Contributions to Economic Analysis & Policy

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1 Conribuions o Economic Analysis & Policy Volume 4, Issue Aricle 13 An Index For Venure Capial, Min Hwang John M. Quigley Susan E. Woodward Naional Universiy of Singapore, rshm@nus.edu.sg Universiy of California, Berkeley, quigley@econ.berkeley.edu Sand Hill Economerics, swoodward@sandhillecon.com Copyrigh c 2005 by he auhors. All righs reserved. No par of his publicaion may be reproduced, sored in a rerieval sysem, or ransmied, in any form or by any means, elecronic, mechanical, phoocopying, recording, or oherwise, wihou he prior wrien permission of he publisher, bepress, which has been given cerain exclusive righs by he auhor. Conribuions o Economic Analysis & Policy is one of The B.E. Journals in Economic Analysis & Policy, produced by The Berkeley Elecronic Press (bepress). hp://

2 An Index For Venure Capial, Min Hwang, John M. Quigley, and Susan E. Woodward Absrac In his paper we build an index of value for venure capial. Our approach overcomes he problems of inermien, infrequen pricing of privae company deals by using a repea valuaion model o build he index, and i correcs for selecion bias in he reporing of values. We use a unique daa se from Sand Hill Economerics which repors 50,734 funding evens, which include he conemporaneous valuaions of 9,092 privae equiy firms disclosed 19,208 imes over almos 17 years. The resuling index measures he reurn and risk for venure capial. Is covariance wih oher asse classes from 1987 hrough 2003 enables us o explore he role of venure capial in diversified porfolios during a period of increased imporance of venure capial in he economy. KEYWORDS: Privae Equiy, Price Index Previous versions of his paper were presened a he Financial Markes Conference sponsored by he Alana Federal Reserve Bank and he NYU Sern School of Business, Sea Island Georgia, May 2002, and a he Conference on Price Indices and Qualiy Change sponsored by he Zenrum für Europaïsche Wirschafsforschung, Mannheim, April An early version of his paper (Quigley, 2001) was prepared for Offroad Securiies. We are graeful for he assisance of Shawn Blosser, Min Hwang, and Zach McRenolds and for he commens of Rober Gary-Bobo, Bruce Lehmann, and Rober Hall.

3 Hwang e al.: An Index for Venure Capial, I. Inroducion Over he pas decade, venure capial has grown enormously in economic imporance. I was esimaed ha in 1990 abou $3 billion flowed ino venure funds. A decade laer he corresponding figure was $103 billion. A he same ime, he ousanding oal value of such firms was roughly $500 billion; in comparison, he marke value for companies lised on US sock exchanges was roughly $10 rillion. The economic imporance of he privaely held companies ha seek financing from ouside invesors probably exceeds heir curren share of business value, because some of oday s privae companies will become highvalue public companies in he fuure. Roughly wo-hirds of he companies ha go public had venure capial funding prior o heir public offering. Some of he ownership ineress in privae companies are held direcly as sock in he issuing company, and some are held as limied parnerships in venure capial funds. Holders are primarily pension plans, endowmens, corporaions, and wealhy individual invesors. Companies funded by primary invesors and by venure capial funds find heir way o he public markes. During he lae 1990s, roughly wo-hirds of he companies making iniial public offerings had backing from venure capial funds, and many of he ohers had subsanial funding from ouside primary invesors. Invesmen in pre-public companies 1 is no longer experimenal or exploraory, bu is a permanen feaure of he U. S. financial landscape. There is lile sysemaic informaion on he resuls of venure invesmens. By conras, for publicly raded holdings, quaniaive performance evaluaion is sraighforward. Sandard indices, such as he S&P500 and he Wilshire 5000, provide measures of overall marke reurns. For non-raded holdings, such as venure capial, invesors have no similar benchmark. This paper builds an index for venure capial o provide a clear benchmark. Such a benchmark is useful: for evaluaing he performance of paricular venure holdings; for evaluaing he performance of specific funds, including venure capial limied parnerships, corporae venure funds, and venure holdings of pension and endowmen funds; for comparing he performance of venure capial wih ha of oher asse classes; for deermining he 1 By privae equiy we mean equiy in pre-public companies. These firms raise money from ouside invesors wih he hope and inenion of becoming public corporaions. We do no include leveraged buy-ous (LBOs), managemen buy-ous (MBOs), or privae placemens in oherwise public companies (PIPEs) in our analysis, alhough hey are privae in he sense ha here are resricions on he sale of hese ypes of securiies o he general public. Furher, by common usage, venure capial refers o invesmens in pre-public companies made hrough venure capial funds and hose made direcly by primary invesors. We hus use venure capial and privae equiy as synonyms. Conribuions o Economic Analysis & Policy

