money illusion in the stock market: the modigliani-cohn hypothesis
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1 money lluson n he sock marke: he modglan-cohn hypohess Chrsopher Polk Norhwesern Unversy (wh Randy Cohen and Tuomo Vuoleenaho) Froners of Fnance 2005 Bonare
2 money lluson n he sock marke OVERVIEW
3 Research quesons Can sudyng he cross-secon of average reurns shed lgh on wheher nvesors confuse nomnal and real raes of cash-flow growh? How does one generae a conssen spread n marke bea among socks? Is here a posve cross-seconal premum for marke rsk? Does keepng nflaon under conrol have mplcaons for marke effcency? money lluson n he sock marke
4 Conrbuons Presen evdence for a perssen behavoral bas on he par of nvesors: Modglan and Cohn s (1979) money lluson Inroduce a new mehodology for esmang he excess slope and nercep of he secury marke lne Explan he emprcal puzzle ha hgh-bea socks have no hsorcally ouperformed low-bea socks by he marke premum Take a dscplned approach o behavoral fnance: use a smple plausble heory and es mplcaons he heory was no desgned o explan money lluson n he sock marke
5 money lluson n he sock marke THE IDEA
6 Effec of money lluson Assume nflaon s hgh (e.g. 1982) Bond yelds are hgh AGGREGATE MARKET EFFECT (pror papers) Invesors sell socks buy bonds unl sock yelds (mnus a rsk premum) are reasonably close o bond yelds However sock and bond yelds are no drecly comparable Socks are clams on real asses whle bonds are no In ha sense he nomnal componen of he bond yeld s only an llusonary reurn So socks have hgher expeced reurns han hey would n he absence of hs lluson money lluson n he sock marke
7 Effec of money lluson Assume nflaon s hgh (e.g. 1982) Bond yelds are hgh INDIVIDUAL STOCK EFFECT (hs paper) Illuson makes he aggregae sock marke cheap Invesors hnkng he forward-lookng premum s modes prce hgh-bea socks only a lle cheaper han low-bea socks The realzed marke premum wll exceed he (erroneous) expecaon by nflaon (plus nose). CAPM ess wll fal hgh bea socks were prced o only ouperform low bea socks by he dfference n beas mes he modes expeced premum no by he dfference n beas mes he acual equy premum (plus nose) money lluson n he sock marke
8 Effec of money lluson - example Sock A has a β=1.5 sock B has a β=0.5 Invesors demand a consan equy premum of four percen Inflaon s hree percen CAPM Sock A earns a premum of sx percen over he T-bll Sock B earns a premum of wo percen over he T-bll SML slope (four percen) = equy premum (four percen) CAPM and money lluson Invesors fal o realze ha socks are clams on real asses Socks are undervalued The raonal expecaon of he equy premum becomes seven percen Sock A earns a premum of nne percen over he T-bll Sock B earns premum of fve percen over he T-bll SML slope (four percen) equy premum (seven percen) money lluson n he sock marke
9 money lluson n he sock marke THE FED MODEL
