Venture Capital, Double-sided Adverse Selection, and Double-sided Moral Hazard

Transcription

1 Vntur Cpitl Doul-sidd Adrs Sltion nd Doul-sidd Morl Hzrd ik Houn Unirsity of Kil First Vrsion: Mr 2002 Tis Vrsion: Dr 2002 grtful to Tos lndnr Ptr Nippl Rolnd Sinrt Flix Stritfrdt nd sinr prtiipnts t t Unirsitis of ou nd Kil t Kil nstitut of World onois t 14 t Austrlsin Finn nd nking Confrn in Sydny 2001 t Annul Mting of t Assoition Frnçis d Finn in Strsourg 2002 nd t 14 t APFA / PACAP / FMA Finn Confrn in Tokyo 2002 for lpful onts nd suggstions on n rlir drft of tis ppr. Finnil support y Duts Forsungsginsft is grtfully knowldgd. Dipl.-Vw. ik Houn Cristin-Alrts-Unirsität zu Kil nstitut für triswirtsftslr Lrstul für Finnzwirtsft Olsusnstrß Kil Grny. Tl Fx il: oun@wl.uni-kil.d.

2 Astrt T ppr offrs nw xplntion for t widly osrd us of rdl nd onrtil prfrrd stok in ntur pitl finn. Rdl nd onrtil prfrrd stoks n usd to ndognously llot s flow nd ontrol rigts s funtion of t stt of ntur t ntrprnur s nd ntur pitlist s ffort nd t signls plyr s rld out is prit infortion rgrding t projt s prsptis. Tis proprty n usd to indu ot plyrs to rl tir prit infortion trutfully nd to spnd t ffiint ffort. Tis rsult olds irrspti of t ssud distriution funtion of t stt of ntur. T odl is onsistnt wit t osrtion tt onrsion is oftn utoti nd tt tr is n inrs orrltion twn risk nd ontrol rigts. Furtror it xplins wy ntur pitlists n rn positi xptd rturns in optiti ntur pitl rkt. JL Clssifition: D23 D82 G24 G32 Ky words: ntur pitl orl zrd drs sltion signling

3 1 ntrodution T rkt for ntur pitl in Grny s grown trndously in t pst fw yrs. n t yr 2000 t olu of ntur pitl funds ros 47.6 % up to or tn 20.1 illion uro wil t instd pitl ws up 43.1 % to nrly 11.5 illion uro. 1 n oprison to 1999 wr t growt rts wr 43.2 % nd 41.7 % rsptily tis is furtr lrtion of t growt of t Grn ntur pitl rkt nd xprsss t inrsing iportn of ntur pitl for t onoy. Howr t finning of strt-up opnis is ound up wit spil prols rsulting fro t xtr infortion sytris twn t ntrprnur nd t ntur pitlist. n our iw ts infortion sytris r doul sidd i.. not only t ntrprnur y suprior infortion out t lu of t instnt projt rsulting fro is R&D ut lso t ntur pitlist y on. At first gln tis is surprising sin t ntrprnur is t on wo knows is projt st. ut sids t projt's tnologil qulity its suss proility nd n its lu lso dpnds on its onoi qulity. Wit onoi qulity w n t onoi iility of t projt i.. t qustion wtr tr is rkt for t projt t ll nd ow ig is t optition on tis rkt. n tis rspt t ntur pitlist y suprior infortion du to is industry xprtis. Togtr t two kinds of qulity dtrin t projt's totl qulity. To lu t projt proprly ot prtis sould rl tir prit infortion trutfully. Howr it y dntgous for sid to isstt its prit infortion. y orstting is infortion t ntrprnur otins iggr stk in t finnil rturn of t opny sin t ontriution of is projt id to t lu of t projt inrss. Furtror if t ntrprnur ris prit nfit fro running t opny n possily i y orstting tt lso projt wit ngti nt prsnt lu is finnd. For t ntur pitlist undrstting is prit infortion n dntgous sin it inrss is stk in t finnil rturn of t opny. Tt olds spilly if t stk of t ntur pitlist is dtrind y t rtio of is pitl ontriution to projt lu. Witout undrstting t ntur pitlist gts only is rsrtion utility. sids its tnologil nd onoi qulity t suss nd tus t lu of strt-up opny ruilly dpnds on t fforts spnt y t ntrprnur nd t ntur pitlist. On t sid of t ntrprnur tr n n innti prol. Wil tr 1 VK (2001). 1

4 igt no dout out t ntrprnur working rd t llotion of is ffort y inffiint. For xpl t ntrprnur y spnd too u ti wit R&D nd too fw wit rkting ounting t. 2 ut tr y lso n innti prol on t sid of t ntur pitlist. As Gorn nd Sln (1989) rport on rg ntur pitlist spnds or tn on undrd ours yr in onsulting portfolio opny. Tis onsulting is on of t in diffrns twn ntur pitl finning nd stndrd dt or quity finning. T onsulting tiity of t ntur pitlist is n iportnt suss ftor sin ntrprnurs oftn lk t ility to run opny on t ''usinss'' sid i.. doing rkting ounting or rruit stff. Howr sin tis ounsling is xpnsi t ntur pitlist y n innti to spnd too fw ffort if is stk in t opny's rturns is low. Sin t ffiint lls of onsulting nd ntrprnuril ffort y dpnd on t opny s futur prsptis trutful rltion of t prit infortion is not only nssry for propr lution of t opny ut lso for n ffiint ffort dision. To sol t trut-rling nd t ffort innti prol spil finning ontrts r ndd. Goprs (1997) nd Kpln nd Strörg (2001) rport tt onrtil suritis r widly usd in ntur pitl finn nd tt tr is oftn sprtion of s flow nd ontrol rigts. n our odl w offr n xplntion for ts stylizd fts. t is sown tt wit rdl prfrrd nd onrtil prfrrd stok ontrt t prit infortion of ot plyrs is rld trutfully t ffiint instnt dision is d 3 nd t ffiint fforts r iplntd. T onoi intuition ind tis rsult is tt wit rdption nd onrsion lus rsptily t inntis of t ntrprnur nd t ntur pitlist n lignd. Tis lignnt rsults fro t stt ontingnt llotion of t s flow nd ontrol rigts inrnt to rdl nd onrtil prfrrd stok ontrts. T si nis is tt onrsion is profitl for ot plyrs: t ntrprnur gts k ontrol nd n tn onsu prit nfits wil t ntur pitlist n ris is stk in t opny's s flow. y dsigning t onrsion lus su tt onrsion n tk pl only if t ffiint disions n tkn y ot plyrs t ffiint solution is id. T s olds for t rdption lus. To k our solution lr suppos tt t ffiint instnt dision nd t ffiint fforts dpnd on t projt's futur prsptis i.. t stt of ntur wi is d- 2 3 S Sidt (2000) for tis point. Tt is to strt or not to strt t projt. 2

