Comments on "Time-varying Risk Premia and the Cost of Capital: An Alternative. Implication of the Q Theory of Investment" Janice C.

Transcription

1 Commens on "Tme-varyng Rsk Prema and he Cos of Capal: An Alernave Implcaon of he Q Theory of Invesmen" Jance C. Eberly * Kellogg School of Managemen, Norhwesern Unversy, Evanson, IL and Naonal Bureau of Economc Research * I hank Rav Jagannahan for helpful dscussons and Anono da Slva for provdng he daa on equy ssues.

2 Inroducon Marn Leau and Sydney Ludvgson have wren a seres of papers explorng he ably of he consumpon-wealh rao o predc excess sock reurns. The curren paper akes hs agenda anoher sep by nsead predcng real economc acvy - specfcally, nvesmen n physcal capal. The goal s an excng and ambous one: o connec he real and fnancal componens of he macroeconomy. In he pece of he agenda underaken here, he auhors provde compellng evdence ha he consumpon-wealh rao s a useful predcor of fuure nvesmen growh. In my commens, I frs summarze he heorecal connecon beween he consumponwealh rao and fuure nvesmen growh. Ths requres wo basc equaons. Frs, he neremporal budge consran for consumpon lnks he consumpon-wealh rao o fuure reurns. Second, he Q-heory of nvesmen lnks asse reurns o nvesmen. Leau and Ludvgson's earler work examnes he frs alone, whle hs paper adds he second and ess he forecasably of nvesmen usng he consumpon-wealh rao. However, hs second sep also requres ha he consumpon-wealh rao forecas changes n Tobn Q. Ths concepual lnk s no esed n he paper, bu s easly examned. I show n Secon 3 ha Q s ndeed forecasable, conssen wh he argumen of he paper. 2

3 The more challengng queson lad down by hs lne of research, however, s he source of forecasably. In mos sandard models whou arbrage, equy reurns are no forecasable. Emprcal evdence o he conrary has movaed a number of models ha can generae hs feaure. Whle he evdence here conssen wh forecasably of reurns, s slen on he source of hs forecasably. However, he paper dscusses he possbly ha he forecasng power of he consumpon-wealh rao arses from changes n nvesors' requred reurn o rsk and hence, equy rsk prema. Such a uly-based explanaon mgh leave s fooprns n consumpon behavor, and ndeed, he auhors have examned wheher he consumpon-wealh rao predcs fuure changes n consumpon of nondurables and servces. Whle hey fnd no evdence of hs, ha resul s no surprsng. Alernavely, one mgh examne consumer durables expendures for evdence of me varyng rsk prema. Snce durables expendures are physcal capal nvesmens made by households, hey mgh be a more promsng landscape n whch o search for evdence of me varyng rsk averson. I show below ha here s only weak evdence relang he consumpon-wealh rao o fuure durable expendures. The weakness of hs fndng may be because here are conflcng effecs a work, bu he evdence here s decdedly less compellng han for busness nvesmen. Anoher mplcaon explored by he auhors s he presence of "nvesmen lags". Whle hs s no her man focus, he auhors argue ha a me lag n he dynamcs of he nvesmen response o changes n reurns s evdence of an nvesmen lag. I wll argue below ha such a me lag s no conssen wh nvesmen lags ha nvolve me-obuld or oher nsallaon lags. These lags would quash raher han shf he nvesmen 3