10 The Fed model The Fed model saes ha he aggregae sock yeld (earnngs yeld or dvdend yeld) should equal he bond yeld plus a rsk premum From he Federal Reserve Board s Moneary Polcy Repor o he Congress of July 1997: Sll he rao of prces n he S&P 500 o consensus esmaes of earnngs over he comng welve monhs has rsen furher from levels ha were already unusually hgh. Changes n hs rao have ofen been nversely relaed o changes n long-erm Treasury yelds bu hs year s sock prce gans were no mached by a sgnfcan ne declne n neres raes. The nuon s ha socks and bonds compee for space n nvesors' porfolos. For boh o be held n equlbrum hey mus have equal rskadjused yelds Asness (2000): If he marke uses he Fed model he dvdend yeld on socks should be well explaned by he bond yeld and a proxy for he relave rskness of socks. money lluson n he sock marke
11 The Fed model explans prces... Source: Campbell and Vuoleenaho (2004) money lluson n he sock marke
12 ...bu does no forecas reurns Cross-seconal prce of rsk s black. Smooh earnngs/prce s blue. Smooh earnngs/prce mnus T-bond yeld s green. Source: Polk Thompson and Vuoleenaho (2004) money lluson n he sock marke
13 Money lluson n he Fed model Modglan and Cohn (1977) Rer and Warr (2000) Asness (2003) and Campbell and Vuoleenaho (2004) pon ou a serous logcal flaw whn he Fed model: Sock yelds are "real" fuure nomnal earnngs and dvdends grow wh nflaon Bond yelds are "nomnal" fuure coupons and prncpal do no grow wh nflaon Comparng real sock yelds o nomnal bond yelds assumes ha he nomnal growh rae of socks' cash flows s consan Consequence: Model undervalues socks a mes of posve (hgh) nflaon and overvalues socks a mes of negave (low) nflaon money lluson n he sock marke
14 Money lluson n he Fed model Pu dfferenly Fed-model nvesors apparenly use he followng npus n her presen value calculaon Consan nomnal cash-flow growh raes (perhaps a hsorcal average) Dscoun raes equal o he nomnal bond yeld plus a rsk premum Bu whle he nomnal bond yeld adjuss for curren nflaon he hsorcal nomnal growh rae does no Consequence: Model undervalues socks a mes of posve (hgh) nflaon and overvalues socks a mes of negave (low) nflaon money lluson n he sock marke
15 Tme-seres decomposon Sandard VAR analyss provdes hree facs Inflaon s posvely correlaed wh expeced dvdend growh Inflaon s negavely correlaed wh he subjecve rsk premum Inflaon s posvely correlaed wh fuure rsk-adjused reurns Source: Campbell and Vuoleenaho (2004) money lluson n he sock marke
16 Money lluson n he Fed model Tme-seres evdence Msprcng Inflaon 0.88 correlaon!!! Source: Campbell and Vuoleenaho (2004) money lluson n he sock marke
17 money lluson n he sock marke MODELING
18 Frm-level valuaon e e D / P 1 = R G = R G D s dvdend P s prce R s he subjecve dscoun rae and G s expeced dvdend growh. All varables are eher n real erms or n nomnal erms. The subscrp e denoes varables n excess of he rsk-free rae Ths equaon holds for all frms Raonal prcng: R corresponds o he long-horzon expeced excess reurn (f reurns are consan over me) e OBJ e OBJ D / P 1 = R G Irraonal prcng: G corresponds o based expeced longhorzon dvdend growh e SUBJ e SUBJ D / P 1 = R G money lluson n he sock marke
