Capital Commitment Considerations

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1 UBS Alernave Invesmens 6 Sepember Invesng n Prvae Equy apal ommmen onsderaons ghlghs Page ommmen Issues omplcaons Framework for eermnng ommmens and ash Flows ommmen Sraegy Insghs 4 Seady Sae Invesmen and Lqudaon aes 5 Lmaons of Ths Framework 6 oncluson 6 UBS Fnancal Servces Inc. (UBS FS) s pleased o provde you wh nformaon abou alernave nvesmens. There are a few pons we would lke o rase wh you a he ouse. Ths arcle s for educaonal and nformaonal purposes only. I does no consue nvesmen advce. Among oher hngs, does no ake no accoun your personal fnancal suaon, or your nvesmen goals or sraeges. You should no consrue any nformaon provded here o be an nvesmen recommendaon for you o follow. You should conac your Fnancal Advsor for nformaon or recommendaons ha may be useful specfcally o you. Alhough all nformaon and opnons expressed n hs documen were obaned from sources beleved o be relable and n good fah, no represenaon or warrany, express or mpled, s made as o s accuracy or compleeness, and may no be reled upon as such. Any opnons expressed or nformaon provded n hs documen s subjec o change whou noce, and UBS FS has no oblgaon o updae such opnon or nformaon. Ths paper explores capal commmen ssues and cash-flow managemen ssues n prvae equy fund nvesng. We fnd ha achevng a argeed level of allocaon o prvae equy s a funcon of he pace of capal deploymen as well as dependen upon he desred amoun of argeed exposure. I s also dependen on he spread of realzed reurns n prvae equy versus oher asse classes, as well as on mng and realzaon perods for capal already nvesed. I provdes a heorecal framework o srucure prvae equy capal commmen ssues n a formal manner, defnes varables, nerrelaonshps and boundares n such a way ha he problem can be worked upon. We wll be buldng on hs foundaon o creae an mplemenable praccal mehodology n a subsequen repor. Key Takeaways gher argeed levels of prvae equy allocaons requre hgher upfron commmen levels. Faser growh n prvae equy reurns reduces requred commmens, snce he nvesor can reach he same seady sae allocaon as a percenage of he overall porfolo, wh less capal. Faser overall porfolo growh ncreases requred upfron commmens, snce he desred allocaon n dollar erms ncreases as he porfolo growh ncreases. Longer drawdown perods requre hgher nal commmen levels o reach seady sae allocaons, snce he capal accumulaon rae s slower. Longer lqudaon perods reduce nal commmen levels, snce he capal lqudaon rae s slower.

