r) l . zz1 y , .g -) s) J ', - . -) lnvestment tlnder Uncertainty f'shri 11:1 s 11 1Q. 1) ixi t :.1 114.1 Illlbert S. I'i lltl),ck- ee >e ' 1%; 14X'aZl>l&l u . , . N #- 1 a a jl I'rincetoll UI1 ivers ity I'ress Prillcetoll, NcAy Jersey [...]... return ()n tilis ptlrtllitl- rel-nembcring that the short position will require a paymdnt () 1- () 1 ?? J1) I /1) l ()t) That return 6:1() Since the return is risk-free, i t mtlst cqtlal () l *t) is 6.6() /-1 ) -8 .25 = 2000 W l 4,5 - - 1 r tt 1600 = ww - w 12Oo 80O y-1500 - '.0.455 / - - I I 1 l I ' 400 80O = - Fz l ) 400 O O - 6) l xw N x xv N 1600 12O0N 1284 / Pa '-' -> ' Nw N N N N 2000 = 2 =... when J'l) = 64.65 I-lence if /$) < 64.65 wtt will never invest at 1111, even if the price goes up in both periods Als(? suppllse we invest in peritld 1 rather than waiting until period 2 Then &ve would obtain a net value 1z'1 l 11 ( 1 #()) 1600 Setting this equal to h and solving for /1)gives /'!) l 66.23 = = , = - )-N't7 - = - - - -( ).25 5 = - - - -fr(2tl - - = E) = l 0 l= 2 = l = 3 - = 5 J2 J2 Pj =... be exercised now- and hence the valtle ()f the option is jtlst its net payoff, K) I In the terminology of options when / is small tht, nttt payllff thlm imin the mtlney.'' At mediate investment becomes large ()r the (lption is critical point or threshold where it is stltliciently deep the ctlst of waiting a - = - - = - - - (?1% tllltyvtriglls - = = ,$ -l - = 5 -. ().5 5 = - 's - K&dtlep w /1)+ 81)1)... patla / s,av,'' ovcrtimc -v ti-l d ibi-gth -d -l-p -t pp di-th-x v kvimesonthesame May Jzbs Filled as Factories Rcly on day.sunday, !6, !993: Sbaky Economy Even Professionals Are Temps.'' uyeq-ver and '.In a jj i'x 't u yt L Nt, k 'h.h ,, , i ' $- 'ikyk ,; q 11 u 'fK ''e ot ,, ,- ''' i l8 lntrodttctil they can have different implications for investment: aggregate uncertainty that affects... /'!) l 66.23 = = , = - )-N't7 - = - - - -( ).25 5 = - - - -fr(2tl - - = E) = l 0 l= 2 = l = 3 - = 5 J2 J2 Pj = 1 Pa = 2.25/% -' '>' Pz = 2.25P -' -' '' >- - 25 = 5/% L 2 Pv Pz = 0.75/% '-' '-' >' Pz = Q.75Pz ' '-> ' = J2 2 % = - 5 - = 0.5/% L 2 % = 0.25/% -' '-* ' Pz = 0.25/% ' ' *- ''l''l''hc method of kecping a ptlrtl'lllitl riskless by changing its ctlmpllsititln through repeatcd hedging str:ltetzy.''... terms of the underlying Interest Rates and Investment Once we understand why and how (irms should be cautious when deciding whether to exercise their investment options, we can also understand why interest rates seem to have so Iittle effect on investment Econometric tests of the orthodox theory generally 5nd that interest rates are only a weak or insignihcant determinant of investment demand Recent... period-l) price.? Thus rt)( ) ((/ + 0.5) f'1) Pb Therefore the expectcd rate of capital gain on 11 widget is g-()( ) Jl)J/ ) P3 C q 0.5 Hence the required payment per widget in the short position is 0.5)1 /l) (0.6 f/ ) J1).Setting * 1 *t) ((1.6 t/ ) l /1) t).I *()s t0 l ( and setting 11 8.5, we find that if Jl) > $97, the value ()f the option is = , = = - - - = - - - - = - = 8) = 15 (? Jl) l455 q - ... the option unexorcised- at to invest is worth lnore than I l J$) 1()()1) ,and should be Ie until next year least ' - - - y' 1800 1600 = 1400 - 1 1 Pz 1200 - ur z 1000 800 ,' 7.5/% 727 - - 'Ybu might think that immediate investment woultl be justifie only if we wouitl invest ncxt year irrespective of whether the price went up or down In fact thc critical price for immediatll investment is Iower Assuming... which case t' l will equal -( ).25 11 J:1y quating these two possible values ()f tp 1 and solving for ?? gives -free = - 75 , 75 = = - n (Then, * - C) + 267 irrespective -3 .21 1 l 2.83 = = 1()f)7/ /!) t)f 141 Remembcring ) /'$) position will require a payment of () l n J'll l portfolio is 8.34 Jl) 8) 693 Setting tllis equal to t).l 107 and solving for 6) gives 28 = - - - that thtl shtlrt l ()7, the... intbrmation (but never, Most -rcb'o-sible future 'Tllese th rct: cllari.ti-iit.: ritii itisill ic I itt;i ((? dcfcl I l 111lc i.llc t?I?(ilI lul dcttisioldsol' investors is interacton is the focus ()f t his bf.)tlk.bl'.t dklvclllpth e theof'y ()f 'l-h lntrodttcliolt irreversible investment applications-l under uncertainty, and illustrate it with some practical The orthodox theory of investment has ntt recognized . .g -) s) J ', - . -) lnvestment tlnder Uncertainty f'shri 11:1 s 11 1Q. 1) ixi t :.1 114.1 Illlbert S. I'i lltl),ck- ee >e ' 1%; 14X'aZl>l&l u . , . N #- 1 a a jl I'rincetoll UI1 ivers ity. Congress Cataloging-in-ablication Data Dixit, Avinash K. Investment under uncertainty / by Avinash K. Dixit and Robert S. Pindyck P. C n1. Includes bibliographical references and index. ISBN 0-6 9 1-0 341 0-9 1. Capital investments-Decision. Temps.'' jj affect it. In this respect, two types ofcertainty must 6' v distinguished because i'x u q ' t. 'h.h i ,; 'ikyk j ' $- yt . L , o t q j k Nt, u ,, 'f- 11 . ,, . . . . . . . ,- . K .''e ''' i In Chapters 8 and 9 the focus turns from a hrm's The path dependence can leatl to the lbilowing kind of sequence ot' events. When the tirm (irst arrives on the scene and contemplates investment. the current protit is in the intermediate range between the two thrcsholds. Theretbre the lirm decides to wait. Then proiit rises past the upper thresllold. so the lirm invests. Finally. profit falls back to its old intermediate Ievcl. btlt that does not take it down to the Iower threshold where abandonment would occur. Thus the underlying cause (current proiitability) has been restored to its old level. but its