Joural of Appld Busss ad Eoos Vtur Captal Fag : A Thortal odl odhr Chrf Uvrsty of Rs O-LAE Saa Elouar SG Souss Ths papr vstgats vtur aptal fag a vrot whr a aagr fas a prft aptal arkt ad a vtur aptalst fas a oral hazard ad urtaty. Atv otorg, stagd fudg ad sydato a allvat oral hazard ad rdu rsk. At frst stag, w opar th soal wlfar as of up-frot fudg wth otorg, ad as of stagd fudg wthout otorg. W fd that up-frot fudg a provd gratr bfts tha as of stagd fudg. orovr, udr gv odtos, w fd that stagd fudg ats as a sussful dv otrollg forato asytrs. At a sod stag, w fd that sydatd vstts usd wth atv otorg gvs th hghr proft to th start-up du to th s fr-rdg probl otorg. NTRODUCTON Vtur aptal s oft th sour of fag th sstal stags of th arly dvlopt of ay frs. Th fudatal d for fudg start-up frs os fro th trprur s walth ostrats. O portat haratrst of ay start-ups s th hgh rsk du to th grat urtaty about rturs, th lak of substatal tagbl assts ad th lak of a trak rord opratos. ay start-ups ay fa ay yars of gatv args bfor thy start to s profts. Gv ths stuato, baks ad othr trdars ar avrs to or v prohbtd fro ldg oy to suh frs. orovr, ths faal trdars usually lak xprts vstg youg ad hgh-rsk opas. Cosqutly, ths start-ups oft sk vtur aptalsts to b volvd thr atvts by offrg rvu sharg th for of quty ot vturs ordr to obta ssary fudg ad to bft fro th vtur aptalsts xpr aagt ad fa (Wag ad Zhou, 4). Vtur aptal frs ar faal trdars fousd o provdg aptal to sall, fastgrowth start-up opas that ar typally hgh rsk ad ot aabl to or tradtoal fag altratvs. oparso wth tradtoal sours of fuds, vtur aptal frs hav so partular haratrsts. Aordg to Goprs (995), vtur aptal s vstts tal hghr tsts of urtaty, asytr forato ad gral hghr tagbl
assts ad dvlopt opportuts. Sapza ad Gupta (994) assrt that vtur aptalsts obta a quty posto th orporato ad play a atv rol th orporat govra. othr words, thy st th board of drtors ad rgularly otor prfora (Shala, 99). Ky haratrsts vtur aptal fag ar stagg th ott of aptal ad prsrvg th opto to abado th prot. stad of provdg all th ssary aptal upfrot, vtur aptalsts vst stags to kp th prot udr otrol. Stagd vstt allows vtur aptalsts to otor th fr bfor thy ak rfag dsos. Th forato about th vablty of a prot aqurd through suh otorg hlps vtur aptalsts to avod throwg oy at bad prots. t rdus losss fro fft otuato ad rats a xt opto for vtur aptalsts. ths papr, w vstgat vtur aptal fag a vrot whr a trprur fas a prft aptal arkt ad a vstor fas oral hazard ad urtaty. W osdr a up-frot fudg, ad th w osdr a stag fudg ad sydato, to opar th ffts of ths fag stratgs o th aagr s bhavor. Stagd fag a play two rols ths odl: to otrol rsk ad to allvat oral hazard. Stagd fag has b wdly usd vtur aptal, spally th Utd Stats. Ca stagd fag b usd by vtur aptalsts to rdu probls of asytry forato? To aswr ths qusto, w prst a oprhsv, two stags odl of th vtur aptal otratg pross, orporatg oral hazard ad asytr forato probls. Th strutur of th odl volvg aagral ffort, stagd vstt rprodus what w kow of vtur aptal fag. Usg paratr futos, w dsovr a fw trstg proprts of stagd fag. partular, w show that wh usd togthr wth a sharg otrat, stagd fag ats as a fftv opltary has to otratg otrollg agy probls. orovr, vtur aptalsts oft bad togthr groups to vst opas. Covtoal wsdo says thy gag ths prat, alld sydato, to bttr sr pottal vstts. or ys th thkg gos yld bttr vstts (At, 3). Fro th lad vtur aptalst s pot of vw, th bft of skg sydato s that th valu of th prot rss f othr vtur aptalsts bo volvd. Sydato, for xapl, lts th to shar rsk ad dvrsfy thr portfolos, At foud so vd of that. Badg togthr ght also gv th a strogr bargag posto vs-à-vs th opas whh thy vst. Forally, w osdr a faally ostrad aagr ad a vtur aptalst who s trstd vstg th aagr s prot. Th prot s rsky ad th aagr s ffort s ot vrfabl. W assu that th aagr fas a prft aptal arkt ad th vtur aptal s th oly pottal vstor who apts to fa th prot. Th vtur aptal offrs a sharg otrat ad fas th prot stratgally stags o had, ad sydatd th vstt o th othr had. Usg paratr futos, w ar abl to drv so trstg proprts of vtur aptal fag. Our rsults show that, addto to otratg, stagd fag s a fftv has for vtur aptalsts to rdu probls of asytry forato ad to otrol rsks rsultg fro th aagr s bhavor. By takg to aout th atv otorg rol of th vtur aptalst w show that up-frot fudg provds a hghr proft tha as of stagd fudg, or sydato.