4 2 Vol. 4 [2005], No. 1, Aricle 13 appropriae porfolio allocaions of differen asse classes; and for oher applicaions as well. There are several major problems in consrucing such an index. To begin wih, pricing evens for privae companies are inermien and infrequen, no regular and almos coninuous as for raded securiies. A price is se for sock in an individual company when i raises new capial, when i sells shares o he public (hrough an IPO), when i is acquired, or when i ceases operaions. These companies are privae heir sock is no regisered wih he Securiies and Exchange Commission (SEC); hey do no repor financial resuls o he SEC or o he public unless hey choose o, and heir sock is no raded in any organized marke. Nearly all such companies are organized as C-corporaions (and are hus hemselves axable eniies). These companies may be valued only a handful of imes during he inerval beween esablishmen and IPO, acquisiion, or cessaion of operaions. 2 Moreover, because hey are privae, disclosures are volunary. Hence, even when firms are valued, hey need no reveal he price a which hey sold sock in heir mos recen round. More imporan for our analysis is he fac ha companies may simply forgo an opporuniy o raise money if hey find he available erms unappealing. In oher words, some rades happen and he prices a which hey occur are repored, some rades occur bu prices are no repored, and some poenial rades do no occur a all. To measure movemens in he value of hese privaely held firms over ime, we develop a mehod for creaing a sandardized price index for such firms. We build he index using a modern hybrid version of he repea-sales echnique inroduced by Bailey e al. (1963) for measuring price changes for real propery sold infrequenly, and we correc i for selecion bias. There are wo seps o building he index. In he firs sep, o measure he sample seleciviy in he ransacions ha do reveal value, we consruc he hisories of pricing evens for all of he companies for which we have daa (hose evens ha reveal value and hose ha do no) o esimae he probabiliy ha a company will reveal value (hrough an IPO, acquisiion, privae funding, or by ceasing operaions). We hen use his esimaed probabiliy in consrucing he index by a hybrid version of he repea-valuaion mehod ha uses informaion on he ransacions for companies which revealed value and for which we can observe a price or a reurn in some inerval. The approach is similar o ha used o consruc price indices for residenial real esae by governmen agencies (OFHEO), governmen-sponsored enerprises (Freddie Mac and Fannie Mae), and privae firms such as MRAC, Inc. 2 Privae companies ha raise money from ouside invesors and cease operaions can do so eiher hrough windup or shudown (in principle, credior s bills are paid in full in his even) or hrough Chaper 7 bankrupcy liquidaion. If here is no hope for a company, he board of direcors is obliged o wind i up raher han coninue sruggling unil remaining asses can no longer saisfy crediors. Windups (or shudowns) are far more frequen han bankrupcies. hp://

5 Hwang e al.: An Index for Venure Capial, The novelies in our applicaion lie in he exension of he hybrid repea sales approach o privae companies, he correcion for selecion bias made necessary by he non-random naure of he reporing of ransacions, and --imporanly-- he analysis of a imely and unique daa se which spans he recen period of volailiy in asse markes. The uni of observaion is a pricing even for a privae company. This includes any privae round of fund raising, which necessarily produces a company value (repored or no) deermined by negoiaion beween he issuing company and is invesors (which may include venure capial limied parnerships, individuals, and corporaions). Pricing evens also include IPOs, acquisiions, and windups or bankrupcies. The index hus reflecs gross reurns from direc invesmens in he companies, no he reurns o venure fund limied-parner invesors afer he fees and expenses of heir funds. 3 Ohers have acknowledged he imporance and difficuly of esimaing reurns for privae equiy invesmens. Bygrave and Tymmons (1992) calculaed average inernal raes of reurn for compleed venure funds; hey repored an average annual reurn of 13.5 percen from 1974 o 1989, using an approach ha provides no risk measuremen. Reyes (1997) used a se of 175 compleed venure capial funds o calculae beas, and found hem o lie beween 1 and 3.8. Gompers and Lerner (1997) repored an arihmeic average annual reurn of 30.5 percen on compleed venure funds from 1972 o Long (1999) calculaed risk by inferring he shorer-erm sandard deviaion from variaions in longererm reurns, and repored an esimae of he annual sandard deviaion of 8.23 percen per year for compleed venure funds. This analysis was based upon nine unidenified, successful VC invesmens. Moskowiz and Vissing-Jorgenson (2002) measured reurns o all privae equiy, conceived very broadly o include closely-held businesses wih no inenion of going public and no money from ouside invesors. They used daa from he Survey of Consumer Finances, including self-repored valuaions. They were puzzled ha he reurns were so low. 4 Chen, Baierl, and Kaplan (2000) examined compleed venure funds o calculae average annual arihmeic and geomeric reurns, sandard deviaions, and correlaions wih marke indices. They repored a geomeric average reurn of 13 percen, an annual sandard deviaion per fund of percen, and a 3 Venure capial funds ypically charge heir limied parner invesors an annual managemen fee of wo o hree percen of ne asse value, and hen also ake 20 o 35 percen of he gains (20 percen is a sandard carry, while 35 percen is a premium carry ) on he companies wih posiive reurns when hey are acquired or go public. 4 Companies issuing pre-public privae equiy are a iny fracion of privae businesses. There are more han 20 million companies ha file income ax reurns. Roughly 5 million have a payroll. Of hese, roughly 1.5 million are organized as C corporaions. Conribuions o Economic Analysis & Policy

6 4 Vol. 4 [2005], No. 1, Aricle 13 correlaion wih he public sock marke of None of his work considers selecion bias. Two pieces of research on venure risk and reurn ha do address he selecion issue are Cochrane (2005) and Peng (2001). Boh empirical analyses rely upon a subse of our daa ha was available in 2000 covering he period These daa are for venure-backed firms only, primarily from he VenureOne daabase (described below). Peng (2001) builds a venure valuaion index accouning for selecion by combining wo sub-indices, one for shudowns and he oher for successful exi. He correcs for selecion bias approximaely, by assigning weighs o hese wo indices based on he likelihood ha companies will go ou of business or will succeed, esimaed from observable characerisics. Cochrane analyzes 16,613 observaions on 7,765 sarup firms observed beween January 1, 1999 and June 30, He uses a maximum likelihood approach o esimae reurns, sandard deviaion, and correlaion wih he marke, accouning for probabiliy of new funding rounds as a funcion of firm values, and correcing for selecion bias in he reporing of valuaions. His approach esimaes risk and reurn direcly, bu does no build an index of valuaion. He finds ha he selecion-bias-correced log reurn is 15 percen during , compared o he bias-uncorreced reurn of 108 percen, and ha alpha from he log marke model is -7 percen, compared o he bias uncorreced alpha of 92 percen. He also finds ha log reurns are sill quie volaile, wih sandard deviaion of 89 percen. 5 In Secion II we describe he economic problem and review models ha have been employed in analogous seings o develop indexes of value. Secion III provides a deailed descripion of observaions on 50,734 rounds of financing for 9,092 sar-up firms during he period January 1, 1987 hrough June 30, These daa are used o esimae a valuaion index for his secor of he economy. Secion IV repors our principal empirical resuls, measuremen of a price index for privae equiy correced for selecion bias. Secion V explores an applicaion of his analysis o porfolio allocaion. Secion VI is a brief conclusion and discussion of fuure work. II. Venure Firm Values, Index and Selecion Bias 2.1 A Hybrid Index Model wih Selecion Bias Correcion Mehods for esimaing marke prices for heerogeneous goods or for iems raded infrequenly have received considerable aenion among applied 5 However, he arihmeic reurn is sill large and volaile even afer correcing for selecion bias. He finds ha he mean arihmeic reurn is 59 percen wih a sandard deviaion of 107 percen. The arihmeic alpha is as high as 32 percen. hp://

