A Model of Private Equity Fund Compensation


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1 A Model of Prvate Equty Fund Compensaton Wonho Wlson Cho Andrew Metrck Ayako Yasuda KAIST Yale School of Management Unversty of Calforna at Davs June 26, 2011 Abstract: Ths paper analyzes the economcs of the prvate equty fund compensaton. We buld a novel model to estmate the expected revenue to fund managers as a functon of ther nvestor contracts. In partcular, we evaluate the present value of the farvalue test (FVT) carred nterest scheme, whch s one of the most common proftsharng arrangements observed n practce. We extend the smulaton model developed n Metrck and Yasuda (2010a) and compare the relatve values of the FVT carry scheme to other benchmark carry schemes. We fnd that the FVT carry scheme s substantally more valuable to the fund managers than other commonly observed (and more conservatve) carry schemes, largely due to the early tmng of carry compensaton that frequently occurs under the FVT scheme. Interestngly, condtonal on havng a FVT carry scheme, fund managers ncremental gans from nflatng the reported values of the funds unexted portfolo companes are neglgble. JEL classfcaton: G1, G2 Keywords: prvate equty; venture captal; fund managers; Ths paper was prevously ttled as Expected Carred Interest for Prvate Equty Funds. All errors and omssons are our own. 1
2 1. Introducton Prvate equty funds are typcally organzed as lmted partnershps, wth prvate equty frms servng as general partners (GPs) of the funds and nvestors provdng captal as lmted partners (LPs). These partnershps usually last for ten years, and partnershp agreements (nvestor contracts) sgned at the funds nceptons clearly defne the expected GP compensaton. Snce the payments to GPs can account for a sgnfcant porton of the total cash flows of the fund, the fund fee structure s a crtcal determnant of the expected net fund returns that the LPs receve. Metrck and Yasuda (2010a) estmate the expected present value of the compensaton to GPs as a functon of the fee structure specfed n nvestor contracts, but do not consder the farvalue test (FVT) scheme, whch s one of the most commonly used carred nterest schemes n practce. In ths paper, we evaluate the present value of the FVT carred nterest scheme by extendng the smulaton model developed n Metrck and Yasuda (2010a), and compare the relatve values of the FVT carry scheme to other benchmark carry schemes. The FVT carred nterest scheme allows early carry payments before the fund s carry bass has been returned to nvestors f certan condtons are met. The FVT scheme s almost always accompaned by clawback; thus, the fnal nomnal amount of carry for the fund s lfetme s unchanged whether the fund uses a FVT scheme or a more conservatve carry tmng scheme, holdng all other fund terms (such as carry % level) equal. In other words, the man mpact of the FVT scheme derves from the tme value of money. The condtons for the FVT scheme are twofold. Frst, upon any ext, the cost bases of all exted or wrttenoff companes to date must be returned to LPs before any dstrbuton to GPs. In addton, the dstrbuton to GPs s made only f the sum of the far values of all unexted (.e., remanng) companes under management at the tme of the ext equals or exceeds a threshold 2
3 value, defned as a multple of the total cost bases of unexted nvestments wth the most typcal multple beng 1.2 (120%). The far values of remanng nvestments cannot be easly marked to market snce these prvate equty nvestments are llqud by nature; n practce, estmate values that are reported by GPs are used. Snce GPs are thought to possess an nformaton advantage over LPs as nsders, the nformaton asymmetry between them gves rse to a potental agency problem when GPs use selfreported portfolo values to calculate ther carred nterest. We nvestgate whether GPs are tempted to nflate the portfolo values of unexted companes by examnng the effects of nflated values on the expected PV of GP compensaton. In our analyses, we extend the model employed n Metrck and Yasuda (2010a) by mappng the ext tmng and ext values of portfolo nvestments as well as the nterm values of unexted nvestments nto the tmng and amount of GP carry accordng to the FVT carry scheme. We obtan detaled nformaton on the terms and condtons for farvalue tests used n practce from a large anonymous nvestor who also provded other nformaton for the analyses n Metrck and Yasuda (2010a). We match the parameter values of our FVT model to the values most commonly used n these actual funds. We then compare the expected GP compensaton of the fund wth a FVT carry scheme to those of two other benchmark funds. Our fndngs generally ndcate that the FVT carry scheme s substantally more valuable to the fund managers than other commonly observed (and more conservatve) carry schemes, but nterestngly, condtonal on havng a FVT carry scheme, fund managers ncremental gans from nflatng the reported values of the funds unexted portfolo companes are neglgble. The remander of the paper s organzed as follows. In secton 2, we descrbe a model of prvate equty fund compensaton n a rskneutral prcng framework. In secton 3, we report the model outputs as a functon of varous nput values. We conclude n secton 4. 3
