A Model of Private Equity Fund Compensation

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "A Model of Private Equity Fund Compensation"

Transcription

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 far-value test (FVT) carred nterest scheme, whch s one of the most common proft-sharng 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 wrtten-off 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 un-exted (.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 un-exted 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 self-reported portfolo values to calculate ther carred nterest. We nvestgate whether GPs are tempted to nflate the portfolo values of un-exted 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 un-exted 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 far-value 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 un-exted 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 rsk-neutral 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 un-exted portfolo companes. In ths secton, we descrbe a rsk-neutral 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 un-exted 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 Rsk-neutral 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 tme-seres correlatons wth the market and other factor returns. Many of the studes that employ fund-level cash flow data make an effectve assumpton that market beta for the asset class s 1. 1 In ths analyss, we take a rsk-neutral 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 sem-fxed 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 rsk-free 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 rsk-neutral valuaton method consstent. Although the nterm values of un-exted 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 un-exted companes s not nconsstent wth the rsk-neutral 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 one-factor 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 log-normal 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 log-normal 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 far-value 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 far-value test s met. If a far-value test s met, t s the case n whch the far values of all un-exted 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 far-value 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 far-value 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% rsk-free rate, the amounts of GP carres are dentcal across these three funds. However, wth a non-trval rskfree rate, t s always the case that; 10

11 Present value of GP carry n a fund that apples the far-value 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 rsk-free 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 un-exted nvestment values We nvestgate whether GPs are tempted to nflate the portfolo values of un-exted 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 un-exted 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 far-value 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% far-value 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 far-value threshold levels are the multples for the cost bases of remanng portfolo companes. For the FVT to be passed, the far-values 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 far-value test GP carry scheme on the tme value of carred nterests. We fnd that whle the use of a far-value 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 un-exted (and therefore llqud) nvestments remanng n ther fund portfolos. Our fndngs suggest that the far-value 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, Pearson-Prentce 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 Closed-Form 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 rsk-free 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 far-value test s 120%, and the reported value of un-exted 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 un-exted nvestments determne the carry tmng. X t Benchmark Varaton Ext probablty 20% 10%, 30% Rsk-free 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% Far-value threshold level 120% 112%, 125%, 130% Inflated value of un-exted 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 rsk-free 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 wrtten-off) nvestments and meetng the 120% far-value test crtera for un-exted nvestments. The rsk-free rates vary from 0% to 5% by 1% ncrements. Rsk-Free 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 far-value 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 Un-exted 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 un-exted nvestments. The actual portfolo values of un-exted 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 Un-exted Investments 100% 125% 150% Fund III: wth a far-value 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 far-value 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% far-value 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% far-value test threshold and 130% far-value 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 % far-value threshold level % far-value threshold level % far-value 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 % far-value threshold level % far-value threshold level % far-value threshold level

An Alternative Way to Measure Private Equity Performance

An Alternative Way to Measure Private Equity Performance An Alternatve Way to Measure Prvate Equty Performance Peter Todd Parlux Investment Technology LLC Summary Internal Rate of Return (IRR) s probably the most common way to measure the performance of prvate

More information

THE DISTRIBUTION OF LOAN PORTFOLIO VALUE * Oldrich Alfons Vasicek

THE DISTRIBUTION OF LOAN PORTFOLIO VALUE * Oldrich Alfons Vasicek HE DISRIBUION OF LOAN PORFOLIO VALUE * Oldrch Alfons Vascek he amount of captal necessary to support a portfolo of debt securtes depends on the probablty dstrbuton of the portfolo loss. Consder a portfolo

More information

Chapter 15: Debt and Taxes

Chapter 15: Debt and Taxes Chapter 15: Debt and Taxes-1 Chapter 15: Debt and Taxes I. Basc Ideas 1. Corporate Taxes => nterest expense s tax deductble => as debt ncreases, corporate taxes fall => ncentve to fund the frm wth debt

More information

benefit is 2, paid if the policyholder dies within the year, and probability of death within the year is ).

benefit is 2, paid if the policyholder dies within the year, and probability of death within the year is ). REVIEW OF RISK MANAGEMENT CONCEPTS LOSS DISTRIBUTIONS AND INSURANCE Loss and nsurance: When someone s subject to the rsk of ncurrng a fnancal loss, the loss s generally modeled usng a random varable or

More information

Solution: Let i = 10% and d = 5%. By definition, the respective forces of interest on funds A and B are. i 1 + it. S A (t) = d (1 dt) 2 1. = d 1 dt.

Solution: Let i = 10% and d = 5%. By definition, the respective forces of interest on funds A and B are. i 1 + it. S A (t) = d (1 dt) 2 1. = d 1 dt. Chapter 9 Revew problems 9.1 Interest rate measurement Example 9.1. Fund A accumulates at a smple nterest rate of 10%. Fund B accumulates at a smple dscount rate of 5%. Fnd the pont n tme at whch the forces

More information

Lecture 3: Force of Interest, Real Interest Rate, Annuity

Lecture 3: Force of Interest, Real Interest Rate, Annuity Lecture 3: Force of Interest, Real Interest Rate, Annuty Goals: Study contnuous compoundng and force of nterest Dscuss real nterest rate Learn annuty-mmedate, and ts present value Study annuty-due, and

More information

Vasicek s Model of Distribution of Losses in a Large, Homogeneous Portfolio

Vasicek s Model of Distribution of Losses in a Large, Homogeneous Portfolio Vascek s Model of Dstrbuton of Losses n a Large, Homogeneous Portfolo Stephen M Schaefer London Busness School Credt Rsk Electve Summer 2012 Vascek s Model Important method for calculatng dstrbuton of

More information

A Model of Private Equity Fund Compensation!