LTERATURE REVEW A portat sour of fag for th trprural stor s th vtur aptal dustry. dd, vtur aptal atvty s usually dfd as th provso of quty fag to youg frs. addto, thy oft provd aagral adv to thr vsts. Th vtur aptal dustry s haratrzd by grat urtaty about rturs ad forato asytrs btw prpals ad agts. Th strutur of ths sto appls so aspts of th thory of asytr forato to a faal otratg sttg whh a trprur ay obta fudg fro a vtur aptalst. oral hazard probls ar partularly portat stuatos whr o party ats as a agt for aothr party: th prpal. ths stuatos, th prpal a t prftly obsrv th ffort (or othr atos) of th agt. Js ad klg [976] argud that agy aalyss was th ky to udrstadg th odr fr. Othr lass paprs o th agy probl lud Holstro [979] ad Grossa ad Hart [983]. Th rol of asytry of forato faal otratg vtur aptal s ooly rogzabl. Shala [99] postulatd that otratg prats th vtur aptal dustry rval urtaty about payoffs ad forato asytrs btw vtur aptalsts ad aagrs. H prsly argud that th lak of opratoal hstory tsfs th advrs slto dla. Durg th srg stag, vtur aptalst rvws busss plas of startups ad proposs to th aagr otrats that rdu agy osts. Shala [99] osdrs vtur aptal as otrol hass usd to allvat agy osts. Goprs [995] assrts that thr otrol hass ar oo to arly all vtur aptal fag: - Th us of ovrtbl surts; - Th sydato of vstt; - Th stagg of aptal fusos. So rsarhrs suggstd solutos grd by th vtur aptal dustry to ovro probls arsg fro th asytry of forato lud th us of ovrtbl prfrrd stok (Bary, 994), Trstr (998) otrol rghts (Hlla, 998) whh ay lud rprstato o th boards of start-ups (Lrr, 995) ad sydato (Lrr, 994), Bradr, At ad Atwlr (995). Th sydato ay b a has through whh vtur aptalsts dtr foratoal urtats about pottal vstts. Adat ad Pfldrr (994) dvlop a ratoal for sydato latr vtur rouds that s basd o foratoal asytrs btw th tal vtur vstor ad othr pottal vstors. A vtur aptalst who s volvd th fr s opratos ay utlz ths foratoal advatag, ovrstatg th approprat pr for th surts th xt fag roud. Th oly way to avod ths opportust bhavor s wh th lad vtur aptalst atas a ostat shar of th fr s quty. Sydato ay also b a has through whh vtur aptalsts xplot foratoal asytrs ad ollud to ovrstat thr prfora to pottal vstors. Vtur aptalsts prfr sydatg ost dals for a spl raso; t as thy hav a ha to hk out thr ow thkg agast othr kowldgabl. f two or thr othr fuds whos thkg you rspt agr to go alog, that s a doubl hk to your ow thkg. ost fag volvs a sydat of two or or vtur groups, provdg or aptal avalablty
for urrt ad follow-o ash ds. Sydato also sprads th rsk ad brgs togthr or xprts ad support. Ths bfts prta oly to start-up fag rqurg th vtur aptalst s frst vstt dso. Thr ar dffrt stratgs ad otvatos for sydato follow-o fag. Lad vtur aptalsts who bo volvd th fr s opratos a solv ths forato probl. Othr lss wll-ford vstors wll vst f ths lad o dos. Vtur aptalsts, howvr, ay xplot thr foratoal advatag ad ovrstat th propr pr for th surts th fr s fag. Stagd vstt, whh rats th opto to abado a vtur, s a portat a for vtur aptalsts to z th prst valu of agy osts. Th atv volvt of vtur aptalsts th opratos of thr vstd opas ay also tgat th oral hazard probl. Stagg aptal allows th vtur aptalst to gathr forato ad otor th progrss of th frs wth atag th opto to prodally abado prots. Th rol of stagd fudg s slar to that of dbt hghly lvragd trasatos, kpg th owr/aagr o a tght lash ad rdug pottal losss fro bad dsos. Total vtur fag ad th ubr of fag rouds should also b hghr for sussful prots tha for falurs f vtur aptalst uss forato vstt dsos. othr words, vtur aptalsts otor fr s progrss ad dsotu fudg th prot f thy lar gatv forato about futur prospts. At, Glost ad ullr (99a) rlatd th vtur aptal fag dso to th trprur s skll lvl ad prdtd whh trprurs would dd to tr to a agrt wth vtur aptalsts. Thy also osdrd oral hazard probls, but tratd advrs slto oly th stuato whr th trprur s typ bos oo kowldg btw hdg ad otratg. Hrao (993) assud that th agt s (th aagr s) uobsrvabl atos afft th larg pross. Sh foud that baus of th trato btw larg ad oral hazard, a log-tr otrat s ot quvalt to a srs of short tr otrats. Brga ad Hg (998) aalyzd a slar stuato whh thr s a lk btw oral hazard ad gradual larg about prot qualty. Thy assud that a trprur a t afft th up-sd pottal of hr vtur; sh a oly prvt trsally good prots fro falg. Wthholdg ffort (oral hazard) ot oly dagrs th suss of th vtur but also auss th trprur s ad th vtur aptalst (tally sytr) larg about prot qualty to dvrg. Brga ad Hg (998) foud that th optal otrat ths stuato s a t varyg shar otrat. At, Glost ad ullr (99b) osdrd th rol of dffrt hass for athg trprurs ad vtur aptalsts tgatg advrs slto probls. thr work, trprurs ar assud to hav prvat forato about thr typs ad vtur aptalsts