibited, as wee company stock epuchases; thee wee also estictions on inteest ates, on pivate oveseas boowing, on foeign-owned companies access to domestic financial makets, and on the ability of NZ esidents to puchase foeign exchange fo investment puposes. All of these egulations effectively esticted infomation flows and abitage, and so encouaged mispicing. By Mach 1985, most had been emoved; in addition, openmaket opeations in govenment secuities had begun, the exchange ate had been floated, and the banking secto deegulated. 2 1 The isk and mispicing stoies ae often associated with 2013 Nobel Laueates Eugene Fama and Robet Shille espectively. Academy of Sciences, 2013). Fo a nice summay, see the Pize Committee s citation (Royal Swedish Fo an even bette (and shote) summay, see John Cochane s blog post: http://johnhcochane.blogspot.co.nz/2013/10/bob-shilles-nobel.html 2 The estictions on shot selling and stock epuchases wee not escinded until the ealy 1990s. Fo a 1
The speed of this libealisation povides an ideal setting fo compaing etun pedictability in makedly diffeent envionments within the same maket. The potential fo mispicing would seem to be consideably geate in the pe-efom peiod, and Goenwald (1997) epots evidence (albeit faily weak) that this is indeed the case. Consequently, if etun pedictability in the NZ maket is pimaily due to mispicing, then the estimated magnitude of this pedictability should be lowe in the post-efom peiod. In the next section, we set out ou appoach in moe detail and descibe ou data. Section 3 contains ou esults and section 4 offes some concluding emaks. 2 Methods and Data We follow the appoach of Cochane (2011). The Campbell-Shille (1988) etun appoximation yields: dp t k ρ j 1 t+j j=1 k ρ j 1 d t+j + ρ k dp t+k j=1 whee dp is the log dividend-pice atio, is the log of the eal etun facto (i.e., the log of 1+nominal stock etun 1+inflation ate ), d is log eal dividend gowth, and ρ = e E[dp] 1+e E[dp] is a constant of appoximation. This in tun implies: va(dp t ) cov(dp t, k ρ j 1 t+j ) + cov(dp t, j=1 o, dividing though by va(dp t ), whee cov(dpt, k j=1 ρj 1 t+j) va(dp t) 1 k ρ j 1 d t+j ) + ρ k cov(dp t, dp t+k ) j=1 + d + ρk dp (1) is the coefficient fom a egession of weighted k peiod futue eal etuns k j=1 ρj 1 t+j on the cuent dividend yield dp t ; d and b dp ae defined similaly. Equation (1) tells us that, d and ρk dp ae the popotions of dividend yield volatility attibutable to time vaying expected etuns, time vaying expected (negative) dividend gowth, and dividend yield pesistence espectively. A consideable liteatue epots estimates pedictable, but dividend gowth is not. 3 ˆb > 0 and ˆb d = 0, i.e., etuns ae Howeve, much disageement emains ove the souce of etun pedictability: is it time vaiation in isk pemia, o iational mispicing? To make this distinction moe concete, let be the component of expected (eal) etun justified by isk consideations and z denote the mispicing component. Then = + z, i.e., etun pedictability is due to isk picing ( In pactice, of couse, the econometician obseves only ) o mispicing ( z ) o both. ˆb, not the individual components. Howeve, if the elative stength of the two components vaies ove time, then it potentially summay of some of the moe impotant financial secto efoms, see Magaitis et al. (1992). 3 Fo summaies of this evidence, see Cochane (2008, 2011) and Koijen and Nieuwebugh (2011) 2
becomes possible to infe something about the impotance of each fom ˆb alone. Suppose, fo example, that ational picing involves setting expected etuns equal to a constant. Then ational etun pedictability is, by definition, zeo, and any etun pedictability obseved by the econometician must be the esult of mispicing. That is ˆb = ˆb z > 0; ˆb = 0 But fo etun pedictability to be due to mispicing, an obvious peequisite is that mispicing actually occu. So if the maket envionment then changes in a way such that mispicing is completely o substantially eliminated, then z estimate of. 4 must fall, and so theefoe does the While this example is exteme, it illustates a geneal point: if mispicing-induced etun pedictability is the null, then a eduction in the capacity fo mispicing (i.e., fewe limits to abitage, as in Shleife and Vishny, 1997) should see a fall in ˆb. 5 On the othe hand, if the null is that etun pedictability is pimaily due to isk picing, then the same eduction in the capacity fo mispicing should have no effect on effect if maket libealisation allows fo moe accuate isk picing). ˆb (o possibly a positive We investigate this idea using 1931 2012 data fom NZ. As explained in the Intoduction, NZ expeienced a compehensive, and apid, maket