The textbook expresses the stock price as the present discounted value of the dividend paid and the price of the stock next period.

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1 coomcs 435 Meze. Ch Fall 07 Socal Sceces 748 Uversy of Wscos-Madso Sock rces, News ad he ffce Markes Hypohess The rese Value Model Approach o Asse rcg The exbook expresses he sock prce as he prese dscoued value of he dvded pad ad he prce of he sock ex perod. [8.] I realy, we do kow he prce ex perod. Raher we have a expecao of he prce ex perod, ad for ow we assume for ow Raoal xpecaos (such ha he marke expecao s he mahemacal codoal expecao. Hece he expecaos operaor refers o he codoal mahemacal expecaos operaor. I oe-perod: [8. ] Where for smplcy, he eres rae used o dscou he fuure s a cosa, ad (Z+ = (Z formao avalable a me +. Assume a me, ha s kow. Noe ha he prce ex perod s gve by: [8. ] Subsug o [8. ] yelds: ( ( ( ( ( ( ( Noe ha by he Law of Ieraed xpecaos, vz., ( ( Z Z quao ( becomes: ( ( [8.3 ] Oe ca coue o subsue ou for + o oba he Geeralzed vded Valuao Model: ( (... ( [8.4 ] Noe ha hs expresso mples, uder cera codos:

2 ( ( ( ( ( Lm quao ( rules ou bubbles. Tha s, s assumed ha 0 ( k The Gordo Growh Model assumes ha dvdeds are expeced o grow deermscally a rae g, such ha ( g (whch s equao [8.6]. Subsug [8.6] o ( yelds, for < : ( g ( g ( g... [8.7] ( ( If oe allows o go o fy: ( g ( g ( g... (3 ( ( ( g ( g ( g... ( g ( ( ( g I geeral, wll o grow a smooh deermsc fasho, or wll be cosa. As a cosequece, he flucuaos prces wll o move oe for oe wh coemporaeous dvdeds. The prevous calculaos assume ha he eres rae used o dscou he fuure values s cosa, ad equal o a rsk free rae. I geeral, he eres rae used s he sum of he rsk free rae ad a rsk premum (rf ad rp, respecvely, he exbook. Subsug: e (4 ( g (5 ( rf rp g I he below fgures, mohly daa from Rober Shller s webse ( hp:// are used o hghlgh he relaoshps bewee sock prces, dvdeds ad eres raes. I Fgure, real (CI deflaed sock prces ad dvdeds are show; ad Fgure real prces ad e year eres raes.

3 5, ,500,500,500, Real S& [lef scale] Real dvded [rgh scale] RALS_AN_ RALIVIN Fgure : Real (CI deflaed Sadard ad oor dex (lef scale, log, ad real dvdeds (rgh scale, log. Source: Rober Shller, hp:// accessed 0/5/07. 5,000 3,500,500,500 Te year rae, % [rgh scale] 6 4, Real S& [lef scale] RALS_AN_ GS0 Fgure : Real (CI deflaed Sadard ad oor dex (lef scale, log, ad e year eres rae (rgh scale. Source: Rober Shller, hp:// accessed 0/5/07. As predced, he sock prce dex covares posvely wh dvdeds (dvdeds are hghly serally correlaed, so a moveme up dvdeds persss, ad s egavely relaed o he eres rae. Noe ha dvdg boh sdes of equao 5 by leads o he relaoshp ha he prce/dvded rao s versely relaed o he eres rae (mus he growh rae of dvdeds. 3

4 ( g ( g... ( g rf rp ( rf rp ( rf rp ( rf rp g (6 The posed verse relaoshp s show Fgure Te year rae, % [rgh scale] S& rcedvded rao [lef scale] S_AN_/IVIN GS0 Fgure 3: Sadard ad oor prce o dvded rao (lef scale, ad e year eres rae (rgh scale. Source: Rober Shller, hp:// accessed 0/5/07. News Le s reur o a rsk eural model. Recall he prese value of a sock s gve by: [8. ] ( (7 The las erm afer he secod equal sg (7 obas by he Law of Ieraed xpecaos, vz., ( ( Z Z Now decompose he chage he prce of he asse: [( ] (8 ( 4