4 2. A Model of Prvate Equty Fund Compensaton Whle management fees are based on the cost bases of fund portfolo nvestments (and/or the fund sze), the amount of carred nterest (= carry) receved by GPs s based n general on the tmng and ext values of portfolo companes and thus s senstve to fund performance. In the FVT carry scheme, the tmng and amount of GP carry also depends on the nterm values of unexted portfolo companes. In ths secton, we descrbe a rskneutral valuaton method for the estmaton of the PV of carry startng wth determnng the ntal nvestment value of a portfolo company. We then specfy the dynamcs of the company value durng the holdng perod, the stochastc ext tme pont, and the values of exted and all other unexted nvestments n the fund portfolo at every ext tme pont. We fnally apply varous functons that correspond to specfc proft sharng rules by mappng the ext values of portfolo companes to the amount of GP carry. 2.1 Rskneutral valuaton The estmaton of the present value of GP carry for a VC/PE fund s complcated because approprate dscount rates are hard to be estmated emprcally. Snce nvestments are llqud and ndvdual project returns are not fully realzed untl the end of the fund lfe, usually ten years, t s not easy to measure rsk ( beta ) at the fund level, usng standard tmeseres correlatons wth the market and other factor returns. Many of the studes that employ fundlevel cash flow data make an effectve assumpton that market beta for the asset class s 1. 1 In ths analyss, we take a rskneutral valuaton approach and buld a smulaton model to overcome ths data problem whle matchng parameter values of the smulaton model to those that are 1 See Secton 4.1 of Metrck and Yasuda (2011) and the ctatons theren. 4
5 supported by emprcal evdence wherever estmates are avalable Intal nvestment values Snce GPs receve a stream of semfxed compensaton through management fees and these fees come out of commtted captal, the nvestment captal that can be used for nvestments s always less than the commtted captal that s delegated by LPs. Snce a mnmum necessary condton for any type of equlbrum should state that at least the commtted captal be returned to LPs n expectaton, GPs must somehow create values to reconcle the gap between the nvestment captal and the commtted captal. For example, the value creaton may come from the possblty that GPs make a lucratve purchase at a low prce, and from the possblty that GPs has a specal skll to mprove the value through tme. We estmate the amount of the value creaton by mposng the condton that the commtted captal s guaranteed to be returned to LPs, and calculate the ntal nvestment value of $110M by addng the estmated amount of the value creaton to the nvestment captal. Then, for the ntal nvestment value, we smulate the value paths by assumng processes as descrbed n the followng secton. 2.3 The dynamcs of the value of a portfolo company Let X t be the market value of a portfolo company. It s assumed to follow a Gaussan dffuson process n a rsk neutral world of the followng form: dx t, (1) rdt 1 2 dw F t dw t X t where r s the rskfree rate and s the volatlty of the nvestment. Note that W F and t W t 2 See Secton 2.2 of Metrck and Yasuda (2010) for more detaled dscussons. 5