19 Model of marke equlbrum Assume he followng 1) The only valuaon msake made by nvesors s o fal o adjus expeced nomnal growh raes wh nflaon Specfcally prcng errors are ε = ε M = γ 1 + γ 2 π -1 where γ 2 > 0 (snce nflaon s he same for all socks) 2) Subjecve expeced reurns are deermned by he Sharpe-Lnner CAPM Specfcally nvesors prce he cross secon of socks o yeld a rsk premum equal o bea mes he subjecve equy premum Implcaon: Low nflaon mples an expeced-reurn bea relaon ha s oo seep hgh nflaon mples an expecedreurn bea relaon ha s oo shallow money lluson n he sock marke
20 money lluson n he sock marke Money Illuson klls he CAPM! ) )( ( ) ( ) )(1 ( ) ( ) ( / Lnner CAPM Objecve Sharpe Lnner CAPM Subjecve Sharpe 1 OBJ OBJ M OBJ OBJ e M OBJ e M M OBJ e M OBJ e SUBJ e M OBJ e SUBJ e OBJ e SUBJ e OBJ e SUBJ e OBJ e SUBJ e OBJ e SUBJ e SUBJ e R R R R R R R R G G G G R G G R P D β π γ γ π γ γ α α β π γ γ ε β ε α β ε β ε ε β ε β ε ε + + = = + = = = = = = + + = = Defne msprcng Assumpon 2: CAPM benchmark Assumpon 1: Money Illuson msprcng
21 Excess nercep and slope of SML Calculae he objecve Sharpe - Lnner alpha for a zero bea asse : OBJ UB OBJ ZB Calculae he objecve Sharpe - Lnner alpha for a un bea asse : 1 0 OBJ UB excess nercep of α α OBJ ZB = 0 1 he SML : γ 1 + γ 2π excess slope of he SML : α α = γ 1 + γ 2π = γ 1 γ 2π 1 1 money lluson n he sock marke
22 10 bea-sored porfolos money lluson n he sock marke
23 money lluson n he sock marke METHODOLOGY
24 Formal ess Three-sage process Sage 1: Creae porfolos Sor socks no N porfolos on pas esmaed beas Esmae he pos-rankng beas for hese N porfolos wh a K- monh ralng wndow We focus on N=20 K=36 bu resuls are robus o hese choces money lluson n he sock marke
25 Formal ess Three-sage process Sage 2: Fama-MacBeh cross-seconal regressons Each monh regress he fuure excess reurns of hese N porfolos on an nercep and pas esmaed pos-rankng beas The me seres of coeffcens represens he reurns on a managed porfolo wh pas bea of 0 (for he coeffcens on he consan) or 1 (for he coeffcens on bea) Call hese he nercep porfolo and he slope porfolo respecvely Inercep porfolo s un-nvesmen; slope s zero-nvesmen money lluson n he sock marke
26 Formal ess Three-sage process Sage 3: Black-Jensen-Scholes me-seres regressons Run wo me seres regressons: Regress he nercep porfolo's reurns and he slope porfolo's reurns on a consan he marke's conemporaneous excess reurn and lagged nflaon Solve for he excess slope and excess nercep of he SML as a funcon of nflaon (.e. adjus for fac ha acual beas of slope and nercep porfolo are no exacly 0 and 1) money lluson n he sock marke
27 money lluson n he sock marke RESULTS
28 Table 1: Tme-Seres Regressons of Inercep and Slope Porfolos K N a 1 a 2 b 1 b 2 c 1 c 2 R 2 nercep R 2 slope % 58.03% (0.36) (-0.40) (0.14) (34.38) (2.41) (-2.35) % 57.69% (0.33) (-0.40) (-1.12) (34.15) (2.23) (-2.16) % 58.58% (0.33) (-0.21) (2.07) (34.75) (2.57) (-2.65) % 57.19% (-0.06) (-0.03) (2.10) (34.02) (2.73) (-2.57) % 57.23% (0.70) (-0.72) (-0.53) (33.55) (1.86) (-1.85) money lluson n he sock marke
29 Excess slope and nercep Excess slope: Defne π -1 as demeaned nflaon g 0 + g 1 π -1 g 0 a 2 /b 2 g 1 c 2 /b 2 Excess nercep (or excess zero-bea rae) Defne π -1 as demeaned nflaon h 0 + h 1 π -1 h 0 a 1 -a 2 *(b 1 /b 2 ) h 1 c 1 -c 2 *(b 1 /b 2 ) money lluson n he sock marke