a partpat th aagt of vstd frs (at so ost) ad thus otrbut drtly to th vtur s suss. aagrs ay stop aroud or vtur aptalsts ay atvly sk out attratv vstt opportuts. Wth a thr-stag ga, th authors xad possbl poolg ad sparatg qulbru. To haratrz th otrat that allows optal otuato dsos wth a stagd fa, Adat ad Pfldrr (994) foud that vtur aptalsts should prfr a fxd frato otrat. Ths otrat stpulats that th vtur aptalst ows a rta frato of th fal payoffs, ad fas th sa frato of ay futur vstt (f th otuato of th prot s dsrabl). Ths rsult xplas why latr stags ar ot fully fad by th lad vtur aptalst. t also attrbuts a postv rol to th vtur aptalst as a faal trdary btw th aagr ad outsd vstors. O th sa drto, Hlla (994) bult a ult-stag odl volvg stagd vstt. H xplad rta sttutoal faturs that dstgush vtur aptal fro or
tradtoal thods of fa. For xapl, h xplad that oly wh th vtur aptalst has a otratd stak vstd opas wll thr b a sufftly hgh tv for atv otorg. Th otorg gos byod what a tradtoal fag sttuto would do ad luds spdg t at th opas, frqut tgs wth aagrs, ad bg volvd th dfto of th opas stratgs, hrg dsos (Hlla ad Pur, ), ad top aagt opsato (Kapla ad Strobrg, ). addto, vtur aptalsts brg thr xpr valuatg th prospts of start-ups through thr srg of pottal vstts (Hall ad Hofr, 993), thr ollaborato wth othr start-ups, thr udrstadg of th solutos to th probls that ths frs ay fa, ad wh stat-ups ar bst postod to ras oy (Goprs ad Lrr, 999). Fally thy provd ass to a stratg twork ludg pottal lts ad supplrs, aagt talt (Bygrav ad Tos, 99), stratg partrs (Bau, Calabrs t.al; ). Our odl trs to xplor, at a frst stag, th arbtrag btw up-frot fudg ad stagd fudg for th vtur aptalst. Sod, w aalyz vtur aptalsts ho btw fag th prot dvdually ad splttg fag wth othr vtur aptalsts: sydatg vtur vstts. THE ODEL Cosdr a trprur dowd wth a ovatv vstt prot. Th prot rqurs a tal vstt, dotd, ad ylds a outo R. Th trprur s walthostrad. To plt th prot, h ust ras fuds fro outsd vstors. So of thos vstors hav spal xprts fag ovatv prots. W all th vtur aptalsts. Th ovatv aagr (dotd by ) rls o a vtur aptalst (dotd by ) for vstt. W assu that th prot rqurs a u aout of aptal vstt. Thus, s a gv ostat. Th prot lasts two prods. Th vtur aptalst provds a total vstt. Th vtur aptalst rqurs that th aagr xrts a ffort xhag for fag th prot. Th aagr s ffort, s appld durg th two prods. Th ost of ffort for th aagr s (). Th xptd rtur of th prot s futo of th ffort of th aagr durg th two prods, ad th otorg tsty of th vtur aptalst f otorg our. W suppos that th xptd rtur s subt to a rado fft z suh that th ralzd rtur s r z.r. At th bgg of th frst prod, th vtur aptalst kows th dstrbuto futo of z, ad th rado fft s ralzd ad publly rvald at th bgg of th sod prod. Th vstt a b ad o aout, or two stags ad. Although s fxd, th vtur aptalst a dvd, as of stagd fudg, th rqurd aout to two parts, ad for th two prods, ad th vtur aptalst also has th opto to abado th prot x post by ot provdg th rag vstt. our odl, stagd fag doats th altratv of gvg th aagr all th oy at th sa t, s stagd fag abls th vtur aptalst to ut hs losss ad to shut dow udrprforg prots arly. Thus, th vtur aptalst proposs to supply a total of rsours at th bgg of th frst prod. Aftr th rado fft s ralzd at th start of th sod prod, th vtur aptalst thks about supplyg a total of rsours. f th prot s gltd th ddl by thr th aagr or th vtur aptalst, th prot fals wthout ay output ad th tal vstt s lost. f t s ot th as, th prot otus. To ralz th rtur by th d of th sod prod, th ssary aout, of vstt ust b ad,..,. f both vstts ar ad, th start-up otus to dat ad th
trprur ad th vtur aptalst a splt th fal rtur of th prot. Th splt dpds o thr owrshp prtags, whh ar assud, fxd o th xstg otrat. THE CONTRACT a typal agy odl, otrats ar typally basd o so wll-kow aggrgat asurs. W assu that oly th rtur of th prot s otratbl at th bgg of th frst prod (x at). W wll otrat o a rta typ of foratoal asytry, havg to do wth th bhavor of th aagr durg th vstt. W shall assu that th agt s bhavor s obsrvabl by th prpal, but t s ot vrfabl. Ths asytr forato probl s kow as oral hazard. That ffort s ot vrfabl as that t aot b ludd th trs of th otrat. Th, th aagr s ffort s ot vrfabl. Corg th vtur aptalst s vstt stratgy, t s ot otratbl th otrat. Th aagr s stady wth th ralty that th orally has th opto of abadog th prot th futur. Typally, vtur aptal vstors provd aptal usurd by assts to youg, prvat opas wth th pottal for rapd growth. Suh vstg ovrs ost dustrs ad s approprat for bussss through th rag of dvloptal stags. vstg w or vry arly opas hrtly arrs a hgh dgr of rsk. But vtur aptal s log tr or patt aptal that allows opas th t to atur to proftabl orgazatos. Vtur aptal fag ossts a quty fag, whh s rprstd