6 are standard Brownan motons, whch are mutually ndependent where W t s specfc to a portfolo company and W tf s common across portfolo companes. By assumng the dffuson process as such, captures the correlaton between the values of a portfolo company and the common factor. We further assume that W t and W t j j are uncorrelated so that corr d ln X j t, d ln X t 2. 3 It s mportant to pont out that the process s not for the ntrnsc value of a company, but for ts market value. The ntrnsc value of an llqud asset s generally dfferent from ts market value that would be apprased once t becomes tradable. However, the carry dstrbutons to GPs could occur only when a fund makes any ext after whch the exted company becomes less llqud. For ths reason, we assume that the proceeds from an exted company at any ext are equvalent to ts market value whle gnorng some frctons 4. It s also mportant to note that ths assumpton makes our rskneutral valuaton method consstent. Although the nterm values of unexted companes under management mght not be close to the market values, the nterm values are not correlated wth the exted values n our model, so the assumpton of the market value for unexted companes s not nconsstent wth the rskneutral valuaton. 2.4 Random nvestment duraton and random ext tme pont Random nvestment duraton d Let be the nvestment duraton for a portfolo company. We specfy d as a 3 Ths correlaton structure n a stochastc process s wdely used n credt rsk management and commonly known as onefactor Gaussan copula (see, e.g., Brys and De Varenne (1997), Duffe and Sngleton (2003), Hull (2007), and Schonbucher (2003)). 4 A majorty of exts are made through IPOs or sales to other companes. Whle the proceeds from an IPO are close to the market value (net of underwrtng fees and etc.), the proceeds from prvate sales may be dfferent from the market value. For the purpose of our analyss, we gnore these dfferences. 6
7 random varable that follows an exponental dstrbuton wth the nstantaneous hazard rate of. Furthermore, d s assumed to be ndependent of the company value. d f ( d ) e ( d 0) (2) For the benchmark case, we use the ext rate of 20% snce the nvestment perod for early VC nvestments typcally lasts for 5 years. 5 Random ext tme Prvate equty funds make an nvestment n a portfolo company at any tme pont durng the nvestment perod of the frst several years. Denote the tme pont of an nvestment n a portfolo company by s. Then, the ext tme pont t for a portfolo company s the sum of s and d. 2.5 Far value and ext value The far value of a managed portfolo s the sum of the far values of ndvdual portfolo companes under management. At tme t, a portfolo company s under management f and only f s t t. Gven the dffuson process (1), the far value of an ndvdual portfolo company ( FV t ) follows a lognormal dstrbuton: For s t, t FV t X t where ln X t ~ N ln X S r 2 t s, 2 t s 2. (3) 5 See Metrck and Yasuda (2010b). 7
8 Smlarly, the ext value of a portfolo company ( EV t ) at ts ext t follows a lognormal dstrbuton: For t, t EV t X t where ln X t ~ N ln X S r 2 t s, 2 t s 2. (4) 2.6 Mappng to carry amount In our analyss, we consder three funds that apply dfferent carry rules separately as follows. Fund I: a fund wth no hurdle, contrbuted/nvested captal returned frst, wth clawback If the carry base s the commtted captal (nvestment captal), ths fund stpulates a rule that LPs receve the contrbuted captal (nvested captal) before any dstrbuton of carred nterests where the contrbuted captal (nvested captal) s the aggregated cash flow from LPs to GPs for annual fee payments and captal calls (only for captal calls). If ths rule s volated, 6 GPs should return some porton of ther early carred nterests as clawback to adhere to the rule at the end of the fund lfe. Fund II: a fund wth commtted/nvestment captal returned frst If the carry base s the commtted captal (nvestment captal), ths fund guarantees that LPs receve the commtted captal (nvestment captal) before any dstrbuton of carred nterests. 6 Ths rule s often volated f the proceeds from later exts are not suffcent. 8
9 Fund III: a fund wth a farvalue test, wth clawback If the carry base s the commtted captal (nvestment captal), ths fund stpulates a rule that LPs receve the cost bases of all exted companes before any dstrbuton of carred nterests where the cost bases are the aggregated captal nvested n all exted companes plus prorated management fees (only the aggregated captal nvested n all exted companes). The dfference n the amounts between cumulatve ext values and the cost bases can be dstrbuted to GPs at a certan multple (= carry level) f a farvalue test s met. If a farvalue test s met, t s the case n whch the far values of all unexted companes under management exceed the cost bases of these companes multpled by a certan percentage (= FVT threshold level) that s greater than or equal to 100%. If a farvalue test s not met, the dfference n the amounts can be pad to LPs for the reducton of cost bases untl the FVT s met. If ths rule s volated, GPs should return some porton of ther early carred nterest as clawback to adhere to the rule at the end of the fund lfe. 3. Model Outputs Assessng the present value of a GP carry scheme s analogous to prcng a basket call opton. Although a basket opton can be prced approxmately n a closed form, 8 the evaluaton of a GP carry scheme s more complcated manly because (1) the number of assets n the portfolo changes over tme, and (2) the strke prce ether gradually ncreases durng the nvestment perod, or fluctuates throughout the fund lfe, dependng on the carry schemes. For these reasons, we rely on Monte Carlo smulaton. To analyze the GP carry as a functon of the value paths of portfolo companes wth smulaton, we take the followng assumptons. 