7 Hwang e al.: An Index for Venure Capial, economericians and finance professionals. Mehods o accoun for he heerogeneiy of goods were exended in he early 1970s (Kain and Quigley, 1970, Griliches, 1971) and have been applied quie widely in he analysis of durables, such as auomobiles (Oha and Griliches, 1975), housing (Kain and Quigley, 1975), home appliances (Hausman, 1979), and compuers (Pakes, 2003). Hedonic price models accoun for he heerogeneiy of commodiies by relaing he observed ransacion prices or marke values, V, (or someimes, in he case of auomobiles, lis prices) o a vecor, X =(x 1, x 2,..., x n ) describing he qualiaive and quaniaive aribues of he goods. The esimaed coefficiens, b, represen he implici marginal prices of each aribue. n (1) V = b bi xi p δ ξ b x p τ τ + = + δ + ξ i= 1 τ = 1 where δ τ is an indicaor variable wih a value of one for all ime periods up o, and p τ is he change in prices during period τ. ξ is a random error wih mean zero. I is ofen assumed ha he saisical relaionship is semi-logarihmic. The underlying logic is ha marke value V is he produc of price P imes quaniy X, i.e., (2) V = X P. The logarihm of he ransacion price is regressed upon variables measuring he physical characerisics of he commodiies x i and dummy variables represening ime δ. In his formulaion, exp τ = 1 pτδ τ is he price index a. Despie he populariy of he semi-log form, few economically meaningful resricions can be placed on he form of he hedonic relaionship (Rosen, 1974). Because heory provides lile guidance in he formulaion of saisical models of hedonic prices and because many durables are raded infrequenly in hin markes, repea-sales mehods have been developed o absrac from measuring he hedonic characerisics of hese goods. Consider he difference beween ransacion prices measured a and T.. (3) V VT = b ( x xt ) + p ( δ δ T ) + ξ ξt If he form of he hedonic price funcion is semi-logarihmic and if he characerisics of he commodiy are unchanged beween sales, he model reduces o, (4) V VT = p ( δ δ T ) + ξ ξt where he lef hand side is a logarihmic difference. Conribuions o Economic Analysis & Policy

8 6 Vol. 4 [2005], No. 1, Aricle 13 The advanage of his formulaion is ha, for repea sales of unchanged commodiies, i is no necessary o measure he deailed characerisics of he commodiies o esimae he price index implied by equaion (1). In he fory years since hey were inroduced (Bailey, e al., 1963), hese models have been applied exensively o he housing marke, and hey form he basis for mos commercially developed measures of local housing price variaion (for example, indexes markeed by Fiserv CSW, Inc.) as well as he regional housing price informaion produced by he Federal Governmen (he OFHEO house price series for saes and meropolian areas). Goezmann (1993) applied he same echnique o valuing fine ar. The repea-sales mehod encouners wo major challenges. Firs, muliple sales may be non-random samples of he underlying populaion (Hwang and Quigley, 2004). If he objecive is o esimae he value of he sock of he asse, raher han merely he value of hose unis ha have been sold in any period, his selecion bias may be imporan. In an applicaion o privae companies, i seems clear ha firms receiving financing a any poin in ime are hose whose prospecs are more promising han are hose of oher firms. Thus, bias in sample selecion is poenially quie imporan. Second, characerisics of he produc may change. To address hese issues, a variey of hybrid models have been developed. These models combine he desirable properies of hedonic and repea sales esimaors. For example, join esimaion of equaions (1) and (3) for single sales and repea sales combine hedonic adjusmens wih changes in marke value. (5a) V = b x + p δ + ξ i i ˆ i (5b) Vi ViT = b ( xi xit ) + p ( δ i δ it ) + ξi ξit (5c) b = bˆ and p = pˆ. i ˆ More general hybrid specificaions wih more realisic specificaions of he error srucure are also possible. (See Englund, e al., 1998, for a survey and applicaion.) A sensible specificaion of he error srucure in (5) may be a firsorder auogressive process, (6) ξ i = ε i + ηi and ε i = λε i, 1 + μi where η i and μ i are whie-noise innovaions. ( μ ) = E( η μ ) 0 E( η ) E = i = i i i (7) E 2 2 ( η i ) = ση hp://