5 trind y t projt s tnologil nd onoi qulity. n ontrst to t ug ount of inoplt ontrt ppros wi n found in t litrtur w ssu tt t stt of ntur is lrdy dtrind t t ti of ontrt losing. Howr t stt of ntur is not oon knowldg. nstd t ntrprnur knows only t projt's tnologil qulity wil ntur pitlist knows only t onoi on. y oining tir prit infortion t stt of ntur n opltly rld. n our odl tr r tr possil stts of ntur. n t d stt t projt sould not strtd sin t rturns r not suffiint to roup t instnt xpnditur. n t diu stt t projt sould strtd ut ffort sould low. Only in t good stt of ntur ot prtis sould spnd ig ffort. For t ntrprnur strting t opny is purpos of its own spilly if t ntrprnur insts only littl or n noting of is own pitl. Tt is us dris prit nfits fro t ontrol of ''is'' opny. 4 Tus tr is n innti for t ntrprnur to orstt is infortion in ordr to indu t ntur pitlist to finn t opny. Wit prfrrd stok ontrt t ontrol is siftd to t ntur pitlist nd n t onsuption of prit nfits is prntd. Howr tis sift is inffiint if t projt is suss or t lst no totl loss. Wit proprly dsignd rdption or onrsion lus t ntrprnur s t opportunity to gt k ontrol in t diu nd t good stt of ntur if told t trut. Furtror ts luss lso prnt isstting y t ntur pitlist. f t ntur pitlist orstts is prit infortion nnot onrt nd tus is stk in t opny's s flow is liitd t lowr ll. f undrstts is prfrrd stoks r rdd t low pri nd n t ntur pitlist nnot profit fro igr tn ntiiptd s flow. Hn is stk in t opny's rturn is liitd t lowr ll. To our knowldg tis is t first ppr nlyzing doul-sidd drs sltion nd orl zrd prol siultnously. Tr is on ppr y Mskin nd Tirol (1992) wi fouss on t ontrt dsign if ot plyrs rlnt prit infortion. Howr ty do not tk orl zrd prol into ount. Altoug tr is yt no ppr dling siultnously wit doul-sidd drs sltion nd doul-sidd orl zrd prol tr is ug ount of pprs xplining t us of onrtil suritis in ntur pitl finn. For sury of ts pprs w 4 S Wstd nd Wrigt (1998). 3

6 rfr to t surys y Forn (1998) nd Srtlr (2000). Hr w just wnt to ont on two losly rltd pprs. Sidt (2002) dls wit doul-sidd orl zrd prol in n inoplt ontrting frwork. H sows tt wit onrtil ond t first st ffort n iplntd. As in our odl t projt's rturn dpnds on t stt of ntur nd t fforts spnt y t ntrprnur nd t ntur pitlist. n ontrst to our odl t t ti of ontrt losing t stt of ntur is unknown to ot prtis. ut it is rld for fforts r spnt nd n osrd fr of osts y prty. Furtror for t ntur pitlist spnds is ffort n fr of osts osr t ntrprnur's ffort. Sidt lso onsidrs tr possil stts wr spnding ffort y t ntur pitlist is only ffiint in t good stt of ntur. To proid t ntur pitlist n innti to spnd ffort in t good stt ust gin s flow snsiti ontrt (quity). Howr tis dstroys t ntrprnur's inntis. Sidt sows tt wit proprly dsignd onrtil ond tis prol n iruntd. n t odl y D'Souz (2001) t t ti of ontrt losing t stt of ntur is unknown to t ntrprnur nd t ntur pitlist. ut it is oon knowldg tt tr r tr possil stts: d diu nd good. Aftr t stt of ntur is rlizd only t ntrprnur n osr wtr t diu or t good stt pprd. n D'Souz's odl only t ntur pitlist s to spnd ffort. Sin t ffiint ount of ffort dpnds on t stt of ntur t ntrprnur s to rport t stt of ntur trutfully. D Souz sows tt trutful rltion nd n ffiint ffort spnding n id wit onrtil surity. A ondition for tis rsult to old is tt t ntrprnur n onsu suffiintly lrg prit nfit in t diu stt of ntur. T strutur of our ppr is s follows. n ptr two t si odl is prsntd. n ptr tr w nlyz ow dt nd quity ontrts work in t spil ntur pitl nironnt nd sow tt ty fil in soling t prols dsrid. n ptr 4 w introdu propr dsignd prfrrd quity ontrts wi n sol ts prols. n ptr 5 w nlyz t ipt of rngotitions on ontrt dsign nd sow t roustnss of our rsults. n ptr 6 w onlud our ppr. 2 T Modl A risk nutrl ntrprnur s ss to n instnt projt wi rquirs n instnt of > 0. us s no initil wlt s to onin ntur pitlist (VC) to 4

7 proid. T ntur pitl rkt is optiti nd t disount ftor is qul to zro. T rsulting s flow fro t projt dpnds on t produt qulity θ { θ; θ } t prsptis of t produt rkt η { η; η } nd on. Sin is t tniin w ssu tt s suprior prit infortion out t produt qulity i.. knows t tru stt of. Sin VC gind so xprin in t ntur pitl rkt w ssu tt s suprior prit infortion out t prsptis of t produt rkt i.. knows t tru stt of. T two prit infortion for Crtsin produt dfind s t t stt of ntur wr 5 ( θ η) ( θ η ) ( θ η) ( θ η ) l sids t stt of ntur t s flow lso dpnds on t ffort { ; } spnt y t ost of nd rsptily nd t ffort { ; } spnt y VC t ost of nd rsptily. W intrprt s t ffort instd in t tnologil running of t opny.g. prodution nd will tus proidd y. ut y lk t ility to run opny on t usinss sid.g. rkting ounting t. Tis usinss xprtis s tus proidd y VC nd is odld y. T projt if strtd dos not only yild ontry rturn ut lso prit nfit to if nd only if s t ontrol or t opny. Tus is in ontrol s long s olds t jority of t oting rigts nd t opny is not nkrupt. Assuption 1: T 12 possil s flows r ordrd s follows ( ) > ( ) ( ) > ( ) ( ) > ( ) ( ) > ( ) ( ) ( ) ( ) ( ) > > wr l l l 1. ( ) < 0 wit { ; } nd { } l ; l 5 W onsidr only tr possil stts sin s Sln (1990) rports tr is tr lss pttrn in t stylizd fts: on tird of ll instnts nd in totl loss 50 % roup tir instnt nd only 15 % rn xtrordinry rturns. 5