libealisation in 1984 1985, so we compae estimates of obtained fom the 1931 1984 peiod with those fom the 1985 2012 peiod. Annual data on stock maket etuns, bond etuns, dividend yields, and dividend gowth between 1931 and 2002 come fom Lally and Masden (2004) and wee kindly supplied to us by Matin Lally. Subsequent stock maket data wee obtained fom the NZX Company Reseach database and bond and inflation data fom the Reseve Bank of NZ. 6 3 Results To facilitate compaison with existing eseach, we fist use the full 1931 2012 sample to estimate and d fo vaious values of k. Fo k > 1, we epot both diect and VARimplied estimates, with the latte given by (see Cochane, 2008, 2011) ˆb j = k (1) 1 (ρ ˆφ) ˆb j [ 1 ρ ˆφ ] whee ρ = 0.95 and ˆφ = 0.81 is the log dividend yield autocoelation estimate. Standad eos ae Newey-West and, in the case of the implied estimates, obtained using the delta method. 4 By (1), d + ρk dp must coespondingly incease. 5 Fo a ecent summay of the limits-to-abitage liteatue, see Gomb and Vayanos (2010). 6 See http://companyeseach.nzx.com/cust/sevices.php and http://www.bnz.govt.nz/statistics/tables/b2/ espectively. 3
Table 1: Foecasting Regessions: Full Sample Pedictability coefficient estimates fom the full 1931 2012 data sample. is the coefficient fom a egession of weighted k peiod futue log etuns k j=1 ρj 1 t+j on the cuent dividend yield dp t, whee ρ = 0.95 is a constant of appoximation; e is the analogous coefficient fom a egession whee the dependent vaiable is excess log etuns. Each implied k 1 (ρ ˆφ) estimates equals 1 ρ ˆφ x its coesponding 1-yea estimates (Cochane, 2008, 2011), whee ˆφ = 0.81 is the log dividend yield autocoelation estimate. Tems in backets ae t statistics based on Newey-West standad eos; implied standad eo estimates ae obtained using the delta method. k d e 1 0.27 0.03 0.24 (3.2) ( 0.5) (2.9) 3 0.53 0.08 0.47 (3.1) (0.7) (2.3) 3 (implied) 0.63 0.08 0.56 (3.5) ( 0.5) (3.4) 5 0.64 0.07 0.54 (3.3) (0.4) (2.1) 5 (implied) 0.84 0.11 0.76 (3.5) ( 0.5) (3.3) (implied) 1.15 0.15 1.03 (3.3) ( 0.5) (3.1) Table 1 confims the pincipal esult of Cochane (2008, 2011) in NZ data: at shot-, medium- and long-tem hoizons, eal stock etuns ae pedictable but eal dividend gowth is not. All estimates of the etun pedictability coefficient ae economically lage and significantly diffeent to zeo at the 0.005 level o bette, while the dividend pedictability estimates ae small, often have the wong sign, and ae not emotely close to being statistically significant. The etun point estimates ae somewhat highe than Cochane finds fo the US: 1-yea expected etun vaiation accounts fo appoximately 27% of dividend yield volatility, ising to 53% ove thee yeas, 64% ove five yeas, and to 115% in the long-un; implied estimates ae somewhat highe still, and have bigge t-statistics. The last column of Table 1 epots excess etun pedictability coefficients, whee excess etun is the log of 1+nominal stock etun 1+nominal iskless bond etun. Unlike Cochane (2008) who epots stonge etun pedictability fo excess etuns, ou estimates ae slightly smalle than thei eal etun countepats and less pecisely estimated. This is almost cetainly due to the noise in ou bond etun seies. All that we have available ae yields on the NZ Govenment 10- yea bond, so we calculate 1-yea bond etuns as the beginning-of-yea yield, an assumption that is obviously sensitive to tem stuctue shifts. 7 Nevetheless, the same pictue emeges: (excess) etuns ae pedictable, but (excess) dividend gowth is not. The main question of inteest is whethe o not the obseved etun pedictability epesents maket isk picing o mispicing. Table 2 attempts to shed light on this issue by 7 The 10-yea bond is the only NZ govenment bond to exist fo the entie 1931 2012 peiod. 4
Table 2: Foecasting Regessions: Pe- and Post-Refom Sub-Peiods Retun pedictability coefficient estimates fom the pe-efom 1931 1984 and post-efom 1985 2012 peiods. e is the excess etun pedictability coefficient assuming the iskless bond 1-yea etun equals its beginning-of-peiod yield; ep is the excess etun pedictability coefficient assuming the iskless bond is a pepetuity. indicates that the post-efom coefficient is geate than the pe-efom coefficient at the 0.05 level o bette, based on a Welch t test. k 1931 84 1985 2012 1931 84 1985 2012 1931 84 1985 2012 e ep 1 0.23 0.50 0.23 0.50 0.30 0.54 (2.7) (2.4) (3.1) (2.4) (3.6) (2.6) 3 0.5 1.01 0.51 1.07 0.67 1.17 (2.3) (5.6) (3.1) (5.9) (3.2) (6.4) 3 (implied) 0.56 1.01 0.56 1.02 0.72 1.09 (3.0) (2.6) (3.5) (2.5) (4.1) (2.8) 5 0.63 1.08 0.61 1.25 0.78 1.60 (3.0) (3.2) (3.2) (3.8) (3.0) (5.1) 5 (implied) 0.77 1.21 0.77 1.22 0.99 1.30 (3.2) (2.4) (3.7) (2.4) (4.3) (2.6) (implied) 1.13 1.33 1.12 1.34 1.44 1.44 (2.9) (2.2) (3.4) (2.2) (3.4) (2.3) compaing the etun pedictability estimates fo the pe-efom 1931 84 peiod with those fo the post-efom 1985 2012 peiod. If the Table 1 esults pimaily eflect mispicing, then these estimates should be lowe in the latte peiod. The fist fou columns of Table 2 eveal no such tend. In fact, at all hoizons, the etun pedictability estimate is stictly geate in the post-efom peiod, in some cases at the 0.05 significance level despite the elatively small numbe of obsevations in the postefom peiod making it difficult to eject the null of no diffeence. Fo 1- and 3-yea hoizons, and fo both eal and excess etuns, the pedictability estimates appoximately double following libealisation, while at 5 yeas the incease is 60 70%; only in the long un do the estimates come close to conveging, but even then the diffeence emains stictly in favou of the late peiod. As noted above, ou iskless etun poxy is likely to contain significant measuement eo due to ou assumption that the 10-yea bond fo which we have data is identical to a 1-yea bond. To check whethe this has any effect on ou esults, we move to the othe end of the scale and assume the 10-yea bond is identical to a pepetuity, since this also allows us to calculate an appoximate annual etun. 8 The esults fom calculating excess etuns in this altenative way appea in the last two columns of Table 2, and ae essentially indistinguishable fom those in the pevious fou columns: etun pedictability estimates ae much highe in the post-efom peiod. 8 Specifically, in this case the bond etun between t and t + 1 is y t + y t y t+1, whee y y t is the bond yield t at the beginning of yea t. 5
4 Concluding Remaks Based on the null of mispicing-induced etun pedictability, we expect to see weake pedictability in the post-efom peiod when limits to abitage ae less appaent. But we do not. Instead, we see consideably stonge etun pedictability following maket libealisation. One facto potentially contibuting to this phenomenon is lowe dividend yield pesistence afte 1984 ( ˆφ = 0.66 vesus 0.83 in the pe-efom peiod), as the pesent value identity tells us that the sum of etun and dividend gowth pedictability must then ise mechanically as a esult. Howeve, ou esults show that the slack is entiely taken up by etuns, and none by dividend gowth. To econcile this with the mispicing explanation of etun pedictability, one would have to believe eithe that the NZ libealisation inceased limits to abitage, o that lowe limits to abitage esulted in lage and longe-lasting mispicing. Both ae had stoies to tell. In a simila vein, Maio and Santa-Claa (2013) epot that etun pedictability is much weake amongst small stocks. As small stocks ae moe likely to encounte abitage difficulties, this esult also implies that educing limits to abitage is associated with stonge etun pedictability. Again, this seems difficult to econcile with a mispicing stoy. Nevetheless, we ecommend some caution. Ou post-efom sample is elatively shot, and contains two majo maket coections. As moe data become available, thus lessening the impact of these two events, it is possible that etun pedictability estimates fo the post-1984 peiod could fall substantially. Refeences Campbell, J. and R. Shille, 1988. The dividend-pice atio and expectations of futue dividends and discount factos. Review of Financial Studies 1, 195 228. Cochane, J., 2008. The dog that did not bak: a defense of etun pedictability. Review of Financial Studies 21, 1533 1575., 2011. Discount ates. Jounal of Finance 66, 1047 1108. Goenewold, N., 1997. Shae maket efficiency: tests using daily data fo Austalia and New Zealand. Applied Financial Economics 7, 645-657. Gomb, D. and D. Vayanos, 2010. Limits of abitage. Annual Review of Financial Economics 2, 251 275. Koijen, R. and S. Nieuwebugh, 2011. Pedictability of etuns and cash flows. Annual Review of Financial Economics 3, 467 491. 6
Lally, M. and A. Masden, 2004. Histoical tax-adjusted maket isk pemiums in New Zealand: 1931-2002. Pacific Basin Finance Jounal 3, 423 449. Maio, P. and P. Santa-Claa, 2013. Dividend yields, dividend gowth, and etun pedictability in the coss-section of stocks. Jounal of Financial and Quantitative Analysis, fothcoming. Magaitis, D., D. Hyslop and D. Rae, 1992. Financial policy efom in New Zealand, Reseve Bank of New Zealand Discussion Pape G92/2. Royal Swedish Academy of Sciences, 2013. Undestanding asset pices. Available at: http://www.kva.se/documents/pise/ekonomi/2013/sciback ek en 13.pdf Shleife, A. and R. Vishny, 1997. The limits of abitage. Jounal of Finance 52, 35 55. 7