5 The frs erm s he expeced poro of he prce chage. The secod erm he brackes s he uexpeced poro. Ths secod poro square brackes ca be furher broke up. ( (9 ( rp rf ( rp rf News cludes he dvdeds aouced for perod +. I s uforecasable. Ths ews may also affec people s expecaos regardg he fuure, ad hece he fuure (whch ur affecs expecaos of perod +. Hece, ew formao drecly resuls a ew prce, ad revsos expecaos. Noce he secod erm he square bracke s ( rp rf whch s he chage he expecaos regardg he asse prce perod +, based upo wha he marke kew perod + versus wha kew perod. Noe ha oher ews ha does affec perod + could sll affec expeced asse prces he fuure, ad hece he asse prce oday. A example: The sock marke (Goldma Sachs sued by SC, aouceme approx. 0:30am 5

6 Wha equao ( says s ha he prce wll evolve as expecaos of dvdeds o he fuure chage over me ( rf rp ( ( rf rp ( ( rf rp ( ( rf rp ( ( rf rp ( Those dvded sreams deped par upo he eargs ha frms are expeced o ear he fuure. As he ecoomy looks more lkely o slow dow, expecaos of eargs (ad hece dvdeds are lkely o be revsed dowward. I addo, here s o reaso he requred reur o equy has o rema cosa. If vares over me, he ( becomes: ( rf rp ( ( rf 3 ( ( rf rp ( ( rf rp ( rp ( ( rf ( ( rf rp rp... ( ( rf rp...( ( rf rp To he exe ha he requred reur vares wh he eres rae (say o he 3 moh Treasury ad rsk averso, a addoal source of varao s roduced o he sock prce. Aouceme ffecs Oher Markes Ths framework for aalyzg asse prces has bee appled umerable cases. Mos recely, has bee appled o he Fed s mplemeao of large scale asse purchases of log erm Treasures ad morgage backed secures. Gago e al. (00 s he mos well kow aalyss of he LSA s effec o log erm bod raes. Neely (00 aalyses he mpac of LSA aoucemes o bod raes ad exchage raes. 6

7 7

8 ffce Markes Hypohess I he above dscusso, I have assumed ha he subjecve marke expecao of fuure dvdeds ad prces equals he mahemacal expecaos. Ths assumpo s called he raoal expecaos hypohess. Oe mplcao of raoal expecaos s: X X u u _ d(0, u Tha s, he acual realzao of X equals he expecao of X based o me - formao, plus a uforecasable radom error, u. Cosder for sace f dvdeds were pad oly every year, ad each perod was oe day. The equao ( becomes: ( rf rp Use he defo of raoal expecaos above, ad assume log-ormaly of he error erm: p p l( rf rp p p rf rp u~ ( So sock prces follow a radom walk (wh drf. I s o que rgh o say he bes predcor of omorrow s sock prce s oday s. Raher here s a small predcable compoe (ke, whch from oe day o aoher s quaavely very small. Refereces Joseph Gago, Mahew Rask, Jule Remache, ad Bra Sack, 00, Large-Scale Asse urchases by he Federal Reserve: d They Work? Saff Repor o. 44 (Federal Reserve Bak of New York. Chrsopher J. Neely, 00, The Large Scale Asse urchases Had Large Ieraoal ffecs, Workg aper 00-08A (Federal Reserve Bak of S. Lous _emh_f7 8

The textbook expresses the stock price as the present discounted value of the dividend paid and the price of the stock next period.

The textbook expresses the stock price as the present discounted value of the dividend paid and the price of the stock next period. ublc Affars 974 Meze D. Ch Fall Socal Sceces 748 Uversy of Wscos-Madso Sock rces, News ad he Effce Markes Hypohess (rev d //) The rese Value Model Approach o Asse rcg The exbook expresses he sock prce

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