by fuds that ar rasd by a busss, xhag for a shar of owrshp th opay. Equty fag allows a busss to obta fuds wthout urrg dbt, or wthout havg to rpay a spf aout of oy at a partular t. Takg to aout th aagr s ffort, ad th rado fft z, th vtur aptalst proposs a sharg otrat ad fas th prot stratgally two stags. As osqu, th otrat proposd by th vtur aptalst s a sharg otrat (, ) whr s th rtur shar for th vtur aptalst, ad th rag part ( ) s th rtur shar for th aagr. At th d of th prot, w wll sk for th soal optu. Th dtrato of a fasbl soal optu aouts to axz th olltv utlty futo that s th dvdual utlty obato. W dfd th optal soal wlfar by: SW Whr: SW : s th Soal Wlfar; : s th optal proft lvl of th aagr; : s th optal proft lvl of th Vtur Captalst. Th varabls,, ad ar dtrd dogously qulbru. Tg Th odl has thr prods: t,,. All agts ar rsk utral. Thr s o dsoutg. Th tg of th atos s gv blow: At t, th vtur aptalst dds o a vstt pla (, ) ( as of up-frot fudg ad ). But frst, th vtur aptalst proposs a sharg otrat (,
) to th aagr; th f th aagr apts th sharg otrat, th vtur aptalst vsts, ad th aagr appls ffort ad urs ost (). Th vtur aptalst ay bft fro th rsoluto of urtaty by vstg x post. Howvr, x post vstt wll pos a rsk o th aagr (fro th vtur aptalst s opto to qut ad to rgotat), whh ay lad to a hghr ffort. At t, th vtur aptalst thks about th dso to lav th prot, to rgotat th otrat, or to provd th rag vstt. Th urtaty s rsolvd; th, f th prot s good, th vtur aptalst otus to vst th prot ad offrs th ssary vstt. f th prot s avrag, th vtur aptalst wll ask for rgotatg a w otrat. Ad f th prot s bad, th vtur aptalst wll abado th prot wthout vstg. At t, th prot s fshd, ad th vtur aptalst ad th aagr splt th rtur basd o th xstg otrat. Assuptos W suppos that vtur aptalst wll xrt otorg as of up-frot fudg, ad as of stagd fag, otorg wll ot our. as of sydatd vtur vstts, vtur aptalsts wll otor th prot. Vtur aptalst a alorat aagr s oral hazard probl through otorg. Vtur aptalst hooss to otor th prot wth a tsty whh has a pat o th aagr s bhavor. otorg s ostly, a tsty osts C () wth [, ] ad,. W suppos that th xptd rtur s a lar futo of th aagr ffort ad th otorg tsty. f th aagr s ffort s rasg, th xptd rtur of th prot s rasg, ad f th otorg tsty of th vtur aptalst s hgh, th output xptd of th prot s hgh. W assu that: R R ad Thus, th ralzd rtur wth z a obsrvabl rado fft s: zr(, ) r zr( ) For splty, w osdr th dtty futo for th xptd rtur of th prot. W wll ot osdr th as of rgotato ths papr.
W assu that th rado fft s dstrbutd aordg to th Ufor dstrbuto o trval[,]. orovr w assu that th ffort ost futo () of th aagr s suh that: ' '' ad For xapl, w assu that: whr Vtur Captal Fudg Th bas d for fudg start-up frs os fro th trprur s walth ostrats. Th trprur ds fuds to fa th fr fro bgg utl t gvs postv rturs. Vtur aptalsts provd th fuds rqurd to ovro ash ltatos durg th tal stags of a fr s lf, bfor th urtaty of th vtur s rdud ad altratv sours of fudg bo avalabl. Stagd fudg s a a haratrst of vtur aptal fag. Rathr tha provdg thr fudg upfrot, stag fudg allows vtur aptalsts to prodally updat thr forato about th fr, otor ts progrss, rvw ts prospts, ad valuat whthr to provd addtoal fudg or abado th prot. Stagd fag provds vtur aptal wth a ral opto. Ths opto a b xrsd or abadod ovr t as th urtaty about th start-up fr s rdud. Stagd fag s also advoatd as a otrol has. Thortal odls xpla ths fag strutur as a govra has to rdu th agy osts plt vturbakd start-ups. Ths thortal odls ar portat to udrstad th uqu atur of vtur fag. Nhr (999) studs th suprorty of stagd fudg ovr up-frot fudg a prft rtaty, full forato sttg (thus wthout a ral opto). A walth-ostrad trprur stablshs a agy rlatoshp wth a vstor who provds th fuds rqurd to start th busss. Th vstt that th trprur aks s partly suk, thus th rlatoshp s op to th hold-up probl assoatd wth th trprur rgotatg th otrat aftr th vstt has b ad. Stagg th vstt a rdu ths hold-up probl f th valu of th vtur s assts wthout th trprur rass ovr t as th trprur s spf kowldg s bddd th assts of th fr. Th ash ostrats assoatd wth follow-up rouds, whl vr bdg qulbru, provd th bargag powr that th vstor ds to rdu th osts assoatd wth th hold-up probl. Koks ad Ozrturk () adopt a oplt otratg strutur to dogously drv th optalty of stagd vtur aptal fudg. Thr odl assus a walthostrad trprur ad a tal vstor who provds a frst roud of fudg, but dos ot ot to furthr fudg. Bfor th sod roud fudg dso, w forato bos avalabl. Ths forato s avalabl to both th trprur ad th sd vstor but ot to pottal outsd vstors. Cosqutly, th sd vstor has a foratoal advatag that allows h to offr bttr trs f th prot ras attratv as wll as aptur A ufor dstrbuto s o for whh th probablty of ourr s th sa for all valus z Z.