8 A basket opton s an opton on a portfolo of assets wth a predetermned strke prce. A basket opton can be prced only approxmately n a closed form. See Gentle (1993) and Huynh (1994) for lognormal approxmatons and Mlevsky and Posner (1998) for a recprocal Gamma approxmaton. 9
10 (1) A fund makes the predetermned number of nvestments wth equal szes. (2) Investments are made at the begnnng of each calendar year durng the frst 5 years. All possble exts are also made at the begnnng of each calendar year. (3) A fund s lqudated at the end of the 12 th year from ts ncepton. Under these assumptons, we make 10,000 Monte Carlo smulatons and get the average of GP carry usng the varous set of nput numbers n the table Effect of carry tmng A farvalue test, f t s passed, would enable GP to collect early carry, but a clawback condton states that at the end of a fund lfe, GP has to return the dfference n the amounts between what he has receved by then (nclusve) and what he would be elgbly enttled wthout the prepayment condton. Due to the clawback condton, the total undscounted amount of GP dstrbuton (Fund III) would be the same as for a fund that returns the commtted captal frst (Fund II). For a smlar reason, when the contrbuted captal s the barrer above whch GP starts to get pad the carred nterests (Fund I), GP possbly receves early carry, but a clawback condton offsets the early payments and makes the aggregate undscounted amount of GP dstrbuton the same as for a fund that returns the commtted captal frst (Fund II). Table 2 llustrates the effect of early carry payments. When the amounts of GP carres are aggregated through tme wthout dscountng as seen n the case of the 0% rskfree rate, the amounts of GP carres are dentcal across these three funds. However, wth a nontrval rskfree rate, t s always the case that; 10
11 Present value of GP carry n a fund that apples the farvalue test (Fund III) > Present value of GP carry n a fund that returns the contrbuted captal frst (Fund I) > Present value of GP carry n a fund that returns the commtted captal frst (Fund II) Ths result shows that n expectaton, GP takes n a larger amount of early carry n Fund III than n Fund I n present value. Furthermore, wth the ncrease of rskfree rates, the dfference between the frst two amounts above gets larger than the dfference between the last two amounts. It ndcates that the present value of GP carry n Fund III s more senstve to rskfree rate ncreases than that n Fund I. 3.2 Effect of nflaton of unexted nvestment values We nvestgate whether GPs are tempted to nflate the portfolo values of unexted companes. Table III examnes the effects of nflated values on the GP compensaton. The benchmark case of 100% s the case n whch the market values are accurately apprased. Relatve to the benchmark case, the present value of GP carry before clawback ncreases slghtly wth the nflated level of 125% from $10.25 to $10.40, and ncreases further but only margnally wth the level of 150% from $10.40 to $ However, t s notceable that a clawback condton eventually kcks n and offsets much of these ncreases. A clawback condton makes the amount of clawback bgger wth a hgher nflaton level of unexted nvestment. Ths s because the total amount of GP dstrbuton (undscounted) s unaffected by the nflaton level. Wth ths offset amount, the present values of GP carry net of clawback across three dfferent nflaton levels exhbt only small dfferences where the small dfferences ndcate the tme value of early carry. 11
