MONEY ILLUSION IN THE STOCK MARKET: THE MODIGLIANICOHN HYPOTHESIS*


 Polly Bridges
 2 years ago
 Views:
Transcription
1 MONEY ILLUSION IN THE STOCK MARKET: THE MODIGLIANICOHN HYPOTHESIS* RANDOLPH B. COHEN CHRISTOPHER POLK TUOMO VUOLTEENAHO Modigliani and Cohn hypothsiz that th stock markt suffrs from mony illusion, discounting ral cash flows at nominal discount rats. Whil prvious rsarch has focusd on th pricing of th aggrgat stock markt rlativ to Trasury bills, th monyillusion hypothsis also has implications for th pricing of risky stocks rlativ to saf stocks. Simultanously xamining th pricing of Trasury bills, saf stocks, and risky stocks allows us to distinguish mony illusion from any chang in th attituds of invstors toward risk. Our mpirical rsults support th hypothsis that th stock markt suffrs from mony illusion. I. INTRODUCTION Do popl suffr from mony illusion, confusing nominal dollar valus with ral purchasing powr? Whn th diffrnc btwn ral and nominal quantitis is small and staks ar rlativly low, quating th nominal dollar amounts with ral valus provids a convnint and ffctiv rul of thumb. Thrfor, it sms plausibl that popl oftn ignor th rat of inflation in procssing information for rlativly small dcisions. 1 Modigliani and Cohn [1979] hypothsiz that stock markt invstors may also suffr from a particular form of mony illusion, incorrctly discounting ral cash flows with nominal discount rats. An implication of such an rror is that tim variation in th lvl of inflation causs th markt s subjctiv xpctation of th futur quity prmium to dviat systmatically from th * An arlir draft of th papr was circulatd undr th titl How Inflation Illusion Killd th CAPM. W would lik to thank Clifford Asnss, John Campbll, Edward Glasr, Jussi Kppo, Stfan Nagl, Andri Shlifr, Jrmy Stin, and thr anonymous rfrs for hlpful commnts. 1. Th trm mony illusion was coind by John Maynard Kyns arly in th twntith cntury. In 1928 Irving Fishr gav th subjct a thorough tratmnt in his book Th Mony Illusion. Sinc thn, numrous paprs hav dscribd implications of mony illusion to tst for its xistnc. Th most widly discussd of ths implications is stickinss in wags and prics (s Gordon [1983] for a rviw of th vidnc on this topic). Although mony illusion can xist vn in th absnc of inflation, inflation is cntral to most mony illusion storis. Fishr and Modigliani [1978] catalog th ways in which inflation could affct th ral conomy, with mony illusion as on important sourc of ral ffcts. Shafir, Diamond, and Tvrsky [1997] xamin in dtail potntial ffcts of mony illusion and prsnt vidnc on ths ffcts along with a thory of th psychological undrpinnings of th illusion by th Prsidnt and Fllows of Harvard Collg and th Massachustts Institut of Tchnology. Th Quartrly Journal of Economics, May
2 640 QUARTERLY JOURNAL OF ECONOMICS rational xpctation. Thus, whn inflation is high (low), th rational quityprmium xpctation is highr (lowr) than th markt s subjctiv xpctation, and th stock markt is undrvalud (ovrvalud). Th claim that stock markt invstors suffr from mony illusion is a particularly intriguing and controvrsial proposition, as th staks in th stock markt ar obviously vry high. Nvrthlss, rcnt timsris vidnc suggsts that th stock markt dos suffr from mony illusion of Modigliani and Cohn s varity. Sharp [2002] and Asnss [2000] find that stock dividnd and arnings yilds ar highly corrlatd with nominal bond yilds. Sinc stocks ar claims to cash flows from ral capital and inflation is th main drivr of nominal intrst rats, this corrlation maks littl sns, a point mad rcntly by Rittr and Warr [2002], Asnss [2003], and Campbll and Vuoltnaho [2004]. Ths aggrgat studis suffr from on srious waknss, howvr. Inflation may b corrlatd with invstors attituds toward risk, which dirctly influnc stock prics vn if invstors do not suffr from mony illusion. To th xtnt that ths aggrgat studis fail to fully control for risk, th rsults may confound th impact of risk attituds and mony illusion. Our novl tsts xplor th crosssctional asstpricing implications of th ModiglianiCohn monyillusion hypothsis. Simultanously xamining th pricing of Trasury bills, saf stocks, and risky stocks allows us to distinguish mony illusion from changing attituds of invstors toward risk. Th ky insight undrlying our tsts is that mony illusion will hav a symmtric ffct on all stocks yilds, rgardlss of thir xposur to systmatic risk. In contrast, th impact of invstor risk attituds on a stock s yild will b proportional to th stock s risk, as risky stocks yilds will b affctd much mor than saf stocks yilds will b. This insight allows us to clanly sparat th two compting ffcts. Spcifically, w assum that invstors us th logic of th SharpLintnr capital asst pricing modl (CAPM) [Sharp 1964; Lintnr 1965] to masur th riskinss of a stock and to dtrmin its rquird risk prmium. According to th CAPM, a stock s bta with th markt is its sol rlvant risk masur. In th absnc of mony illusion (and othr invstor irrationalitis), th SharpLintnr CAPM prdicts that th risk compnsation for on unit of bta among stocks, which is also calld th slop of th scurity markt lin, is always qual to th rationally x
3 MONEY ILLUSION IN THE STOCK MARKET 641 pctd prmium of th markt portfolio of stocks ovr shorttrm bills. For xampl, if a risky stock has a bta of 1.5 and th rationally xpctd quity prmium is 4 prcnt, thn that stock should hav a rationally xpctd rturn of th Trasurybill yild plus 6 prcnt. Convrsly, a saf stock with a bta of 0.5 should only arn a 2 prcnt prmium ovr Trasury bills, and th risky stock will thrfor rturn a prmium of 4 prcnt ovr th saf stock. Th joint hypothsis of mony illusion and th CAPM offrs a sharp, quantitativ prdiction. W show that mony illusion implis that, whn inflation is low or ngativ, th compnsation for on unit of bta among stocks is largr (and th scurity markt lin stpr) than th rationally xpctd quity prmium. Convrsly, whn inflation is high, th compnsation for on unit of bta among stocks is lowr (and th scurity markt lin shallowr) than what th ovrall pricing of stocks rlativ to bills would suggst. Suppos that, in our abov xampl, high inflation lads monyillusiond invstors, who still dmand a 4 prcnt quity prmium, to undrvalu th stock markt to th xtnt that th rational xpctation of th quity prmium bcoms 7 prcnt. Thn ths invstors will pric th risky stock to yild only a 4 prcnt rturn prmium ovr th saf stock. Consquntly, whn inflation is high, th avrag ralizd quity prmium (7 prcnt) will b highr than th avrag rturn prmium of th risky stock ovr th saf stock (4 prcnt). Our mpirical tsts support this hypothsis. First, as an illustration, w sort th months in our sampl into quartils basd on laggd inflation and xamin th pricing of btasortd portfolios in ths quartils. Th slop of th solid lin in Figur I dnots th pric of risk implid by th pricing of th ovrall stock markt rlativ to that of shorttrm bills, i.., th quity prmium that a rational invstor should hav xpctd. Th dashd lin is th scurity markt lin, th slop of which is th pric of risk implid by th pricing of highrisk stocks rlativ to that of lowrisk stocks. As prdictd by th monyillusion hypothsis, th figur shows that during months that ar prcdd by inflation in th lowst quartil of our sampl, th rlation btwn avrag rturns and CAPM btas is stpr than th slop prdictd by th SharpLintnr CAPM and no mony illusion. Convrsly, during months that ar prcdd by inflation in th highst quartil of our sampl, th scurity markt lin
4 642 QUARTERLY JOURNAL OF ECONOMICS FIGURE I Avrag Excss Rturns and Bta in Diffrnt Inflation Environmnts W first crat tn portfolios by sorting stocks on thir past stimatd btas. W thn rcord th xcss rturns on ths portfolios. Nxt, w sort months in our 1927: :12 sampl into four groups basd on laggd inflation (dfind as th smoothd chang in th producr pric indx). For ach group, w thn stimat th postformation btas and avrag xcss rturns. Th avrag annualizd xcss rturns ( yaxis) and btas ( xaxis) of ths portfolios form th graphs. Th solid lin (drawn from th [0,0] to [1, avrag markt s xcss rturn in this subsampl]) is th rlation prdictd by th SharpLintnr CAPM. Th dashd lin is th fittd lin computd by rgrssing th avrag rturns on btas in ach subsampl. stimatd from th cross sction of btasortd portfolios is much shallowr than th xpctd quity prmium. Scond, w introduc a nw mthod for stimating th xcss slop and xcss intrcpt of th scurity markt lin among stocks, rlativ to th prdictions of th SharpLintnr CAPM. Our statistical tst combins FamaMacBth [1973] crosssctional and BlackJnsnSchols [1972] timsris rgrssions to solv for th xcss slop and xcss intrcpt as a function of th btas and conditional alphas from th timsris rgrssion s paramtrs. Th ida bhind this statistical tst is xactly th
5 MONEY ILLUSION IN THE STOCK MARKET 643 sam as th on illustratd in Figur I, but allows for a convnint and powrful statistical hypothsis tst. Our tsts indicat that th xcss intrcpt of th scurity markt lin comovs positivly and th xcss slop ngativly with inflation, as prdictd by th ModiglianiCohn monyillusion hypothsis. At first, it may sm incrdibl that stock markt invstors, with trillions of dollars at stak, mak such a pdstrian mistak. Fortunatly, or prhaps unfortunatly, w nd not look any furthr than to th lading practitionr modl of quity valuation, th socalld Fd modl, 2 to find corroborating vidnc of stock markt invstors falling pry to mony illusion. Th Fd modl rlats th yild on stocks to th yild on nominal bonds. Practitionrs argu that th bond yild plus a risk prmium dfins a normal yild on stocks, and that th actual stock yild tnds to rvrt to this normal yild. Consistnt with this practitionr argumnt, Sharp [2002], Asnss [2000], and Campbll and Vuoltnaho [2004] find that th Fd modl is quit succssful as an mpirical dscription of aggrgat stock prics prics ar st as if th markt usd th Fd modl to pric stocks. Logically, howvr, th Fd modl is on wak grounds, as it is basd on prcisly th monyillusion rror notd by Modigliani and Cohn. Evn if most stockmarkt invstors confus nominal and ral quantitis, could a small numbr of walthy and rational arbitragurs still liminat any potntial mispricing? W bliv that rational arbitragurs would b vry consrvativ in accommodating supply and dmand du to mony illusion. Th Sharp ratio (th xpctd xcss rturn dividd by th standard dviation of xcss rturn) of a bt against th monyillusion crowd is likly to b rlativly low, bcaus on can only mak a singl bt at a tim and bcaus th mispricing may b corrctd vry slowly. This potntial slow corrction of mispricing is a particularly important limiting factor of arbitrag, as any attmpt to corrct th inflationrlatd mispricing xposs th arbitragur to th uncrtain dvlopmnt of th stock markt s fundamntals. Mispricing that corrcts slowly ncssarily rquirs long holding priods for arbitrag positions along with significant xposur to volatility, as th varianc of fundamntal risk grows linarly in tim. In fact, if a rational arbitragur had bt against mony illusion by buying stocks on margin in th arly 1970s, his profits 2. Dspit this nam, th modl has absolutly no official or spcial status within th Fdral Rsrv systm.