a surplus assoatd wth th prvat forato. Stagd fudg provds th sd vstor wth a surplus that othrws h would ot aptur. As prvous odls, th frst roud rovs th tal ash ostrat ad allows th trprur to grow ts vtur. Th sod roud gvs th vtur aptalst bargag powr to xtrat addtoal rts. Th ash ostrat plt th sod roud s th thrat that strgths th vtur aptalst bargag posto v f ratoal xptatos sur that t s vr arrd out. Caada, sydatd vstts yldd sgfatly hghr rturs tha thos by a sgl vtur aptalst. At foud that "uotd vstts had avrag aual rats of rtur o th ordr of 5% to % whras th sydatd vstts had avrag rturs of about 35% to 39%". Wag ad Zhou (4) drv th advatag of stagd fag ovr up-frot fag a stuato whr thr s forato asytry btw th vtur aptal ad th trprur. Th trprur provds ffort, w forato bos avalabl ovr t ad oly th fal output s otratbl. th stagd fudg soluto, th vtur aptalst kps th opto of abadog th prot f th w forato s ot attratv. Stagd fudg provds two bfts. Frst, t rdus th ost assoatd wth th rsk of bad forato bog avalabl. Ad sod, t drass th osts of th oral hazard probl that rgs fro th agy rlatoshp stablshd wh th frst vstt ours. Th tal fudg provds th rsours that th walth ostrad trprur ds. otrast, follow up fudg rls o th thrat that th trprur rus out of rsours to urv dow oral hazard, v f qulbru ths thrat s vr arrd out. Ths odls sparat a tal stag whr th ash-ostrad trprur rvs fudg ad whr a agy rlatoshp s stablshd fro follow-up rouds. Ths follow-up rouds rly o th thrat to th trprur of httg hs ash ostrat to rdu agy osts. Up-frot Fudg ths paragraph, w study th altratv whr th vtur aptalst provds th fuds rqurd by th aagr o aout. At th bgg of th frst prod, th vtur aptalst has th ho btw two possblts: fag or ot th prot. as of upfrot fudg th vtur aptalst loss th opto to abodo th prot. S th ffort s ot vrfabl, th sharg otrat ad atv otorg srvs as as of otrol of oral hazard probl to th vtur aptalst. Th vtur aptalst should hoos th otrat (,( ) that axzs hs xptd proft ad takg to aout th osqus of ths otrat o th aagr s dsos. Dfto : Lt th aagr s xptd proft fro th prot b: ( ) zr(, ) h( z). dz ( ) () Whr z s th rado fft dstrbutd aordg to th ufor dsty dstrbuto h( z) wth a ad vara. W assu that th aagr s rsrvato utlty s. qual to zro ( ) Th aagr s wll apt th otrat f ad oly f t gvs h a proft o sallr tha that rprsts th utlty th aagr a obta by brakg hs rlatoshp wth th vtur aptalst.
Th partpato ostrat (th dvdual Ratoalty ostrat) thus a b wrtt: ( ) zr(, ) h( z). dz ( ) (R) Wh th vtur aptalst offrs h a otrat (, ( )), th aagr hooss hs ffort by solvg th followg progra: ax ( ) zr(, ) h( z). dz ( ) E Th FOC gvs us th sod ostrat that th vtur aptalst has to tak to aout: t s th tv Costrat. Thus th tv opatblty ostrat a b wrtt: ( ) zr(, ) h( z) dz '( ) (C) Dfto : Lt th vtur aptalst s xptd proft fro th prot as of upfrot fudg b: U. zr(, ) h( z). dz C( ) Th, th vtur aptalst wll hoos th otrat whh rsolvs th followg progra: ax [ ]. zr(, ) h( z). dz C( ),, Subt to : (P.) ( C) ( R) Fro th (C) ostrat w obta: () Th FOCs odtos ar: U U ( ) Th FOCs odtos of th progra abov ply that th vtur aptalst wll xrt otorg (whh as ) f ad oly f th aagr wll xrt a ffort lvl sallr tha s.
Aothr oluso s that th optal ffort lvl whh aks th proft lvl of th vtur aptalst optal s: (3) By substtutg w obta: Ad: s postv f ad oly f: as of upfrot fudg, th sod bst soluto s: SW U U U U Proof. S Appdx Stagd Fudg Vtur Captal ths sto w osdr stag fudg vtur aptal. W assu that th vtur aptalst wll ot xrt otorg, ad that th aagr s ffort s ot vrfabl.a prot haratrst of vtur aptal vstg s ts stagg strutur through squtal fag rouds. At ah roud of fag, a vtur aptal fr suppls w faal rsours to th start-up. Ths rouds of fag ar dsrt vts stagd ovr th lf of th opay as a prvat tty. Rouds of fudg ar rtal th rlatoshp btw vtur aptalsts ad th start-ups that thy vst. Thy ar ot a spl trasfr of faal rsours; thy also volv th rdfto of th govra strutur of th fr ad provd a sgal about ts
prospts. Ths w owrshp strutur affts th otrol strutur of th opay as wll as th payoffs of a futur lqudty vt. At th bgg of th frst prod, th vtur aptalst vsts, th aagr appls ffort. At th bgg of th sod prod, th urtaty s rsolvd. Gv th vstt, th aagr s ffort, ad th rsolvd urtaty z, th vtur aptalst dds whthr to otu vstg th prot or to abado t. W assu that th vtur aptalst wll apt to provd th rag aout to th aagr f ad oly f th rado fft valu s suh that: ( zr ) Ths as that th vtur aptalst wll apt to otu fag th prot f hr xptd rtur s at last qual to. Lt assu that: z R( ) f z z, th vtur aptalst wll provd th rfag; othrws th vtur aptalst wll stop vstg th prot. Thus: z z Th prot otus z z Th prot s abadod Dfto 3: Lt th vtur aptalst s xptd proft fro th prot b: (.. R() ) h( z). dz z z (4) Forally, th vtur aptalst s progra to rsolv s gv by: ax, E z Subt to : (. zr( ) ) h( z). dz (R) ( ) zr( ) h( z). dz '( ) (C) z (RC), ad [,] (PC) Ths probl stablshs that th vtur aptalst axzs th proft that sh obtas fro vstg th prot, udr th rstrto that th aagr s wllg to apt th sharg otrat. Ths odto s kow as th partpato odto (.R). orovr, th vtur aptalst axzs ts proft subt to ts dvdual partpato odto ( z z), th aagr s tv opatblty ostrat (.C) ad th rsours ostrat (R.C). Postvty ostrat (P.C) ust b tak to aout. Th followg soluto haratrzs th qulbru th stuato of stagd fag. th as of stag fudg, th sod bst soluto s:
SW S SB SB Proof. S Appdx. Now assu that th aagr s ffort s vrfabl. W suppos that th vtur aptalst dad a ffort lvl th otrat. Th probl to rsolv s: (RC) (R) : ). ( ) (., to Subt dz z h zr ax z E (P.3) as of stagd fudg ad a vrfabl ffort, th frst bst soluto s:
FB ( ) FB ( ) SW ( ) S ( ) Proof. S Appdx 3. W wll us ths soluto to fd th optal stratgy for th vtur aptalst: up-frot fudg wth atv otorg, stagd fudg wth a ot vrfabl ffort, ad sydatd vstts. Sydatd Vtur vstts W ow tur to th qulbru wth ultpl vtur fag: sydatd vtur fudg. Sydato s th pross whrby a group of vtur aptalsts wll ah put a proporto of th aout of oy dd to fa a sall busss. Two a optg sghts xst as to why vtur aptalsts sydat vstts. Th tradtoal sd dvlopd fro fa thory osdrs sydato as a as of rsk sharg va portfolo dvrsfato (Bygrav, 987, 988) ad Sth & Khol Sth, ). otrast th rsour basd sd vws sydato as a as to shar rsours suh as forato th slto (bfor th vstt s ad) ad aagt (aftr th vstt s ad) of vstts. Rlatd to th rsour basd vw, sydato s osdrd as a a to assur, ras or rproat trasato flow of th vtur aptalst. Cosdr ow that w hav urous frs ad vtur aptalsts. As bfor frs hav ass to a vstt prot ah ad d xtral fuds to fa th. Oly vtur fag s avalabl. Vtur aptalsts a dd thr to fa frs o thr ow dvdual vtur fag or to shar fag wth othr vtur aptalst: ultpl vtur fag (sydatd vstts). aagr s bhavoral hos ar ot obsrvabl: thr s a oral hazard probl. Frs rv fag oly f vtur aptalsts xpt o-gatv profts... f thy xpt a rtur at last qual to th o fro a altratv vstt. Suppos that w hav vtur aptalsts (hforth dxd by...), ah vtur aptalst fas k prots (hforth dxd by...k). Th dffr wth th up-frot fudg dpds o how vtur aptalsts shar fag wth othr ( ) vtur aptalsts so that t vsts ut ah of th k prots. W assu that all th prots hav th sa dstrbuto futo of urtaty. W a hav fr-rdg probl baus otorg s prvatly ostly ad ot
obsrvabl, ah vtur aptalst has a tv to rdu ts ow ffort ad bfts fro th othr vtur aptalsts otorg. orovr, thr s a duplato of fforts baus vtur aptalsts do t oordat th ho of thr otorg tsts. Th da s that otorg dlvrs a publ good, ad all vtur aptalsts fag a start-up bft fro th hghr rtur of th prot. Th xptd rtur of th prot s: R(, ) Whr s th ffort lvl xrtd by th aagr of th prot ad s th total otorg tsts that all vtur aptalsts xrt o th prot. S vtur aptalsts (s) fag th sa prot wll at as oly o, thy wll propos to th aagr as of suss. Th thy wll splt qually btw th. Th: Th vtur aptalst wll dad to th aagr as of suss of th prot. Thus th proporto of th aagr fro th prot s ( ). Vtur aptalst s xptd proft fro a prot s gv by: z R( ) h z dz..,.. Vtur aptalst s xptd proft fro th k prots s gv by: k k. z. R,. h( z). dz k Whr th frst tr rprsts th xptd rtur fro th k prots vtur aptalst fas, ad th sod tr s th total ost of otorg k prots. Vtur aptalst hooss ad to axz (5). Vtur aptalsts a fa or prots ad rah a gratr dgr of dvrsfato tha wth dvdual vtur fag. Eah vtur aptalst a fa k prots stad of o. Th xptd rtur of ah prot dpds o th otorg of all k vtur aptalsts. Vtur aptalsts wll dad th sa shar of rtur as of suss of th prot. Th progra to rsolv s: (5)
:, k k to Subt ax Fro, w obta. Takg to aout ths rsult to th obtv futo, w fd: k k ax, Th thrd ostrat as that th vtur aptalst wll otor th prot f ts xptd proft s postv, whh gvs us: Th total otorg tsts that s xrt for th prot thy fa s: Th FOCs Codtos gv. Th avrag otorg tsty xrtd by th s o th prot s. Vtur aptalsts wll xrt otorg f th aagr s ffort s lowr tha, whh axzs thr xptd proft. W ot that th ssary total otorg tsty to otrol aagr s sbhavor s lowr as of sydato tha as of sgl vtur fudg (hr up-frot fudg) s otorg s dsprsd through vtur aptalsts provdg fa to th aagr. Th followg proposto haratrzs th qulbru of th sydatd vstt. Th uqu sytr qulbru of th sydatd vtur vstt, whh ah vtur aptal otors th prot wth tsty ad dads th shar of rtur s gv by:
f f k SW k SyF SyF SyF SyF f th Vtur aptalst wll hoos to otor th prot losly ad wth a hgh otorg tsty suh that hr xptd proft wll b k SyF. Th s obtv s to axz ts xptd proft, sh wll hoos to provd a lowr otorg lvl s th lad vtur aptalst wll otor th prot losly (Fr-rdg probl), thus: S s do t oprat oopratvly, all s wll provd a otorg tsty suh that:, ad th oly agt who wll proft fro th fr-rdg probl s th aagr. Proposto : Ev wh th ubr of vtur aptalsts fag ay prots sultaously s hgh, th t proft of th aagr s postv., l SyF k