A Model of Private Equity Fund Compensation! A Model of Private Equity Fund Compensation! Wonho Wilson Choi Andrew Metrick Ayako Yasuda KAIST Yale School of Management University of California at Davis September 15, 2011 Abstract: This paper analyzes

More information

Can Auto Liability Insurance Purchases Signal Risk Attitude?

Can Auto Liability Insurance Purchases Signal Risk Attitude? Internatonal Journal of Busness and Economcs, 2011, Vol. 10, No. 2, 159-164 Can Auto Lablty Insurance Purchases Sgnal Rsk Atttude? Chu-Shu L Department of Internatonal Busness, Asa Unversty, Tawan Sheng-Chang

More information

Staff Paper. Farm Savings Accounts: Examining Income Variability, Eligibility, and Benefits. Brent Gloy, Eddy LaDue, and Charles Cuykendall

Staff Paper. Farm Savings Accounts: Examining Income Variability, Eligibility, and Benefits. Brent Gloy, Eddy LaDue, and Charles Cuykendall SP 2005-02 August 2005 Staff Paper Department of Appled Economcs and Management Cornell Unversty, Ithaca, New York 14853-7801 USA Farm Savngs Accounts: Examnng Income Varablty, Elgblty, and Benefts Brent

More information

An Interest-Oriented Network Evolution Mechanism for Online Communities

An Interest-Oriented Network Evolution Mechanism for Online Communities An Interest-Orented Network Evoluton Mechansm for Onlne Communtes Cahong Sun and Xaopng Yang School of Informaton, Renmn Unversty of Chna, Bejng 100872, P.R. Chna {chsun,yang}@ruc.edu.cn Abstract. Onlne

More information

Capital asset pricing model, arbitrage pricing theory and portfolio management

Capital asset pricing model, arbitrage pricing theory and portfolio management Captal asset prcng model, arbtrage prcng theory and portfolo management Vnod Kothar The captal asset prcng model (CAPM) s great n terms of ts understandng of rsk decomposton of rsk nto securty-specfc rsk

More information

Inequality and The Accounting Period. Quentin Wodon and Shlomo Yitzhaki. World Bank and Hebrew University. September 2001.

Inequality and The Accounting Period. Quentin Wodon and Shlomo Yitzhaki. World Bank and Hebrew University. September 2001. Inequalty and The Accountng Perod Quentn Wodon and Shlomo Ytzha World Ban and Hebrew Unversty September Abstract Income nequalty typcally declnes wth the length of tme taen nto account for measurement.

More information

ECONOMICS OF PLANT ENERGY SAVINGS PROJECTS IN A CHANGING MARKET Douglas C White Emerson Process Management

ECONOMICS OF PLANT ENERGY SAVINGS PROJECTS IN A CHANGING MARKET Douglas C White Emerson Process Management ECONOMICS OF PLANT ENERGY SAVINGS PROJECTS IN A CHANGING MARKET Douglas C Whte Emerson Process Management Abstract Energy prces have exhbted sgnfcant volatlty n recent years. For example, natural gas prces

More information

DEFINING %COMPLETE IN MICROSOFT PROJECT

DEFINING %COMPLETE IN MICROSOFT PROJECT CelersSystems DEFINING %COMPLETE IN MICROSOFT PROJECT PREPARED BY James E Aksel, PMP, PMI-SP, MVP For Addtonal Informaton about Earned Value Management Systems and reportng, please contact: CelersSystems,

More information

Risk Model of Long-Term Production Scheduling in Open Pit Gold Mining

Risk Model of Long-Term Production Scheduling in Open Pit Gold Mining Rsk Model of Long-Term Producton Schedulng n Open Pt Gold Mnng R Halatchev 1 and P Lever 2 ABSTRACT Open pt gold mnng s an mportant sector of the Australan mnng ndustry. It uses large amounts of nvestments,

More information

Pricing Multi-Asset Cross Currency Options

Pricing Multi-Asset Cross Currency Options CIRJE-F-844 Prcng Mult-Asset Cross Currency Optons Kenchro Shraya Graduate School of Economcs, Unversty of Tokyo Akhko Takahash Unversty of Tokyo March 212; Revsed n September, October and November 212

More information

Number of Levels Cumulative Annual operating Income per year construction costs costs ($) ($) ($) 1 600,000 35,000 100,000 2 2,200,000 60,000 350,000

Number of Levels Cumulative Annual operating Income per year construction costs costs ($) ($) ($) 1 600,000 35,000 100,000 2 2,200,000 60,000 350,000 Problem Set 5 Solutons 1 MIT s consderng buldng a new car park near Kendall Square. o unversty funds are avalable (overhead rates are under pressure and the new faclty would have to pay for tself from

More information

FINANCIAL MATHEMATICS. A Practical Guide for Actuaries. and other Business Professionals

FINANCIAL MATHEMATICS. A Practical Guide for Actuaries. and other Business Professionals FINANCIAL MATHEMATICS A Practcal Gude for Actuares and other Busness Professonals Second Edton CHRIS RUCKMAN, FSA, MAAA JOE FRANCIS, FSA, MAAA, CFA Study Notes Prepared by Kevn Shand, FSA, FCIA Assstant