8 6 2. ( ) { } l ; 0 wit < 3. ( ) ( ) ( ) ( ) 0 > > > 4. ( ) 0 > 5. ( ) ( ) ( ) ( ) 0 > > > 6. ( ) 0 > 7. 0 nd 0 > > Assuption 2: > Assuption 1 stts tt n instnt in t projt sould not undrtkn if ot prtis rid t d signl. n spnding t ig ffort will not ris t s flow in t d stt of ntur. Furtror t s flow will nr suffiint to opnst VC for is instnt. f only on prty s rid d signl t projt sould strtd ut no on sould spnd t ig ffort. f ot prtis rid t good signl tn t instnt sould rrid out nd t ig ffort sould spnt y ot prtis. To k t odl non-triil ssuption 2 xprsss t rln of t prit nfits for. Sin xds t ost of t low ffort lwys wnts strt t projt. T ti strutur of t odl is s follows. At t 0 ntur drws nd nd nd VC ri tir prit infortion. At t 1 offrs VC (nu of) ontrt(s). f VC pts is instd. At t 2 spnds ffort nd VC spnds ffort. At t 3 t s flow rlizs nd t ontrt is xutd. y running t opny n onsu is prit nfits in t priod fro t 1 to t 3 if is in ontrol. As w will sow wit onrtil or rdl surity y not in ontrol fro t 1 to t 3 ut only t point t 3 wn nd if onrsion or rdption tks pl. Howr w ssu tt ing in ontrol only t t 3 is suffiint to onsu prit nfits. T ti strutur is displyd in figur 1.

9 t 0 t 1 t 2 t 3 ntur drws θ nd η ontrt losing - ontrt xutd Figur 1: Ti strutur Fro t ti strutur it os lr tt trutful rltion of t prit infortion is ruil nssity. Tt is not only us t dision wtr t projt sould strtd or not dpnds on t stt of ntur ut lso t ffiint lls of ffort. Tus w nlyz in t nxt stion if trutful rltion of t prit infortion n id in t prft ysin-ns quiliriu wit lssi finn ontrts i.. strigt dt nd quity. Aftr sowing tt tis i nnot id wit lssi finn ontrts w look t prfrrd stok ontrts s nis. for w do so w wnt to xplin t ontrt offring nd pting stg in or dtil. Aftr riing is signl knows in wi of t possil tr stts of ntur t projt is not in. ut tr r still two possil stts of ntur. Sin pursus t ojti to rl VC's prit infortion nd to dri down VC to is rsrtion utility s to offr two ontrts dsignd for t two possil stts. Dpnding on t signl rid tr r two possil nus of ontrts wi ould offr. T first on onsists of ontrt for t d stt of ntur nd on for t diu stt of ntur t sond on of ontrt for t diu nd ontrt for t good stt of ntur. 6 T first (sond) nu sould offrd if s rid t d (good) signl. Fro 's oi of nu VC n onlud t signl s rid. Tus trnsits is prit infortion troug t nu of ontrts offrd. Howr s w will sow wit inpproprit dsignd ontrts y n innti to offr t ''wrong'' nu i.. t on wi dos not rl is prit infortion trutfully Not tt t first nu fftily onsists only of t diu stt ontrt. Tt is us in t d stt t s flow is not suffiint to opnst VC for is xpnditurs. Hn ontrt for t d stt would nr signd. As w will sow s nr n innti to offr t first nu inditing tt s rid t d signl if s rid t good on. ut y n innti to offr t sond nu n if s rid t d signl. W rfr to tis ior s orstting. 7

10 Fro t two ontrts offrd y VC signs on. Wit is ontrt oi VC rls is prit infortion. 8 f ot prtis trnsit tir prit infortion trutfully t tru stt of ntur n onludd fro t signd ontrt. W ssu in our odl tt ot prtis lif in t quiliriu nd oos tir fforts ording to t ontrt signd s long s ty do not know for sur tt t ''wrong'' on ws signd. Tt is t s if t plyr lid. 3 Clssi Finn Contrts 3.1 Dt ontrts Wit dt ontrt VC ris fix pynt irrspti of t rlizd s flow. 9 To indu VC to sign dt ontrt ust offr i dt rpynt oligtion D wi t lst opnsts VC for is instnt nd is ffort ost. To sow tt VC nnot lwys indud to rl is prit infortion trutfully nd to spnd t ffiint ffort suppos for sipliity tt t projt is of good tnologil qulity i.. θ θ. Sin dos not know wtr t projt is of good or d onoi qulity ut wnts to dri down VC to is rsrtion utility offrs two ontrts. n dsigning t dt ontrts s to tk VC s prtiiption onstrints into ount wi is in t diu stt of ntur (1) D 0 nd in t good stt of ntur (2) D 0 sin tn wnts VC to spnd t ig ffort. ut us VC ris fix pynt indpndntly fro t rlizd s flow s no innti to spnd t ig ffort if ( ) >. us tn t dt is not t risk. Furtror sin > D ust 8 9 As w xplind o t first nu onsists only of on ontrt. Hn VC trnsits is prit infortion y pting or rjting tis ontrt. Of ours if t dt is risky VC s pynt dpnds on t stt of ntur. 8

11 lrgr tn D. ut tn VC will lwys oos D nd tus orstts is prit infortion if. Tus w n stt t following l. L 1: Wit dt ontrts VC nnot lwys indud to rl is prit infortion trutfully nd to spnd t ffiint ffort. Proof: T proof follows dirtly fro t o rgunttion. Wit dt ontrt nnot lwys indud to rl is prit infortion trutfully itr. f s rid t d signl s n innti to orstt is prit infortion. Tt is us in t d stt of ntur n y orstting ssur islf is prit nfit sin t projt is tn rrid out. Tus t slf-sltion onstrint of in t d stt of ntur (3) π x[ ( ) D ; 0] π tru 0 l fls is nr fulfilld du to ssuption 2. Tus w n stt t following l. 10 L 2: Wit dt ontrts trutful rltion y nnot id if. Proof: T proof follows dirtly fro t o rgunttion. 3.2 quity ontrts Wit n quity ontrt VC olds linr stk in t opny s rturns. n ordr to indu VC to sign n quity ontrt ust offr n quity wi t lst opnsts VC for t instnt of nd is ffort ost. f s rid t d signl nd offrs only on ontrt for t diu stt of ntur trutful rltion y VC n id wit n quity ontrt. n ontrst if s rid t good signl nd tus offrs ontrt for t diu nd ontrt for t good stt of ntur trutful rltion y VC is not ssurd. t rtr dpnds on t odl s prtrs s it is sttd in t following l. 10 S lso Houn nd Nippl (2001). 9