12 3.3 Effect of other parameter values We examne the effects of varous parameter values on the present value of GP compensaton across three dfferent funds to nvestgate whether these effects are more or less substantal for Fund III that apples the FVT. We examne the effects along 6 dmensons of ext probabltes, carry levels, carry bass, total volatltes of companes, parwse correlatons between any two portfolo companes, and farvalue threshold levels. Table 4 presents the effects of alterng parameter values for three dfferent funds. The parameter values for the benchmark case are 20% ext probablty, 20% carry level, $100 carry bass (= commtted captal), 90% total volatltes, 50% parwse correlaton, and 120% farvalue threshold level. The present value of GP carry net of clawback s shown n Panel A. The ext probabltes have negatve effects on the present values of GP carry n a concave way across the three levels of 10%, 20%, and 30%. The carry levels have postve effects n a concave way across the three levels of 20%, 25%, and 30%, but the concavty s qute neglgble. When the carry bass changes to the nvestment captal of $82, the magntude and the percentage of the ncreases n the value s the largest for Fund III, and the smallest for Fund II. As expected, ncreases n ether the volatlty of an ndvdual company and or the parwse correlaton lead to hgher compensaton to GPs. However, gven the levels of GP carry net of clawback, the effects of ether volatlty or parwse correlaton are about the same across three dfferent funds. The farvalue threshold levels are the multples for the cost bases of remanng portfolo companes. For the FVT to be passed, the farvalues of remanng portfolo companes should 12
13 exceed the product of ths multple and the managed value. Hence, ths multple affects only Fund III, and makes negatve effects on the present value of GP carry. Panel B presents the effects of varous parameter values on the present values of the clawback. These results generally ndcate that excessve early carry payments are frequently made for Fund III relatve to Fund I. 4. Concluson Ths paper analyzes the economcs of the prvate equty fund compensaton. We analyze the effect of usng a farvalue test GP carry scheme on the tme value of carred nterests. We fnd that whle the use of a farvalue test n GP compensaton tself has a sgnfcant postve effect on the PV of carry relatve to other commonly used carry schemes, GPs gan only a margnal ncrease n ther expected PV of carry by reportng nflated values for the unexted (and therefore llqud) nvestments remanng n ther fund portfolos. Our fndngs suggest that the farvalue test scheme s a favorable compensaton scheme for GPs, but does not seem to nduce GPs to sgnfcantly msreport portfolo values. 13
14 References Brys, E., and F. De Varenne, 1997, Valung Rsky Fxed Rate Debt: An Extenson, Journal of Fnancal and Quanttatve Analyss, 32 (2), Duffe, D. J., and Sngleton, K. J., 2003, Credt Rsk, Prnceton Unversty Press. Gentle, D., 1993, Basket Weavng, Rsk (6) Hull, J. C., 2007, Rsk Management and Fnancal Insttutons, PearsonPrentce Hall. Huynh, C. B., 1994, Back to Baskets, Rsk (7) Metrck, A., and Yasuda, A., 2010a, The Economcs of Prvate Equty Funds, Revew of Fnancal Studes 23, Metrck, A., and Yasuda, A., 2010b, Venture Captal and the Fnance of Innovaton, Hoboken, NJ: John Wley and Sons. Metrck, A., and Yasuda, A., 2011, Venture Captal and Other Prvate Equty: A Survey, European Fnancal Management, forthcomng. Mlevsky, M. A., and S. E. Posner, 1998, A ClosedForm Approxmaton for Valung Basket Optons, Journal of Dervatves, (5) Schonbucher, P.J., 2003, Credt Dervatves Prcng Models, Wley and Sons, New York. 14
15 Table 1. Parameter values for the smulaton model Ths table summarzes the default parameter values for the benchmark case and other nput values consdered for senstvty analyss. In the benchmark case, a venture captal fund makes a total of 25 nvestments of equal szes at the pace of 8, 6, 7, 3, and 1 nvestment(s) at the begnnng of each of the frst 5 years, respectvely. The nvestment pace follows the emprcally observed average nvestment pace as dscussed n Metrck and Yasuda (2010a). From the tme of the nvestment, each portfolo company s assumed to have the nstantaneous hazard rate (= death rate, or ext probablty) of 20%, ndependently wth respect to any other portfolo companes. The market value of a portfolo company at tme t,, s dx t assume to follow rdt 1 2 dw F where the default rskfree rate (r) s 5%, the t dw t X t, volatlty (σ) s 90%, and the parwse correlaton (= ρ 2 ) s 50%. For a gven carry scheme, the default carry level s 20%, the carry bass s 100, the threshold level for the farvalue test s 120%, and the reported value of unexted nvestments s 100% of the actual value (that s prvately observed/assessed by GPs). Whle the carry level and bass determne the amount of carry that GPs are enttled to, the farvalue threshold level and the rato of reported to actual values of unexted nvestments determne the carry tmng. X t Benchmark Varaton Ext probablty 20% 10%, 30% Rskfree rate 5% 4%, 3%, 2%, 1%, 0% Carry level 20% 25%, 30% Carry bass (commtted captal=100, nvestment captal=82) Total volatlty of an nvestment 90% 60%, 120% Parwse correlaton 50% 30%, 70% Farvalue threshold level 120% 112%, 125%, 130% Inflated value of unexted nvestments 100% 125%, 150% 15