9 Hwang e al.: An Index for Venure Capial, E 2 2 ( μ i ) = σ μ The original Bailey, e al. (1963) model assumes he λ = 0 while he Case-Shiller (1987) model assumes λ = 1. In his formulaion, he error variances in equaions (5a) and (5b) are: 2 σ μ 2 (8a) Var( ξ i ) = + σ 2 η. 1 λ (8b) 2σ (1 λ ) Var( ξ + 1 λ 2 τ μ i ξi τ ) = 2 2 σ 2 η σ λ 1 2 μ γ τ τ γ (8c) [( ξ ξ )( ξ ξ )] g g = ( λ λ λ + λ ) E i iτ ig iγ 2 ( I ( = g) I( = γ ) I( τ = g) + I( = g) ) 2 + σ η τ Now consider selecion bias. Successful firms are more likely o arac addiional rounds of privae equiy finance, are more likely o reveal value when hey do arac money, are more likely o be acquired by publicly raded firms, and are more likely o raise capial hrough an iniial public offering. In any period, we observe ha firm i akes one of he following acions: (1) i ceases operaions; (2) i is acquired by anoher firm which does no reveal is value; (3) i underakes no funding even; (4) i obains a new round of privae equiy financing, bu chooses no reveal is valuaion; (5) i obains a new round of financing, revealing is value; (6) i is acquired by anoher firm which reveals is valuaion; (7) i sells shares hrough an IPO, going public and revealing is value. These alernaives form a naural ordering, from he leas desirable (1, a shudown) o he mos desirable (6 or 7, an IPO or an acquisiion revealing value). Of hese seven evens, only four of hem resul in an observaion on he valuaion of he firm (1, 5, 6 and 7). We assume here is an unobserved revelaion index, I i, for each firm and unobserved hresholds, I k 1, such ha if I i I, he firm is shu down; if I < I i I, he firm is acquired wihou revealing value; if I < I i I, he 3 4 firm underakes no funding even; if I < I i I, he firm obains a new round of 4 5 privae equiy financing, wihou revealing value; if I < I i I, he firm obains 5 a new round of financing and reveals is valuaion; if I i > I, he firm goes public hrough an IPO or is acquired wih revelaion of is value. Noe ha I i Conribuions o Economic Analysis & Policy

10 8 Vol. 4 [2005], No. 1, Aricle 13 may vary over ime and wih he characerisics of firm (e.g. he sae of firm developmen). Suppose (9) I i = z i γ + ς i, where z i = (z 1i, z 2i,..., z mi ) are he characerisics of firm i a ime ha affec funding and oher aspecs of value revelaion, and ς i is a random error. The revelaion index depends posiively on he firm s need o obain funding and negaively on he firm s value in relaion o is earlier value. We observe a firm s 4 1 value only a he ime of a revelaion even, I i > I or I i I. Thus, he expecaion of equaion (1) for firm i is E V = b x + p δ + E ξ Funding even for firm i a, (10) ( ) ( ) i i i i where a funding even is eiher { ω I I 5 i > }, { ω I 5 I I 4 i > } or { I I 1 i } Similarly, from equaion (3) (11) E( V V ) = b ( x x ) + p ( δ δ ) + i it i it i it ω. ( E( ξ Funding even for firm i a ) E( ξ Funding even for firm i a T )) i it Clearly, he coefficiens esimaed from equaion (10) or (11) are biased if he condiional expecaion of he error erm is no zero. Following Heckman (1979), we model he process ha selecs firms ino he se of observaions of hose funded. Denoe he correlaion of he random elemen of his selecion model, ς i, wih he random elemen of value, ξ i, by ρ. Wihou loss of generaliy, we assume ha he variance of ς i is one. Then equaion (10) becomes: δ ρσ ϖ (5d) E( Vi ) = b xi + p + i where and ϖ ϖ i i = Φ φ = Φ 5 φ( I z iγ ) 5 ( ( I z γ ) i ξ when 4 5 ( I z iγ ) φ( I z iγ ) 5 4 ( I z γ ) Φ( I z γ ) i i 5 I i > I when 5 I Ii > I 4 hp://

11 Hwang e al.: An Index for Venure Capial, ϖ i φ = Φ 1 ( I z iγ ) 1 ( I z γ ) i when 1 I i I. φ denoes he pdf and Φ denoes he cdf of he sandardized normal disribuion. Thus, ϖ i is he inverse Mills raio in he conex of ordered probi. Is inclusion in he valuaion regression yields unbiased esimaes of he parameers in he presence of non-random sample selecion. The selecion bias-correced valuaion model associaed wih equaions (10) and (11) is (5e) V V = b ( x x ) + p ( δ δ ) + θ ( ϖ ϖ ) + ( ξ ξ ) i it i it i it i it i it for a firm wih muliple funding evens, and (5e ) V j = b x + p δ + θϖ + ξ for a firm wih a single funding even, j j j j where θ is he parameer ρσ ξ. Esimaion of he model can be accomplished in a wo-sep procedure. Firs, an ordered probi wih he seven alernaives is esimaed o calculae Mills raio, ϖ i, for each observaion. Second, wih he Mills raios compued in he firs sage, equaions (5e) and (5e ) are esimaed joinly by maximum likelihood using he error srucure assumed in (6), (7) and (8). We can hus obain unbiased esimaes of he price movemen of privae equiy firms using he non-random sample of firms whose valuaions are acually observed. 2.2 Cochrane s Model wih Selecion Bias Correcion As noed above, here exis few approaches o venure firm valuaion which ake ino accoun selecion bias. The closes work o ours is Cochrane (2005), which uses a subsample of preliminary daa from he same source as ours, bu here are several differences beween his approach and ours. Firs, for valuaion of venure firms, Cochrane uses a CAPM ype marke model in logarihms while we use a hybrid hedonic pricing model. Cochrane s marke model does no allow for he idiosyncraic differences of individual firms, bu only he marke-wide alpha and bea for venure invesmen, while he hybrid model presened here allows separae esimaes of marke-wide valuaion and idiosyncraic componens of individual firms. Second, in he selecion bias correcion, Cochrane does no differeniae among very differen ypes of exis and financing rounds, enforcing a single hreshold for various valuaion evens. In conras, our correcion procedure allows differen hresholds for various ypes of funding evens. Third, in he selecion bias correcion, in Cochrane, he hreshold is derived from he reurns of individual firms during he specified inervals wihou Conribuions o Economic Analysis & Policy