6 644 QUARTERLY JOURNAL OF ECONOMICS would hav bn ngativ for mor than a dcad. As Modigliani and Cohn notd in 1979: On th othr hand, thos xprts of rational valuation who could corrctly assss th xtnt of th undrvaluation of quitis, had thy actd on thir assssmnt in th hop of acquiring richs, would hav mor than likly ndd up with substantial losss. In summary, mispricing causd by mony illusion has prcisly thos charactristics that Shlifr and Vishny [1997] suggst ffctivly prvnt arbitrag activity. II. MONEY ILLUSION AND ITS IMPLICATIONS II.A. Modigliani and Cohn s MonyIllusion Hypothsis Th corrct application of th prsntvalu formula discounts nominal cash flows at nominal discount rats or ral cash flows at ral discount rats. Modigliani and Cohn [1979] propos that stock markt invstors, but not bond markt invstors, suffr from mony illusion, ffctivly discounting ral cash flows at nominal rats. What mchanism could caus th bond markt to corrctly rflct inflation, whil th stock markt suffrs from mony illusion? According to th ModiglianiCohn hypothsis, mony illusion is du to th difficulty of stimating longtrm futur growth rats of cash flows. Considr an invstor who thinks in nominal trms. Sinc nominal bonds hav cash flows that ar constant in thos trms, stimating a growth rat for bonds is not difficult. In contrast, th task of stimating th longtrm xpctd cashflow growth for stocks is far from trivial. For xampl, suppos that this invstor rronously assums that longtrm arnings and dividnd growth ar constant in nominal trms, and uss all past historical data to stimat a longtrm growth rat for a stock. Of cours, a mor rasonabl assumption would b that xpctd longtrm growth is constant in ral trms. If xpctd longtrm growth is constant in ral trms, yt th invstor xpcts it to b constant in nominal trms, thn in quilibrium stocks will b undrvalud whn inflation is high and ovrvalud whn inflation is low. Th basic intuition of th ModiglianiCohn hypothsis can asily b capturd by xamining a monyillusiond invstor s approach to stock valuation. Considr th classic Gordon growth modl [Williams 1938; Gordon 1962] that quats th dividnd
7 MONEY ILLUSION IN THE STOCK MARKET 645 pric ratio with th diffrnc btwn th discount rat and xpctd growth: (1) D t /P t 1 R G, whr R is th longtrm discount rat and G is th longtrm growth rat of dividnds. R and G can b ithr both in nominal trms or both in ral trms, but th Gordon growth modl dos not allow mixing and matching nominal and ral variabls. If th xpctd rturns ar constant, th discount rat is xactly qual to th xpctd rturn on th asst. If conditional xpctd rturns vary ovr tim, howvr, th discount rat is only approximatly qual to th longhorizon xpctd holding priod rturn on th asst. Th Gordon growth modl can also b thought of in trms of th invstor s firstordr condition. If an invstor is at th optimum portfolio allocation, thn th discount rat or xpctd rturn R on stocks must qual th yild on bonds plus a prmium du to th highr covarianc of stock rturns with th invstor s consumption. If an othrwis optimizing invstor suffrs from mony illusion of Modigliani and Cohn s varity, thn h thinks of R in nominal trms and xpcts G to b constant in nominal trms. If th inflation is tim varying, howvr, th assumption of constant nominal G dos not mak any sns, as it would imply a wildly variabl ral G. In ral trms, thr is no obvious rason why ithr R or G should chang mchanically with xpctd inflation, if th consumr is rational. 3 If stock markt invstors suffr from mony illusion and xpct constant longtrm growth in nominal trms, what will happn whn inflation riss? Highr nominal intrst rats rsulting from inflation ar thn usd by stock markt participants to discount unchangd xpctations of futur nominal dividnds. Th dividndpric ratio movs with th nominal bond yild bcaus stock markt invstors irrationally fail to adjust th nominal growth rat G to match th nominal discount rat R. From th prspctiv of a rational invstor, stocks ar thus undrvalud whn inflation is high and ovrvalud whn inflation is low. A singl small rational invstor, facing a markt populatd by monyillusiond invstors, would thn tilt his portfolio toward 3. Som businsscycl dynamic (such as Fama s [1981] proxy hypothsis) might crat a corrlation btwn inflation and ithr nartrm discount rats or nartrm growth rats. Howvr, such movmnts ar a priori unlikly to mov longtrm discount rats or growth rats much.
8 646 QUARTERLY JOURNAL OF ECONOMICS stocks whn inflation is high and away from stocks whn inflation is low, so that th quilibrium risk prmium of stocks would b justifid by stock rturns covarianc with his consumption. To adapt th notation to conform with our subsqunt mpirical tsts, first subtract th risklss intrst rat from both th discount rat and th growth rat of dividnds. W dfin th xcss discount rat as R R R f and th xcss dividnd growth rat as G G R f, whr all quantitis should again b ithr nominal or ral. As w ar considring th possibility that som invstors ar irrational, w follow Campbll and Vuoltnaho [2004] and distinguish btwn th subjctiv xpctations of irrational invstors (suprscript SUBJ) and th objctiv xpctations of rational invstors (suprscript OBJ). As long as irrational invstors simply us th prsnt valu formula with an rronous xpctd growth rat or discount rat, both sts of xpctations must oby th Gordon growth modl: (2) D/P R,OBJ G,OBJ R,SUBJ G,SUBJ G,OBJ R,SUBJ G,OBJ G,SUBJ. In words, th dividnd yild has thr componnts: (1) th ngativ of objctivly xpctd xcss dividnd growth, (2) th subjctiv risk prmium xpctd by irrational invstors, and (3) a mispricing trm du to a divrgnc btwn th objctiv (i.., rational) and subjctiv (i.., irrational) growth forcast, ε G,OBJ G,SUBJ. Notic that mispricing ε is spcifid in trms of xcss yild, with ε 0 indicating ovrpricing and ε 0 undrpricing. Notic also that th Gordon growth modl rquirs that th xpctational rror in longtrm growth rats, G,OBJ G,SUBJ, b qual to th xpctational rror in longtrm xpctd rturns, R,OBJ R,SUBJ. Campbll and Vuoltnaho [2004] formaliz th Modigliani Cohn monyillusion story by spcifying that mispricing or xpctational rror is a linar function of past smoothd inflation: (3) ε G,OBJ G,SUBJ R,OBJ R,SUBJ 0 1, whr is th xpctd inflation and 1 0. If on taks th ModiglianiCohn hypothsis litrally, on could argu that 1 1, i.., inflation is (irrationally) fully pricd into stock yilds. Th cas in which 1 1 is consistnt with th simpl form of mony illusion in which invstors assum that futur xpctd cashflow growth is constant in nominal trms.
9 MONEY ILLUSION IN THE STOCK MARKET 647 II.B. CrossSctional Implications of Mony Illusion Whil prvious rsarch has tstd th aggrgat timsris prdictions of th ModiglianiCohn monyillusion hypothsis, th crosssctional implications of this hypothsis hav bn largly unxplord in ithr th litratur on bhavioral financ thory or th mpirical litratur in gnral. (Th main xcption is Rittr and Warr s [2002] study, which xamins th diffrntial impact of inflation on a firm s stock pric as a function of its financial lvrag.) W fill this gap in th litratur by dvloping and tsting crosssctional prdictions rsulting from th original ModiglianiCohn hypothsis. W bas our crosssctional prdictions on thr substantiv assumptions. First, w assum that th markt suffrs from mony illusion of th typ dscribd by quation (3). Scond, w assum that th markt maks no othr typ of systmatic mistak in valuing stocks. Togthr, ths two assumptions imply that quation (3) holds not only for th markt but also for ach individual stock: (4) ε i G i,obj G i,subj R i,obj R i,subj 0 1. An important rsult of ths assumptions is that mony illusion s influnc on mispricing is qual across stocks, i.., ε i ε M 0 1. Our final assumption is that invstors bhav according to modrn portfolio thory in valuating risks; that is, thy us th SharpLintnr CAPM to st rquird risk prmiums. This implis that th slop of th rlation btwn th subjctiv rturn xpctation on an asst and that asst s CAPM bta is qual to th subjctiv markt prmium: (5) R i,subj i R M,SUBJ. This is in contrast with th usual, rationalxpctations spcification of th CAPM: R i,obj i R M,OBJ. Not that w implicitly assum that btas ar known constants so that subjctiv and objctiv xpctations of btas ar thus qual. Ths assumptions allow us to driv th crosssctional implication of th ModiglianiCohn [1979] monyillusion hypothsis. Substituting th subjctiv SharpLintnr CAPM into (4) yilds (6) ε i R i,obj i R M,SUBJ.