sydatd vtur vstts wth atv otorg, th vtur aptalst dos ot obta postv rturs. Ths s du to th probl of fr-rdg. Th t proft of th aagr as of sydatd vstts wth atv otorg s lowr tha as of up-frot fudg. Aalyss To apprat th rol of vtur aptalst fag stratgy allvatg oral hazard, w osdr th followg ass: up-frot fudg, stagd fudg ad sydatd vstts. W wll us UF, SF ad Sy for up-frot fudg, stagd fudg ad sydato, rsptvly. f w opar th soal wlfar wh th ost of otorg gos to ad wh th ost of otorg s hgh, ad gos to. W fd: SW ( ) SW ( ) Up-frot fudg Stagd fudg (FB) Stagd fudg (SB) Sydato ( ) ( ) 4 ( ) k k Proposto : Wh gos to fty, th Soal Wlfar as of up-frot fudg s hghr th as of sydato, wh th ost of otorg s hgh, ad wh th ost of otorg s low, sydatd vstts ras th soal wlfar of th agts. Th proposto abov suggsts that as of sydatd vtur vstts th soal proft of th agts s hghr tha as of a sgl vtur fudg (up-frot fudg) wh otorg s ot ostly. s wll otor losly th prot. Othrws, sydato s ot th optal stratgy for th vtur aptal vstor wh otorg s ostly, s otorg s ot a obsrvabl ato btw th s; thy wll fr-rd to axz thr xptd proft. Thus, wh otorg s ostly, up-frot fudg wth atv otorg s a optal stratgy. otorg tsts ar hghr wh thr s oly o vtur aptalst that fas th prot, ths s th drt rsult of th urous vtur aptalst that provd fudg to th start-up. As up-frot fudg, th aagr of th prot ust provd a ffort lvl lowr tha to gv tvs for th s to otor th prot.
Th oparso of four soal wlfar urvs wh th ost of otorg s low s show Fgur. Fgur Th fgur abov dats that th soal wlfar as of up-frot fudg wth atv otorg wh s low, whh as that th ost of th ffort provdd by th aagr s hghr tha th soal wlfar for th frst bst soluto. Th sydatd vstts provd th lowr soal wlfar; ths s th drt rsult of fr-rdg probl. W olud that wh provdg ffort s ostly for th aagr, up-frot fudg wth atv otorg s th optal stratgy to obta hghr rsults. th othr as, wh supplyg ffort s t ostly ( ), stagd fudg wth vrfabl ffort s th optal stratgy. Th oparso of four soal wlfar urvs wh th ost of otorg s hgh s show Fgur.
Fgur Th soal wlfar as of up-frot fudg wth atv otorg s hghr tha th soal wlfar as of stagd fudg for gv valu of (th ost of ffort ovrgs to zro as ). fat atv otorg wll hav a pat o th aagr s bhavor whh gvs a rasg th t proft of th agts. Stagd fudg a rdu urtaty ad allvat oral hazard. our odl, th otorg up-frot fudg ras th t proft of th vtur aptalst ad th start-up. For lowr valu of, whh as a hgh ost of ffort for th aagr, th ust otor th prot losly to otrol th aagr s sbhavor. othr words, th aagr wll ot provd a hghr ffort s t s ostly. otorg wll b a good has to otrol ths probl. But wh s hgh, th ost of th ffort s low, ad th aagr wll provd a hghr ffort to ras th xptd rtur of th prot ad th thr s o raso for th to otor losly th prot. For that raso, th soal wlfar as of stagd fudg (FB) s hghr tha th soal wlfar as of up-frot fudg wth atv otorg. Wh th ost of otorg s hgh, th soal wlfar as of sydatd vstts approahs th soal wlfar as of up-frot fudg: vtur aptalsts wll oprat as o "far". CONCLUSON Ths study has xtdd th vtur aptal ltratur by aalyzg th rol of asytr forato odtos, whh ay ars subsqut to th t of otratg, a play th ho of otrat typ. Howvr, th trprur has a tv to bhav opportustally udr asytr forato. our odl w osdr a trprur fag a prft aptal arkt ad a vtur aptal vstor fag urtaty ad oral hazard. W study how
atv otorg a ras th xptd t proft of ths two agts, ad thus th soal wlfar. Udr rta assuptos, w obta so uqu rsults o th prfora ad rol of th otorg that th vtur aptalst uss to tgat oral hazard probl ad to rdu urtaty. W fd that up-frot fudg ay b soally bttr ho wh th ost of th ffort s hgh. partular otorg up-frot fudg a lat th tvs of th aagr to sbhav s provdg ffort s ostly. orovr, ths papr aalyzs s tvs to tr sydatd vstts wth othr s a otxt whr both start-ups ad s ar subt to oral hazard, ad otorg s sstal. s hoos sydatd vtur vstts whvr th bft of a gratr dvrsfato trs of hghr ovrall otorg doats th drawbaks of fr-rdg probl. W fd that wh th ubr of s fag th sa prot s hgh th soal wlfar as of sydato s lowr tha as of up-frot fudg. W dvlop th aalyss udr th assupto that all s shar fag qually wh thy sydat th vstt ad rv th sa shar of bfts as of suss of th prot. Allowg for asytr shars would lad to dffrt rsults. How th s splt th vstt aout btw th? Usg a bargag odl, w a hav a aswr to ths da. Ths aalyss osttuts a trstg avu for futur rsarh. REFERENCES Adat, A & Pfldrr, P. (994). Robust Faal Cotratg ad th Rol of Vtur Captalsts. Joural of Fa, 49, 37-4. At, R. (3). Vtur aptal sydato pays off-ad ot ust for th vtur aptalst", Workg Papr, Wharto Shool.. At, R. Bradr, J. & Atwlr, W. (995). Why Do Vtur Captal Frs Exst? Thory ad Caada Evd. Workg Papr, Uvrsty of Brtsh Coluba. At R, Glost, L & ullr, E. (99a). Etrprural ablty vtur vstts, ad rsk Sharg. aagt S, 36, 3-45. At, R. Glost, L. & ullr, E. (99b). Dos vtur aptal fostr th ost prosg trprural frs? Calfora aagt Rvw, 3, -. Bary, C.B. (994). Nw drtos s rsarh o vtur aptal fa. Faal aagt, 3 3-5. Brglof, E. (994). A Cotrol Thory of Vtur Captal Fa. Joural of Law, Eoos ad Orgazato,, 47-67. Brga, D. & Hg, U. (998). Dya Vtur Captal Fag, Larg, ad oral Hazard. Joural of Bakg ad Fa., 73-35. Goprs, P.A. (995). Optal vstt, otorg, ad th Stagg of Vtur Captal. Joural of Fa, 5, 46-49.