12 10 Vol. 4 [2005], No. 1, Aricle 13 reference o marke condiions. In our approach, hresholds are derived wih direc reference o marke condiions since our ordered probi equaion includes a complee se of indicaor variables for ime. Fourh, Cochrane s analysis is based on informaion only up o he second quarer of 2000, which is he very peak for public and privae equiy valuaions. Our daase covers hree addiional years, up o he second quarer of 2003, which reflecs a complee cycle of firm valuaions, for boh privae and public equiy firms. III. Daa The daa used o esimae he venure index come from he Sand Hill Economerics daabase and cover he period from January 1, 1987 hrough June 30, he period covering he rise in he imporance of privae equiy and he subsanial marke declines beginning in he second quarer of Consrucion of his daabase began wih daa purchased from proprieary daa vendors (iniially VenureOne) and has since been subsanially augmened by Sand Hill s own research. Subsanial effor was invesed o make he daa suiable for analyical purposes eliminaing duplicae rounds of funding (by maching company names, daes of funding, and amouns raised, and by consolidaing muliple closings of he same round) and obaining precise exi daes for companies ha have been shu down, been acquired, or gone public. The daa conain records on 15,583 privae firms wih a oal of 50,734 rounds of financing. Of hese, 19,208 rounds include informaion on pos-round valuaion, including 14,012 rounds of privae-equiy financing, 2,116 IPO s, 1,905 acquisiions, and 1,175 shu downs. Table 1 repors he number of observaions of valuaion by sage of business developmen and ype of financing. Abou 2,900 financing rounds ook place during he produc developmen phase, and 6,700 ook place when he firm was delivering produc o cusomers. The average firm valuaion a hese financing rounds varies sysemaically. A laer rounds of financing, average firm valuaions are higher. No surprisingly, valuaions for IPOs are subsanially higher han for oher funding evens, and valuaions of firms furher along in he developmen process are also considerably higher. Table 2 repors more deail on he firms ha exied from he privae equiy daa se hrough IPO, acquisiion, or shu down. The able indicaes ha he average valuaion a exi for IPOs is $319 million, more han wice as large as he repored value a exi for acquisiions ($129 million). A he penulimae round of financing, firms ha exied hrough IPO had almos wice he value as hose exiing hrough acquisiion. Significanly, firms exiing hrough bankrupcy were no much differen from hose exiing hrough acquisiion in heir valuaion, as hp://

13 Hwang e al.: An Index for Venure Capial, Table 1. Summary of Privae Financing Informaion: By Rounds of Financing and Businses Developmen Sage A. Number of Rounds Produc Sarup Developmen Bea Tesing Clinical Shipping Profiable Unknown Toal Trials Seed Firs 358 1, , ,743 4,905 Early , ,846 6,824 Lae ,399 Mezzanine IPO ,116 Acquisiion ,905 Shudowns ,175 Toal 705 2, ,674 1,203 7,080 19,208 Conribuions o Economic Analysis & Policy

14 12 Vol. 4 [2005], No. 1, Aricle 13 Table 1. (coninued) Summary of Privae Financing Informaion: By Rounds of Financing and Businses Developmen Sage B. Mean Value of Firms wih Revelaion of Values ($M) Produc Sarup Developmen Bea Tesing Clinical Shipping Profiable Unknown All Sages Trials Seed $6.04 $4.70 $10.24 $1.70 $ $6.09 $6.69 Firs $13.85 $16.66 $25.26 $28.44 $24.47 $28.52 $27.56 $22.96 Early $11.76 $40.85 $35.88 $34.55 $55.28 $43.47 $64.39 $55.67 Lae ---- $74.82 $48.58 $53.06 $90.19 $57.09 $80.82 $82.02 Mezzanine ---- $76.32 $ $66.77 $ $65.22 $22.40 $ IPO ---- $ $ $ $ $ $ $ Acquisiion $ $ $ $53.85 $ $62.68 $ $ Shudowns $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 Toal $10.78 $45.88 $68.21 $66.73 $93.29 $93.69 $78.37 $76.81 hp://

15 Hwang e al.: An Index for Venure Capial, Table 2. Summary of Privae Financing Informaion a Final Financing Round for Firms ha Have Exied For Preceding Round: A Exi: Toal Number of Firms Mean Number of Days beween Exi and Preceding Rounds Mean Valuaion Pre-Round (Million) Mean Valuaion Pos-Round (Million) Mean Valuaion (Million) IPOs whose preceding round was: Seed $2.53 $3.20 $ Firs $28.55 $38.58 $ Early $76.07 $88.90 $ Lae $ $ $ Mezzanine $87.16 $ $ Average 592 $81.00 $94.36 $ Acquisiions whose preceding round was: Seed $4.08 $5.90 $33.14 Firs $17.64 $23.78 $76.03 Early $48.72 $58.59 $ Lae $49.17 $58.36 $ Mezzanine $95.35 $ $ Average 872 $40.61 $49.30 $ Shudowns whose preceding round was: Seed $5.79 $7.62 $0.00 Firs $16.41 $23.11 $0.00 Early $49.51 $61.96 $0.00 Lae $61.44 $74.07 $0.00 Mezzanine $ $ $0.00 Average 1369 $40.96 $51.36 $0.00 Conribuions o Economic Analysis & Policy

16 14 Vol. 4 [2005], No. 1, Aricle 13 repored afer he round immediaely preceding exi ($49 million versus $51 million) For IPOs, on average, he penulimae round of financing raised abou $13 million, while he public offering raised $225 million. For acquisiions, he penulimae round of financing raised abou $6 million, while he acquisiion raised $80 million. For firms ha exied hrough bankrupcy, he las round of financing raised abou $10 million, and more han $51 million was los, on average, in shudowns. For firms ha exied hrough an IPO, he average ime beween rounds of financing was 592 days. For firms ha were ulimaely acquired, he average ime beween rounds was significanly higher, 872 days. For firms exiing hrough bankrupcy, he elapsed ime beween rounds was higher sill, 1,369 days. IV. Empirical Analysis For each firm, we observe he daes of all funding evens and exis beginning on January 1, 1987 (or when he firm is firs recorded in he daa se) and ending wih is las valuaion before June 30, 2003 (or when he firm exied by acquisiion, IPO, or windup). A hese daes, we observe he business group of he firm in one of four caegories (he healhcare indusry, informaion echnology, reail and services, and oher ), is sage of developmen in seven caegories (as repored in Table 1), and is region of he counry. A each of he funding daes, we observe he ype of valuaion even (IPO, acquisiion, privae equiy funding, shudown). For some of hese evens, we also observe he valuaion of he firm. (We always observe firm valuaion when i has been funded hrough a public offering or i has gone bankrup; someimes we observe a valuaion when i is acquired or when i receives a round of privae equiy finance.) 4.1 The Selecion Model: The Probabiliies of Privae Equiy Financing and Exis We esimae he probabiliy ha a firm will be valued and ha valuaion will be revealed a any poin in ime by consrucing and analyzing he even hisories of funding opporuniies for hese firms. An even is an observaion on each firm in he sample in each quarer year. In paricular, we observe wheher a firm has been funded, he ype of funding, and, someimes he revelaion of value. These even hisories are analyzed by esimaing an ordered probi model using he seven oucomes possible in each quarer. They are: 1) revelaion of value hrough shudown; 2) funding hrough acquisiion, wihou revelaion of value; 3) no funding a all; 4) privae equiy funding wihou revelaion of value; 5) privae hp://