2 UBS Alernave Invesmens 6 Sepember ommmen Issues As descrbed n greaer deal n edons of he UBS Prvae Equy Educaon Seres, prvae equy fundrasng and deploymen s referred o as makng commmens because no all fundng s made avalable mmedaely o he fund vehcle. aher, funds are called up as projecs covered by he prvae equy vehcle s mandae become avalable. When commng o a prvae equy fund, he commmen s ypcally o provde cash o he fund on shor noce from he eneral Parner. eneral Parners of a fund draw down capal from he Lmed Parners as and when hey make nvesmens. eneral Parners call down capal only as hey requre, raher han n pre-se amouns accordng o a rgd meable. If an nvesor fals o fund a capal call from a fund when due, he fund may exercse varous remedes wh respec o such nvesors o forfe, or sell, all or a poron, of s neres n he fund or requrng ha he nvesor mmedaely pay up he full amoun of her remanng capal commmen. Invesors are ypcally requred o fund only a small percenage of her oal capal commmen a he ouse. Ths nal fundng s followed by subsequen capal draw-downs (he mng and sze of whch are generally made known o he nvesor a few days n advance), as needed by he fund o make new nvesmens. Jus-n-me draw-downs are used o mnmze he amoun of me ha a fund holds unnvesed cash, whch s a drag on fund performance, All of hs nroduces uncerany n he cash flows of prvae equy nvesmens. The unpredcably of cash flows apples o boh capal calls, whch he nvesor mus fulfll a earler sages, and dsrbuons o he nvesor a laer sages. In boh cases he amoun and mng of cash flows s a he dscreon of he fund manager. ence, he mporance of carefully consderng cash flow needs n porfolos and plannng for commmens ha have already been made. omplcaons Unceran ash-flows Lead o Unceran ommmen Sraeges I gves rse o quesons of wha s an approprae commmen sraegy gven: () Uncerany abou capal draw-downs, () Uncerany abou capal dsrbuons, (3) Meeng arge allocaons o porfolo allocaon over long me perods. Oher quesons arse such as wha does one do wh undrawn, commed nvesmens? Invesors are requred o make a range of decsons: keep n cash (rskless), allocae proporonaely o he res of he porfolo and so on. Naurally hs depends a lo on he nvesmen objecves and he characerscs of he exsng porfolo. Added rsks (e.g., wha happens f one pus he unnvesed, bu commed capal no a publc proxy and markes are depressed a he precse me capal s beng called?) are consderaons worh nvesgang. ebalancng ebalancng s a relaed ssue; clearly here s an asymmery n he ably o rebalance a porfolo ha consss of llqud nvesmens n prvae equy and lqud radonal nvesmens such as publcly raded socks. If prvae equy, for example, grows faser han oher asse classes, hen one canno easly rebalance he rsks n one's porfolo necessarly; f grows more slowly, hen here s no ssue. Wha does hs mean for he porfolo over he long erm? learly, one approach s o accoun for hs before happens and moderae one's nvesmens. Bu, when does, should one rebalance no more fxed ncome whle one s over-allocaed? Ignore? Ths s parcularly neresng when one consders ha here mgh be accal mplcaons abou mng of enry no he prvae space whch also mus be houghfully addressed. Transonal Plannng A relaed ssue s ranson plannng n he sense ha he commmen sraegy wll dffer beween an nvesor sarng a a zero allocaon and rampng up o a arge allocaon versus one who s replacng a pece of a regular program every year. The reason here s ha cash ouflows from a rampng up program are no he same from a regular, vnage-year dversfed program. onracng oss Fnally, here are oher ssues whch are clearly mporan: ax, ransacon coss, ec. Framework for eermnng ommmens and ash-flows In order o brng rgor o an approach ha may help elucdae mporan consderaons n makng prvae equy commmens, whn he larger conex of a porfolo allocaon, we propose a heorecal model here. Unforunaely here s no escapng he algebra behnd hs model, bu we do hope ha our conclusons follow logcally from.

3 UBS Alernave Invesmens 6 Sepember We assume a model n whch each asse class grows a a deermnsc rae, and he mng of prvae equy drawdown and lqudaons s ceran. We furher assume ha an nvesor would lke o manan a consan percenage allocaon o prvae equy, and needs o choose a commmen sraegy o oban hs desred allocaon. Model We can model he nvesor s porfolo as follows: I Inal value of nvesor s capal (.e., oal sarng porfolo value) TPE Invesor s arge prvae equy allocaon, n percen rowh facor of prvae equy nvesmens rowh facor of opmal porfolo Inal commmen a = Years o nves commmen (.e., / raw own ae) Invesmen holdng perod I New amoun nvesed, or drawn down, a end of perod L Lqudaons a me perod. Ths amoun may be renvesed n he fund or reurned o nvesors. P Toal prvae equy dollars nvesed a end of perod Inuvely, n order o manan a consan seady sae allocaon o prvae equy, he growh n commmens over me mus equal he growh n he opmal porfolo. Ths mples ha =. Furhermore, he dsbursemens a any me wll equal he new amoun nvesed a me, mulpled by he growh facor n prvae equy. In oher words, L = I -. Usng hs ermnology, we can model he prvae equy dollars nvesed a any pon n me as: P P I L () Each commmen,, s nvesed unformly a he end of each year for years. Therefore, f an nvesor comms n year, / s nvesed each year beween years and +. Based on hs, we can defne I as: I () Snce -(- ) s equal o -(-), we can re-wre () as: I (3) ( ) Smlarly, we can defne L as: L I (4) ( ) whch may be eher renvesed or reurned o nvesors. Subsung (3) and (4) no () provdes: P P ( ) Ths can be smplfed as: P P (5) ( ) (6) ( ) ven (6), how should he nvesor manage hs commmens n order o reach hs desred prvae equy allocaon? Assume ha he nvesor wans o acheve a 3