10 648 QUARTERLY JOURNAL OF ECONOMICS Rcognizing that markt mispricing ε M quals th wdg btwn objctiv and subjctiv markt prmiums rsults in (7) ε i R i,obj i R M,OBJ ε M N i OBJ R i,obj i R M,OBJ ε i i ε M. Abov, i OBJ is an objctiv masur of rlativ mispricing, calld Jnsn s [1968] alpha in th financ litratur. Sinc mispricing for both th markt and stock i is qual to th sam linar function of xpctd inflation, 0 1, w can writ (8) i OBJ 0 1 i 0 1. Equation (8) prdicts that th (conditional) Jnsn s alpha of a stock is a linar function of inflation, th stock s bta, and th intraction btwn inflation and th stock s bta. If th markt suffrs from mony illusion, thn whn inflation is high a rational invstor would prciv a positiv alpha for lowbta stocks and a ngativ alpha for highbta stocks. Convrsly, whn inflation is low (or ngativ), a rational xpctation of a stock s alpha is ngativ for lowbta stocks and positiv for highbta stocks. Rcall that th scurity markt lin is th linar rlation btwn a stock s avrag rturn and its bta. Equivalntly, quation (8) stats that both th intrcpt and th slop of th obsrvd scurity markt lin dviat systmatically from th rationalxpctation SharpLintnr CAPM s prdiction. Morovr, this dviation is a function of inflation. Dfin th xcss slop of th scurity markt lin as th crosssctional slop of (objctiv) alpha on bta. Dfin th xcss intrcpt of th scurity markt lin as th (objctiv) alpha of a unitinvstmnt stock portfolio that has a zro bta. Equation (8) prdicts that th xcss intrcpt of th scurity markt lin quals 0 1 and th xcss slop quals ( 0 1 ) undr th joint hypothsis of mony illusion and th SharpLintnr CAPM. Th abov rasoning assums that prics ar xclusivly st by invstors who suffr from mony illusion. What happns if som invstors suffr from mony illusion whil othr invstors do not, and th two groups intract in th markt? In th Appndix w dscrib a vry stylizd quilibrium modl, in which a fraction of th riskbaring capacity in th markt suffrs from mony illusion. This stylizd modl givs an intuitiv prdiction: th xcss slop of th scurity markt lin is dtrmind by th
11 MONEY ILLUSION IN THE STOCK MARKET 649 product of inflation and th fraction of th markt s riskbaring capacity controlld by monyillusiond invstors. Th abov hypothss ti in closly with rcnt rsarch on quityprmium prdictability and inflation. A papr by Polk, Thompson, and Vuoltnaho [forthcoming] assums that th CAPM holds in trms of invstors subjctiv xpctations, and uss th rlativ prics of high and low bta stocks to driv an stimat of th subjctiv quity prmium. Polk, Thompson, and Vuoltnaho find that this stimat corrlats wll with proxis for th objctiv quity prmium such as th dividnd yild, and also has prdictiv powr for th futur quity prmium. Th major xcption to thir finding occurs in th arly 1980s, whn thir subjctiv quity prmium masur is low but th dividnd yild, as wll as th subsqunt aggrgat stock markt rturn, is high. It is notworthy that this priod was also th pak of U. S. inflation. Campbll and Vuoltnaho [2004] assum th validity of Polk, Thompson, and Vuoltnaho s [2004] masur of th subjctiv quity prmium. Campbll and Vuoltnaho combin this masur with th Gordon growth modl for th aggrgat markt to stimat th subjctivly xpctd growth rat of aggrgat cash flows. It appars that inflation drivs a wdg btwn th subjctiv and objctiv stimats of aggrgat growth, just as prdictd by th ModiglianiCohn hypothsis. In contrast, w ssntially circl back to ask how mony illusion affcts th objctiv validity of th CAPM. Evn if invstors subjctivly us th CAPM, dos th CAPM dscrib th pattrn of objctiv rturns in th cross sction? Th answr is that thr should b an objctiv scurity markt lin, but it can b stpr or flattr than th prdiction of th SharpLintnr CAPM, i.., th rational xpctation of th quity prmium. III. EMPIRICAL METHODOLOGY AND RESULTS Our main tsts xamin tim variation in th xcss intrcpt and slop of th scurity markt lin, and th rlation of this tim variation to inflation. Our stimation stratgy is th following. First, w construct dynamic stock portfolios that ar likly to show a larg and consistnt crosssctional sprad in thir CAPM btas. Th natural way to construct such portfolios is to sort stocks into portfolios ach month on thir past stimatd stock
12 650 QUARTERLY JOURNAL OF ECONOMICS lvl btas. W rcord th rturns on ths valuwight portfolios, which bcom our basis assts. Spcifically, w gnrat our basis asst rturns from th Cntr for Rsarch in Scuritis Prics (CRSP) monthly stock fil, which provids monthly prics; shars outstanding; dividnds; and rturns for availabl NYSE, AMEX, and NASDAQ stocks. W masur btas, ˆ i,t, for individual stocks using at last on and up to thr yars of monthly rturns in a marktmodl OLS rgrssion on a constant and th contmporanous rturn on th valuwight NYSEAMEXNASDAQ portfolio. 4 As w somtims stimat bta using only twlv rturns, w cnsor ach firm s individual monthly rturn to th rang ( 50 prcnt, 100 prcnt) in ordr to limit th influnc of xtrm firmspcific outlirs. W us ths stocklvl stimats to form btasortd portfolios. Th portfolios ar valuwight and rformd ach month using th most rcnt availabl btas. W considr sorts into 10, 20, and 40 portfolios. Th rsults ar not snsitiv to th numbr of portfolios, and w thus concntrat on th twntyportfolio data st for most tsts. Ths portfoliorturn sris span th 895month priod, 1927: :12. Scond, w stimat rolling btas on ths 20 btasortd portfolios using a trailing window of 36 months. (W hav rplicatd our rsults using 24 and 48month btastimation windows, and th rsults ar robust to variation in window lngth.) W dnot th tim sris of ths rolling btas as th postformation btas of th basis assts. Ths postformation bta sris span th 860month priod, 1930: :12. At this stag of th analysis, it is important to vrify that our stocklvl bta stimats ar actually usful and rsult in crosssctional sprad in th avrag postformation btas. W find that thy ar, as th avrag postformation bta of th lowst bta portfolio is 0.63 whil th postformation bta of th highst bta portfolio is Howvr, th stimatd postformation btas for a particular portfolio ar not constant through tim. For th lowst bta portfolio, th postformation bta varis from 0.35 to 1.92, whil th highst bta portfolio s postformation bta varis from 0.59 to Of cours, most of this timsris variation in th postformation btas is simply du to sampling variation. Third, w form two portfolios from ths 20 basis assts using 4. W skip thos months in which a firm is missing rturns. Howvr, w rquir all obsrvations to occur within a fouryar window.
13 MONEY ILLUSION IN THE STOCK MARKET 651 Fama and Macbth s [1973] crosssctional rgrssion tchniqu. Th purpos of this stp is to dirctly control for th tim variation in postformation btas documntd abov. Spcifically, for ach cross sction, w rgrss th futur xcss rturn on th 20 basis assts on a constant and th portfolios trailingwindow postformation bta. As shown by Fama and Macbth, th tim sris of ths crosssctional rgrssion cofficints ar xcss rturns on portfolios as wll: (9) r intrcpt,t r slop,t 1 ˆ t 1 1 ˆ t ˆ t 1 r t. Abov, 1 is a vctor of constants and ˆ t 1 a vctor of postformation btas of btasortd portfolios stimatd using a trailing window that nds at t 1. r t is th vctor of xcss rturns on th btasortd portfolios. W prsnt th rgrssion cofficints in matrix notation in quation (9) to highlight th fact that th crosssctional rgrssion cofficints ar portfolios. As long as th trailing postformation btas ar accurat forcasts of futur postformation btas, th intrcpt portfolio rturn will b th xcss rturn on a unitinvstmnt zrobta stock portfolio and th slop portfolio rturn will b th xcss rturn on a unitbta zroinvstmnt portfolio. Furthrmor, ths portfolio stratgis ar implmntabl as long as th xplanatory variabls (i.., th btas) ar known in advanc of th dpndnt variabls (i.., th basisasst xcss rturns). Th intrcpt and slop portfolio hav avrag rturns of 44 and 19 basis points pr month rspctivly, though only th intrcpt portfolio s man rturn is statistically significantly diffrnt from zro. Ths two xcssrturn sris span th 859month priod, 1930: :12. Though th stps takn so far ar complicatd, ths complications ar justifid as thy will produc two portfolio rturn sris with rlativly constant, prcisly masurd btas of zro and on for th intrcpt and slop portfolios, rspctivly. This is dsirabl, as th timsris rgrssions in th nxt stag critically rquir that th portfolios w us hav constant btas. Fourth, w rgrss th intrcpt and slop portfolio s xcss rturns on a constant, th contmporanous markt xcss rturn, and laggd inflation. As abov, w us th valuwight NYSEAMEXNASDAQ portfolio as our proxy of th markt portfolio. Th xcss rturn is computd by subtracting th thr
14 652 QUARTERLY JOURNAL OF ECONOMICS month Trasurybill rat from CRSP. Our masur of inflation is th sris usd by Campbll and Vuoltnaho [2004] in thir study invstigating aggrgat markt valuations and inflation. W first comput log growth rats on th producr pric indx. As ths growth rats ar vry noisy spcially in th first part of our sampl, w smooth ths log growth rats by taking an xponntially wightd moving avrag with a halflif of 36 months (i.., monthly dcay to th powr of ). Not that th xponntially wightd moving avrags us trailing inflation data, so thr is no lookahad bias in our smoothing. W also dman this inflation sris using its full sampl man in ordr that th subsqunt rgrssion paramtrs ar asir for th radr to intrprt. Th two timsris rgrssions (10) ar analogous to Black, Jnsn, and Schols [1972] and Gibbons, Ross, and Shankn [1989] timsris rgrssions with timvarying Jnsn s [1968] alphas: (10) r intrcpt,t r slop,t a 1 b 1 r M,t c 1 t 1 u 1,t a 2 b 2 r M,t c 2 t 1 u 2,t. Th mpirical stimats of th two rgrssion quations in (10) show that both portfolios hav vry prcisly masurd btas. Tabl I shows that for our prfrrd spcification (20 btasortd portfolios whr postformation btas ar stimatd using a 36 month trailing window), th intrcpt portfolio has a bta of with a tstatistic of 0.14, whil th slop portfolio has a bta of with a tstatistic of W also find that th conditional alpha of th intrcpt portfolio varis positivly with laggd inflation as th stimat of c 1 is 1.50 with a tstatistic of Our stimat of c 2 is rliably ngativ (valu of 1.48, tstatistic of 2.35) indicating that inflation tracks th conditional alpha of th slop portfolio in an opposit fashion. Bcaus of our novl mthodology, w now hav idntifid two portfolios with rlativly stabl btas. If w could b confidnt that th trailingwindow postformation bta stimats ar prfct forcasts of th futur basisasst btas, th xcss intrcpt and xcss slop of th scurity markt lin would b givn by a 1 c 1 t 1 and a 2 c 2 t 1. In that hypothtical cas, th timsris rgrssion cofficints b 1 and b 2 would b xactly qual to zro and on. Dspit th usfulnss of our nw approach, ralistically spaking, th trailingwindow btas w us as inputs of
15 MONEY ILLUSION IN THE STOCK MARKET 653 TABLE I TIMESERIES REGRESSIONS OF INTERCEPT AND SLOPE PORTFOLIOS 2 K N a 1 a 2 b 1 b 2 c 1 c 2 R intrcpt 2 R slop % 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) Th tabl shows OLS rgrssions of th intrcpt portfolio s (r intrcpt,t ) and th slop portfolio s (r slop,t ) xcss rturn on a constant, contmporanous xcss markt rturn (r M,t ), and dmand laggd inflation ( t 1 ): r intrcpt,t r slop,t a 1 b 1 r M,t a 2 b 2 r M,t c 1 t 1 u 1,t c 2 t 1 u 2,t. Th intrcpt and slop portfolios ar constructd using FamaMacbth [1973] rgrssions of xcss rturns on N bta sortd portfolios on a constant and th portfolios laggd Kmonth postformation btas. tstatistics ar in parnthss. R 2 is adjustd for dgrs of frdom. Th rgrssions ar stimatd from th sampl priod 1930: :12, 859 monthly obsrvations. th FamaMacBth stag will nvr b prfct forcasts of futur btas; thr is no guarant that b 1 0 and b 2 1 xactly. Sinc th point stimats ar always clos for th basis assts w considr, our mthod is informativ nough to allow us to simply modify th formulas for th conditional xcss intrcpt and xcss slop of th scurity markt lin to tak ths small dviations into account. As w can confidntly rjct th hypothss that b 2 0 and b 2 b 1 for all sts of basis assts, straightforward algbra provids th alphas of a zrobta and a unitbta stock portfolio implid by th stimats of quation (10). Th functions that map stimats of th paramtrs in rgrssion (10) into th paramtrs of quation (8) ar as follows. Th xcss slop of th scurity markt lin is g 0 g 1 t 1 (11) g 0 a 2 /b 2 g 1 c 2 /b 2. Th xcss intrcpt of th scurity markt lin is givn by th function,