17 Hwang e al.: An Index for Venure Capial, equiy funding wih revelaion of value; 6) funding hrough acquisiion wih revelaion of value; 7) funding and revelaion of value hrough an IPO. The observaions on individual firms yield 293,927 observaions on he occurrence or non-occurrence of one of hese evens in each quarer. We use his informaion o consruc even hisories, recording he occurrence of each of hese disinc evens in each quarer from 1987 hrough Even hisories are used o esimae he probabiliy of funding and he probabiliy ha valuaion is revealed by any firm in any quarer. The seven possible evens observable in any quarer are raher clearly ordered from he leas desirable for any firm, revelaion of value hrough bankrupcy, hrough he mos desirable, revelaion hrough an IPO. We esimae even probabiliies using an ordered probi model. We esimae he probabiliy of conemporaneous funding of any firm as a funcion of is developmen saus, recorded a is mos recen round of funding, of is indusry group and geographical locaion, he sock marke capializaion a he ime and calendar ime in quarers. We also hypohesize ha he probabiliy of funding is inversely relaed o he elapsed ime since is las injecion of capial, and ha he imporance of elapsed ime varies wih he ype of round of previous financing. The esimaes of he ordered probi model are presened in Table 3, based upon he 293,927 observaions on funding evens. I is widely observed ha privae equiy firms which do no receive regular injecions of capial hrough funding evens are less likely o survive and prosper. The resuls in Table 3 confirm his inuiion. They clearly esablish ha firms whose las round of finding is furher in he pas are less likely o receive funding in he curren period. In paricular, a longer elapsed ime since he seed (he original) round or he mezzanine (he presumed penulimae) round is inversely relaed o funding in he curren period. Longer elapsed imes since funding rounds described as early and lae are also associaed wih lower probabiliies of funding in he curren period. Firms which have no been funded recenly are less likely o be funded oday. There are also sysemaic differences in he probabiliies of funding and revelaion for broad indusry groups. Similarly, he kinds of firms locaed in differen geographical regions are associaed wih differing propensiies o receive funding, ceeris paribus. Firms in he bea esing sage of developmen are sysemaically less likely o receive funding, while firms ha are already profiable are much more likely o obain new funding. The reurn on he S&P500 is included o measure he impac of public equiy invesmen opporuniies. This impac can come from wo differen sources. Higher values of he variable are associaed wih greaer availabiliy of invesmen funds. However, for a given level of funding available, he variable also reflecs he degree of compeiion wih public equiy invesmens. Conribuions o Economic Analysis & Policy

18 16 Vol. 4 [2005], No. 1, Aricle 13 Table 3. Ordered Probi Model of New Privae Equiy Finance and Revelaion of Value by Quarer, 1987:I hrough 2003:II Variables Coefficien -raio Days elapsed x Type of Las Funding Round Elapsed Days ( 10 ) Elapsed Days x Previous Round (Seed) ( 10 ) Elapsed Days x Previous Round (Firs) ( 10 ) Elapsed Days x Previous Round (Early) ( 10 ) Elapsed Days x Previous Round (Laer) ( 10 ) Elapsed Days x Previous Round (Mezzanine) ( 10 ) hp://

19 Hwang e al.: An Index for Venure Capial, Table 3. (coninued) Ordered Probi Model of New Privae Equiy Finance and Revelaion of Value by Quarer, 1987:I hrough 2003:II Variables Coefficien -raio Developmen Saus Produc Developmen Bea Tesing Clinical Trials Shipping Produc Profiable Geographical Locaion Norhern California Souhern California Massachuses Texas Norhern Virginia NY-NJ Conribuions o Economic Analysis & Policy

20 18 Vol. 4 [2005], No. 1, Aricle 13 Table 3. (coninued) Ordered Probi Model of New Privae Equiy Finance and Revelaion of Value by Quarer, 1987:I hrough 2003:II Variables Coefficien -raio Technology Group Healh Care Informaion Technology Reail and Services Oher S&P Cuoff Poins Acquisiion wihou Valuaion No Funding Privae Equiy Financing wihou Valuaion Privae Equiy Financing wih Valuaion Acquisiion wih Valuaion IPO Noe: The ordered probi model also conains 65 indicaor variables for ime in quarers, from 1987:II hrough 2003:II. The esimaion is derived from 293,927 observaions on one of 7 funding evens observed each quarer for each firm from 1987:I (or when he firm eners he daa se) hrough 2003:II (or when he firm exis he daa se). hp://