More information

Analysis of Premium Liabilities for Australian Lines of Business

Analysis of Premium Liabilities for Australian Lines of Business Summary of Analyss of Premum Labltes for Australan Lnes of Busness Emly Tao Honours Research Paper, The Unversty of Melbourne Emly Tao Acknowledgements I am grateful to the Australan Prudental Regulaton

More information

The impact of hard discount control mechanism on the discount volatility of UK closed-end funds

The impact of hard discount control mechanism on the discount volatility of UK closed-end funds Investment Management and Fnancal Innovatons, Volume 10, Issue 3, 2013 Ahmed F. Salhn (Egypt) The mpact of hard dscount control mechansm on the dscount volatlty of UK closed-end funds Abstract The mpact

More information

Nasdaq Iceland Bond Indices 01 April 2015

Nasdaq Iceland Bond Indices 01 April 2015 Nasdaq Iceland Bond Indces 01 Aprl 2015 -Fxed duraton Indces Introducton Nasdaq Iceland (the Exchange) began calculatng ts current bond ndces n the begnnng of 2005. They were a response to recent changes

More information

Stress test for measuring insurance risks in non-life insurance

Stress test for measuring insurance risks in non-life insurance PROMEMORIA Datum June 01 Fnansnspektonen Författare Bengt von Bahr, Younes Elonq and Erk Elvers Stress test for measurng nsurance rsks n non-lfe nsurance Summary Ths memo descrbes stress testng of nsurance

More information

SPEE Recommended Evaluation Practice #6 Definition of Decline Curve Parameters Background:

SPEE Recommended Evaluation Practice #6 Definition of Decline Curve Parameters Background: SPEE Recommended Evaluaton Practce #6 efnton of eclne Curve Parameters Background: The producton hstores of ol and gas wells can be analyzed to estmate reserves and future ol and gas producton rates and

More information

Time Value of Money. Types of Interest. Compounding and Discounting Single Sums. Page 1. Ch. 6 - The Time Value of Money. The Time Value of Money

Time Value of Money. Types of Interest. Compounding and Discounting Single Sums. Page 1. Ch. 6 - The Time Value of Money. The Time Value of Money Ch. 6 - The Tme Value of Money Tme Value of Money The Interest Rate Smple Interest Compound Interest Amortzng a Loan FIN21- Ahmed Y, Dasht TIME VALUE OF MONEY OR DISCOUNTED CASH FLOW ANALYSIS Very Important

More information

Answer: A). There is a flatter IS curve in the high MPC economy. Original LM LM after increase in M. IS curve for low MPC economy

Answer: A). There is a flatter IS curve in the high MPC economy. Original LM LM after increase in M. IS curve for low MPC economy 4.02 Quz Solutons Fall 2004 Multple-Choce Questons (30/00 ponts) Please, crcle the correct answer for each of the followng 0 multple-choce questons. For each queston, only one of the answers s correct.

More information

On the pricing of illiquid options with Black-Scholes formula

On the pricing of illiquid options with Black-Scholes formula 7 th InternatonalScentfcConferenceManagngandModellngofFnancalRsks Ostrava VŠB-TU Ostrava, Faculty of Economcs, Department of Fnance 8 th 9 th September2014 On the prcng of llqud optons wth Black-Scholes

More information

Macro Factors and Volatility of Treasury Bond Returns

Macro Factors and Volatility of Treasury Bond Returns Macro Factors and Volatlty of Treasury Bond Returns Jngzh Huang Department of Fnance Smeal Colleage of Busness Pennsylvana State Unversty Unversty Park, PA 16802, U.S.A. Le Lu School of Fnance Shangha

More information

Kiel Institute for World Economics Duesternbrooker Weg 120 24105 Kiel (Germany) Kiel Working Paper No. 1120

Kiel Institute for World Economics Duesternbrooker Weg 120 24105 Kiel (Germany) Kiel Working Paper No. 1120 Kel Insttute for World Economcs Duesternbrooker Weg 45 Kel (Germany) Kel Workng Paper No. Path Dependences n enture Captal Markets by Andrea Schertler July The responsblty for the contents of the workng

More information

DO LOSS FIRMS MANAGE EARNINGS AROUND SEASONED EQUITY OFFERINGS?

DO LOSS FIRMS MANAGE EARNINGS AROUND SEASONED EQUITY OFFERINGS? DO LOSS FIRMS MANAGE EARNINGS AROUND SEASONED EQUITY OFFERINGS? Fernando Comran, Unversty of San Francsco, School of Management, 2130 Fulton Street, CA 94117, Unted States, fcomran@usfca.edu Tatana Fedyk,

More information

Lecture 3: Annuity. Study annuities whose payments form a geometric progression or a arithmetic progression.

Lecture 3: Annuity. Study annuities whose payments form a geometric progression or a arithmetic progression. Lecture 3: Annuty Goals: Learn contnuous annuty and perpetuty. Study annutes whose payments form a geometrc progresson or a arthmetc progresson. Dscuss yeld rates. Introduce Amortzaton Suggested Textbook

More information

Underwriting Risk. Glenn Meyers. Insurance Services Office, Inc.