12 L 3: Dpnding on t odl's prtrs tr n xist nu of pur quity ontrts induing VC to rl is prit infortion trutfully nd to spnd t ffiint ffort gin tt s rid t good signl nd rls it trutfully. n iing tis it y nssry to py VC n infortion rnt if η η. Proof: S Appndix A. A nssry ondition for trutful rltion of VC's prit infortion is tt t quity stk for t diu stt of ntur is lrgr tn t on for t good stt. Tt is us otrwis VC ould gin twi y orstting. On t on nd riss is quity stk nd on t otr nd indus to spnd t (inffiint) ig ffort wi riss t s flow. 11 ut t quity stk for t good stt ust not ''too low'' in oprison to t on for t diu stt. us dpndnt on t odl's prtrs VC igt tn n innti to undrstt is prit infortion. n ordr to indu VC to spnd t ig ffort 12 or n to sign t ontrt in t good stt of ntur it igt nssry to offr i n quity stk igr tn t on for t diu stt of ntur. Oiously trutful rltion of t prit infortion nd n iplnttion of t ffiint ffort is tn not possil. Furtror if it is not VC's prtiiption onstrint in t good stt of ntur wi dtrins t siz of t quity stk s to py n infortion rnt in ordr to indu VC to slt t trut-rling ontrt nd to spnd t ig ffort rsptily. W ould introdu or ssuption on t odl's prtrs in ordr to sow undr wi onditions solution xists. Howr sin our ojti ws to sow tt wit pur quity ontrt VC nnot lwys indud to rl is prit infortion trutfully nd to spnd t ffiint ffort w py no furtr ttntion to tis point. Wtr n indud to rl is prit infortion wit pur quity ontrts dpnds on t ontrol rigts ssoitd wit VC s quity stk. f VC is in ontrol s no innti to orstt is prit infortion if θ θ. Tt is us n tn nr onsu prit nfits in t d stt of ntur. Howr grnting VC ontrol is inffiint. ut if ontrol is lft to orstting n no longr prntd. Tt is us y orstting t projt will lwys strtd n in t d stt of ntur. nstd of gtting no utility t ll gts is prit nfits nd ontry rturn on is quity. n t W ssu tt ooss is ffort ording to t ontrt osn Tt is us VC ooss is ffort ording to is quity stk. 10

13 diu stt n y orstting ris is quity stk nd t s flow sin y signing t good-stt-ontrt VC is indud to spnd t ig ffort. 13 A pur quity ontrt n tus not t solution to our odl s is sttd in t following l. L 4: Wit pur quity ontrts orstting y nnot oidd if θ θ nd ontrol is lft to. f ontrol is siftd to VC pur quity ontrts r inffiint. Proof: S Appndix. Oiously ointion of dt nd quity nnot solution to t prol itr. us to indu to rl is prit infortion trutfully ontrol ust siftd to VC. Howr tis is inffiint. To onlud tis stion w n n stt t following proposition. Proposition 1: Wit dt nd quity ontrts it is not possil to siultnously ssur trutful rltion of t prit infortion t iplnttion of t ffiint fforts nd t ffiint llotion of ontrol. Proof: T proof follows dirtly fro l 1 l 2 l 3 nd l 4. 4 Prfrrd stok ontrts n s of pur dt finning trutful rltion fils us VC n gurnt islf igr stk in t opny's pyoff y orstting is infortion. Furtror n iplnttion of t ffiint ffort nnot id if ( ) >. n s of pur quity finning tr y xist st of ontrts induing VC to slt t trut-rling ontrt nd to spnd t ffiint ffort. Howr tis rsult olds only for spil ointion of t odl's prtrs. Furtror s to py VC n infortion rnt if VC's prtiiption onstrint in t good stt of ntur is not t inding onstrint for t dtrintion of t quity stk. Trfor diffrnt typ of ontrt s to found wi rls VC's prit infortion indpndnt of t odl's prtrs iplnts t ffiint ffort nd dris VC down to is rsrtion utility. 13 As w rgud o for solution to xist nssry ondition is tt VC's quity stk in t diu stt ontrt is igr tn in t good stt ontrt. 11

14 As w sown o tr is lso n innti prol on 's sid. Sin wit lssi finnil ontrts n lwys onsu is prit nfits n in t d stt of ntur trutful rltion of is prit infortion fils. Furtror wit pur quity ontrts tr y n innti prol in t good stt of ntur if is not t sol rsidul lint. Tus diffrnt typ of ontrts s to found wi rls s prit infortion trutfully nd iplnts t ig ffort in t good stt of ntur. n t following proposition w sow ow su ontrts to dsignd to trutfully rl t prit infortion of plyr nd iplnt t ffiint fforts in t prft ysin-ns quiliriu. Proposition 2: offrs VC t following nus of ontrts wi r trut-rling nd iplnt t ffiint fforts on ot sids if ( ) ( ) ( ) ( ) >. > nd f θ θ offrs VC rdl non-oting prfrrd stok ontrt Z : { } n P n wi gis VC prfrrd diidnd of n P. Furtror t ontrt ontins rdption lus wi gis t rigt to rd t prfrrd stok t pri P instd of pying t diidnd. n f θ θ offrs VC nu of ontrts onsisting of 1. rdl oting prfrrd stok ontrt Z : { } P wi gis VC ontrol nd prfrrd diidnd of P. Furtror t ontrt ontins rdption lus wi gis t rigt to rd t prfrrd stok t pri P instd of pying t diidnd. 2. nd onrtil prfrrd stok ontrt { P s } Z : ; p p wi gis VC ontrol nd liitd prfrrd diidnd of P. Furtror t ontrt ontins onrsion lus wi gis VC t rigt to onrt 12

