*************************************************************************************************** Doit3: starting new run If bankrupt, interpreting as before reported date Index = S&P500 Results for round 1.00 All industries together Using round to IPO/Acquisition returns. Returns overlap for same company! Doing model with k, bankruptcy minage parameter 0.25 using all rounds, even those that take less than 60 days deleting 4 huge returns Using S&P500 for betas There are data points in this estimation before cleaning = 7765.00 elminated observations with unknown fate: 0 Eliminated observations with >100% or <0% shareholder value 31.00 Eliminated observations with missing round date 0 Note. Beta procedure -- cannot handle missing round date, so eliminating those. Eliminating observations that start in second quarter 2000. Need one quarter lag for probability. 61.00 If out date is before or equal to begin date, treat out date as missing. This affects 12.00 Relabeling all ipo, acquisition or new round with zero return as out of business. This affects 10.00 deleting observations with > 300x returns. 4.00 deleting observations with log annualized return greater than 15 1.00 Remaining data: 7668.00 Note: following refers to round, not company. Round may end in another round, though company eventually goes public Percent bankrupt 9.17 Percent ipo 17.10 Percent acquired 19.95 Percent with subsequent round 0 Percent Private 51.12 Percent Ipo registered 2.66 Percent fate unknown 0 0 Percent of bankrupt have good data. Using this parameter in simulation Note: good means round date and exit date not -99 93.03 Percent of new valuation (ipo,acquired,new round) that have good data. Using this parameter in simulation. Note: good means final date not -99, return not missing or 0 37.96 Directional Iteration Func-count f(x) Step-size derivative 1 7 25528.7 0.001 -1.63e+008 2 18 25528.7 1e-011 -1.63e+008 3 26 25528.7 5e-012 -1.63e+008 4 37 25528.7 9.3086e-012 -7.02e+008 5 45 25528.7 4.6543e-012 -7.02e+008 6 56 22317.9 1.12493e-005 -3.3e+006 7 67 21566.4 1.93589e-005 -2.05e+004 8 79 21532.6 0.000107534 -363 9 91 21529.1 0.0141794 32.1 10 103 21520.3 0.0204184 -476 11 111 22120.6 0.231042 4.72e+003 12 119 21513.3 0.013951 -515 13 127 21528.3 0.097603 1.99e+003 14 135 21499.8 0.0269224 -454 15 146 21485.4 0.0651252 -2.4 16 158 21451 2.09886 -2.5 17 169 21446.7 0.38623 -4.89 18 181 21444.8 0.987459 -0.0174 19 192 21444.7 0.623862 0.0154 20 204 21444.6 1.05979 0.00181 21 216 21444.4 14.5837 -0.000939 22 227 21442.1 15.702 -0.000708 23 238 21430.3 3.89179 -1.69 24 249 21403.8 1.15273 -10.6 25 260 21349.7 1.87917 -0.906 26 271 21307.9 2.10722 -0.0223 27 282 21293.8 0.847274 0.0629 28 294 21287 2.26806 0.00595 29 306 21284.7 1.93108 0.00691 30 317 21284.6 0.86534 -0.0079 31 328 21284.5 0.978357 -0.0015 Optimization terminated successfully: Current search direction is a descent direction, and magnitude of directional derivative in search direction less than 2*options.TolFun initial and final parameters 0.01 1.50 0.90 0.10 1.00 3.00 0.01 0.01 0.97 0.48 0.17 1.04 4.21 0.08 chi2 tests. NOTE NO MINIMIZATION OVER OTHER PARAMETERS YET test for gamma = 0, and all other parameters unchanged. chi2 value, chi2(1) and chi2(#pars) 21.73 3.84 14.07 test for delta = 0, and all other parameters unchanged. chi2 value, chi2(1) and chi2(#pars) 213.50 3.84 14.07 test for gamma= 0 and delta = 0, and all other parameters unchanged. chi2 value, chi2(2) and chi2(#pars) 350.37 5.99 14.07 looking for most influential observations 30 most influential observations and their contrib to lkly co. no. round date post value exit date exit typ post value gross ret age(mo) lkly contrib 3815.00 19980507.00 8.68 19990819.00 1.00 1026.60 91.14 15.39 12.06 6529.00 19870701.00 13.50 19901228.00 2.00 1.40 0.09 41.89 12.07 2694.00 19890901.00 15.50 19901129.00 2.00 1.80 0.11 14.92 12.07 4811.00 19990324.00 17.00 20000301.00 1.00 1655.80 61.24 11.24 12.07 5398.00 19931231.00 11.90 19990720.00 2.00 2.50 0.16 66.64 12.10 594.00 19981231.00 8.50 19990922.00 1.00 244.30 13.50 8.70 12.13 635.00 19890201.00 31.00 19941101.00 2.00 20.00 0.16 69.00 12.13 5345.00 19870801.00 16.10 19901201.00 2.00 2.40 0.07 40.00 12.14 5493.00 19981015.00 11.00 20000201.00 2.00 3250.00 186.73 15.54 12.15 1765.00 19970531.00 108.00 19980626.00 1.00 104.00 0.03 12.84 12.18 6787.00 19930219.00 2.20 19971007.00 1.00 38.20 0.01 55.61 12.22 6934.00 19981023.00 7.88 19991209.00 1.00 1191.00 102.89 13.54 12.22 1702.00 19950714.00 33.50 19960514.00 2.00 2.50 0.07 10.00 12.35 1115.00 19960603.00 7.30 19961220.00 2.00 150.00 20.55 6.56 12.37 1049.00 19990810.00 20.60 19991203.00 2.00 162.40 7.88 3.77 12.40 1690.00 19870601.00 12.50 19941101.00 2.00 4.10 0.19 89.00 12.42 2040.00 19911201.00 11.75 19980624.00 2.00 5.94 0.12 78.76 12.44 3966.00 19891024.00 10.00 19901001.00 1.00 22.80 0.00 11.24 12.45 4471.00 19981115.00 2.40 19990923.00 1.00 618.00 98.61 10.26 12.46 2923.00 19920901.00 9.70 19980731.00 2.00 0.90 0.09 70.99 12.53 1885.00 19890101.00 50.00 19940726.00 2.00 5.80 0.07 66.82 12.54 1267.00 19950901.00 5.00 19951130.00 2.00 41.60 8.32 2.95 12.55 4082.00 19880601.00 20.00 19950503.00 2.00 4.00 0.13 83.07 12.59 3859.00 19990115.00 43.55 19990721.00 1.00 1914.60 37.31 6.20 12.60 6146.00 19941115.00 6.40 19950302.00 1.00 88.60 10.89 3.57 12.60 3623.00 19870601.00 46.20 19930817.00 1.00 49.10 0.08 74.53 12.64 378.00 19920101.00 24.00 19920306.00 1.00 293.10 9.05 2.16 12.66 7460.00 19990518.00 25.40 19990922.00 1.00 242.00 8.06 4.13 12.73 2196.00 19870201.00 13.70 19960711.00 2.00 6.80 0.17 113.33 13.02 4191.00 19900207.00 16.80 19990518.00 2.00 1.50 0.05 111.36 13.29 998.00 19870301.00 5.55 19971107.00 1.00 24.80 0.17 128.20 13.32 Table . Maximum Likelyhood estimates A. Parameter Estimates and Standard Errors Parameter estimate std err gamma % 3.65 1.23 delta 0.97 0.05 sig % 95.19 1.75 k % 17.26 0.94 a 1.04 0.04 b 4.21 0.11 pim * 100 7.96 1.00 c 0.93 d 0.38 log likelyhood -21284.54 gamma and sigma are reported on an annualized basis - 4*gamma and 2*sigma. pim is times 100 Implied Er sigr ER alpha and beta Using parameters (annualized percentages) ElogRf, ElogRm, sigmalogRm 6.82 15.92 14.94 beta is at a quarterly frequency, alpha is annualized Implied mean and sd of log returns (annualized) 19.29 96.29 Implied mean and sd of return levels (annualized) 71.34 120.36 alpha 52.94 beta 1.09 Continuous time alpha (q) (a) (in percent) 12.23 48.93 correlation matrix of estimated parameters 1.00 -0.75 -0.22 0.56 -0.35 0.46 0.10 -0.75 1.00 0.38 -0.71 0.57 -0.62 -0.25 -0.22 0.38 1.00 -0.80 -0.30 0.32 -0.25 0.56 -0.71 -0.80 1.00 0.14 -0.10 0.22 -0.35 0.57 -0.30 0.14 1.00 -0.97 0.06 0.46 -0.62 0.32 -0.10 -0.97 1.00 -0.01 0.10 -0.25 -0.25 0.22 0.06 -0.01 1.00 NOTE: Doit3 is incrementing tablerow