Underwriting Risk. Glenn Meyers. Insurance Services Office, Inc. Underwrtng Rsk By Glenn Meyers Insurance Servces Offce, Inc. Abstract In a compettve nsurance market, nsurers have lmted nfluence on the premum charged for an nsurance contract. hey must decde whether

More information

Portfolio Loss Distribution

Portfolio Loss Distribution Portfolo Loss Dstrbuton Rsky assets n loan ortfolo hghly llqud assets hold-to-maturty n the bank s balance sheet Outstandngs The orton of the bank asset that has already been extended to borrowers. Commtment

More information

The Application of Fractional Brownian Motion in Option Pricing

The Application of Fractional Brownian Motion in Option Pricing Vol. 0, No. (05), pp. 73-8 http://dx.do.org/0.457/jmue.05.0..6 The Applcaton of Fractonal Brownan Moton n Opton Prcng Qng-xn Zhou School of Basc Scence,arbn Unversty of Commerce,arbn zhouqngxn98@6.com

More information

Multivariate EWMA Control Chart

Multivariate EWMA Control Chart Multvarate EWMA Control Chart Summary The Multvarate EWMA Control Chart procedure creates control charts for two or more numerc varables. Examnng the varables n a multvarate sense s extremely mportant

More information

DI Fund Sufficiency Evaluation Methodological Recommendations and DIA Russia Practice

DI Fund Sufficiency Evaluation Methodological Recommendations and DIA Russia Practice DI Fund Suffcency Evaluaton Methodologcal Recommendatons and DIA Russa Practce Andre G. Melnkov Deputy General Drector DIA Russa THE DEPOSIT INSURANCE CONFERENCE IN THE MENA REGION AMMAN-JORDAN, 18 20

More information

7.5. Present Value of an Annuity. Investigate

7.5. Present Value of an Annuity. Investigate 7.5 Present Value of an Annuty Owen and Anna are approachng retrement and are puttng ther fnances n order. They have worked hard and nvested ther earnngs so that they now have a large amount of money on

More information

CHOLESTEROL REFERENCE METHOD LABORATORY NETWORK. Sample Stability Protocol

CHOLESTEROL REFERENCE METHOD LABORATORY NETWORK. Sample Stability Protocol CHOLESTEROL REFERENCE METHOD LABORATORY NETWORK Sample Stablty Protocol Background The Cholesterol Reference Method Laboratory Network (CRMLN) developed certfcaton protocols for total cholesterol, HDL

More information

Communication Networks II Contents

Communication Networks II Contents 8 / 1 -- Communcaton Networs II (Görg) -- www.comnets.un-bremen.de Communcaton Networs II Contents 1 Fundamentals of probablty theory 2 Traffc n communcaton networs 3 Stochastc & Marovan Processes (SP

More information

Traffic-light a stress test for life insurance provisions

Traffic-light a stress test for life insurance provisions MEMORANDUM Date 006-09-7 Authors Bengt von Bahr, Göran Ronge Traffc-lght a stress test for lfe nsurance provsons Fnansnspetonen P.O. Box 6750 SE-113 85 Stocholm [Sveavägen 167] Tel +46 8 787 80 00 Fax

More information

9.1 The Cumulative Sum Control Chart

9.1 The Cumulative Sum Control Chart Learnng Objectves 9.1 The Cumulatve Sum Control Chart 9.1.1 Basc Prncples: Cusum Control Chart for Montorng the Process Mean If s the target for the process mean, then the cumulatve sum control chart s

More information

Module 2 LOSSLESS IMAGE COMPRESSION SYSTEMS. Version 2 ECE IIT, Kharagpur

Module 2 LOSSLESS IMAGE COMPRESSION SYSTEMS. Version 2 ECE IIT, Kharagpur Module LOSSLESS IMAGE COMPRESSION SYSTEMS Lesson 3 Lossless Compresson: Huffman Codng Instructonal Objectves At the end of ths lesson, the students should be able to:. Defne and measure source entropy..

More information

A Critical Note on MCEV Calculations Used in the Life Insurance Industry

A Critical Note on MCEV Calculations Used in the Life Insurance Industry A Crtcal Note on MCEV Calculatons Used n the Lfe Insurance Industry Faban Suarez 1 and Steven Vanduffel 2 Abstract. Snce the begnnng of the development of the socalled embedded value methodology, actuares

More information

Intra-year Cash Flow Patterns: A Simple Solution for an Unnecessary Appraisal Error

Intra-year Cash Flow Patterns: A Simple Solution for an Unnecessary Appraisal Error Intra-year Cash Flow Patterns: A Smple Soluton for an Unnecessary Apprasal Error By C. Donald Wggns (Professor of Accountng and Fnance, the Unversty of North Florda), B. Perry Woodsde (Assocate Professor

More information

ADVERSE SELECTION IN INSURANCE MARKETS: POLICYHOLDER EVIDENCE FROM THE U.K. ANNUITY MARKET *

ADVERSE SELECTION IN INSURANCE MARKETS: POLICYHOLDER EVIDENCE FROM THE U.K. ANNUITY MARKET * ADVERSE SELECTION IN INSURANCE MARKETS: POLICYHOLDER EVIDENCE FROM THE U.K. ANNUITY MARKET * Amy Fnkelsten Harvard Unversty and NBER James Poterba MIT and NBER * We are grateful to Jeffrey Brown, Perre-Andre