15 is prfrrd stok into t frtion p of t opny s s flow if t s flow xds t strik s ( ) p ( ). for proing proposition 2 forlly w wnt to gi so si onoi intuition for it. y offring just on ontrt n rdily signl VC tt s rid t d signl. Tt is us nnot profit fro undrstting is prit infortion y offring just on ontrt if s rid t good signl. Sin VC tn onluds fro s ontrt oi tt s rid t d signl rjts t ontrt in t diu stt of ntur. tus loss t opportunity to strt t projt. Altoug VC pts t ontrt in t good stt of ntur is innti to spnd t ig ffort is dstroyd wi is disdntgous for. Sin dos not wnt to indu VC to spnd t ig ffort in t diu stt of ntur n do no ttr tn offring rdl non-oting prfrrd stok ontrt wi fulfills VC s prtiiption onstrint. n ontrst offring t nu of ontrts is no rdil signl for riing t good signl y if t ontrts r not proprly dsignd. Furtror offring t nu of ontrts ls roo for or- or undrstting y VC. Tus nd sin t ontrt for t good stt of ntur sould indu VC to spnd t ig ffort t ontrt dsign ust or dnd. As w sn in t d stt of ntur t driing for ind 's dision to strt t opny is is ility to onsu prit nfits. Tus y sifting t oting rigts to VC is prntd fro onsuing prit nfits. Hn dos not wnt to strt n inffiint projt. Tnilly t sift of ontrol is id y tting ll t oting rigts or t lst t jority to VC's prfrrd stoks. Howr tis sift of ontrol is only ffiint in t d stt of ntur. ust gin t opportunity to gt k t ontrol in t diu nd t good stt of ntur if told t trut. For t diu stt tis n id wit rdption lus wi gis t rigt to rd t prfrrd stok t n in dn dtrind pri. y stting t rdption pri igr tn t s flow in t d stt of ntur nnot profit fro orstting 13

16 >. 16 in t d stt of ntur sin tn lks t ony to rd t prfrrd stoks. 14 H tus dos not gt k ontrol nd du to t prfrrd diidnd dos not ri ontry rturn on is quity itr. Hn nnot gin y orstting. Furtror rdption lus liits VC s s flow prtiiption. y undrstting VC n tn no longr profit fro t unxptd prt of t s flow sin is prfrrd stoks r rdd y. Tus if VC s rid t good signl dos not wnt to sign t diu instd of t good stt ontrt. A sipl rdption lus for t good stt of ntur nnot iplnt t ffiint fforts sin rdption lus s t s pyoff strutur s strigt dt. ut wit onrsion lus t ffiint fforts n indud on sid if t strik is st t s flow ll wi n only id in t good stt of ntur if ot plyrs spnt t ig ffort. Wit su strik VC s s flow prtiiption is liitd to t liitd prfrrd diidnd if spnds only t low ffort. Tus nnot profit fro ig s flows. ut s innti to spnd t ig ffort is strngtnd too sin y onrsion gts k ontrol. 15 Furtror y stting VC s post onrsion quity stk t ll t wi is xtly opnstd for is xpnditurs os t sol rsidul lint. Howr for n iplnttion of t ffiint fforts it is nssry tt t rginl rturns xd rginl osts wi is xprssd y t ondition ( ) ( ) ut su onrsion lus dos not only iplnt t ffiint fforts it lso ssurs trutful rltion of t prit infortion. Gin tt on prty orstts t otr prty spnds t ig ffort wi riss t diu stt s flow. ut sin in t diu stt of ntur t strik is issd for sur VC nnot profit fro induing to spnd t ig ffort y orstting is prit nfit. n ontrst y ontrily profit. Tt is us ris ll t s flow o t liitd prfrrd diidnd. Howr sin t strik is issd VC nnot onrt nd dos not gt k ontrol. n is dision to orstt tus fs trd off wi is rprsntd y t ondition ( ) ( ) >. Hn dos not orstt if t loss in prit nfits xds Not tt if orstts is prit infortion in t d stt of ntur iplying tt VC s rid t good signl it is t diu stt ontrt tt is signd. n gnrl ntur pitlists spil ontrol rigts ttd to tir prfrrd stoks lik t rigt to dtrin t CO. n s of onrsion ty los ts rigts nd ontrol is siftd. Howr if t prfrrd r onrtd into oon stok VC y old jority of t oting rigts. To xlud tis possiility w ssu tt in tis s t prfrrd stoks r onrtd into non-oting quity. At first gln it is surprising to intrprt t prit nfits s rginl rturn. ut not tt n only onsu prit if t prfrrd stoks r onrtd. 14

17 t xtr s flow. t nnot onludd fro t ssuptions wtr ( ) ( ) > is fulfilld or not ut it ss plusil to ssu tt it is. 17 Proof: W to proof tt it is possil to rl t prit infortion of plyr trutfully nd to indu i to spnd t ffiint ffort in t prft ysin-ns quiliriu. n t proof w to distinguis two ss θ θ nd θ θ. 1. d tnologil qulity θ θ f s rid t d signl t projt n itr in t d or in t diu stt of ntur. d stt of ntur Suppos tt ot plyrs rid t d signl su tt t projt is in t d stt of ntur. Fro ssuption 1 follows dirtly tt VC s no innti to orstt is prit infortion if offrs just t ontrt Z n. Sin s ontrt oi indits t d stt of ntur pting t ontrt would ld to rtin loss for i. n ontrst to VC orstting y dntgous for. y orstting is prit infortion indus VC to sign t diu stt ontrt Z nd n t projt will rrid out. Howr it is sy to sow tt tis ontrt oi is disdntgous for. n t d stt of ntur t s flow is not suffiint to py t prfrrd diidnd sin (4) P > ( ) l dos tn not ri pynt on is quity. Tus t only innti to strt n inffiint projt is 's ility to onsu prit nfits. Howr n do so only if is ontrol i.. s t oting rigts. ut wit prfrrd quity ontrt t oting rigts r siftd to VC. Sin t s flow is not suffiint to rd t prfrrd stok nnot gt k t oting rigts. Hn nnot onsu prit nfits. 17 rly nd Holdrnss (1989) rport tt on rg prit nfits r round 20 % of opny lu. Altoug tis nur is drid fro lok trds in our iw it n lso pplid to strt-up opnis. 15

18 Furtror strting n inffiint projt is ostly for sin s to r ffort osts. His totl pyoff fro lying nd tus strting n inffiint projt is tn (5) π li. n oprison to tis s pyoff fro tlling t trut is (6) π 0. tru Oiously tlling t trut is doinnt strtgy. 18 t is lso sy to s tt will nr spnd t ig ffort if t projt is strtd. Mdiu stt of ntur Suppos now tt VC s rid t good signl nd tus t diu stt of ntur ourrd. Lt us first sow tt ot plyrs r intrstd in strting t projt if offrs only t rdl prfrrd stok ontrt Z n. t is sy to s tt VC s prtiiption onstrint VC (7) π P 0 n nd s prtiiption onstrint (8) π ( ) P > 0 n r ot fulfilld for P. n Wit t rdl prfrrd ontrt VC s no inntis to undrstt is prit infortion sin tis would iply rjtion of t ontrt ltoug VC s prtiiption onstrint is fulfilld. Undrstting would tus irrtionl. 18 Tis rsult olds irrspti of t siz of. n for tr is no rson to ssu tt will orstt is prit infortion. 16