4 UBS Alernave Invesmens 6 Sepember arge prvae equy allocaon, TPE, of hs porfolo value. If he porfolo s compoundng a a facor, hen he nvesor s desred dollar nvesmen n prvae equy a me s:. Targe Prvae Equy Invesmen, P gher levels of prvae equy allocaons requre hgher commmen levels. P TPE I P (7) Subsung (7) no (6) and rearrangng he erms yelds: P P (8) We dsngush he sgn of he frs paral dervave by conemplang equaon and fnd o be posve. P P d dp P (9). Prvae Equy rowh ae, Faser growh n prvae equy reduces requred commmens, snce he nvesor can reach he same seady sae allocaon wh less capal. P () Equaon () esablshes he nal level of commmen an nvesor ough o make o prvae equy assumng ha a varey of varables are perfecly predcable ( as we have made smplfyng assumpons). espe he consrans we have mposed hs s a powerful equaon for provdes neresng nsghs. ommmen Sraegy Insghs Equaon () llusraes ha he prvae equy commmen level depends on fve facors: Assumpons:,,. We nend o explore he effec of hese varables, acng severally as well as jonly on opmal commmen sraegy, furher n a fuure research paper. We dsngush he sgn of he frs paral dervave by conemplang equaon and fnd o be negave. d For, d le K P d d d d ( ) 3 d d K d d Alernavely, we may also use nuon.. 4

5 UBS Alernave Invesmens 6 Sepember As ncreases, each erm n he denomnaor ncreases, so and decreases as well. d, d < decreases d For, d le M P d ( )( ln ) d d d 3. Porfolo rowh ae, Faser porfolo growh ncreases requred commmens, snce he desred allocaon n dollar erms ncreases as he porfolo growh ncreases. s exremely complex n s analycal form so s helpful o examne hs nuvely P P P / / / / As ncreases, every erm n he denomnaor decreases, whch means ha he denomnaor decreases and ncreases..e. d d > 4. rawdown ycle, Longer drawdown perods requre hgher nal commmen levels o reach seady sae allocaons, snce he capal accumulaon rae s slower. We dsngush he sgn of he frs paral dervave by conemplang equaon and fnd o be posve. ( ) and d d ln x e x x x ln whch shows ha, so For he laer, we use for all and se d d 5. Lqudaon Perod, L Longer lqudaon perods reduce nal commmen levels, snce he capal lqudaon rae s slower. Ths s self evden from our defnon: L = I - when d combned wh Insgh # e., d < Seady Sae Invesmen and Lqudaon aes Usng he above model, we can compue he seady sae nvesmen and lqudaon raes as a funcon of unfunded commmens and oal nvesmens, respecvely. More formally, we would lke formulas for IN and I, where: I = IN x -, and () 5

6 UBS Alernave Invesmens 6 Sepember L = I x P - () We know ha n perod, a poron of he new commmens from -, -,, - wll be nvesed. Therefore, we can resae I as: I (3) Also, n he real world one needs o make accommodaons for exogenous facors. For nsance, cyclcal facors such as perods of under commmen and over commmen nfluence capal deploymen raes. In general drawdown raes are lower when commmen raes are hgh. The effec s more pronounced n frs-year nvesmen raes. Ths phenomenon may parally be explaned by he followng hypohess: ecognzng ha he commmens grow each year a he same rae as he porfolo, we can rewre (3) as: emand for prvae equy funds s cyclcal and s a funcon of he busness cycle. I (4) Equaon 4 denfes he new amoun nvesed, or drawn down, a end of perod o compue he seady sae nvesmen rae for mananng dynamc equlbrum. Lmaons of Ths Framework The model we have descrbed here, whls useful o frame ssues deermnscally suffers naurally from shorfalls; n he real world nvesors face many ypes of uncerany ha mpac her prvae equy allocaons such as : eurns The reurns for boh he porfolo and he prvae equy allocaon are unceran. ash Flows The drawdown schedule and he nvesmen horzon/ realzaon mngs are unceran. Valuaon Invesors do no observe rue prvae equy valuaons; he observed valuaons conan some error, snce he prces are no marked-o-marke. These forms of uncerany have wo mplcaons for nvesors. Frs, hey change he arge prvae equy allocaon for mos nvesors. Second, hey may change he opmal commmen sraegy. There are no easy soluons o addressng hese ssues. Answers range from assumng ha expeced reurns, draw-downs/ cash-flows and valuaons are () sorcally arrved a, or () Mone arlo smulaed under smplfyng dsrbuonal assumpons. Supply of prvae equy funds s scky n he shor run and responds o demand wh a lag. Increases n he supply of prvae equy mply ougher compeon for capal deploymen n subsequen perods ( money chasng deals ). Thus, we ofen observe anecdoally reduced capal deploymen n he frs hree years The mplcaons of hs observaon are ha nvesors may expec her money o be nvesed a lower raes afer srong fundrasng perods. onsequen reurns, as measured by Is, may be lower because dsrbuons are also lkely o ake longer. oes hs means ha nvesors should say away from prvae equy when fund rasng s srong? Probably no. oes hs means ha nvesors should gravae o prvae equy when fund rasng s weak? Probably no, once agan. oncluson Invesors n a prvae equy fund comm o provdng a pre-agreed sum of capal o he fund over a specfed perod of me. Ths s called he Lmed Parners apal ommmen. owever, he enre fundng may no be needed mmedaely. The eneral Parner draws down or calls he capal over a perod of me when nvesmen opporunes arse. rawdown usually occurs over a four o fve year nvesmen perod, hough hs can be sooner as seen n some recen vnages. The flexbly o call capal on an as needed bass, wh a few weeks noce, reduces cash drag on overall fund reurns. Some nvesors monor for mng ssues beween drawdown and deploymen when hey qualavely evaluae performance. ven uncerany n capal calls nvesors need o plan her cash flows as well as develop nvesng sraeges o mee desred exposure levels o prvae equy over a long perod of me. Ths paper provdes a framework o explore hese ssues sll furher. 6