More information

Multiple discount and forward curves

Multiple discount and forward curves Multple dscount and forward curves TopQuants presentaton 21 ovember 2012 Ton Broekhuzen, Head Market Rsk and Basel coordnator, IBC Ths presentaton reflects personal vews and not necessarly the vews of

More information

Risk-based Fatigue Estimate of Deep Water Risers -- Course Project for EM388F: Fracture Mechanics, Spring 2008

Risk-based Fatigue Estimate of Deep Water Risers -- Course Project for EM388F: Fracture Mechanics, Spring 2008 Rsk-based Fatgue Estmate of Deep Water Rsers -- Course Project for EM388F: Fracture Mechancs, Sprng 2008 Chen Sh Department of Cvl, Archtectural, and Envronmental Engneerng The Unversty of Texas at Austn

More information

Gender differences in revealed risk taking: evidence from mutual fund investors

Gender differences in revealed risk taking: evidence from mutual fund investors Economcs Letters 76 (2002) 151 158 www.elsever.com/ locate/ econbase Gender dfferences n revealed rsk takng: evdence from mutual fund nvestors a b c, * Peggy D. Dwyer, James H. Glkeson, John A. Lst a Unversty

More information

Using Series to Analyze Financial Situations: Present Value

Using Series to Analyze Financial Situations: Present Value 2.8 Usng Seres to Analyze Fnancal Stuatons: Present Value In the prevous secton, you learned how to calculate the amount, or future value, of an ordnary smple annuty. The amount s the sum of the accumulated

More information

An Analysis of Pricing Methods for Baskets Options

An Analysis of Pricing Methods for Baskets Options An Analyss of Prcng Methods for Baskets Optons Martn Krekel, Johan de Kock, Ralf Korn, Tn-Kwa Man Fraunhofer ITWM, Department of Fnancal Mathematcs, 67653 Kaserslautern, Germany, emal: krekel@twm.fhg.de

More information

Efficient Project Portfolio as a tool for Enterprise Risk Management

Efficient Project Portfolio as a tool for Enterprise Risk Management Effcent Proect Portfolo as a tool for Enterprse Rsk Management Valentn O. Nkonov Ural State Techncal Unversty Growth Traectory Consultng Company January 5, 27 Effcent Proect Portfolo as a tool for Enterprse

More information

Scale Dependence of Overconfidence in Stock Market Volatility Forecasts

Scale Dependence of Overconfidence in Stock Market Volatility Forecasts Scale Dependence of Overconfdence n Stoc Maret Volatlty Forecasts Marus Glaser, Thomas Langer, Jens Reynders, Martn Weber* June 7, 007 Abstract In ths study, we analyze whether volatlty forecasts (judgmental

More information

Section 5.4 Annuities, Present Value, and Amortization

Section 5.4 Annuities, Present Value, and Amortization Secton 5.4 Annutes, Present Value, and Amortzaton Present Value In Secton 5.2, we saw that the present value of A dollars at nterest rate per perod for n perods s the amount that must be deposted today

More information

Hollinger Canadian Publishing Holdings Co. ( HCPH ) proceeding under the Companies Creditors Arrangement Act ( CCAA )

Hollinger Canadian Publishing Holdings Co. ( HCPH ) proceeding under the Companies Creditors Arrangement Act ( CCAA ) February 17, 2011 Andrew J. Hatnay ahatnay@kmlaw.ca Dear Sr/Madam: Re: Re: Hollnger Canadan Publshng Holdngs Co. ( HCPH ) proceedng under the Companes Credtors Arrangement Act ( CCAA ) Update on CCAA Proceedngs

More information

PSYCHOLOGICAL RESEARCH (PYC 304-C) Lecture 12

PSYCHOLOGICAL RESEARCH (PYC 304-C) Lecture 12 14 The Ch-squared dstrbuton PSYCHOLOGICAL RESEARCH (PYC 304-C) Lecture 1 If a normal varable X, havng mean µ and varance σ, s standardsed, the new varable Z has a mean 0 and varance 1. When ths standardsed

More information

Multiple-Period Attribution: Residuals and Compounding

Multiple-Period Attribution: Residuals and Compounding Multple-Perod Attrbuton: Resduals and Compoundng Our revewer gave these authors full marks for dealng wth an ssue that performance measurers and vendors often regard as propretary nformaton. In 1994, Dens

More information

Is the home bias in equities and bonds declining in Europe?

Is the home bias in equities and bonds declining in Europe? Drk Schoenmaker (Netherlands), Thjs Bosch (Netherlands) Is the home bas n equtes and bonds declnng n Europe? Abstract Fnance theory suggests that nvestors should hold an nternatonally dversfed portfolo.