4 response. The repored daa seem n fac more conssen wh hs mplcaon of quasfxy of he capal sock n he shor run. 2 Concepually Lnkng he Consumpon-Wealh Rao and Invesmen Growh Theorecally, here s a drec lnk beween he consumpon-wealh rao and fuure nvesmen. The paper develops hs n he frs secon, so here I provde only a summary. Two equaons provde he backbone of he emprcal ess. The frs s he neremporal budge consran. Ths lnks consumpon and wealh wh fuure reurns o wealh, snce he consumpon expendures are lmed by he agen s wealh and he reurns ha can be acheved by nvesng. The second man equaon comes from he Q- heory of nvesmen, snce hs relaes nvesmen o asse prces and reurns. Begnnng from he neremporal budge consran, he paper uses Campbell and Mankw's expresson for he log consumpon-wealh rao (equaon (2) n he paper), = ( r c ) c w = E ρ () w w, + + Ths expresson relaes he consumpon-wealh rao o fuure reurns and wealh and he fuure pah of consumpon. If consumpon s expeced o be fla, E c + = 0 for all. In hs case, curren consumpon s jus an annuy paymen from he sock of wealh, and 4

5 he consumpon-wealh rao s jus he annuy facor, E ρ wrw, +. If he curren = consumpon-wealh rao exceeds hs annuy facor, hen fuure consumpon mus fall, = so ha E ρ c < 0. Smlarly, f he curren consumpon-wealh rao s less han w + he annuy facor, hen fuure consumpon may be ncreasng. Concepually, he consumpon-wealh rao hus summarzes agens' vews abou fuure reurns o wealh and planned consumpon profles. In her earler work, Leau and Ludvgson use hs expresson drecly. Snce he consumpon-wealh rao should predc fuure reurns o wealh, hey develop an emprcal proxy, caˆ y, for he consumpon-wealh rao. Ths emprcal proxy s used o predc reurns o one componen of wealh, he sock marke. 2 The lnk from he consumpon-wealh rao o real economc acvy s also concepually drec. Marke effcency mples ha he expeced requred reurn o a frm's margnal un of capal, r K, equals he oal expeced reurn, or he sum of he expeced capal gan and margnal prof derved from he margnal un of capal. The value of he margnal un of capal s margnal Q. Equang he gross requred reurn and he expeced reurn (capal gan plus margnal prof) o he margnal un of capal yelds Campbell (987) used hs nuon by usng a closely relaed measure, savng, o predc fuure labor ncome n hs "savng for a rany day" model. 2 In prncple, equaon () relaes he consumpon-wealh rao o fuure reurns on oal wealh. Leau and Ludvgson predc one componen of hs, he reurns o levered equy. 5

6 E ( + r ) K π ( K ) Q+ + ( δ ) K =, E (2) Q where r K, s he requred reurn o physcal capal, Q s margnal Q, π s cash flow, and δ s he deprecaon rae of capal, K. The frs erm on he rgh hand sde of equaon (2) measures he expeced capal gan on he margnal un of capal, whle he second erm gves he expeced ne margnal cash flow. Togeher hese gve he oal reurn o he margnal un of capal, whch mus equal he requred reurn on he lef-hand sde of he equaon. Leau and Ludvgson hen log-lnearze hs condon o oban a lnear expresson for he requred reurn o capal, whch s equaon (5) n he paper E ( rk, + ) qe q+ + ( ρ q ) E ( m+ q ) + Φ ρ (3) where ρ q s a consan, Φ s a me-varyng varance erm, and m s he log of ( δ ) I have wren he reurn on he lef hand sde as r K,+ o emphasze ha s he requred reurn on he frm's capal. In order o relae he consumpon-wealh rao o q (and subsequenly o nvesmen), he auhors frs equae r w, and r K,,, he reurns o wealh π K. 6

7 and o physcal capal, respecvely. 3 Wh hs assumpon, equaon (3) can be subsued no equaon () o oban [ ρ q + ( ρ )( m q ) + Φ c ] c w = E w q + + q = ρ (4) Ths expresson relaes he curren (log) consumpon-wealh rao no o fuure reurns o wealh, bu raher o fuure reurns o physcal capal, whch are composed of capal gans, q, and margnal profs, m. The fnal sep connecs he value of capal and nvesmen n capal usng Q heory, as suggesed by he le of he paper. Followng Abel (983), he auhors employ an adjusmen cos funcon of he form g(i )=γi β, β >. Equang he margnal value of an addonal un of capal, Q, wh s expeced margnal cos yelds Q =E - β γi β-. The paper agan log-lnearzes hs expresson o oban q 2 2 = ln( γβ ) + ( β ) E + ( β ) σ ( ) (5) 2 3 Ths subsuon equaes he reurn on wealh and a dfferen sub-componen han he auhors examned n her work on equy reurns and n Table. In hs case, he reurns o physcal capal are subsued for he reurns o oal wealh. 7