16 654 QUARTERLY JOURNAL OF ECONOMICS h 0 h 1 t 1 (12) h 0 a 1 a 2 b 1 /b 2 h 1 c 1 c 2 b 1 /b 2. To summariz, ths two formulas ar th rsult of solving for th conditional alpha of a zrobta and a unitbta portfolio implid by stimats of systm (10). It is important to not that quations (11) and (12) also provid a corrction for any potntial masurmnt rror problm causd by th us of stimatd btas at th FamaMacbth stag. Evn if btas ar stimatd with rror in arlir stags, our final stimats of th xcss slop and th xcss intrcpt of th scurity markt lin ar consistnt. Tabl II rports th point stimats of th xcss slop of th scurity markt lin. W focus on th spcification using 20 portfolios and a 36month btastimation window in th FamaMac Bth stag, but as th tabl shows, th rsults ar robust to small TABLE II EXCESS INTERCEPT AND SLOPE OF THE SECURITY MARKET LINE K N g 0 g 1 h 0 h 1 [g 1,h 1 ] 0 g 1 h ( 0.40) ( 2.35) (0.36) (2.40) [0.05] [0.96] ( 0.40) ( 2.16) (0.33) (2.23) [0.07] [0.95] ( 0.21) ( 2.64) (0.32) (2.57) [0.03] [0.99] ( 0.06) ( 2.56) ( 0.05) (2.71) [0.02] [0.93] ( 0.72) ( 1.85) (0.71) (1.86) [0.18] [0.98] Th tabl shows th stimatd function that maps inflation into th xcss slop and intrcpt of th scurity markt lin. First, w rgrss th intrcpt portfolio s (r intrcpt,t ) and th slop portfolio s (r slop,t ) xcss rturn on a constant, contmporanous xcss markt rturn (r M,t ), and laggd inflation ( t 1 ): r intrcpt,t a 1 b 1 r M,t c 1 t 1 u 1,t r slop,t a 2 b 2 r M,t c 2 t 1 u 2,t. Th intrcpt and slop portfolios ar constructd using FamaMacbth [1973] rgrssions of xcss rturns on N bta sortd portfolios on a constant and th portfolios laggd Kmonth postformation btas. Scond, w comput th functions that map th rgrssion paramtrs to th xcss slop and intrcpt of th scurity markt lin. Th xcss slop is dfind as g 0 g 1 t 1, whr g 0 a 2 /b 2 and g 1 c 2 /b 2. Th xcss intrcpt is computd as h 0 h 1 t 1, whr h 0 a 1 a 2 b 1 /b 2 and h 1 c 1 c 2 b 1 /b 2. tstatistics computd using th dlta mthod ar in parnthss. W also rport th tst statistic and th twosidd pvalus [in brackts] for th hypothss that [g 1,h 1 ] [0,0] and g 1 h 1 0. Th rgrssions ar stimatd from th sampl priod 1930: :12, 859 monthly obsrvations.
17 MONEY ILLUSION IN THE STOCK MARKET 655 variations in ths choics. Incrasing th numbr of basisasst portfolios in th tsts typically strngthns our rsults. W stimat g 0 as with a tstatistic of 0.40 and h 0 as with a tstatistic of Th intrprtation of ths narzro intrcpt stimats is that whn inflation is at its man, th mpirical bta slop and th zrobta rat among stocks ar consistnt with th prdiction of th SharpLintnr CAPM. In othr words, whn inflation is at its timsris avrag, th SharpLintnr CAPM works. This is consistnt with a form of mony illusion in which popl us historical avrag nominal growth rats to valu th stock markt, ignoring th currnt lvl of inflation which may b vry diffrnt from inflation s historical avrag. Our stimat for g 1 is with a tstatistic of As prdictd by th ModiglianiCohn hypothsis, th xcss slop of th scurity markt lin comovs ngativly with inflation. Our point stimats for th xcssintrcpt function ar also consistnt with th prdictions of th thory: th stimat of h 1 is with a tstatistic of 2.40, which is statistically significantly diffrnt from zro but not from on. In words, w can rjct th hypothsis that th markt dos not suffr from mony illusion, but w cannot rjct th hypothsis that inflation is (irrationally) fully pricd into ral stock yilds. Furthrmor, g 1 is conomically and statistically vry clos to h 1, as prdictd. Finally, w can rjct th joint hypothsis that both g 1 0 and h 1 0 against th twosidd altrnativ at th 5 prcnt lvl of significanc. III.A. Additional Robustnss Chcks Our rsults ar not snsitiv to small variations in th inflation masur. For xampl, all of our conclusions rmain valid if w us as our masur of inflation th fittd valu from a rgrssion of monthly (unsmoothd) inflation on its laggd valu, th thrmonth Trasurybill yild, and th tnyar Trasurybond yild. W hav also rplicatd our rsults with xpandd sts of basis assts, prsntd in Tabl III. Th first panl uss 20 btasortd and 10 sizsortd portfolios as basis assts. Th scond panl uss 20 btasortd and 10 booktomarktsortd portfolios as basis assts. Th third and final panl uss 20 btasortd, 10 sizsortd, and 10 booktomarktsortd portfolios as basis assts. Th sizsortd and booktomarktsortd portfolios ar providd by Knnth Frnch on his Wb sit. Add
18 656 QUARTERLY JOURNAL OF ECONOMICS TABLE III RESULTS FROM EXPANDED ASSET SETS 20 btasortd and 10 MEsortd portfolios K g 0 g 1 h 0 h 1 [g 1,h 1 ] 0 g 1 h (0.22) ( 2.55) (0.07) (2.41) [0.03] [0.95] 20 btasortd and 10 BE/MEsortd portfolios K g 0 g 1 h 0 h 1 [g 1,h 1 ] 0 g 1 h (0.03) ( 3.12) ( 0.02) (3.23) [0.00] [0.93] 20 btasortd, 10 MEsortd, and 10 BE/MEsortd portfolios K g 0 g 1 h 0 h 1 [g 1,h 1 ] 0 g 1 h (0.52) ( 3.13) ( 0.30) (3.13) [0.01] [0.99] Th tabl shows th stimatd function that maps inflation into th xcss slop and intrcpt of th scurity markt lin, stimatd from xpandd asst sts. First, w rgrss th intrcpt portfolio s (r intrcpt,t ) and th slop portfolio s (r slop,t ) xcss rturn on a constant, contmporanous xcss markt rturn (r M,t ), and laggd inflation ( t 1 ): r intrcpt,t a 1 b 1 r M,t c 1 t 1 u 1,t r slop,t a 2 b 2 r M,t c 2 t 1 u 2,t. Th intrcpt and slop portfolios ar constructd using FamaMacbth [1973] rgrssions of xcss rturns on basisasst portfolios on a constant and th portfolios laggd Kmonth postformation btas. Scond, w comput th functions that map th rgrssion paramtrs to th xcss slop and intrcpt of th scurity markt lin. Th xcss slop is dfind as g 0 g 1 t 1, whr g 0 a 2 /b 2 and g 1 c 2 /b 2. Th xcss intrcpt is computd as h 0 h 1 t 1, whr h 0 a 1 a 2 b 1 /b 2 and h 1 c 1 c 2 b 1 /b 2. tstatistics computd using th dlta mthod ar in parnthss. W also rport th tst statistic and th twosidd pvalus [in brackts] for th hypothss that [g 1,h 1 ] [0,0] and g 1 h 1 0. Th rgrssions ar stimatd from th sampl priod 1930: :12, 859 monthly obsrvations. ing ths charactristicssortd portfolios to th st of basis assts dos not altr our basic conclusions, as th point stimats rmain clos to thos obtaind in th arlir tsts. Thus, w argu that our main conclusions ar not snsitiv to small changs in th st of basis assts. In unrportd tsts, w also xamin th ModiglianiCohn hypothsis using longhorizon rturns. W us th sam portfolios as in our prvious tsts, xcpt w hold th stocks for horizons ranging from 3 to 60 months. Our markt rturn is also compoundd in th sam way, and thn th compoundd thrmonth Trasurybill intrst rat is subtractd. Smoothd inflation is scald to th sam tim units as th rturns. Othr than th chang in th holding priod, th tst procdur is xactly th sam as in th prvious tsts. W find point stimats consistnt
19 MONEY ILLUSION IN THE STOCK MARKET 657 with th joint hypothsis of mony illusion and th CAPM at th quartrly horizons and at horizons of thr yars and fiv yars. Howvr, for intrmdiat horizons (12 24 months), any ffct is small, with point stimats occasionally having th wrong sign. Though unfortunat, th low powr and larg standard rrors of ths longhorizon tsts ar at last partially to blam, as th ModiglianiCohn hypothsis is nvr rjctd statistically. As part of our longhorizon tsts, w also chck to s whthr our point stimats of th crosssctional ffct of mony illusion ar consistnt with th aggrgat mispricing of stocks vrsus bonds by Campbll and Vuoltnaho [2004]. In particular, w stimat a rgrssion forcasting th xcss markt rturn with smoothd inflation, whil controlling for th subjctiv riskprmium masur SRC of Polk, Thompson, and Vuoltnaho [2004]. As prdictd by th ModiglianiCohn hypothsis, th partial rgrssion cofficint on inflation is positiv, significant, and similar to our shorthorizon crosssctional stimat at all horizons. Though w find vidnc of Modigliani and Cohn s mony illusion, our tsts so far hav only considrd th SharpLintnr vrsion of th CAPM. Howvr, it is thortically possibl that our rsults ar simply du to an incorrct rstriction on th intrcpt of th scurity markt lin implicit in that vrsion of th CAPM. Black [1972] considrs th possibility that invstors cannot borrow at th Trasurybill rat. If so, th likly ffct of such inability to borrow is that th zrobta rat among stocks dviats from th Trasurybill rat. In othr words, th Black CAPM allows th xcss intrcpt and slop of th scurity markt lin to b nonzro. Thrfor, an altrnativ xplanation for our findings is that th sprad btwn th tru borrowing rat facing invstors and th Trasurybill rat comovs with inflation. Fortunatly for our conclusions, data on actual borrowing rats indicat that th sprad dos not comov positivly with inflation. Our thr mpirical proxis for th tru borrowing rat ar carloan rats from commrcial banks, prsonalloan rats from commrcial banks, and crditcard intrst rats. W obtain ths quartrly data from th Fdral Rsrv s Wb sit. Th data from commrcial banks bgin 1972:02, whil th crditcard rat data bgin 1994:11. W first comput th yild sprad btwn ths loans and maturitymatchd Trasury yilds. W
20 658 QUARTERLY JOURNAL OF ECONOMICS thn rgrss ths sprads on smoothd inflation (in th sam annualizd units). Th rgrssion rsults in Tabl IV show that th yild sprad btwn individuals borrowing rats and Trasury rats comovs ngativly, not positivly, with laggd inflation. This rsult is not surprising, as Ausubl [1991] finds that crditcard intrst rats appar sticky in rsponding to changs in markt intrst rats. Thus, w rjct th Black CAPM as an altrnativ xplanation for th obsrvd timvariation in th xcss slop of th scurity markt lin. W also considr subjctiv risk prmiums dtrmind in a world whr multipl risk factors dtrmin th cross sction of subjctiv xpctd rturns. That is, w assum a world in which invstors mistaknly misstimat ral cashflow growth of (and thus xpctd rturns on) all stocks du to mony illusion, but othrwis pric stocks corrctly in accordanc with a multifactor modl. Furthrmor, w assum that masurd btas ar not matrially affctd by this mispricing. TABLE IV INFLATION AND THE SPREAD BETWEEN BORROWING AND TREASURY RATES 48month car loans from commrcial banks, sprad ovr th 48month Tnot yild constant (tstatistic) slop on (tstatistic) Adj. R 2 N (13.9) ( 0.9) month prsonal loans from commrcial banks sprad ovr th 24month Tnot yild constant (tstatistic) slop on (tstatistic) Adj. R 2 N (29.4) ( 7.9) Crdit card accounts (intrst rats), sprad ovr th 90day Tbill yild constant (tstatistic) slop on (tstatistic) Adj. R 2 N (22.8) ( 2.0) Crdit card accounts (assssd intrst), sprad ovr th 90day Tbill yild constant (tstatistic) slop on (tstatistic) Adj. R 2 N (21.1) ( 2.0) Th tabl rgrsss proxis for th sprad btwn borrowing rats that individuals fac and Trasury rats on laggd inflation. Th inflation sris ( ) is th smoothd inflation usd in arlir tsts, annualizd by multiplying th sris by twlv. Th tstatistics ar basd on NwyWst standard rrors computd using four lags and lads. Th hading of ach panl spcifis th sprad masur bing usd as th dpndnt variabl. Data ar quartrly.