Goprs, P.A & Lrr J. (996). Th Us of Covats: A Epral Aalyss of Vtur Partrshp Agrts. Joural of Law ad Eoos, 39, 463-498. Goprs, P.A & Lrr, J. (999). Th vtur aptal yl. Th T Prss. Gora,. & Sahla, W.A. (989). What Do Vtur Captalsts Do?. Joural of Busss Vturg, 4, 3-48. Grossa, S & Hart, O. (983). Th osts ad bfts of owrshp: A thory of vrtal ad latral tgrato. Joural of Poltal Eooy, 94, 4, 69-79. Hart, O & oor, J. (994). A Thory of Dbt Basd o th alablty of Hua Captal. Quartrly Joural of Eoos, 9, 84-879. Hlla, T. (994). Th Alloato of Cotrol Rghts Vtur Captal Cotrats. Workg Papr, Staford Uvrsty Graduat Shool of Busss. Hlla, T. & Pur,. (). Th trato btw produt arkt ad faal stratgy: th rol of vtur aptal. Rvw of Faal Studs, 3, (4), 959-984. Holstro, B. (979). oral Hazard ad Obsrvablty" Bll Joural of Eoos,, (), 74-9. Koks, L. & Ozrturk, S. (). Stagd fag ad dogous lok- : A odl of start-up fa, Workg papr, Coluba Uvrsty. Js,.C & klg, W.H. (976). Thory of th Fr: aagral Bhavor, Agy Costs ad Owrshp Strutur. Joural of Faal Eoos, 3, 35-36. Kapla, S.N. & Strobrg, P. (). How do vtur aptalsts hoos ad aag thr vstts? Workg Papr, Uvrsty of Chago. Lrr, J. (994). Th sydato of vtur aptal vstts, Rvw of Eoo Studs, 66,4-55. Lrr, J. (995). Vtur aptalsts ad th ovrsght of prvat frs, Joural of Fa, 5, (), 3-38. Nhr, A. (999). Stag Fag: A Agy Prsptv.Workg Papr, Bosto Uvrsty. Sagar, S & Gudott, G. (99). Vtur Captal Opratos ad Thr Pottal Rol LDC arkts. World Bak, WPS 54. Sahla, W.A. (99). Th Strutur ad Govra of Vtur- Captal Orgazatos. Joural of Faal Eoos, 7, 473-5.
Sapza, H.J. & Gupta, A.K. (994). Wh do vtur aptalst add valu? Joural of Busss Vturg, 7, 9-7. Sth, J.K & Sth, L.S. (). Etrprural Fa, Nw York, Wly. Jffry, J. (997). Vtur Captal Cotratg Udr Asytr forato. Workg Papr Wharto Shool. Wag, Z H. (4). Stagd Fag Vtur Captal: oral Hazard ad Rsks. Joural of Corporat Fa,, (), 3-55. Appdx Proof. Soluto z U,, w hav h( z) Probl (P.) to rsolv s: U ax ( ), Subt to : For [ ] ( )( ) Th (C) ostrat pls th (R) odto; w a osdr th followg progra: U ax ( ), Subt to : ( ) Whh s quvalt to: U ax ( ), Th FOCs odtos ar : Whh gvs,, th U ad ( ) soluto. Proof. Soluto
W kow that: ) ( R z ) ( ) ( ) ( dz z h zr z Ad: dz z h zr z ) ( ) ( Th probl (P.) to rsolv s: ax E Subt to :.., Th two frst ostrats gv us: Ad: Thus, ax E, Th FOC for pls: Whh datly pls ad,, SB soluto. Proof. Soluto 3 Th probl (P.3) to rsolv s:
, Subt to :.. ax U E Cosdrg that: W obta: Ad: Th progra to rsolv s: FOCs ar :., ax E Whh gvs: Whh datly pls ad,, FB soluto 3. Proof. Soluto 4 Th probl (P.4) to rsolv s:
Subt to :, k k ax Th sod ostrat provds us: Cosdrg that wll hoos th otorg tsty whh gvs h a proft at last qual to zro. Th: Th FOCs odtos ar: k SyF SyF Fro th FOCs for w obta: ad SyF SyF Ths gvs: ad Ths datly pls. ad