19 y offring t nu of ontrts nd tus orstting indus VC to oos t onrtil stoks. Sin t strik is issd for sur t prfrrd stoks r nr onrtd n if t ig fforts r spnt us (9) s ( ) > ( ) p dos tn not gt k ontrol nd nnot onsu prit nfits. Howr y orstting indus VC to spnd t ig ffort wi riss t s flow in t diu stt of ntur in oprison to t s wr t orrt i.. t rdl prfrrd stok ontrt Z n is signd. Sin VC is not opnstd for spnding t ig ffort t gin rus opltly to. Tus 's pyoff in t diu stt is 19 (10) ( ) π. li f tlls t trut t rdl prfrrd stok ontrt Z n is signd. Wit tis ontrt is in ontrol nd n onsu prit nfits. His pyoff fro tlling t trut is tn (11) ( ) π. tru tus prfrs tlling t trut if tru ( ) > ( ) π π (12) > ( ) ( ) li f (12) is not fulfilld in is dision to orstt fs trd off. On t on nd wit lying s to r ffort ost in t d stt of ntur nd opportunity ost in t diu stt of ntur sin nnot onsu prit nfits. On t otr nd is ontry rturn in t diu stt riss. 's oi tn gnrlly dpnds on t 19 Not tt t s flow is suffiint to py t liitd prfrrd diidnd of P. 17

20 proilitis of t stts of ntur. 20 Howr s w rgud o (12) is likly to fulfilld. 2. Good tnologil qulity θ θ f s rid t good signl t projt is itr in t diu or in t good stt of ntur. Mdiu stt of ntur Suppos tt VC s rid t d signl nd tus t diu stt ourrd. Lt us first sow tt ot prtis r intrstd in strting t projt if t rdl prfrrd stok ontrt Z is signd. t is sy s to tt VC s prtiiption onstrint VC (13) π P 0 nd s prtiiption onstrint (14) π ( ) P > 0 r fulfilld for P. f offrs t nu of ontrts VC n orstt is prit infortion y oosing t onrtil prfrrd stok ontrt. ut sin t strik is issd for sur is pyoff is liitd to t liitd prfrrd diidnd. VC dos not orstt if is slfsltion onstrint (15) π P P π VC tru VC li is fulfilld wi is oiously t s for P nd P f VC knows lso knows if (12) is fulfilld or not. f (12) is not fulfilld VC inntis r ltrd. Sin VC nnot onlud fro t offrd nu of ontrts wi stt of t world ourrd is ontrt nd ffort oi dpnds on t proilitis ssigns to t stts of world. f VC s rid t d signl tn igt n rjt t offrd ontrts in ordr to prott islf ginst n inffiint instnt. f s rid t good signl tn igt undrstt is prit infortion nd / or spnd only t low ffort sin wit positi proility will not opnstd for spnding t ig ffort. Atully VC is indiffrnt. Howr tr is no rson to ssu tt dos not oos t diu stt ontrt. 18

21 t is intuitily lr tt dos not undrstt is prit infortion sin tn VC will rjt t ontrt offrd y. T projt will not strtd ltoug it is ffiint. s pyoff is tus (16) π 0 li n ontrst if tlls t trut gts ontry rturn nd is prit nfits i.. (17) π ( ) tru Oiously undrstting is disdntgous for. t rins to sow tt no prty s n innti to xris t ig ffort. VC s innti onstrint (18) π P P π VC low VC ig is oiously fulfilld for P nd P. s innti onstrint (19) π ( ) ( ) π low ig is lso fulfilld du to ssuption 1. Good stt of ntur f VC s rid t good signl t good stt of ntur ourrd. Lt us gin first sow tt t prtiiption onstrint of VC VC (20) π ( ) 0 p nd t on of (21) π ( ) 0 19

22 r fulfilld wit t onrtil prfrrd stok ontrt Z. Oiously VC s prtiiption onstrint is fulfilld for p wil s prtiiption onstrint is ( ) fulfilld y ssuption. f VC undrstts is prit infortion t rdl prfrrd ontrt Z is signd. Sin t s flow is suffiint to rd t prfrrd stoks VC s pyoff is liitd to t rdption pri nd tus is profit is VC (22) π P 0 li Copring VC s profits fro (20) nd (22) sows tt VC nnot profit fro undrstting. f undrstts is prit infortion t rdl prfrrd ontrt Z n is signd instd of t onrtil prfrrd ontrt. Altoug is in ontrol wit t ontrt Z n nd n onsu prit nfits dstroys VC's innti to spnd t ig ffort. Tus 's profit fro undrstting is (23) ( ) π li f rls is infortion trutfully t pynt to VC riss ut lso t s flow. Howr sin VC is xtly opnstd for is xpnditurs nd spnding t ig ffort is ffiint t xtr rturn outwigs t xtr ost. 's profit fro tlling t trut nd spnding t ig ffort is tn (24) π ( ) tru Tlling t trut nd spnding t ig ffort is dntgous if tru ( ) > ( ) π π (25) ( ) ( ) > li wi is tru y ssuption. 20

23 Howr it ould dntgous for plyr to rl is prit infortion trutfully ut to spnd only t low ffort. For VC t innti ould to rdu is ffort ost. ut sin t strik is issd for sur is pyoff is gin liitd to t prfrrd diidnd su tt is profit in s of sirking is VC (26) π P 0 low wil wit spnding t ig ffort it is VC (27) π ( ) 0 ig p Hn VC is in ot ss xtly opnstd for is xpnditurs. Tr is tus no rson to ssu tt VC will sirk. For sirking ould dntgous sin it lowrs t ffort ost nd rdus t pynt to VC wo ould not onrt is prfrrd stok. ut sirking rdus lso t s flow nd prnts fro onsuing prit nfits. Wit tis s profit fro sirking is (28) π low ( ) n ontrst spnding t ig ffort lds to profit of (29) π ( ) ig Copring t two profits sows tt plying t Ns quiliriu is still dntgous for if ig ( ) > ( ) π π (30) ( ) ( ) > low 21