7 UBS Alernave Invesmens 6 Sepember Alernave Invesmen Funds sk sclosure Ineress of Alernave Invesmen Funds (he Funds ) are sold only o qualfed nvesors, and only by means of offerng documens ha nclude nformaon abou he rsks, performance and expenses of he Funds, and whch lens are urged o read carefully before subscrbng and rean. Ths communcaon s confdenal, s nended solely for he nformaon of he person o whom has been delvered, and should no be reproduced or oherwse dsrbued, n whole or n par, o hrd pares. Ths s no an offer o sell any neress of any Fund, and s no a solcaon of an offer o purchase hem. An nvesmen n a Fund s speculave and nvolves sgnfcan rsks. The Funds are no muual funds and are no subjec o he same regulaory requremens as muual funds. The Funds' performance may be volale, and nvesors may lose all or a subsanal amoun of her nvesmen n a Fund. The Funds may engage n leveragng and oher speculave nvesmen pracces ha may ncrease he rsk of nvesmen loss. Ineress of he Funds ypcally wll be llqud and subjec o resrcons on ransfer. The Funds may no be requred o provde perodc prcng or valuaon nformaon o nvesors. Fund nvesmen programs generally nvolve complex ax sraeges and here may be delays n dsrbung ax nformaon o nvesors. The Funds are subjec o hgh fees, ncludng managemen fees and oher fees and expenses, all of whch wll reduce profs. The Funds may flucuae n value. An nvesmen n he Funds s long-erm, here s generally no secondary marke for he neress of he Fund, and none s expeced o develop. Ineress n he Funds are no deposs or oblgaons of, or guaraneed or endorsed by, any bank or oher nsured deposory nsuon, and are no federally nsured by he Federal epos Insurance orporaon, he Federal eserve Board, or any oher governmenal agency. Prospecve nvesors should undersand hese rsks and have he fnancal ably and wllngness o accep hem for an exended perod of me before makng an nvesmen n a Fund. Invesors should consder a Fund as a supplemen o an overall nvesmen program. In addon o he rsks ha apply o alernave nvesmens generally, here are rsks specfcally assocaed wh nvesng n hedge funds, whch may nclude hose assocaed wh nvesng n shor sales, opons, small-cap socks, junk bonds, dervaves, dsressed secures, non-u.s. secures and llqud nvesmens. Ths documen s for educaonal and nformaonal purposes only. I does no consue nvesmen advce. Among oher hngs, does no ake no accoun your personal fnancal suaon, or your nvesmen goals or sraeges. You should no consrue any nformaon provded here o be an nvesmen recommendaon for you o follow. You should conac your Fnancal Advsor for nformaon or recommendaons ha may be useful specfcally o you. Alhough all nformaon and opnons expressed n hs documen were obaned from sources beleved o be relable and n good fah, no represenaon or warrany, express or mpled, s made as o s accuracy or compleeness, and may no be reled upon as such. Any opnons expressed or nformaon provded n hs documen s subjec o change whou noce, and UBS Fnancal Servces Inc. has no oblgaon o updae such opnon or nformaon. Neher UBS Fnancal Servces nor s Fnancal Advsors provde ax or legal advce. lens should be advsed o conac her personal ax and/or legal advsors regardng her ndvdual suaons. Opons are rsky and are no suable for everyone. Please read he Opons learng orporaon Publcaon led "haracerscs and sks of Sandardzed Opons Tradng". Ths Publcaon can be obaned from a Fnancal Advsor, or can be accessed under he Publcaons Secon of he Opon learng orporaon's webse a oponsclearng.com. 7