More information

Small pots lump sum payment instruction

Small pots lump sum payment instruction For customers Small pots lump sum payment nstructon Please read these notes before completng ths nstructon About ths nstructon Use ths nstructon f you re an ndvdual wth Aegon Retrement Choces Self Invested

More information

STAMP DUTY ON SHARES AND ITS EFFECT ON SHARE PRICES

STAMP DUTY ON SHARES AND ITS EFFECT ON SHARE PRICES STAMP UTY ON SHARES AN ITS EFFECT ON SHARE PRICES Steve Bond Mke Hawkns Alexander Klemm THE INSTITUTE FOR FISCAL STUIES WP04/11 STAMP UTY ON SHARES AN ITS EFFECT ON SHARE PRICES Steve Bond (IFS and Unversty

More information

Istituto Italiano degli Attuari Riunione di Seminario Attuariale. A Collective Risk Model for Claims Reserve Distribution

Istituto Italiano degli Attuari Riunione di Seminario Attuariale. A Collective Risk Model for Claims Reserve Distribution Isttuto Italano degl Attuar Runone d Semnaro Attuarale Unverstà Cattolca del Sacro Cuore Mlano, 12 Maggo 2011 A Collectve Rsk Model for Clams Reserve Dstrbuton no Savell Full Professor of Rsk Theory Catholc

More information

Management Quality, Financial and Investment Policies, and. Asymmetric Information

Management Quality, Financial and Investment Policies, and. Asymmetric Information Management Qualty, Fnancal and Investment Polces, and Asymmetrc Informaton Thomas J. Chemmanur * Imants Paegls ** and Karen Smonyan *** Current verson: December 2007 * Professor of Fnance, Carroll School

More information

Simple Interest Loans (Section 5.1) :

Simple Interest Loans (Section 5.1) : Chapter 5 Fnance The frst part of ths revew wll explan the dfferent nterest and nvestment equatons you learned n secton 5.1 through 5.4 of your textbook and go through several examples. The second part

More information

ENTERPRISE RISK MANAGEMENT IN INSURANCE GROUPS: MEASURING RISK CONCENTRATION AND DEFAULT RISK

ENTERPRISE RISK MANAGEMENT IN INSURANCE GROUPS: MEASURING RISK CONCENTRATION AND DEFAULT RISK ETERPRISE RISK MAAGEMET I ISURACE GROUPS: MEASURIG RISK COCETRATIO AD DEFAULT RISK ADIE GATZERT HATO SCHMEISER STEFA SCHUCKMA WORKIG PAPERS O RISK MAAGEMET AD ISURACE O. 35 EDITED BY HATO SCHMEISER CHAIR

More information

The Cox-Ross-Rubinstein Option Pricing Model

The Cox-Ross-Rubinstein Option Pricing Model Fnance 400 A. Penat - G. Pennacc Te Cox-Ross-Rubnsten Opton Prcng Model Te prevous notes sowed tat te absence o arbtrage restrcts te prce o an opton n terms o ts underlyng asset. However, te no-arbtrage

More information

Cautiousness and Measuring An Investor s Tendency to Buy Options

Cautiousness and Measuring An Investor s Tendency to Buy Options Cautousness and Measurng An Investor s Tendency to Buy Optons James Huang October 18, 2005 Abstract As s well known, Arrow-Pratt measure of rsk averson explans a ratonal nvestor s behavor n stock markets

More information

10.2 Future Value and Present Value of an Ordinary Simple Annuity

10.2 Future Value and Present Value of an Ordinary Simple Annuity 348 Chapter 10 Annutes 10.2 Future Value and Present Value of an Ordnary Smple Annuty In compound nterest, 'n' s the number of compoundng perods durng the term. In an ordnary smple annuty, payments are

More information

Interest Rate Fundamentals

Interest Rate Fundamentals Lecture Part II Interest Rate Fundamentals Topcs n Quanttatve Fnance: Inflaton Dervatves Instructor: Iraj Kan Fundamentals of Interest Rates In part II of ths lecture we wll consder fundamental concepts

More information

A Probabilistic Theory of Coherence

A Probabilistic Theory of Coherence A Probablstc Theory of Coherence BRANDEN FITELSON. The Coherence Measure C Let E be a set of n propostons E,..., E n. We seek a probablstc measure C(E) of the degree of coherence of E. Intutvely, we want

More information

LIFETIME INCOME OPTIONS

LIFETIME INCOME OPTIONS LIFETIME INCOME OPTIONS May 2011 by: Marca S. Wagner, Esq. The Wagner Law Group A Professonal Corporaton 99 Summer Street, 13 th Floor Boston, MA 02110 Tel: (617) 357-5200 Fax: (617) 357-5250 www.ersa-lawyers.com

More information

Section 2.3 Present Value of an Annuity; Amortization

Section 2.3 Present Value of an Annuity; Amortization Secton 2.3 Present Value of an Annuty; Amortzaton Prncpal Intal Value PV s the present value or present sum of the payments. PMT s the perodc payments. Gven r = 6% semannually, n order to wthdraw $1,000.00

More information

The OC Curve of Attribute Acceptance Plans

The OC Curve of Attribute Acceptance Plans The OC Curve of Attrbute Acceptance Plans The Operatng Characterstc (OC) curve descrbes the probablty of acceptng a lot as a functon of the lot s qualty. Fgure 1 shows a typcal OC Curve. 10 8 6 4 1 3 4

More information

Solutions to First Midterm

Solutions to First Midterm rofessor Chrstano Economcs 3, Wnter 2004 Solutons to Frst Mdterm. Multple Choce. 2. (a) v. (b). (c) v. (d) v. (e). (f). (g) v. (a) The goods market s n equlbrum when total demand equals total producton,.e.

