The P/B-ROE Model Revisited. Jarrod Wilcox Wilcox Investment Inc & Thomas Philips Paradigm Asset Management

Transcription

1 The /B-ROE Model Revisied Jarrod Wilcox Wilcox Invesmen Inc & Thomas hilips aradigm Asse Managemen

2 Agenda Characerizing a good equiy model: Is virues and uses Saic vs. dynamic models The /B-ROE model: Closed form & approximae soluions Cross-secional explanaion using he /B-ROE model Cross-secional predicion using he /B-ROE model Time-series explanaion using he /B-ROE model Time-series predicion using he /B-ROE model 2

3 Wha Characerizes a Good Model? Economic realism in is inellecual underpinnings Mus be grounded in a realisic view of he firm Mus allow he incorporaion of economic consrains e.g. Earnings canno grow faser han revenues in perpeuiy arsimony and compuabiliy Should require relaively few inpus Inpus should be readily available or easily esimaed from daa Widespread applicabiliy Model prices should explain prevailing prices wihou significan bias Model residuals should predic fuure reurns Should be applicable in cross-secion and ime-series 3

4 Who Migh Use a Good Model? Corporae officers If he model can guide hem on how bes o increase firm value Fundamenal analyss If he model can help hem beer evaluae a firm and is managemen Invesmen bankers and buyers and sellers of companies If he model can generae unbiased valuaions Invesors If he model s residuals are predicive of fuure reurns 4

5 Models in Widespread Use Today Dividend Discoun Model (J.B. Williams, 1938): Inellecual roo of almos all models in use oday 0 = E[ FCFi ] i = (1+ k) i 1 Gordon Growh model (1962): Free cash flows grow a a consan rae in perpeuiy Edward-Bell-Ohlson Equaion (1961): = Free Cash Flow 1 k g i= 1 Apply clean surplus relaionship o DDM and rearrange erms = B 0 + E[( ri k) B i (1 + k) i 1 ] Various muli-sage versions of he DDM 3 sages model growh, seady sae and decline 5

6 Saic vs. Dynamic Models A saic model evaluaes price a a poin in ime Esimae inpus a fixed poins in ime, discoun back o ge oday s price Examples: DDM, EBO A dynamic model evolves some funcion of price over ime Some evolve price, ohers evolve a valuaion raio Trajecory mus be consisen wih he model: a hin of coninuous ime Examples: Opions (Black-Scholes), pricing a zero-coupon bond Bond price rajecory mus be consisen wih he yield curve Boh saic and dynamic models can have he same inellecual roos Boh ulimaely give us a fix on oday s price Choice of one over he oher is empirical which works beer in pracice 6

7 A Brief Hisory of Dynamic Models Jarrod Wilcox (FAJ 1984): /B-ROE model. Two sage growh model,wih firs phase ending a ime T. Deermine he rajecory of /B subjec o he consrain /B T =1 Obain oday s /B from rajecory & erminal condiion: ln ( / B) = ( r k) T Tony Esep (FAJ 1985, JM 2003): T (or Toal Reurn) model Follows /B-ROE logic, bu arbirarily ses ime horizon o 20 years Derives and ess a holding period reurn: r g / B T = g / B / B Mary Leibowiz (FAJ 2000): /E Forwards And Their Orbis /E mus evolve along cerain pahs (orbis) deermined by k Has implicaions for curren /E Theoreical, no ess of explanaory or predicive power ( g) 7

8 Our Two-Sage Dynamic Model Firm has wo sages growh phase (<T) and equilibrium phase (>T) Disinc growh raes, ROEs, and dividend yields in hese wo phases Capial srucure is ime-invarian firm is self financing Exogenously deermined expeced reurn is ime-invarian GROWTH HASE EQUILIBRIUM HASE Growh rae of book = g Growh rae of book = g eq Reurn on equiy = r Reurn on equiy = r eq Dividend yield on book = d Dividend yield on book = d eq 0 T 8

9 Economic Inuiion and More Noaion We evolve / B = rice-o-book raio a ime Trajecory of /B in he growh phase mus be consisen wih k / B / B T Growh hase Equilibrium 0 T D = Cumulaive dividend process a ime r = Insananeous ROE = growh + dividend yield on book = g+d k = Required shareholder reurn, assumed consan for all >0. 9