21 MONEY ILLUSION IN THE STOCK MARKET 659 In our robustnss chcks blow, w mploy th wllknown thrfactor modl of Fama and Frnch [1993], but th stps blow will asily gnraliz to any multifactor modl for which th additional factors ar xprssd as longshort stock portfolios. Th quations givn abov for th SharpLintnr CAPM cas, and thrfor th rgrssions w will run to tst th modl and th ModiglianiCohn hypothsis, asily gnraliz to this cas. W bgin by rplacing quation (5) with th multifactor bta rprsntation of assts subjctiv risk prmiums: (13) R i,subj i R M,SUBJ i f. f is a column vctor of factor ralizations for th givn priod and i is a column vctor of asst i s multiplrgrssion loadings on thos factors. Hr w assum that th factormimicking portfolios ar long and short stocks in qual dollar amounts. Undr ths conditions thr is no nd for SUBJ suprscripts, as th inflationrlatd mispricing affcts th yilds of all stocks idntically so that th xpctd rturn of any longshort stock portfolio is unaffctd. Thus, (14) ε i R i,obj i R M,SUBJ i f, and thrfor, (15) ε i R i,obj i R M,OBJ i f ε M i OBJ N i OBJ R i,obj i R M,OBJ i f ε i i ε M. dnots th Jnsn s alpha rlativ to th multifactor modl, and is almost idntical to th xprssion drivd in th CAPM cas, xcpt that is a multifactor snsitivity on th markt rturn: (16) i OBJ 0 1 i 0 1. In th FamaMacBth rgrssions w now includ as xplanatory variabls th stimatd loadings on all thr factors, including multifactor markt btas. Lt th additional nonmarkt factor loadings b dnotd by ˆ t 1 whr ˆ t 1 has on row for ach asst and on column for ach nonmarkt factor. Th rturns on th intrcpt and (all) slop portfolios ar thn givn by
22 660 QUARTERLY JOURNAL OF ECONOMICS (17) r intrcpt,t r intrcpt,t r allslops,t 1 ˆ t 1 ˆ t 1 1 ˆ t 1 ˆ t ˆ t 1 ˆ t 1 r t. rprsnts th rturn (in xcss of th risklss rat) on a portfolio anticipatd to hav zro loadings on all factors (including th markt) and a unit nt invstmnt in stocks. r slop,t, which is dfind as th first lmnt of r allslops,t, is th rturn on a portfolio anticipatd to hav a unit markt loading and a zro loading on th othr factors. Th rmaining lmnts of r allslops,t, ar rturns on portfolios with unit loadings on th othr factors; thy ar not usd in our subsqunt analysis. Th actual factor loadings of th r intrcpt,t and r slop,t portfolios ar again rasonably clos to thir hypothtical valus. W obsrv this by rgrssing th tim sris of rturns on th factors, as wll as on, our inflation variabl: (18) r intrcpt,t r slop,t a 1 b 1 r M,t B 1 f t c 1 t 1 u 1,t a 2 b 2 r M,t B 2 f t c 2 t 1 u 2,t. f t is a vctor of factor ralizations at tim t. B 1 and B 2 ar rgrssion cofficints on th nonmarkt factors. As abov, in ordr to stimat th slop of th scurity markt lin, w nd to adjust th intrcpt and slop portfolios slightly to gt portfolios that (in sampl) actually hav th ncssary loadings. Again, th procss of claning out any xtranous loadings on othr factors convnintly lavs us with scurity markt lin quations that ar virtually idntical to thos in th CAPM cas (xcpt that th b 1 and b 2 now com from th rgrssion that includs th othr factors (i.., thy ar multifactor btas). Th xcss slop and xcss intrcpt of th scurity markt lin ar again givn by quations (11) and (12). Tabl V contains our stimats for th Fama and Frnch [1993] multifactor modl, which contains two factors in addition to th markt factor. Th factor sris ar providd by Knnth Frnch on his Wb sit. Th first is SMB, th diffrnc btwn th rturn on small and big marktcapitalization stocks. Th scond is HML, th diffrnc btwn th rturn on high and low booktomarkt ratio stocks. In Tabl V w find that th stimatd g 1 is clos to 1, th stimatd h 1 is clos to 1, and th two ar clos to qual in absolut valu but opposit in sign, just
23 MONEY ILLUSION IN THE STOCK MARKET 661 TABLE V RESULTS FOR THE FAMAFRENCH THREEFACTOR MODEL 20 btasortd portfolios K g 0 g 1 h 0 h 1 [g 1,h 1 ] 0 g 1 h (0.11) ( 1.75) ( 0.13) (1.71) [0.21] [1.00] 20 btasortd and 10 MEsortd portfolios K g 0 g 1 h 0 h 1 [g 1,h 1 ] 0 g 1 h ( 0.76) ( 1.51) (0.75) (1.52) [0.32] [0.99] 20 btasortd and 10 BE/MEsortd portfolios K g 0 g 1 h 0 h 1 [g 1,h 1 ] 0 g 1 h ( 0.40) ( 3.12) (0.35) (1.36) [0.32] [0.99] 20 btasortd, 10 MEsortd, and 10 BE/MEsortd portfolios K g 0 g 1 h 0 h 1 [g 1,h 1 ] 0 g 1 h ( 0.62) ( 1.80) (0.60) (1.84) [0.17] [0.98] Th tabl rpats th tsts of Tabl II using th FamaFrnch [1993] thrfactor modl. First, w rgrss th xcss rturns on th basisasst portfolios on a constant and th portfolios laggd Kmonth postformation factor loadings. Th intrcpt portfolio s (r intrcpt,t ) and th slop portfolio s (r slop,t ) xcss rturns ar th cofficint tim sris corrsponding to th intrcpt and th thrfactor modl s markt loading, rspctivly. Scond, w rgrss ths rturns on a constant, contmporanous factor rturns, and laggd inflation ( t 1 ): r intrcpt,t a 1 b 1,1 r M,t b 1,2 r SMB,t b 1,3 r HML,t c 1 t 1 u 1,t r slop,t a 2 b 2,1 r M,t b 2,2 r SMB,t b 2,3 r HML,t c 2 t 1 u 2,t. Th xcss slop is dfind as g 0 g 1 t 1, whr g 0 a 2 /b 2,1 and g 1 c 2 /b 2,1. Th xcss intrcpt is dfind as h 0 h 1 t 1, whr h 0 a 1 a 2 b 1,1 /b 2,1 and h 1 c 1 c 2 b 1,1 /b 2,1. tstatistics computd using th dlta mthod ar in parnthss. W also rport th tst statistic and th twosidd pvalus [in brackts] for th hypothss that [g 1,h 1 ] [0, 0] and g 1 h 1 0. Th rgrssions ar stimatd from th sampl priod 1930: :12, 859 monthly obsrvations. as prdictd by th Modigliani and Cohn hypothsis (and just as w found using th CAPM as th risk modl). For our prfrrd spcification (36 months in postformation loading rgrssions, 20 tst asst portfolios) w obtain point stimats of 1.28 for g 1 (tstatistic of 1.75) and 1.28 for h 1 (tstatistic of 1.71). Th tsts using th multifactor modl hav lss powr, but w can still rjct at th 10 prcnt lvl th hypothsis that inflation plays no rol in th dtrmination of th crosssctional bta prmium. Th rsults for othr spcifications ar qualitativly similar, as can b sn in Tabl V.
QUANTITATIVE METHODS CLASSES WEEK SEVEN
QUANTITATIVE METHODS CLASSES WEEK SEVEN Th rgrssion modls studid in prvious classs assum that th rspons variabl is quantitativ. Oftn, howvr, w wish to study social procsss that lad to two diffrnt outcoms.