21 Hwang e al.: An Index for Venure Capial, The able also repors he esimaed value of he shif in he probi plane (he cuoff poins ) associaed wih each of he poenial evens. 6 The magniudes of he shifs are ordered wih he desirabiliy of he oucome. The esimaed probi model also includes 65 indicaor variables represening ime in quarer years beginning wih 1987:II. These coefficiens are no repored in he able. We use his ordered probi model o esimae he probabiliy ha each firm will experience one of hese funding and valuaion evens in each period. For each observaion on firm value, we include he inverse Mill s raio calculaed from his probabiliy as a variable, correcing he esimaion for selecion bias Esimaion of Venure firm valuaion and Index Table 4 repors he coefficien esimaes for he valuaion models. For comparison, he simple repea valuaion model, equaion (3), is presened as well as he hybrid model, equaions (5) hrough (8), esimaed by maximum likelihood. Resuls are repored boh wih and wihou he bias correcion facor. Since he dependen variable is expressed in logarihms, he coefficiens are inerpreed as he percenage change in firm valuaion associaed wih a one-uni change in each independen variable. These models have been esimaed in wo varians: including a se of 197 indicaor variables represening monhs, beginning wih February 1987, and also including a se of 65 indicaor variables represening quarer years, beginning wih 1987:II. There are only very small differences in he coefficien esimaes of he oher variables when calendar ime is represened in hese wo varians. Table 4 repors he coefficiens when ime is measured in quarer years. As he able indicaes, laer rounds of financing are generally associaed wih higher firm valuaions. In paricular, lae rounds of privae finance, acquisiions, and IPOs are all associaed wih higher valuaions. Firms reporing profis are valued subsanially higher, by abou weny five percen, han oher firms a he same round in he same line of business. 6 There is no uniform agreemen abou he appropriae ordering of evens in he ordered probi model. In paricular, one reviewer quesioned he ordering of evens 2 ( funding hrough acquisiion, wihou revelaion of value ) and 3 ( no funding a all ) and evens 5 ( privae equiy funding wih revalaion of value ) and 6 ( funding hrough acquisiion wih revalaion of value ). To es he sensiiviy of our resuls o he ordering of evens, we re-esimaed he probi models wih several varians on ordering. When oucomes 2 and 3 are re-ordered, he log likelihood is reduced from o , and he scaled R 2 (See Esrella, 1998) drops from o When oucomes 5 and 6 are re-ordered, he log likelihood and scaled R 2 saisics are reduced only marginally o and 0.170, respecively. (See also noe 17 below.) 7 The deails of calculaing he Mills raio in he conex of ordered probi are repored in Appendix A. Conribuions o Economic Analysis & Policy

22 20 Vol. 4 [2005], No. 1, Aricle 13 Curren Financing Round Table 4. Valuaion of Privae Equiy Firms 1987:I hrough 2003:II (-raios in parenheses) Uncorreced Models Selecion Correced Models Repea Hybrid Repea Hybrid Seed (162.39) (199.23) (102.32) (128.44) Firs (217.98) (293.71) (109.62) (144.52) Early (247.94) (320.42) (101.62) (130.86) Lae (233.90) (284.00) (103.91) (131.79) Mezzanine (199.11) (222.46) (100.30) (124.17) IPO (241.56) (309.74) (92.63) (119.66) Acquisiion (225.69) (292.63) (92.81) (118.94) Developmen Saus Produc Developmen (2.25) (1.54) (2.12) (1.16) Bea Tesing (2.76) (2.74) (2.23) (2.06) Clinical Trials (0.1622) (0.61) (0.11) (0.70) hp://

23 Hwang e al.: An Index for Venure Capial, Table 4. (coninued) Valuaion of Privae Equiy Firms 1987:I hrough 2003:II (-raios in parenheses) Uncorreced Models Selecion Correced Models Repea Hybrid Repea Hybrid Shipping Produc (6.22) (6.67) (6.20) (6.54) Profiable (4.930) (5.11) (4.98) (5.01) Geographical Locaion Norhern California (3.07) (3.19) Souhern California (1.16) (1.20) Massachuses (1.11) (1.19) Texas (2.41) (2.41) Norhern Virginia (0.51) (0.43) NY-NJ (0.28) (0.23) Technology Group Healh Care (1.11) (1.24) Informaion Technology (2.04) (2.20) Conribuions o Economic Analysis & Policy

24 22 Vol. 4 [2005], No. 1, Aricle 13 Table 4. (coninued) Valuaion of Privae Equiy Firms 1987:I hrough 2003:II (-raios in parenheses) Uncorreced Models Selecion Correced Models Repea Hybrid Repea Hybrid Reail and Services (1.41) (1.48) Mills raio (5.46) (6.28) Consan (7.05) (54.96) (6.85) (48.37) λ (167) (7855) (165) (4935) 2 σ μ (19.91) (53.09) (19.79) (52.42) 2 σ η (24.49) (36.64) (24.48) (36.64) R Number of Firms 4,412 9,092 4,412 9,092 Number of Observaions 8,797 13,477 8,797 13,477 Number of Rounds 14,528 19,208 14,528 19,208 Noe: The esimaed model also conains 65 indicaor variables for ime in quarers, from 1987:II hrough 2003:II. (Resuls from comparable models conaining 197 indicaor variables for ime in monhs beginning in February 1987 are available on reques.) The coefficiens of boh ses of hese variables represening ime are repored in Figure 1. hp://