30 Hypohess ess We es predcons of he CAPM and of he jon hypohess of he CAPM and money lluson: Hypohess 1 (CAPM): g 1 = h 1 = 0 Hypohess 2 (Jon): g 1 = -h 1 Hypohess 1 s generally rejeced; Hypohess 2 s no rejeced money lluson n he sock marke
31 Table 2: Excess Inercep and Slope of he Secury Marke K N g 0 g 1 h 0 h 1 [g 1 h 1 ] =0 g 1 + h 1 = (-0.40) (-2.35) (0.36) (2.40) 5.82 [0.05] 0.00 [0.96] (-0.40) (-2.16) (0.33) (2.23) 5.20 [0.07] 0.00 [0.95] (-0.21) (-2.64) (0.32) (2.57) 7.12 [0.03] 0.00 [0.99] (-0.06) (-2.56) (-0.05) (2.71) 8.37 [0.02] 0.01 [0.93] (-0.72) (-1.85) (0.71) (1.86) 3.46 [0.18] 0.00 [0.98] money lluson n he sock marke
32 Table 3: Resuls from Expanded Asse Ses 20 bea-sored and 10 ME-sored porfolos K g 0 g 1 h 0 h 1 [g 1 h 1 ] =0 g 1 + h 1 = (0.22) (-2.55) (0.07) (2.41) 6.94 [0.03] 0.00 [0.95] 20 bea-sored and 10 BE/ME-sored porfolos K g 0 g 1 h 0 h 1 [g 1 h 1 ] =0 g 1 + h 1 = (0.03) (-3.12) (-0.02) (3.23) [0.00] 0.01 [0.93] 20 bea-sored 10 ME-sored and 10 BE/ME-sored porfolos K g 0 g 1 h 0 h 1 [g 1 h 1 ] =0 g 1 + h 1 = (0.52) (-3.13) (-0.30) (3.13) [0.01] [0.99] money lluson n he sock marke
33 Table 4: Inflaon and he Spread beween Borrowng and Treasury Raes 48-monh car loans from commercal banks spread over he 48-monh T-noe yeld consan (-sa) slope on π (-sa) Adj. R 2 N (13.9) (-0.9) monh personal loans from commercal banks spread over he 24-monh T-noe yeld consan (-sa) slope on π (-sa) Adj. R 2 N (29.4) (-7.9) Cred card accouns (neres raes) spread over he 90-day T-bll yeld consan (-sa) slope on π (-sa) Adj. R 2 N (22.8) (-2.0) Cred card accouns (assessed neres) spread over he 90-day T-bll yeld consan (-sa) slope on π (-sa) Adj. R 2 N (21.1) (-2.0) money lluson n he sock marke
34 Table 5: Resuls for he Fama-French Three-Facor Model 20 bea-sored porfolos K g 0 g 1 h 0 h 1 [g 1 h 1 ] =0 g 1 + h 1 = (0.11) (-1.75) (-0.13) (1.71) 3.13 [0.21] 0.00 [1.00] 20 bea-sored and 10 ME-sored porfolos K g 0 g 1 h 0 h 1 [g 1 h 1 ] =0 g 1 + h 1 = (-0.76) (-1.51) (0.75) (1.52) 2.30 [0.32] 0.00 [0.99] 20 bea-sored and 10 BE/ME-sored porfolos K g 0 g 1 h 0 h 1 [g 1 h 1 ] =0 g 1 + h 1 = (-0.40) (-3.12) (-0.35) (1.36) 2.28 [0.32] 0.00 [0.99] 20 bea-sored 10 ME-sored and 10 BE/ME-sored porfolos K g 0 g 1 h 0 h 1 [g 1 h 1 ] =0 g 1 + h 1 = (-0.62) (-1.80) (0.60) (1.84) [0.17] [0.98] money lluson n he sock marke
35 money lluson n he sock marke CONCLUSIONS
36 Conclusons Puzzle: hgh-bea socks fal o suffcenly ouperform low bea socks n several sub-perods (e.g. 1950s 1980s) Money lluson s one of he oldes and mos plausble heores n behavoral fnance The heory s me-seres predcons f he daa bu hs fndng suffers from he problems of all such ess (few daa pons) Our cross-seconal es does no have hs problem and s ruly ouof-sample Daa are enrely conssen wh he jon hypohess of money lluson and he CAPM Our paper boh suppors he money lluson heory and explans he bea-reurn puzzle Mulfacor models and Black s CAPM do no explan our fndngs Moneary polcy amed a keepng nflaon low and predcable may make markes more effcen mprovng capal allocaon money lluson n he sock marke
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