More informationEcon 371: Answer Key for Problem Set 1 (Chapter 1213)
con 37: Answr Ky for Problm St (Chaptr 23) Instructor: Kanda Naknoi Sptmbr 4, 2005. (2 points) Is it possibl for a country to hav a currnt account dficit at th sam tim and has a surplus in its balanc
More informationIntermediate Macroeconomic Theory / Macroeconomic Analysis (ECON 3560/5040) Final Exam (Answers)
Intrmdiat Macroconomic Thory / Macroconomic Analysis (ECON 3560/5040) Final Exam (Answrs) Part A (5 points) Stat whthr you think ach of th following qustions is tru (T), fals (F), or uncrtain (U) and brifly
More informationQuestion 3: How do you find the relative extrema of a function?
ustion 3: How do you find th rlativ trma of a function? Th stratgy for tracking th sign of th drivativ is usful for mor than dtrmining whr a function is incrasing or dcrasing. It is also usful for locating
More informationNonHomogeneous Systems, Euler s Method, and Exponential Matrix
NonHomognous Systms, Eulr s Mthod, and Exponntial Matrix W carry on nonhomognous firstordr linar systm of diffrntial quations. W will show how Eulr s mthod gnralizs to systms, giving us a numrical approach
More informationAdverse Selection and Moral Hazard in a Model With 2 States of the World
Advrs Slction and Moral Hazard in a Modl With 2 Stats of th World A modl of a risky situation with two discrt stats of th world has th advantag that it can b natly rprsntd using indiffrnc curv diagrams,
More informationThe example is taken from Sect. 1.2 of Vol. 1 of the CPN book.
Rsourc Allocation Abstract This is a small toy xampl which is wllsuitd as a first introduction to Cnts. Th CN modl is dscribd in grat dtail, xplaining th basic concpts of Cnts. Hnc, it can b rad by popl
More informationLong run: Law of one price Purchasing Power Parity. Short run: Market for foreign exchange Factors affecting the market for foreign exchange
Lctur 6: Th Forign xchang Markt xchang Rats in th long run CON 34 Mony and Banking Profssor Yamin Ahmad xchang Rats in th Short Run Intrst Parity Big Concpts Long run: Law of on pric Purchasing Powr Parity
More informationBasis risk. When speaking about forward or futures contracts, basis risk is the market
Basis risk Whn spaking about forward or futurs contracts, basis risk is th markt risk mismatch btwn a position in th spot asst and th corrsponding futurs contract. Mor broadly spaking, basis risk (also
More informationThe Matrix Exponential
Th Matrix Exponntial (with xrciss) 92.222  Linar Algbra II  Spring 2006 by D. Klain prliminary vrsion Corrctions and commnts ar wlcom! Th Matrix Exponntial For ach n n complx matrix A, dfin th xponntial
More informationby John Donald, Lecturer, School of Accounting, Economics and Finance, Deakin University, Australia
Studnt Nots Cost Volum Profit Analysis by John Donald, Lcturr, School of Accounting, Economics and Financ, Dakin Univrsity, Australia As mntiond in th last st of Studnt Nots, th ability to catgoris costs
More informationGold versus stock investment: An econometric analysis
Intrnational Journal of Dvlopmnt and Sustainability Onlin ISSN: 2688662 www.isdsnt.com/ijds Volum Numbr, Jun 202, Pag 7 ISDS Articl ID: IJDS20300 Gold vrsus stock invstmnt: An conomtric analysis Martin
More informationLecture notes: 160B revised 9/28/06 Lecture 1: Exchange Rates and the Foreign Exchange Market FT chapter 13
Lctur nots: 160B rvisd 9/28/06 Lctur 1: xchang Rats and th Forign xchang Markt FT chaptr 13 Topics: xchang Rats Forign xchang markt Asst approach to xchang rats Intrst Rat Parity Conditions 1) Dfinitions
More informationRelationship between Cost of Equity Capital And Voluntary Corporate Disclosures
Rlationship btwn Cost of Equity Capital And Voluntary Corporat Disclosurs Elna Ptrova Eli Lilly & Co, Sofia, Bulgaria Email: ptrova.lnaa@gmail.com Gorgios Gorgakopoulos (Corrsponding author) Amstrdam
More information(Analytic Formula for the European Normal Black Scholes Formula)
(Analytic Formula for th Europan Normal Black Schols Formula) by Kazuhiro Iwasawa Dcmbr 2, 2001 In this short summary papr, a brif summary of Black Schols typ formula for Normal modl will b givn. Usually
More informationSTATEMENT OF INSOLVENCY PRACTICE 3.2
STATEMENT OF INSOLVENCY PRACTICE 3.2 COMPANY VOLUNTARY ARRANGEMENTS INTRODUCTION 1 A Company Voluntary Arrangmnt (CVA) is a statutory contract twn a company and its crditors undr which an insolvncy practitionr
More informationTraffic Flow Analysis (2)
Traffic Flow Analysis () Statistical Proprtis. Flow rat distributions. Hadway distributions. Spd distributions by Dr. GangLn Chang, Profssor Dirctor of Traffic safty and Oprations Lab. Univrsity of Maryland,
More informationLecture 3: Diffusion: Fick s first law
Lctur 3: Diffusion: Fick s first law Today s topics What is diffusion? What drivs diffusion to occur? Undrstand why diffusion can surprisingly occur against th concntration gradint? Larn how to dduc th
More informationModern Portfolio Theory (MPT) Statistics
Modrn Portfolio Thory (MPT) Statistics Morningstar Mthodology Papr May 9, 009 009 Morningstar, Inc. All rights rsrvd. Th information in this documnt is th proprty of Morningstar, Inc. Rproduction or transcription
More informationTheoretical aspects of investment demand for gold
Victor Sazonov (Russia), Dmitry Nikolav (Russia) Thortical aspcts of invstmnt dmand for gold Abstract Th main objctiv of this articl is construction of a thortical modl of invstmnt in gold. Our modl is
More informationOverinvestment of free cash flow
Rv Acc Stud (2006) 11:159 189 DOI 10.1007/s1114200690121 Ovrinvstmnt of fr cash flow Scott Richardson Publishd onlin: 23 Jun 2006 Ó Springr Scinc+Businss Mdia, LLC 2006 Abstract This papr xamins th
More informationSUBATOMIC PARTICLES AND ANTIPARTICLES AS DIFFERENT STATES OF THE SAME MICROCOSM OBJECT. Eduard N. Klenov* RostovonDon. Russia
SUBATOMIC PARTICLES AND ANTIPARTICLES AS DIFFERENT STATES OF THE SAME MICROCOSM OBJECT Eduard N. Klnov* RostovonDon. Russia Th distribution law for th valus of pairs of th consrvd additiv quantum numbrs
More informationWORKERS' COMPENSATION ANALYST, 1774 SENIOR WORKERS' COMPENSATION ANALYST, 1769
081685 WORKERS' COMPENSATION ANALYST, 1774 SENIOR WORKERS' COMPENSATION ANALYST, 1769 Summary of Dutis : Dtrmins City accptanc of workrs' compnsation cass for injurd mploys; authorizs appropriat tratmnt
More informationFACULTY SALARIES FALL 2004. NKU CUPA Data Compared To Published National Data
FACULTY SALARIES FALL 2004 NKU CUPA Data Compard To Publishd National Data May 2005 Fall 2004 NKU Faculty Salaris Compard To Fall 2004 Publishd CUPA Data In th fall 2004 Northrn Kntucky Univrsity was among
More informationAP Calculus AB 2008 Scoring Guidelines
AP Calculus AB 8 Scoring Guidlins Th Collg Board: Conncting Studnts to Collg Succss Th Collg Board is a notforprofit mmbrship association whos mission is to connct studnts to collg succss and opportunity.
More informationthe socalled KOBOS system. 1 with the exception of a very small group of the most active stocks which also trade continuously through
Liquidity and InformationBasd Trading on th Ordr Drivn Capital Markt: Th Cas of th Pragu tock Exchang Libor 1ÀPH³HN Cntr for Economic Rsarch and Graduat Education, Charls Univrsity and Th Economic Institut
More informationEFFECT OF GEOMETRICAL PARAMETERS ON HEAT TRANSFER PERFORMACE OF RECTANGULAR CIRCUMFERENTIAL FINS
25 Vol. 3 () JanuaryMarch, pp.375/tripathi EFFECT OF GEOMETRICAL PARAMETERS ON HEAT TRANSFER PERFORMACE OF RECTANGULAR CIRCUMFERENTIAL FINS *Shilpa Tripathi Dpartmnt of Chmical Enginring, Indor Institut
More informationMathematics. Mathematics 3. hsn.uk.net. Higher HSN23000
hsn uknt Highr Mathmatics UNIT Mathmatics HSN000 This documnt was producd spcially for th HSNuknt wbsit, and w rquir that any copis or drivativ works attribut th work to Highr Still Nots For mor dtails
More informationIncomplete 2Port Vector Network Analyzer Calibration Methods
Incomplt Port Vctor Ntwork nalyzr Calibration Mthods. Hnz, N. Tmpon, G. Monastrios, H. ilva 4 RF Mtrology Laboratory Instituto Nacional d Tcnología Industrial (INTI) Bunos irs, rgntina ahnz@inti.gov.ar
More information5 2 index. e e. Prime numbers. Prime factors and factor trees. Powers. worked example 10. base. power
Prim numbrs W giv spcial nams to numbrs dpnding on how many factors thy hav. A prim numbr has xactly two factors: itslf and 1. A composit numbr has mor than two factors. 1 is a spcial numbr nithr prim
More informationPrinciples of Humidity Dalton s law
Principls of Humidity Dalton s law Air is a mixtur of diffrnt gass. Th main gas componnts ar: Gas componnt volum [%] wight [%] Nitrogn N 2 78,03 75,47 Oxygn O 2 20,99 23,20 Argon Ar 0,93 1,28 Carbon dioxid
More informationAnalyzing the Economic Efficiency of ebaylike Online Reputation Reporting Mechanisms
A rsarch and ducation initiativ at th MIT Sloan School of Managmnt Analyzing th Economic Efficincy of Baylik Onlin Rputation Rporting Mchanisms Papr Chrysanthos Dllarocas July For mor information, plas
More informationThe Australian Rules Football Fixed Odds and Line Betting Markets: Econometric Tests for Efficiency and Simulated Betting Systems
Th Australian Ruls Football Fixd Odds and Lin Btting Markts: Economtric Tsts for Efficincy and Simulatd Btting Systms by Adi Schnytzr and Guy Winbrg a Papr to b prsntd at: Th 4 th Binnial Equin Industry
More informationForeign Exchange Markets and Exchange Rates
Microconomics Topic 1: Explain why xchang rats indicat th pric of intrnational currncis and how xchang rats ar dtrmind by supply and dmand for currncis in intrnational markts. Rfrnc: Grgory Mankiw s Principls
More informationHigh Interest Rates In Ghana,
NO. 27 IEA MONOGRAPH High Intrst Rats In Ghana, A Critical Analysis IEA Ghana THE INSTITUTE OF ECONOMIC AFFAIRS A Public Policy Institut High Intrst Rats In Ghana, A Critical Analysis 1 by DR. J. K. KWAKYE
More informationMEASUREMENT AND ASSESSMENT OF IMPACT SOUND IN THE SAME ROOM. Hans G. Jonasson
MEASUREMENT AND ASSESSMENT OF IMPACT SOUND IN THE SAME ROOM Hans G. Jonasson SP Tchnical Rsarch Institut of Swdn Box 857, SE501 15 Borås, Swdn hans.jonasson@sp.s ABSTRACT Drum sound, that is th walking
More informationIMES DISCUSSION PAPER SERIES
IMES DISCUSSIN PAPER SERIES Th Choic of Invoic Currncy in Intrnational Trad: Implications for th Intrnationalization of th Yn Hiroyuki I, Akira TANI, and Toyoichirou SHIRTA Discussion Papr No. 003E13
More informationNew Basis Functions. Section 8. Complex Fourier Series
Nw Basis Functions Sction 8 Complx Fourir Sris Th complx Fourir sris is prsntd first with priod 2, thn with gnral priod. Th connction with th ralvalud Fourir sris is xplaind and formula ar givn for convrting
More informationDeer: Predation or Starvation
: Prdation or Starvation National Scinc Contnt Standards: Lif Scinc: s and cosystms Rgulation and Bhavior Scinc in Prsonal and Social Prspctiv s, rsourcs and nvironmnts Unifying Concpts and Procsss Systms,
More informationPerformance Evaluation
Prformanc Evaluation ( ) Contnts lists availabl at ScincDirct Prformanc Evaluation journal hompag: www.lsvir.com/locat/pva Modling Baylik rputation systms: Analysis, charactrization and insuranc mchanism
More informationME 612 Metal Forming and Theory of Plasticity. 6. Strain
Mtal Forming and Thory of Plasticity mail: azsnalp@gyt.du.tr Makin Mühndisliği Bölümü Gbz Yüksk Tknoloji Enstitüsü 6.1. Uniaxial Strain Figur 6.1 Dfinition of th uniaxial strain (a) Tnsil and (b) Comprssiv.
