An investor simulated his position value for the next day by using a historical simulation method and past 501 days data.

And determined (simulated) next day possible losses. Ordered from the worst losses to the lower are displayed in the following table as well as the weight associate to each scenario.

a) Determine the VaR(99%) as well as the ES(1%) by using results from the classical historical simulation.

b) Determine the VaR(99%) as well as the ES(1%) by using results from weighted historical simulation.

Scenario Loss ('000s) Weight (w) Cumulatives Weight 494.0000 1458.2550 0.0053 0.0053 339.0000 1054.1842 0.0024 0.0077 349.0000 861.2178 0.0026 0.0103 329.0000 845.4629 0.0023 0.0126 487.0000 773.2695 0.0051 0.0177 227.0000 665.2037 0.0014 0.0191 131.0000 617.2349 0.0009 0.0199 238.0000 614.5911 0.0015 0.0214 473.0000 583.7069 0.0048 0.0261 306.0000 583.0373 0.0021 0.0282 477.0000 564.9626 0.0049 0.0330 495.0000 562.8956 0.0053 0.0384 376.0000 557.5782 0.0029 0.0413 237.0000 549.6361 0.0015 0.0427 365.0000 525.5851 0.0028 0.0455 283.0000 525.5492 0.0018 0.0473 378.0000 509.9615 0.0030 0.0503 320.0000 509.8445 0.0022 0.0525 242.0000 509.0323 0.0015 0.0540 322.0000 508.1682 0.0022 0.0562