10 10 Exac Soluion - I Toal Reurn = rice Reurn + Dividend yield If all parameers are ime invarian: (1) In addiion, we always have (2) Differeniae (2) w.r.. ime and divide by price o ge (3) D D k + = + = = 1 1 Reurn Toal B B / = B B B B + = 1 / / 1 1

11 11 Exac Soluion - II Subsiue and rearrange o ge Solve his differenial equaion o give d / k-g = /B* = /B if he iniial condiions prevail in perpeuiy. ( ) d B g k B + = / / ( ) T k g T k g T e g k d e B B ) ( ) ( 0 1 * / / + = T k g g k k r g k k r B B eq eq ) ( * / / ln 0 =

12 Approximaion: All rofis Are Reinvesed In Growh hase Then d=0, r = g, and / B0 = / B T e ( r k ) T Impac of Dividends on /B-ROE Model rice/book % 0% 10% 20% 30% 40% Expeced Reurn on Equiy d = 0% d = 6% 12

13 Approximae Soluion: The /B-ROE Model Take naural log on boh sides o ge ( / B ) = ln( / B ) + ( r k) T = [ ln( / B ) kt ] rt ln 0 In Jarrod s 1984 paper, T T + / =1 B T, bu his is unrealisic oday The /B-ROE model can be esimaed from daa via OLS regression Can proxy r wih ROE, as profiabiliy ends o be sable and mean-revering. Can use analyss esimaes o furher enhance our esimae of r. Hard o exrac informaion from consan, so focus on esimaing T Run cross-secional (U.S. socks) and ime-series (S& 500) regressions Deermine fi of regression (cross-secional & ime-series explanaion) Use residuals o forecas reurns (cross-secional and ime-series predicion) 13

14 Cross Secional Explanaion How much should CEO s expec sock price o increase for each 1% in addiional ROE? Sample: ValueLine Daafile , companies wih fiscal yearends in December, posiive book value, and ROE beween -10% and +40%. Over 20,000 observaions. Run panel regression of ln(/b) agains ROE Slope of regression line depends on pas volailiy of ROE. We inerpre his slope as a measure of he invesmen horizon T. 14

15 Long-erm anel Resuls QUARTILES: Highes 5-year Lowes 5-year ROE Volailiy ROE Volailiy T (years) The pooled slope wihin each year of he period is 3.66 years. For very sable companies i rises o abou 9 years. A sable ROE allows projecing recen values furher ino he fuure. Independen of risk premium, ROE sabiliy can eiher help or hur hrough is impac on invesmen horizon T. 15

16 Example Drawn From Averages Consider a sock wih ROE = 15%, and in he 4 h quarile of ROE sabiliy (5-year sandard deviaion of ROE < 2.5%). Regression slope (our esimae of T): 6.47 years Quesion: Oher hings equal, how much higher would is price be if is ROE were 20%? Answer: Is sock price would have been 38% higher, no couning any increase in book value B. 16

17 How redicable is he Invesmen Horizon? Annual ooled Invesmen Horizon Over Time ln(b) vs ROE Slope (years) Quesion for research: Is invesmen horizon also a predicable funcion of marke-wide variables such as he sae of he economy?

18 Inerpreaion of Explanaory Models Across he full sample, R 2 = 26%. I approaches 50% for more sable companies. R 2 biased upward by random B, and downward by pooling across company ypes and ime. Saisical models involving valuaion raios should be ranslaed ino sandard errors in log price o judge heir meris. Apparen degrees of freedom are inflaed because of clusering of observaions by indusry. However, hey are sill very large. Though useful in pracice, inerpreing slope as T may also incorporae an errors-in-variables bias from using ROE as a proxy for r. In an efficien marke, even a very good explanaory model for prices may no forecas reurns. 18

19 Cross Secion redicion Valuaion Residual Reurn redicion For Successive Monhs afer December Correlaion Quesions for Research: How much, B and ROE informaion was available before December? How lae does he surprise porion become known? How would a risk premium look? Jan Feb Mar Apr May Jun Jul Aug Sep Oc Nov Dec 19