25 Hwang e al.: An Index for Venure Capial, The imporance of sample selecion bias in he saisical models is quie large indeed. Value of a firm ha has a weny five percen probabiliy of having 1 a pricing even revealing value in he sample ( ϖ = φ( Φ ( 0.75) ) 0.75 = ) is abou en percen lower han he value of a firm wih a 75 percen probabiliy 1 ( ϖ = φ( Φ ( 0.25) ) 0.25 = ) of experiencing a pricing even which reveals value. Correcing for selecion bias influences boh he level and precision of he measuremen of he value of he sock of privae equiy which we impue from he sample of firms receiving funding in any period. The coefficiens of he selecionbias-correced models are more precisely esimaed, and he coefficiens of he more-efficienly-esimaed hybrid model differ from hose of he uncorreced model. 8 As noed, each valuaion model also includes a se of variables represening calendar ime. Figure 1 graphs he nominal price index derived from hese variables as well as he 90 percen confidence inerval of ha index. The figure is based upon he preferred specificaion: he bias-correced hybrid model of valuaion repored in Table 4, column 4. Figure 1A presens he resuls based upon he dummy variables represening each quarer. Figure 1B presens he resuls using he dummy variables designaing each quarer. The ime paern of he esimaed subsanially more volaile, bu of course his also reflecs he increased sampling error wih a highly disaggregaed represenaion of ime. The index in Figure 1 racks he valuaion of a sandardized venure firm (where firms are sandardized by he characerisics repored in Table 4). The figure repors ha his index of venure company prices falls during he early days of he sample, sars o rise in he mid-1990s, reaching is peak a he firs quarer of 2000 (he index value of ). Since hen, he index falls dramaically, ending up a less han 50 in he second quarer of I is, of course, possible ha he specific variables which appear in he selecion equaion do no fully idenify ha equaion. For example, he elapsed ime variables which are highly significan in he selecion equaion migh independenly affec firm valuaion, given selecion. In his case, he selecion and valuaion equaions would only be idenified by he funcional form of he equaions and he join normaliy assumed in he error erms. We can provide some evidence on his by relaxing he parameric resricions on he relaionship imposed by he funcional form (See Ahn and Powell, 1993). To do his, we re-esimaed he resuls repored in Table 4 using he inverse Mills raio, is square, and is cube as righ hand side variables. In his reformulaed model, he higher order erms were saisically significan in he valuaion equaion, bu he esimaed index was insensiive o his variaion in funcional form. Of course, his does no insure ha he resuls are insensiive o oher variaions in funcional form which depar from join normaliy. As wih many ohers who have applied he Hecki echnique, we would have preferred o rely upon heoreically unambiguous variables o idenify he selecion mechanism. Conribuions o Economic Analysis & Policy

26 24 Vol. 4 [2005], No. 1, Aricle 13 Figure 1. A. Quarerly Valuaion Index of Privae Equiy Firms, (90 percen confidence inerval in dashed lines) Index (1987:1=100) Year B. Monhly Valuaion Index of Privae Equiy Firms, (90 percen confidence inerval in dashed lines) Index (Jan 1987 =100) Year hp://

27 Hwang e al.: An Index for Venure Capial, Figure 2. Hybrid Quarerly Valuaion Index of Privae Equiy Firms: Seleciviy Correced and Uncorreced Price Indexes Valuaion Index wih Correcion Valuaion Index wihou Correcion Figure 2 compares he seleciviy-correced index of privae equiy wih he uncorreced index. I plos he quarerly index esimaed from column 2 and 4 of Table 4. The seleciviy correced index is lower han he uncorreced index, reflecing he fac ha he firms which reveal value a any ime are no a random sample from he populaion. The uncorreced index is also much higher han he correced index a he peak of privae equiy values in As repored above, we experimened wih alernaive orderings of oucomes in he probi model, finding lile change in he probi resuls when oucomes 5 and 6 were re-ordered, and significanly worse resuls when oucomes 2 and 3 were re-ordered. When Mills raios compued from hese alernaive probi models are included in he valuaion equaion, hey lead o only small changes in valuaion esimaes. When oucomes 5 and 6 are reordered, he R 2 in he valuaion equaion is unchanged, he average log reurn of index is idenical and he sandard deviaion of log reurns is he same. When oucomes 2 and 3 are reordered, he R 2 in he valuaion equaion is marginally reduced, he mean log index of reurns declines from o and he sandard deviaion is marginally reduced as well. The esimaed indexes are virually idenical o hose repored in Figure 1A. Conribuions o Economic Analysis & Policy

28 26 Vol. 4 [2005], No. 1, Aricle 13 V. An Applicaion The price index derived in he previous secion faciliaes some suggesive ex pos comparisons beween invesmen in venure capial and invesmen in oher financial insrumens such as common socks. Of course, wih curren insiuional arrangemens, i is quie easy o inves in a pool of common socks, for example in a muual fund or derivaive of he S&P500. While venure capial was growing in imporance during he 1990s (measured by he amouns ousanding), i is direcly accessible as an invesmen for individuals only if hey are accredied invesors, while indirec invesmens for individuals are possible hrough pension funds. In his secion, we illusrae he poenial role for privae equiy funds in invesmen porfolios and assess he possible improvemens in he efficien mean-variance fronier made possible by including venure capial in a porfolio. Specifically, we consider a fund or a porfolio which consiss of all he firms in he Sand Hill daabase wih valuaion informaion during he period and As noed above, his daabase is he neares hing o a comprehensive invenory of he venure capial secor. The iniial porfolio consiss of he venure firms ha have valuaion evens in he firs quarer of When a new firm has a valuaion even, i eners he porfolio in ha quarer, and when a firm exis by shudown, acquisiion or IPO, i is removed from he porfolio. Therefore, a firm will remain in he porfolio as long as here is no exi even. When a firm exis successfully by acquisiion or IPO, is proceeds are reinvesed in he privae equiy porfolio. For a firm in he porfolio, is value can be affeced by changes in he index or by changes in firm aribues, according o (5e), in a valuaion even. Valuaion evens can be inermediae rounds or exi rounds. Inermediae funding evens can affec he hypoheical privae equiy porfolio value, bu porfolio reurns due o inermediae evens do no represen acual reurns for he invesor since i is quie difficul o realize capial gains (or losses) prior o exi rounds. Table 5 repors he performance of privae equiy invesmens when he invesmen is based solely on he index, on he index and exi rounds, and on he index and all he funding rounds. There are subsanial differences in he invesmen reurns by index only and he invesmen reurns by index and exi rounds. For he whole sample period, he difference is 2.8 percen per quarer, and for he period of 1987 hrough 2000, he difference is 3.2 percen. In conras, he difference beween he invesmen reurns based on exi rounds and he invesmen reurns based on all funding rounds is relaively small, 0.2 percen for he whole sample period and 0.4 percen for he period of 1987 hrough This shows ha mos of invesmen performance comes from exi rounds, no hp://