More information

Chapter 4 Financial Markets

Chapter 4 Financial Markets Chapter 4 Fnancal Markets ECON2123 (Sprng 2012) 14 & 15.3.2012 (Tutoral 5) The demand for money Assumptons: There are only two assets n the fnancal market: money and bonds Prce s fxed and s gven, that

More information

Joe Pimbley, unpublished, 2005. Yield Curve Calculations

Joe Pimbley, unpublished, 2005. Yield Curve Calculations Joe Pmbley, unpublshed, 005. Yeld Curve Calculatons Background: Everythng s dscount factors Yeld curve calculatons nclude valuaton of forward rate agreements (FRAs), swaps, nterest rate optons, and forward

More information

Hedging Interest-Rate Risk with Duration

Hedging Interest-Rate Risk with Duration FIXED-INCOME SECURITIES Chapter 5 Hedgng Interest-Rate Rsk wth Duraton Outlne Prcng and Hedgng Prcng certan cash-flows Interest rate rsk Hedgng prncples Duraton-Based Hedgng Technques Defnton of duraton

More information

Transition Matrix Models of Consumer Credit Ratings

Transition Matrix Models of Consumer Credit Ratings Transton Matrx Models of Consumer Credt Ratngs Abstract Although the corporate credt rsk lterature has many studes modellng the change n the credt rsk of corporate bonds over tme, there s far less analyss

More information

INVESTIGATION OF VEHICULAR USERS FAIRNESS IN CDMA-HDR NETWORKS

INVESTIGATION OF VEHICULAR USERS FAIRNESS IN CDMA-HDR NETWORKS 21 22 September 2007, BULGARIA 119 Proceedngs of the Internatonal Conference on Informaton Technologes (InfoTech-2007) 21 st 22 nd September 2007, Bulgara vol. 2 INVESTIGATION OF VEHICULAR USERS FAIRNESS

More information

ADVERSE SELECTION IN INSURANCE MARKETS: POLICYHOLDER EVIDENCE FROM THE U.K. ANNUITY MARKET

ADVERSE SELECTION IN INSURANCE MARKETS: POLICYHOLDER EVIDENCE FROM THE U.K. ANNUITY MARKET ADVERSE SELECTION IN INSURANCE MARKETS: POLICYHOLDER EVIDENCE FROM THE U.K. ANNUITY MARKET Amy Fnkelsten Harvard Unversty and NBER James Poterba MIT and NBER Revsed May 2003 ABSTRACT In ths paper, we nvestgate

More information

Management Quality and Equity Issue Characteristics: A Comparison of SEOs and IPOs

Management Quality and Equity Issue Characteristics: A Comparison of SEOs and IPOs Management Qualty and Equty Issue Characterstcs: A Comparson of SEOs and IPOs Thomas J. Chemmanur * Imants Paegls ** and Karen Smonyan *** Current verson: November 2009 (Accepted, Fnancal Management, February

More information

Simon Acomb NAG Financial Mathematics Day

Simon Acomb NAG Financial Mathematics Day 1 Why People Who Prce Dervatves Are Interested In Correlaton mon Acomb NAG Fnancal Mathematcs Day Correlaton Rsk What Is Correlaton No lnear relatonshp between ponts Co-movement between the ponts Postve

More information

Assessing the Fairness of a Firm s Allocation of Shares in Initial Public Offerings: Adapting a Measure from Biostatistics

Assessing the Fairness of a Firm s Allocation of Shares in Initial Public Offerings: Adapting a Measure from Biostatistics Assessng the Farness of a Frm s Allocaton of Shares n Intal Publc Offerngs: Adaptng a Measure from Bostatstcs by Efstatha Bura and Joseph L. Gastwrth Department of Statstcs The George Washngton Unversty

More information

Portfolio Performance Manipulation and Manipulation-Proof Performance Measures

Portfolio Performance Manipulation and Manipulation-Proof Performance Measures Portfolo Performance Manpulaton and Manpulaton-Proof Performance Measures Wllam Goetzmann, Jonathan Ingersoll, Matthew Spegel, Ivo Welch March 5, 006 Yale School of Management, PO Box 0800, New Haven,

More information

Evaluating credit risk models: A critique and a new proposal

Evaluating credit risk models: A critique and a new proposal Evaluatng credt rsk models: A crtque and a new proposal Hergen Frerchs* Gunter Löffler Unversty of Frankfurt (Man) February 14, 2001 Abstract Evaluatng the qualty of credt portfolo rsk models s an mportant

More information

What is Candidate Sampling

What is Candidate Sampling What s Canddate Samplng Say we have a multclass or mult label problem where each tranng example ( x, T ) conssts of a context x a small (mult)set of target classes T out of a large unverse L of possble

More information

Fixed income risk attribution

Fixed income risk attribution 5 Fxed ncome rsk attrbuton Chthra Krshnamurth RskMetrcs Group chthra.krshnamurth@rskmetrcs.com We compare the rsk of the actve portfolo wth that of the benchmark and segment the dfference between the two

More information

Discount Rate for Workout Recoveries: An Empirical Study*

Discount Rate for Workout Recoveries: An Empirical Study* Dscount Rate for Workout Recoveres: An Emprcal Study* Brooks Brady Amercan Express Peter Chang Standard & Poor s Peter Mu** McMaster Unversty Boge Ozdemr Standard & Poor s Davd Schwartz Federal Reserve

More information

The DAX and the Dollar: The Economic Exchange Rate Exposure of German Corporations

The DAX and the Dollar: The Economic Exchange Rate Exposure of German Corporations The DAX and the Dollar: The Economc Exchange Rate Exposure of German Corporatons Martn Glaum *, Marko Brunner **, Holger Hmmel *** Ths paper examnes the economc exposure of German corporatons to changes