20 Regression Coefficiens December Residuals vs. Fuure Reurns. eriod OLS Coefficien -saisic Adjused R 2 January March % April June % July Sepember % 20

21 Hypoheical Cross-secional Reurn Forecas Success Abiliy o Forecas April-June Reurn Differences -12 Does /B-ROE capure periods of reversion o fundamenals? 4 0 -Saisic

22 Cross-Secional Summary /B-ROE gives boh he company and he marke a helpful ool o calibrae he impac of financial plans on shareholder value. Model residuals have predicive power, and are likely o be a useful addiion o he invesor s oolbox, even before disaggregaing by ime and indusry. /B-ROE allows a value approach for growh socks, and is less biased agains high qualiy growh han are radiional raios like /E, /B, /S, and /CF. 22

23 Why Improve Explanaory Models for he S& 500? To increase marke sabiliy by showing relevance of fundamenals and idenifying bubbles. To beer show forecasers he impac of changes in fundamenals. If he marke depars from forecasable fundamenals, o help forecas reurns using valuaion residuals. 23

24 Relevan Srucure If ln(/b) = ln(/b T ) + T * (r - k), comparisons of E/ o ineres raes (so-called Fed Model) are badly mis-specified. See also Figh The Fed Model by Cliff Asness (JM, 2003) Changing moneary inflaion complicaes his picure furher Higher raes of inflaion boh: Raise nominal k Lower replacemen cos profiabiliy and hus r from repored ROE. We herefore model ln(/b) as a linear funcion of ROE, inflaion, and real ineres raes. 24

25 Model Inpus (updaed) ROE: S& 500 s S E/ S Inflaion: 12 Monh CI % Change Real Ineres: Moody s AAA Yield 12 Monh CI % Chg. /B-ROE S&500 Model Inpus Annual Rae gdae ROE Inflaion Real_Ineres 25

26 Full Sample S&500 Index Model Because of omied variables, he model errors are highly auocorrelaed. R-squared of he fi is highly inflaed. ln(/b) S&500 = * ROE 15.9 * Inflaion 8.0 * Real Ineres When appraising he model s hypoheical use as an predicion ool, i is imporan o avoid look-ahead bias. Use expanding window regression afer 5-year warm-up period. 26

27 Wha Does /B-ROE Tell US? (updaed) S&500 Acual /B and Expanding Window Explanaion rice-o-book Raio Acual No_LookAhead 27

28 Using A Regression Model Wih Unsable Missing Variables We know ha he regression model is no fully saisfied The process is no sable Residuals are highly auocorrelaed due o missing variables Changes in risk preference? Changing ROE cross-secional dispersion? Changing axaion? Consequenly, we do no assume ha correlaion auomaically ranslaes ino a successful invesmen decision, Bu... 28

29 Correlaion: /B-ROE Residuals vs. 1 monh S& 500 Reurns Do /B-ROE Residuals redic S& 500 Reurns? Lag

30 redicing S& 500 Reurns wih /B-ROE Residuals Sd. Coefficien Error > 95% Confidence Inerval 1 monh reurn monh reurn monh reurn All -saisics are correced for correlaion (Newey-Wes) redicions are boh economically and saisically significan 30

31 /B-ROE Time-Series Confirms Cross-secion Implied invesmen horizon T agains ROE for he S&500 is similar o ha found in cross-secion for socks in he mos sable quarile. When supplemened by allowance for ime-varying inflaion and ineres raes, /B-ROE: Idenifies key fundamenals conrolling valuaion, useful for planning Is srucurally differen from E/ versus ineres rae comparisons See Figh The Fed Model, Cliff Asness (JM 2003) rovides useful shor-erm coinciden explanaion In addiion, is residuals also show poenial for use as an ingredien in acical asse allocaion (TAA) 31

32 Summary /B-ROE is boh simple and effecive for a wide range of problems Some invesmen managers have used /B-ROE for many years as an addiional valuaion facor... Bu i no used as widely as i could be: By CEO s, CFO s and analyss And for idenifying undervalued growh socks And o beer idenify bubbles And as an ingredien in acical asse allocaion And generally o enhance he imporance of fundamenals as opposed o momenum in invesing and pricing. 32