24 t nnot onludd fro t ssuptions wtr (30) is fulfilld or not. 22 Howr if (30) is not lid 's nd VC's inntis r ngd so tt spnding t low ffort y nd t ig ffort y VC is no Ns quiliriu. Furtror it n sown tt t only Ns quiliriu is inffiint. To s tis igin first wi ipt tis s on VC's inntis. f (30) is not fulfilld VC knows tt will spnd only t low ffort. ut tn spnding t ig ffort is disdntgous for i sin will not opnstd for is ig ffort for sur. Hn t ointion of low ffort spnding y nd ig ffort spnding y VC is no Ns quiliriu. ut gin tt VC will spnd only t low ffort spnding t ig ffort is now doinnt strtgy for sin (31) ( ) ( ) > t is sy to s tt ig ffort y nd low ffort y VC is t only Ns quiliriu. 23 Howr tis quiliriu is oiously inffiint. 24 Q..D. Offring just on ontrt is rdil signl for t projt ing t d tnologil qulity us nnot profit fro undrstting is prit nfit. f undrstts t projt will not rrid out in t diu stt of ntur wil in t good stt loss t nt s flow gin for VC s ig ffort. Tus tr is no nssity to trnsfr ontrol fro to VC nd sipl rdl prfrrd stok ontrt is optil. n ontrst offring t nu of ontrts is pr s no rdil signl for t projt ing t good tnologil qulity. For tis to t s s flow ontingnt llo n our iw (30) will norlly fulfilld. Sin spnding t ig ffort is ffiint t opportunity ost fro spnding only t low ffort surd in forgon profits offsts t sd ffort ost. For (30) to lid it would suffiint if t prit nfits xd t diffrn in pynts to VC i.. t diffrn in VC's ffort osts. W tink it is plusil to ssu tt tis is tru. Tr is no Ns quiliriu in ixd strtgis. Tt is us VC is indiffrnt twn spnding t low or t ig ffort gin tt spnds t ig on sin is in ot ss xtly opnstd for is xpnditurs. ut if VC uss ixd strtgy tn using ixd strtgy is t st rspons for. Howr tis iplis tt VC will not opnstd for is ig ffort wit positi proility. ut tn using ixd strtgy is dointd y t pur strtgy ''low ffort''. W do not s ontrt odifition wi n sol t prol. Rising t prfrrd diidnd wi wkns (30) n ld to n orstting y VC. Lowring t strik in ordr to prott VC ginst 's opportunisti ior n ld to sirking y VC. Wit lowr strik s no innti to sirk sin y doing so nnot rdu t pynt to VC. ut if spnds t ig ffort nd n t (lowr) strik is lrdy rd VC s no innti to work rd. 22

25 tion of s flow nd oting rigts is ndd. As w sown ts n iplntd wit rdl nd onrtil prfrrd stoks. A sift of t oting rigts to t ntur pitlist is nssry to prnt t ntrprnur fro onsuing prit nfits in t d stt of ntur. Howr tis sift is inffiint in t diu nd t good stt of ntur. T ntrprnur ust n gin t opportunity to gt k ontrol. Tis n id wit rdption / onrsion lus. A propr dsignd rdption / onrsion lus works tus s nis to llot t oting rigts s flow ontingnt. Tis prnts t ntrprnur fro orstting is prit infortion us it is ssurd tt t ntrprnur n gt k ontrol nd onsu prit nfits only if rld is prit infortion trutfully. Strting n inffiint projt du to prit nfit onsuing oti is tn not dntgous for t ntrprnur. ut lso t otition to orstt is prit infortion in ordr to ris is stk in t finnil rturn is softnd us tis ris s to trdd off ginst t loss of prit nfits. Furtror t onrsion lus lso works s nis to llot t s flow rigts s flow ontingnt. As w sown t ntur pitlist y n innti to undrstt is prit infortion in ordr to ris is stk in t finnil rturns. To prnt tis undrstting it is nssry to xlud t ntur pitlist fro ny s flow wi is igr tn t ntiiptd on. Hn tr is t nd for s flow ontingnt llotion of s flow rigts. y dsigning t onrsion lus proprly it is ssurd tt t ntur pitlist n only prtiipt in ig s flow if s rld is prit infortion trutfully. T onrsion lus is not just iportnt for t trutful rltion of t prit infortion ut lso for t iplnttion of t ffiint fforts. Sin it is indiidul rtionl for prty to oos is ffort ording to t rginl rturn of is stk wit stndrd finning ontrt only t full rsidul lint on t rgin will spnd t ffiint ffort. Hn to iplnt t ffiint ffort on ot sids it would nssry to k prty t rsidul lint on t rgin. Of ours tis not possil. Howr wit onrsion lus it is possil to ''rtifiilly'' k t ntur pitlist t rsidul lint on t rgin in t sns tt is indud to spnd t ffiint ffort. Tt is us y spnding only t low ffort nnot onrt is prfrrd stoks nd n only ris t liitd prfrrd diidnd. n ontrst y spnding t ig ffort n onrt is prfrrd stok nd ris oon quity wit lu qul to is xpnditurs. T ntur pitlist is in ot ss xtly opnstd for is xpnditurs. Sin is tn 23

26 indiffrnt twn spnding t low or t ig ffort tr is no rson to ssu tt will sirk. At lst tr is t nssity of prfrrd diidnd. t is ndd to dstroy t ntrprnur's lst innti to strt n inffiint projt. T prfrrd diidnd ssurs tt t ntrprnur will not ri pynt on is quity in t d stt of ntur. Sin tn gts nitr finnil rturn nor prit nfit is innti to strt n inffiint projt is opltly dstroyd. T liittion of t prfrrd diidnd in t good stt of ntur is nssry ondition to ssur tt t ntur pitlist will lwys spnd t ig ffort nd onrt is prfrrd stoks into oon ons. 5 Rngotitions Sin yt w not onsidrd t possiility of rngotitions. Howr it is plusil to ssu tt t prtis gr to rngotit t initil ontrt if ot prtis n ttr off wit nw ontrt. ut t possiility of rngotitions influns t strtgi ior of ot prtis sin t ngti onsquns of following n inffiint strtgy r softnd. Tus t ontrts to odifid to k t rngotition-proof. n t rngotitions t prtis n gr to sift ontrol wnr tis not possil undr t initil ontrt. Tus t possil surplus is qul to. Howr VC is only intrstd in rngotition if n offr ontry trnsfr. For rngotition to our it is tus nssry tt s so ony lft ftr pying VC t prfrrd diidnd. Sin VC s soting to sll wi is wortlss to i ut lul for it ss plusil to ssu tt t prtis split t surplus in ordr to tir rgining powr in sipl Ns rgining g. 25 Tus ris t frtion (1 ) nd VC t frtion. 26 Oiously prty n for rngotitions y isstting is prit infortion or y spnding only t low ffort in t good stt of ntur. For VC tis y dntgous sin in rngotition n ri ontry pynt wi xds is xpnditurs. y n innti to is sin now tr is t possiility to gt k ontrol n if t inffiint disions n tkn. n t following proposition w stt ow t ontrts to odifid to k t rngotition-proof Sin VC is t only on wo n gi is prit nfit t optition on t pitl rkt dos no longr dris VC s rgining powr to zro. > P tn VC s rgining powr is liitd to f xds s s flow frtion ( ) i δ ( ( ) Pi )/ us is not trnsfrl. 24