More informationGOAL SETTING AND PERSONAL MISSION STATEMENT
Prsonal Dvlopmnt Track Sction 4 GOAL SETTING AND PERSONAL MISSION STATEMENT Ky Points 1 Dfining a Vision 2 Writing a Prsonal Mission Statmnt 3 Writing SMART Goals to Support a Vision and Mission If you
More informationEssays on Adverse Selection and Moral Hazard in Insurance Market
Gorgia Stat Univrsity ScholarWorks @ Gorgia Stat Univrsity Risk Managmnt and Insuranc Dissrtations Dpartmnt of Risk Managmnt and Insuranc 800 Essays on Advrs Slction and Moral Hazard in Insuranc Markt
More informationIn the first years of the millennium, Americans flocked to Paris to enjoy French
14 chaptr Exchang Rats and th Forign Exchang Markt: An Asst Approach 320 In th first yars of th millnnium, Amricans flockd to Paris to njoy Frnch cuisin whil shopping for dsignr clothing and othr spcialtis.
More informationFree ACA SOLUTION (IRS 1094&1095 Reporting)
Fr ACA SOLUTION (IRS 1094&1095 Rporting) Th Insuranc Exchang (301) 2791062 ACA Srvics Transmit IRS Form 1094 C for mployrs Print & mail IRS Form 1095C to mploys HR Assist 360 will gnrat th 1095 s for
More informationCategory 7: Employee Commuting
7 Catgory 7: Employ Commuting Catgory dscription This catgory includs missions from th transportation of mploys 4 btwn thir homs and thir worksits. Emissions from mploy commuting may aris from: Automobil
More informationMETHODS FOR HANDLING TIED EVENTS IN THE COX PROPORTIONAL HAZARD MODEL
STUDIA OECONOMICA POSNANIENSIA 204, vol. 2, no. 2 (263 Jadwiga Borucka Warsaw School of Economics, Institut of Statistics and Dmography, Evnt History and Multilvl Analysis Unit jadwiga.borucka@gmail.com
More informationSPREAD OPTION VALUATION AND THE FAST FOURIER TRANSFORM
RESEARCH PAPERS IN MANAGEMENT STUDIES SPREAD OPTION VALUATION AND THE FAST FOURIER TRANSFORM M.A.H. Dmpstr & S.S.G. Hong WP 26/2000 Th Judg Institut of Managmnt Trumpington Strt Cambridg CB2 1AG Ths paprs
More informationThe Normal Distribution: A derivation from basic principles
Th Normal Distribution: A drivation from basic principls Introduction Dan Tagu Th North Carolina School of Scinc and Mathmatics Studnts in lmntary calculus, statistics, and finit mathmatics classs oftn
More informationDefining Retirement Success for Defined Contribution Plan Sponsors: Begin with the End in Mind
Dfining Rtirmnt Succss for Dfind Contribution Plan Sponsors: Bgin with th End in Mind David Blanchtt, CFA, CFP, AIFA Had of Rtirmnt Rsarch Morningstar Invstmnt Managmnt david.blanchtt@morningstar.com Nathan
More informationAlgorithmic Trading, Market Efficiency and The Momentum Effect. Rafael Gamzo
Algorithmic Trading, Markt Efficincy and Th Momntum Effct Rafal Gamzo Studnt Numbr: 323979 A rsarch rport submittd to th Faculty of Commrc, Law and Managmnt, Univrsity of th Witwatrsrand, in partial fulfilmnt
More informationArchitecture of the proposed standard
Architctur of th proposd standard Introduction Th goal of th nw standardisation projct is th dvlopmnt of a standard dscribing building srvics (.g.hvac) product catalogus basd on th xprincs mad with th
More informationDehumidifiers: A Major Consumer of Residential Electricity
Dhumidifirs: A Major Consumr of Rsidntial Elctricity Laurn Mattison and Dav Korn, Th Cadmus Group, Inc. ABSTRACT An stimatd 19% of U.S. homs hav dhumidifirs, and thy can account for a substantial portion
More informationImproving Managerial Accounting and Calculation of Labor Costs in the Context of Using Standard Cost
Economy Transdisciplinarity Cognition www.ugb.ro/tc Vol. 16, Issu 1/2013 5054 Improving Managrial Accounting and Calculation of Labor Costs in th Contxt of Using Standard Cost Lucian OCNEANU, Constantin
More informationC H A P T E R 1 Writing Reports with SAS
C H A P T E R 1 Writing Rports with SAS Prsnting information in a way that s undrstood by th audinc is fundamntally important to anyon s job. Onc you collct your data and undrstand its structur, you nd
More informationMonetary Policy Shocks and Stock Returns: Evidence from the British Market
Montary Policy Shocks and Stock Rtrns: Evidnc from th British Markt A. Grgorio a, A. Kontonikas b*, R. MacDonald b, A. Montagnoli c a Norwich Bsinss School, Univrsity of East Anglia b Dpartmnt of Economics,
More informationExpertMediated Search
ExprtMdiatd Sarch Mnal Chhabra Rnsslar Polytchnic Inst. Dpt. of Computr Scinc Troy, NY, USA chhabm@cs.rpi.du Sanmay Das Rnsslar Polytchnic Inst. Dpt. of Computr Scinc Troy, NY, USA sanmay@cs.rpi.du David
More informationClosedform solutions for Guaranteed Minimum Accumulation Benefits
Closdform solutions for Guarantd Minimum Accumulation Bnfits Mikhail Krayzlr, Rudi Zagst and Brnhard Brunnr Abstract Guarantd Minimum Accumulation Bnfit GMAB is on of th variabl annuity products, i..
More informationA Theoretical Model of Public Response to the Homeland Security Advisory System
A Thortical Modl of Public Rspons to th Homland Scurity Advisory Systm Amy (Wnxuan) Ding Dpartmnt of Information and Dcision Scincs Univrsity of Illinois Chicago, IL 60607 wxding@uicdu Using a diffrntial
More informationcontent Fresh thinking for decision makers
Roland Brgr Stratgy Consultants contnt Frsh thinking for dcision makrs Think your bank can maintain its liquidity vn undr xtrm strss? Fin, but thr's mor to stratgic liquidity managmnt than that Th prcis
More informationCPU. Rasterization. Per Vertex Operations & Primitive Assembly. Polynomial Evaluator. Frame Buffer. Per Fragment. Display List.
Elmntary Rndring Elmntary rastr algorithms for fast rndring Gomtric Primitivs Lin procssing Polygon procssing Managing OpnGL Stat OpnGL uffrs OpnGL Gomtric Primitivs ll gomtric primitivs ar spcifid by
More informationProduction Costing (Chapter 8 of W&W)
Production Costing (Chaptr 8 of W&W).0 Introduction Production costs rfr to th oprational costs associatd with producing lctric nrgy. Th most significant componnt of production costs ar th ful costs ncssary
More information7 Timetable test 1 The Combing Chart
7 Timtabl tst 1 Th Combing Chart 7.1 Introduction 7.2 Tachr tams two workd xampls 7.3 Th Principl of Compatibility 7.4 Choosing tachr tams workd xampl 7.5 Ruls for drawing a Combing Chart 7.6 Th Combing
More informationRealTime Evaluation of Email Campaign Performance
Singapor Managmnt Univrsity Institutional Knowldg at Singapor Managmnt Univrsity Rsarch Collction L Kong Chian School Of Businss L Kong Chian School of Businss 102008 RalTim Evaluation of Email Campaign
More informationWage Inflation and the Distribution of Output Gaps in Europe: Insiders vs. Outsiders
Economtric Rsarch and Spcial Studis Dpartmnt Wag Inflation and th Distribution of Output Gaps in Europ: Insidrs vs. Outsidrs M. Dmrtzis and A. Hughs Halltt Rsarch Mmorandum WO&E no. 631 Sptmbr 2000 D Ndrlandsch
More informationFactorials! Stirling s formula
Author s not: This articl may us idas you havn t larnd yt, and might sm ovrly complicatd. It is not. Undrstanding Stirling s formula is not for th faint of hart, and rquirs concntrating on a sustaind mathmatical
More informationParallel and Distributed Programming. Performance Metrics
Paralll and Distributd Programming Prformanc! wo main goals to b achivd with th dsign of aralll alications ar:! Prformanc: th caacity to rduc th tim to solv th roblm whn th comuting rsourcs incras;! Scalability:
More informationhttp://www.wwnorton.com/chemistry/tutorials/ch14.htm Repulsive Force
ctivation nrgis http://www.wwnorton.com/chmistry/tutorials/ch14.htm (back to collision thory...) Potntial and Kintic nrgy during a collision + + ngativly chargd lctron cloud Rpulsiv Forc ngativly chargd
More informationAsset set Liability Management for
KSD larning and rfrnc products for th global financ profssional Highlights Library of 29 Courss Availabl Products Upcoming Products Rply Form Asst st Liability Managmnt for Insuranc Companis A comprhnsiv
More informationAbstract. Introduction. Statistical Approach for Analyzing Cell Phone Handoff Behavior. Volume 3, Issue 1, 2009
Volum 3, Issu 1, 29 Statistical Approach for Analyzing Cll Phon Handoff Bhavior Shalini Saxna, Florida Atlantic Univrsity, Boca Raton, FL, shalinisaxna1@gmail.com Sad A. Rajput, Farquhar Collg of Arts
More informationDevelopment of Financial Management Reporting in MPLS
1 Dvlopmnt of Financial Managmnt Rporting in MPLS 1. Aim Our currnt financial rports ar structurd to dlivr an ovrall financial pictur of th dpartmnt in it s ntirty, and thr is no attmpt to provid ithr
More informationKeywords Cloud Computing, Service level agreement, cloud provider, business level policies, performance objectives.
