STRESSATLAS / TAIL PRECISION / SYNTHETIC PORTFOLIO

How stable is
the tail estimate?

Paired path bootstrap for mean loss, VaR and exact empirical ES. Intervals describe numerical sampling uncertainty under fixed model assumptions.

20,000Full simulation paths
300Paired resamples
95%Approximate percentile interval
200ES tail path-equivalents

Absolute risk estimate

All amounts are CNY. Bootstrap SE is the sample standard deviation across resampled estimates. These bounds are approximate, especially for discrete VaR and sparse tails.

ScenarioMetricEstimateLowerUpperBootstrap SE
baselineMean loss3,380,2743,340,9063,427,94623,062
baselineVaR15,140,00014,684,37515,700,250274,701
baselineES18,476,22517,764,28219,116,079326,639
recessionMean loss8,672,3948,599,9438,764,18346,265
recessionVaR29,289,00028,312,72529,921,000459,280
recessionES33,601,69532,777,45034,353,958399,824
severeMean loss19,230,30619,100,43919,392,21481,011
severeVaR51,326,00050,663,86952,296,750411,795
severeES57,175,56656,201,84758,147,089518,028
independentMean loss3,371,4523,345,0413,397,92013,789
independentVaR8,717,5008,590,0008,800,12556,067
independentES9,621,4509,457,1879,780,68287,970
high_correlationMean loss3,378,8383,321,9303,445,47332,637
high_correlationVaR22,085,00021,157,37522,839,062468,870
high_correlationES27,706,33826,589,73628,671,445524,248

Change from baseline

The same resampled path indices are applied to every scenario. Each VaR/ES difference compares two separately recomputed tail statistics; it is not VaR/ES of the pathwise loss difference.

ScenarioMetricPaired changeLowerUpperBootstrap SE
baselineMean loss0000
baselineVaR0000
baselineES0000
recessionMean loss5,292,1215,245,0035,349,56727,832
recessionVaR14,149,00013,413,16214,671,525350,377
recessionES15,125,47014,690,89415,616,604245,027
severeMean loss15,850,03215,745,77415,979,64762,852
severeVaR36,186,00035,426,23136,936,750348,072
severeES38,699,34137,926,43939,466,822383,686
independentMean loss-8,822-51,46032,21121,514
independentVaR-6,422,500-6,984,062-5,974,250274,196
independentES-8,854,775-9,519,947-8,212,318330,784
high_correlationMean loss-1,436-29,25229,03614,734
high_correlationVaR6,945,0006,232,2507,513,812335,373
high_correlationES9,230,1128,630,6309,815,962309,885

Read the limits before interpreting the interval

Resampling cannot generate rare losses absent from the simulated sample. Ties, too few tail paths and too few resamples can make percentile coverage unreliable. These intervals do not measure PD/LGD calibration error, future economic risk or model validity.

Replay the evidence

stressatlas verify-precision --out demo/precision reruns the entire simulation and bootstrap from saved inputs and both seeds, then compares every estimate, resample and report.

Interval rows · All resample statistics · Inputs and settings · Summary