More information

The Cross Section of Foreign Currency Risk Premia and Consumption Growth Risk

The Cross Section of Foreign Currency Risk Premia and Consumption Growth Risk The Cross Secton of Foregn Currency Rsk Prema and Consumpton Growth Rsk By HANNO LUSTIG AND ADRIEN VERDELHAN* Aggregate consumpton growth rsk explans why low nterest rate currences do not apprecate as

More information

PROFIT RATIO AND MARKET STRUCTURE

PROFIT RATIO AND MARKET STRUCTURE POFIT ATIO AND MAKET STUCTUE By Yong Yun Introducton: Industral economsts followng from Mason and Ban have run nnumerable tests of the relaton between varous market structural varables and varous dmensons

More information

FAST SIMULATION OF EQUITY-LINKED LIFE INSURANCE CONTRACTS WITH A SURRENDER OPTION. Carole Bernard Christiane Lemieux

FAST SIMULATION OF EQUITY-LINKED LIFE INSURANCE CONTRACTS WITH A SURRENDER OPTION. Carole Bernard Christiane Lemieux Proceedngs of the 2008 Wnter Smulaton Conference S. J. Mason, R. R. Hll, L. Mönch, O. Rose, T. Jefferson, J. W. Fowler eds. FAST SIMULATION OF EQUITY-LINKED LIFE INSURANCE CONTRACTS WITH A SURRENDER OPTION

More information

Statistical Methods to Develop Rating Models

Statistical Methods to Develop Rating Models Statstcal Methods to Develop Ratng Models [Evelyn Hayden and Danel Porath, Österrechsche Natonalbank and Unversty of Appled Scences at Manz] Source: The Basel II Rsk Parameters Estmaton, Valdaton, and

More information

To manage leave, meeting institutional requirements and treating individual staff members fairly and consistently.

To manage leave, meeting institutional requirements and treating individual staff members fairly and consistently. Corporate Polces & Procedures Human Resources - Document CPP216 Leave Management Frst Produced: Current Verson: Past Revsons: Revew Cycle: Apples From: 09/09/09 26/10/12 09/09/09 3 years Immedately Authorsaton:

More information

Brigid Mullany, Ph.D University of North Carolina, Charlotte

Brigid Mullany, Ph.D University of North Carolina, Charlotte Evaluaton And Comparson Of The Dfferent Standards Used To Defne The Postonal Accuracy And Repeatablty Of Numercally Controlled Machnng Center Axes Brgd Mullany, Ph.D Unversty of North Carolna, Charlotte

More information

Institute of Informatics, Faculty of Business and Management, Brno University of Technology,Czech Republic

Institute of Informatics, Faculty of Business and Management, Brno University of Technology,Czech Republic Lagrange Multplers as Quanttatve Indcators n Economcs Ivan Mezník Insttute of Informatcs, Faculty of Busness and Management, Brno Unversty of TechnologCzech Republc Abstract The quanttatve role of Lagrange

More information

Portfolio Risk Decomposition (and Risk Budgeting)

Portfolio Risk Decomposition (and Risk Budgeting) ortfolo Rsk Decomposton (and Rsk Budgetng) Jason MacQueen R-Squared Rsk Management Introducton to Rsk Decomposton Actve managers take rsk n the expectaton of achevng outperformance of ther benchmark Mandates

More information

Loss analysis of a life insurance company applying discrete-time risk-minimizing hedging strategies

Loss analysis of a life insurance company applying discrete-time risk-minimizing hedging strategies Insurance: Mathematcs and Economcs 42 2008 1035 1049 www.elsever.com/locate/me Loss analyss of a lfe nsurance company applyng dscrete-tme rsk-mnmzng hedgng strateges An Chen Netspar, he Netherlands Department

More information

This study examines whether the framing mode (narrow versus broad) influences the stock investment decisions

This study examines whether the framing mode (narrow versus broad) influences the stock investment decisions MANAGEMENT SCIENCE Vol. 54, No. 6, June 2008, pp. 1052 1064 ssn 0025-1909 essn 1526-5501 08 5406 1052 nforms do 10.1287/mnsc.1070.0845 2008 INFORMS How Do Decson Frames Influence the Stock Investment Choces

More information

HOUSEHOLDS DEBT BURDEN: AN ANALYSIS BASED ON MICROECONOMIC DATA*

HOUSEHOLDS DEBT BURDEN: AN ANALYSIS BASED ON MICROECONOMIC DATA* HOUSEHOLDS DEBT BURDEN: AN ANALYSIS BASED ON MICROECONOMIC DATA* Luísa Farnha** 1. INTRODUCTION The rapd growth n Portuguese households ndebtedness n the past few years ncreased the concerns that debt

More information

Health Insurance and Household Savings

Health Insurance and Household Savings Health Insurance and Household Savngs Mnchung Hsu Job Market Paper Last Updated: November, 2006 Abstract Recent emprcal studes have documented a puzzlng pattern of household savngs n the U.S.: households

More information

The Investor Recognition Hypothesis:

The Investor Recognition Hypothesis: The Investor Recognton Hypothess: the New Zealand Penny Stocks Danel JP Cha, Department of Accountng and Fnance, onash Unversty, Clayton 3168, elbourne, Australa, and Danel FS Cho, Department of Fnance,

More information