8 where ln(i ), and σ 2 ( ) s he condonal varance of log nvesmen. Dfferencng equaon (5) yelds an expresson for q, whch can be subsued no equaon (4) o yeld [ ρ ( β ) + ( ρ )( m q ) + Φ c ] c w = E w q + + q = ρ (6) Equaon (6) relaes he curren (log) consumpon-wealh rao o fuure changes n nvesmen, whch wll be he emprcal subsance of he paper. Ths expresson bulds on wo peces of economc heory. The frs s he neremporal budge consran for consumpon, and he second s he Q heory of nvesmen. The neremporal budge consran relaes he consumpon-wealh rao o fuure reurns. The second lnks asse reurns o nvesmen. In her earler work, he auhors have examned he frs pece. Here hey add he second. 3 Is Tobn's Q forecasable? Before he expresson for opmal nvesmen was subsued above, equaon (4) lnked he consumpon wealh rao o fuure growh n q. Whle he paper moves drecly o examnng equaon (6) by lookng a nvesmen growh, hs lnk s only presen concepually f equaon (4) holds and changes n q are forecasable. 8

9 Snce he auhors gracously provded me her daa, he ably of caˆ y o forecas fuure growh n (log) Tobn's Q s easly esed. The resuls of hs es are repored n Table ; hs able follows he forma of Leau and Ludvgson's (LL) ables by reporng he regresson coeffcen wh he sandard error n parenheses below, followed by he R 2 of he regresson. The frs wo rows of he able reproduce daa from LL Tables and 2, respecvely, for comparson. The hrd row of he able repors he resuls of forecasng fuure growh n log Tobn's Q a he repored quarerly horzons. The resuls sugges ha he ably of caˆ y o predc fuure growh n Tobn's Q s very smlar o s ably o predc sock prces. Ths s reassurng gven he close relaonshp beween Tobn's Q and equy values, as well as he mporan role played by Tobn's Q n he concepual developmen of he subsequen nvesmen regressons. (Table abou here) A poenally relaed effec s shown n he las row of Table. Ths row repors he ably of caˆ y o predc fuure equy ssues a long horzons, whch s subsanal. These daa sugges anoher poenal lnk from forecasable equy reurns o corporae behavor, va corporae fnancng and capal srucure. 4 Wha s he source of caˆ y 's forecasng power? Recall ha n he heorecal developmen of he connecon beween caˆ y and nvesmen, here were wo man equaons. The frs was he neremporal budge 9

10 consran for consumpon, and he second was he Q heory of nvesmen. Neher of hese nvolves uly maxmzaon; ndeed uly s enrely absen from hs concepual framework. Ths srucure s slen on he source of reurn predcably; only requres ha agens respec he neremporal budge consran. The source of reurn predcably s a challengng queson, and he auhors dscuss he possbly ha he forecasng ably of caˆ y derves from s ably o capure movemens n rsk prema. Where mgh one look for evdence of changes n rsk prema? Changes n rsk prema mgh affec consumpon growh; however, n he nroducon of he paper, he auhors say, "movemens n he consumpon-wealh rao bear vrually no relaon o conemporaneous or fuure consumpon growh." Ths s perhaps no surprsng, gven he well-known and heorecally well-movaed smoohness of consumpon. Moreover, evdence suggess ha consumpon s close o a random walk, so changes should be dffcul o predc. However, oher componens of consumpon are no so smooh, and n fac, are concepually and emprcally more smlar o nvesmen. In parcular, one mgh fnd evdence of me varyng rsk prema n consumer durables expendures. Table 2 repors long horzon regressons usng caˆ y o forecas growh n consumer durables expendures. 4 The able has he same forma as Table and he LL ables, reporng he regresson coeffcens, sandard errors, and R 2 a each horzon. The resuls sugges a much weaker relaonshp beween caˆ y and fuure resdenal and durables nvesmen han s found for busness nvesmen. Resdenal nvesmen s he more 0