27 25 Proposition 3: T ontrt Z n is rngotition-proof. To k Z nd Z rngotition-proof ty ust odifid s follows: 1. VC s post onrsion quity stk in ontrt Z ust risd to ( ) rn. δ. 2. T rdption pri nd t prfrrd diidnd in ontrt Z ust ot risd to P δ. For solution to xist t following onditions ust fulfilld: 1. ( ) ( ) > 2. ( ) ( ) ( ) pro < η 3. ( ) δ >. Proof: Oiously Z n is rngotition-proof sin it ls ontrol wit. Tus tr is no roo for rngotitions. To s ow Z nd Z ust odifid w first to k ow t inntis of nd VC r inflund y t possiility of rngotitions. Sin trnsfr of ontrol is possil n if t finnil is r issd s slf-sltion onstrints in t d nd diu stt of ntur o (32) ( ) l P > (33) ( ) ( ) ( ) ( ) ( ) P P P P > > 1 δ δ nd is innti onstrint in t good stt of ntur os (34) ( ) ( ) ( ) ( ) P rn δ > 1 1. VC s slf-sltion onstrint in t diu stt of ntur os (35) P P δ

28 nd is innti onstrint in t good stt os (36) ( ) > P δ rn. Tus to rngotition-proof t odifid ontrts ust t lst offr prty t pyoff it would ri in rngotition. t is sy to s tt t only solution to t o inqulity syst is to inrs t prfrrd diidnd / rdption pri in t diu stt ontrt to (37) P δ nd to ris VC s post onrsion quity stk to (38) rn. δ ( ) Howr for tis solution to xist it is nssry tt t s flow in t diu stt of ntur is suffiint to rd t prfrrd stoks t t nw pri i.. (39) ( ) > δ Furtror sin tr is no ontrt odifition wi n sol (33) n only prntd fro orstting if t xptd loss fro strting n inffiint projt xds t xptd ris in is pyoff. will not orstt if 27 (40) pro( η ) < ( ) ( ) f (40) is not fulfilld tn t ffiint instnts nnot iplntd. Tt is us in ordr to prott islf VC y rjt ontrt offr y if s rid 27 Not tt in t d stt of ntur tr will no rngotition sin t s flow is not suffiint to py VC's prfrrd diidnd. 26

29 t d signl. Furtror sin VC is not opnstd for is ig ffort wit positi proility will lwys spnd t low ffort. y insrting P θ rn. ( ) δ nd P in (34) it follows i- ditly tt spnding t ig ffort is only dntgous for if (41) ( ) ( ) > f (41) is not fulfilld t ffiint fforts nnot iplntd. Q..D. For t ontrts to rngotition-proof ty ust offr prty t lst wt it would gt in rngotition. Sin in rngotition VC prtiipts in s prit nfit s to offr VC n infortion rnt. Otrwis nnot indu VC to rl is prit infortion trutfully nd to spnd t ig ffort rsptily. will lwys offr t infortion rnt us in t diu stt of ntur oids spnding t inffiint ig ffort nd in t good stt of ntur profits fro t nt inrs in s flow rsulting fro VC s ig ffort. Of ours t siz of t infortion rnt dpnds on VC s rgining powr in t rngotition. 6 Conlusion n our ppr w offr n xplntion for t widly osrd sprtion of ontrol nd s flow rigts nd tir inrs orrltion in ntur pitl ontrts s rportd y Goprs (1997) nd Kpln nd Strörg (2001). As w sown t inrs orrltion is nssry to oro t sr infortion sytry twn t ntrprnur nd t ntur pitlist. Witout sift of ontrol to t ntur pitlist nd prfrrd s flow rigt for i t ntrprnur nnot indud to rl is prit infortion trutfully. Howr for t nis to work t ntrprnur ust gin t n to gt k ontrol if told t trut. Sin tis n id wit rdption nd onrsion lus rsptily t prdoinn of rdl nd onrtil prfrrd stoks in ntur pitl finn n xplind wit t infortion sytry. sids t infortion sytry w offr sond xplntion for t us of onrtil stoks t doul-sidd orl zrd prol. To k t opny suss n 27

30 ffort y ot t ntrprnur nd t ntur pitlist is ndd. As w sown wit onrtil stok ot prtis n indud to spnd t ffiint fforts. Sin onrsion dos only tk pl if it is profitl for ot prtis t widsprd us of utoti onrsion proision n xplind s wll wit t doul-sidd orl zrd prol. Furtror w n xplin wy ntur pitlists rn xptd positi rturns on tir instnts n in t urrnt ntur pitl rkt. Tis rkt is rtrizd y n xss supply of pitl wi ould ld to t onlusion tt du to t optition ntur pitlists rn zro xptd rturns. Howr if rngotitions r possil tr is roo for rnts. 7 Appndix 7.1 Appndix A Proof of l 3 Suppos for sipliity tt θ θ nd offrs t nu of ontrts. n dsigning t two ontrt s to tk VC s prtiiption onstrints into ount wi is in t diu stt of ntur (42) ( ) 0 nd in t good stt of ntur (43) ( ) 0 Furtror s to tk VC s innti onstrints into ount wi r (44) ( ) ( ) (45) ( ) ( ) s wll s VC s slf-sltion onstrints (46) ( ) ( ) 28

31 29 (47) ( ) ( ) (48) ( ) ( ) (49) ( ) ( ) t is sy to s tt (44) nd (46) r fulfilld y ssuption. W tus to sow tt tr is ointion of nd for wi (42) (43) (45) (47) (48) nd (49) r fulfilld siultnously. Fro (42) (43) und (45) w otin t iniu solut lus for nd wi r (50) ( ) (51) ( ) (52) ( ) ( ) And fro (47) (48) nd (49) w otin t rlti ons i.. t rltion twn nd (53) ( ) ( ) 1 < (54) ( ) ( ) (55) ( ) ( ) Fro (53) follows dirtly >. 28 Sin (50) is inding w n sustitut fro (50) into (53) (54) und (55). W otin dirtly tt tr is only solution to t prol if 28 Tis rsult is intuitily lr. f tis rltion dos not old VC would lwys oos t good-stt-ontrt.

32 30 (56) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ; ; ; x <. (56) oiously dpnds on t odl s prtrs. s oiously to py n infortion rnt if it is not VC s prtiiption onstrint wi dtrins t siz of t quity stk i.. ( ) >. Q..D. 7.2 Appndix Proof of l 4 Suppos θ θ. s profit in s of rling is prit infortion trutfully is (57) ( ) ( ) η η η η π flls 1 flls 0 wr wil in s of orstting it is (58) ( ) ( ) ( ) ( ) η η η η π flls 1 flls 1 l fls Oiously n ris is profit y orstting is prit infortion. Q..D.

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