Volum 3, Issu 6, Jun 2013 ISSN: 2277 128X Intrnational Journal of Advancd Rsarch in Computr Scinc and Softwar Enginring Rsarch Papr Availabl onlin at: wwwijarcsscom Dynamic Ranking and Slction of Cloud
More informationRural and Remote Broadband Access: Issues and Solutions in Australia
Rural and Rmot Broadband Accss: Issus and Solutions in Australia Dr Tony Warrn Group Managr Rgulatory Stratgy Tlstra Corp Pag 1 Tlstra in confidnc Ovrviw Australia s gographical siz and population dnsity
More informationSIMULATION OF THE PERFECT COMPETITION AND MONOPOLY MARKET STRUCTURE IN THE COMPANY THEORY
1 SIMULATION OF THE PERFECT COMPETITION AND MONOPOLY MARKET STRUCTURE IN THE COMPANY THEORY ALEXA Vasil ABSTRACT Th prsnt papr has as targt to crat a programm in th Matlab ara, in ordr to solv, didactically
More informationOnline Price Competition within and between Heterogeneous Retailer Groups
Onlin Pric Comptition within and btwn Htrognous Rtailr Groups Cnk Kocas Dpartmnt of Markting and Supply Chain Managmnt, Michigan Stat Univrsity kocas@msu.du Abstract This study prsnts a modl of pric comptition
More informationBudget Optimization in SearchBased Advertising Auctions
Budgt Optimization in SarchBasd Advrtising Auctions ABSTRACT Jon Fldman Googl, Inc. Nw York, NY jonfld@googl.com Martin Pál Googl, Inc. Nw York, NY mpal@googl.com Intrnt sarch companis sll advrtismnt
More informationeconstor Make Your Publication Visible
constor Mak Your Publication Visibl A Srvic of Wirtschaft Cntr zbwlibnizinformationszntrum Economics Rich, Robrt; Tracy, Josph Working Papr Th rlationship btwn xpctd inflation, disagrmnt, and uncrtainty:
More informationCostVolumeProfit Analysis
ch03.qxd 9/7/04 4:06 PM Pag 86 CHAPTER CostVolumProfit Analysis In Brif Managrs nd to stimat futur rvnus, costs, and profits to hlp thm plan and monitor oprations. Thy us costvolumprofit (CVP) analysis
More informationUpper Bounding the Price of Anarchy in Atomic Splittable Selfish Routing
Uppr Bounding th Pric of Anarchy in Atomic Splittabl Slfish Routing Kamyar Khodamoradi 1, Mhrdad Mahdavi, and Mohammad Ghodsi 3 1 Sharif Univrsity of Tchnology, Thran, Iran, khodamoradi@c.sharif.du Sharif
More informationB285141. April 21, 2000. The Honorable Charles B. Rangel Ranking Minority Member Committee on Ways and Means House of Representatives
Unit Stats Gnral Accounting Offic Washington, DC 20548 Halth, Eucation, an Human Srvics Division B285141 April 21, 2000 Th Honorabl Charls B. Rangl Ranking Minority Mmbr Committ on Ways an Mans Hous of
More informationVersion 1.0. General Certificate of Education (Alevel) January 2012. Mathematics MPC3. (Specification 6360) Pure Core 3. Final.
Vrsion.0 Gnral Crtificat of Education (Alvl) January 0 Mathmatics MPC (Spcification 660) Pur Cor Final Mark Schm Mark schms ar prpard by th Principal Eaminr and considrd, togthr with th rlvant qustions,
More informationTIME MANAGEMENT. 1 The Process for Effective Time Management 2 Barriers to Time Management 3 SMART Goals 4 The POWER Model e. Section 1.
Prsonal Dvlopmnt Track Sction 1 TIME MANAGEMENT Ky Points 1 Th Procss for Effctiv Tim Managmnt 2 Barrirs to Tim Managmnt 3 SMART Goals 4 Th POWER Modl In th Army, w spak of rsourcs in trms of th thr M
More informationStatistical Machine Translation
Statistical Machin Translation Sophi Arnoult, Gidon Mailltt d Buy Wnnigr and Andra Schuch Dcmbr 7, 2010 1 Introduction All th IBM modls, and Statistical Machin Translation (SMT) in gnral, modl th problm
More informationThe international Internet site of the geoviticulture MCC system Le site Internet international du système CCM géoviticole
Th intrnational Intrnt sit of th goviticultur MCC systm L sit Intrnt intrnational du systèm CCM géoviticol Flávio BELLO FIALHO 1 and Jorg TONIETTO 1 1 Rsarchr, Embrapa Uva Vinho, Caixa Postal 130, 95700000
More information5.4 Exponential Functions: Differentiation and Integration TOOTLIFTST:
.4 Eponntial Functions: Diffrntiation an Intgration TOOTLIFTST: Eponntial functions ar of th form f ( ) Ab. W will, in this sction, look at a spcific typ of ponntial function whr th bas, b, is.78.... This
More informationUse a highlevel conceptual data model (ER Model). Identify objects of interest (entities) and relationships between these objects
Chaptr 3: Entity Rlationship Modl Databas Dsign Procss Us a highlvl concptual data modl (ER Modl). Idntify objcts of intrst (ntitis) and rlationships btwn ths objcts Idntify constraints (conditions) End
More informationunion scholars program APPLICATION DEADLINE: FEBRUARY 28 YOU CAN CHANGE THE WORLD... AND EARN MONEY FOR COLLEGE AT THE SAME TIME!
union scholars YOU CAN CHANGE THE WORLD... program AND EARN MONEY FOR COLLEGE AT THE SAME TIME! AFSCME Unitd Ngro Collg Fund Harvard Univrsity Labor and Worklif Program APPLICATION DEADLINE: FEBRUARY 28
More informationSPECIAL VOWEL SOUNDS
SPECIAL VOWEL SOUNDS Plas consult th appropriat supplmnt for th corrsponding computr softwar lsson. Rfr to th 42 Sounds Postr for ach of th Spcial Vowl Sounds. TEACHER INFORMATION: Spcial Vowl Sounds (SVS)
More informationThe price of liquidity in constant leverage strategies. Marcos Escobar, Andreas Kiechle, Luis Seco and Rudi Zagst
RACSAM Rv. R. Acad. Cin. Sri A. Mat. VO. 103 2, 2009, pp. 373 385 Matmática Aplicada / Applid Mathmatics Th pric of liquidity in constant lvrag stratgis Marcos Escobar, Andras Kichl, uis Sco and Rudi Zagst
More informationCALCULATING MARGINAL PROBABILITIES IN PROC PROBIT Guy Pascale, Memorial Health Alliance
CALCULATING MARGINAL PROBABILITIES IN PROC PROBIT Guy Pascal, Mmorial Halth Allianc Introduction Th PROBIT procdur within th SAS systm provids a simpl mthod for stimating discrt choic variabls (i.. dichotomous
More informationTest of a VShaped Relationship between the Expected Real Effective Exchange Rate and Real Output: The Case of France
Journal of Economics and Businss Vol. II 2009, No 2 Tst of a VShapd lationship btwn th Expctd al Effctiv Exchang at and al Output: Th Cas of Franc u Hsing, SOUTHEASTEN LOUISIANA UNIVESIT Abstract Applying
More informationGlobal Sourcing: lessons from lean companies to improve supply chain performances
3 rd Intrnational Confrnc on Industrial Enginring and Industrial Managmnt XIII Congrso d Ingniría d Organización BarclonaTrrassa, Sptmbr 2nd4th 2009 Global Sourcing: lssons from lan companis to improv
More informationElectronic Commerce. and. Competitive FirstDegree Price Discrimination
Elctronic Commrc and Comptitiv FirstDgr Pric Discrimination David Ulph* and Nir Vulkan ** Fbruary 000 * ESRC Cntr for Economic arning and Social Evolution (ESE), Dpartmnt of Economics, Univrsity Collg
More informationSection 7.4: Exponential Growth and Decay
1 Sction 7.4: Exponntial Growth and Dcay Practic HW from Stwart Txtbook (not to hand in) p. 532 # 117 odd In th nxt two ction, w xamin how population growth can b modld uing diffrntial quation. W tart
More informationCPS 220 Theory of Computation REGULAR LANGUAGES. Regular expressions
CPS 22 Thory of Computation REGULAR LANGUAGES Rgular xprssions Lik mathmatical xprssion (5+3) * 4. Rgular xprssion ar built using rgular oprations. (By th way, rgular xprssions show up in various languags:
More informationA Note on Approximating. the Normal Distribution Function
Applid Mathmatical Scincs, Vol, 00, no 9, 4549 A Not on Approimating th Normal Distribution Function K M Aludaat and M T Alodat Dpartmnt of Statistics Yarmouk Univrsity, Jordan Aludaatkm@hotmailcom and
More informationAre Health Insurance Markets Competitive? By Leemore Dafny*
Ar Halth Insuranc Markts Comptitiv? By Lmor Dafny* To gaug th comptitivnss of th group halth insuranc industry, I invstigat whthr halth insurrs charg highr prmiums, ctris paribus, to mor profitabl firms.
More informationOn the moments of the aggregate discounted claims with dependence introduced by a FGM copula
On th momnts of th aggrgat discountd claims with dpndnc introducd by a FGM copula  Mathiu BARGES Univrsité Lyon, Laboratoir SAF, Univrsité Laval  Hélèn COSSETTE Ecol Actuariat, Univrsité Laval, Québc,
More informationRemember you can apply online. It s quick and easy. Go to www.gov.uk/advancedlearningloans. Title. Forename(s) Surname. Sex. Male Date of birth D
24+ Advancd Larning Loan Application form Rmmbr you can apply onlin. It s quick and asy. Go to www.gov.uk/advancdlarningloans About this form Complt this form if: you r studying an ligibl cours at an approvd
More informationA copy of the Consultation Paper is in the Members Library and further details are available at www.scotland~qov.umpublications/2012/12/5980
To: CORPORATE SERVICES COMMITTEE NORTH LANARKSHIRE COUNCIL REPORT Subjct: CONSULTATION: CIVIL LAW OF DAMAGES  ISSUES IN PERSONAL INJURY From: HEAD OF LEGAL SERVICES Dat: 30 JANUARY 2013 Rf: AL LE CSN
More information