11 relably predced of he wo durables seres, hough he R 2 peaks a shorer horzons (.08 a four quarers) han busness nvesmen (.8 a 2 quarers n LL Table 2). Consumer durables are even less relably predced; he maxmum R 2 s only.03. (Table 2 abou here) These regressons gnore oher sources of varaon n he forecasng relaonshp. Specfcally, equaon (6) suggess ha he consumpon-wealh rao should predc fuure nvesmen, conrollng for he expeced fuure pah of m, or margnal profably. Tha s, f fuure nvesmen s predcable, should be relaed o caˆ y even afer conrollng for profs. However, he predcably of durables expendure found n Table 2 essenally dsappears n he las row of he able, when we conrol for nal ncome. 5 Invesmen Lags Whle unrelaed o her man lne of research, he auhors also examne "nvesmen lags". They argue, followng Lamon (2000), ha hese lags are responsble for he delayed mng observed n her nvesmen daa. Specfcally, hey argue ha when long run reurns rse, he conemporaneous reurn falls. Whou any "nvesmen lag", hs "sgn flp" or reversal would be mrrored n nvesmen growh, leadng o an mmedae decrease n nvesmen growh, followed by a long run ncrease. 4 The daa are real Personal Consumpon Expendures on durable goods and real Resdenal Invesmen, boh n chaned 996 dollars, seasonally adjused annual raes, from he Bureau of Economc Analyss.

12 In her daa, hs sgn reversal occurs mmedaely (as predced) n forecased reurns (LL Table, reproduced n Table here), so ha he effec of caˆ y on fuure reurns has he same sgn from he frs quarer onward. However, n he nvesmen regressons he sgn reversal s delayed unl he fourh quarer. Ths s argued o be evdence of a fourquarer nvesmen lag. However, f by "nvesmen lags" one means me-o-buld or "delvery lags, plannng lags, consrucon lags" (Secon 4.2) as descrbed n he paper, opmal nvesmen would no be smply delayed, or emporally shfed. Insead, he frm chooses opmal nvesmen knowng ha here wll be a delay. For example, f here s a four-quarer nvesmen lag, he frm chooses fuure nvesmen oday based on oday's expecaon of reurns o capal and Q four quarers hence. I would no be opmal o choose nvesmen based on oday's reurns and Q and hen face a four-quarer delay. Invesmen lags ha delay nsallaon would negae any mmedae effec of reurns and Q on curren nvesmen. Thus, lags of hs sor quash he sgn reversal, raher han delayng. Indeed, hs seems more conssen wh he daa repored n Tables 2 hrough 4 and Table 6, where he sgn reversal s only sgnfcanly dfferen from zero n wo of he egh regressons nvolvng caˆ y. Insead, he daa seem o provde evdence of a mued shorrun response and herefore shor-run quas-fxy of he capal sock. 5 5 An "expendure lag", raher han an nvesmen lag, mgh appear o emporally shf nvesmen relave o reurns and Q. Wh such a lag, nvesmen would be nsalled mmedaely, bu he expendure would be recorded a some fuure dae and measured by he economercan as occurrng hen. Ths would 2