16 Table 2. The Effect of Carry Tmng Rules on PV of Carry Ths table presents the smulaton results for the PVs of carred nterest (n $, per $100 of commtted captal) as functons of carry tmng rules and the level of the rskfree rate. PVs of GP carry are calculated for three dfferent fund terms: Fund I: wth no hurdle, contrbuted captal returned frst wth clawback s a fund whose GPs are enttled to carry after returnng the contrbuted captal to LP, subject to clawback. Fund II: wth no early carry s a fund whose GPs must return all of carry bass before they are enttled to carry, thus rulng out any necessty for clawback. Fund III: wth a 120% threshold farvalue test, wth clawback s a fund whose GPs are enttled to carry after returnng the cost bass of all exted (or wrttenoff) nvestments and meetng the 120% farvalue test crtera for unexted nvestments. The rskfree rates vary from 0% to 5% by 1% ncrements. RskFree Rate 5% 4% 3% 2% 1% 0% Fund I: wth no hurdle, contrbuted captal returned frst wth clawback Present value of GP carry before clawback Present value of the clawback Present value of GP carry (net of clawback) Fund II: wth no early carry Present value of GP carry Fund III: wth a 120% threshold farvalue test, wth clawback Present value of GP carry before clawback Present value of the clawback Present value of GP carry (net of clawback)
17 Table 3. The Effect of Inflated (Reported) Values of Unexted Investments on the PVs of Carry Ths table presents the smulaton results for the PVs of GP carry as a functon of the rato of reported to actual values (that are prvately observed/assessed by GPs) of unexted nvestments. The actual portfolo values of unexted nvestments are generated by the stochastc process as descrbed n Equaton (1). For the benchmark case, the reported value s 100% of the actual value (no nflaton). For the results n the last two columns, the reported values are assumed to be nflated by 25% and 50%, respectvely, from the actual (prvately observed) values. Inflaton Level of Unexted Investments 100% 125% 150% Fund III: wth a farvalue test, wth clawback Present value of GP carry before clawback Present value of the clawback Present value of GP carry (net of clawback)
18 Table 4. Senstvty Analyss Ths table presents the effects of alterng the parameter values of the smulaton model on the estmated PV of carry. Fund I s a fund wth no hurdle, contrbuted captal returned frst wth clawback. Fund II s a fund wth commtted captal returned frst. Fund III s a fund wth a farvalue test and wth clawback. The benchmark refers to the base case model. 10% ext probablty refers to an altered model that s the same as the base case mode, except that the ext probablty s set to 10% (nstead of 20%). 30% ext probablty s smlarly defned. 25% carry level refers to an altered model that s the same as the base case model except that the carry level s set to 25%. 30% carry level s smlarly defned. Investment captal bass refers to an altered model that s the same as the base case model except that the carry bass s nvestment captal (whch s set to $82 per $100 of commtted captal). 60% volatlty refers to an altered model that s the same as the base case model except that the annual volatlty of ndvdual nvestments s set to 60%. 120% volatlty s smlarly defned. 30% parwse correlaton s an altered model that s the same as the base case model except that the parwse correlaton between ndvdual nvestments s set to 30%. 70% parwse correlaton s smlarly defned. 112% farvalue test threshold s an altered model that s the same as the base case model except that the threshold level for the farvalue test s set to 112%. 125% farvalue test threshold and 130% farvalue test threshold are smlarly defned. Fund I Fund II Fund III Panel A: the present value of GP carry net of clawback Benchmark case % ext probablty % ext probablty % carry level % carry level Investment captal bass % volatlty % volatlty % parwse correlaton % parwse correlaton % farvalue threshold level % farvalue threshold level % farvalue threshold level
19 Fund I Fund II Fund III Panel B: the present value of clawback Benchmark case % ext probablty % ext probablty % carry level % carry level Investment captal bass % volatlty % volatlty % parwse correlaton % parwse correlaton % farvalue threshold level % farvalue threshold level % farvalue threshold level
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