13 6 Concludng Remarks Leau and Ludvgson provde compellng evdence ha a proxy for he consumponwealh rao forecass fuure nvesmen growh a he wo o four year horzon. They exensvely "sress es" hs resul, showng ha holds, wh only small varaons, n equpmen and srucures separaely, and conrollng for oher varables ofen used o explan nvesmen, such as lagged nvesmen, profs, Tobn's (average) Q, and GDP. Whle hese varables explan a larger share of he varaon n nvesmen growh han he fnancal varables examned n LL Table 2, hey do no elmnae he margnal forecasng power of caˆ y. The concepual lnk beween caˆ y and nvesmen growh developed here bulds from he neremporal budge consran for consumpon and he Q heory of nvesmen. Secon 3 of hs commen shows ha he nermedae lnk from he neremporal budge consran o nvesmen reurns and Q s a sold bass for he subsequen nvesmen regressons. Tha s, caˆ y s hypoheszed o predc nvesmen because predcs he reurn o capal; he resuls n Table 2 sugges ha ndeed changes n Q. caˆ y does predc fuure The deeper queson underlyng hs research agenda, however, s he source of reurn predcably. Whle he heorecal developmen and ess employed here are formally slen on hs pon, he dscusson and resuls mgh provde some clues. Predcably of emporally shf he enre nvesmen seres. Ths expendure lag would generae a "sgn flp" a he fourh 3

14 reurns s conssen wh me varaon n rsk prema, and he auhors argue ha may be measurng hese changes n agens' requred rsk prema. Snce curren forecass changes n nvesmen, hese daa are conssen wh a sgnfcan response from he corporae secor o changes n rsk prema. Less supporve, however, s he evdence n Table 2 of hs noe, suggesng a much weaker response of households' nvesmen n consumer durables. If caˆ y caˆ y caˆ y s measurng changes n agens' rsk prema, would be very convncng o see hese changes refleced n her own nvesmens, n addon o hose made ndrecly va he corporae secor. Whle may be ha he effecs are masked by measuremen or offseng concepual effecs, he resuls for consumer nvesmen are consderably weaker han hose for busness nvesmen. By lnkng forecasably of equy reurns o forecasably of busness nvesmen, hese resuls move forward he enerprse of lnkng fnancal and macroeconomc varables. The emprcal work here connecs he consumpon-wealh rao, asse reurns, and nvesmen. The fascnang queson for fuure work s wheher hs connecon s evdence for a sascal model wh relable forecasng properes, or wheher goes furher oward an asse-prcng model - lnkng uly and asse reurns. quarer f capal were nsalled mmedaely, bu he expendures were no recorded for a year. 4

15 References Abel, A., March 983, Opmal Invesmen under Uncerany. Amercan Economc Revew 73(), Campbell, J., November 987, Does Savng Ancpae Declnng Labor Income? An Alernave Tes of he Permanen Income Hypohess. Economerca 55(6), Lamon, O., December 2000, Invesmen Plans and Sock Reurns. Journal of Fnance 55(6),

16 Table. Forecasng growh n Tobn's Q usng caˆ y cay ˆ forecass: Sock reurns (LL Table ) Growh n oal nvesmen (LL Table 2) Growh n Average Q Growh n Equy Issues Forecas Horzon, H (3.08) (2.98) (2.85) (2.67) (3.85) (-.44) (2.0) (0.97) (-0.24) (3.35) (.94) (2.5) (3.40) (2.85) (4.) (3.89) (4.89) (4.33) (7.74) (4.46) (2.33) (3.86) (8.25) (5.35) 0.7 6

17 Table 2. Forecasng growh n durables and resdenal nvesmen usng caˆ y cay forecass growh n: Consumpon (non-durables & servces) Resdenal Invesmen Durables Invesmen Durables Invesmen, conrollng for nal ncome (-.80) (-.8) (-.2) (-0.7) (-.22) (2.57) (0.20) (0.00).46 (3.6) (.3) (.04) 3.40 (4.45) (2.06) (.72) 3.89 (3.08) (2.05) (.2) 2.27 (.6) (2.79) (0.70) (-.58) (0.0) (.67) (-0.22) 7