Consider a portfolio currently worth $20,000,000. Suppose that a historical simulation of the portfolio's losses based on 1,000 daily observations was performed. The following table shows an excerpt of the ranked losses from this historical simulation: Loss rank 1 2 3 4 5 6 7 8 9 10 11 . 999 1,000 Loss ($000s) 590 484 446 425 391 355 348 332 328 319 295 -423 -504 a) (5%) Estimate the one-day 99.5% VaR and the one-day 99% ES. b) (5%) Suppose that an EVT model fitted to the losses from the historical simulation results in the following estimates for the generalised Pareto distribution's parameters: The shape parameter isestimated as 0.50, while the scale parameter is estimated as 50. Under the assumption that there are 50 scenarios where the loss is greater than 268 (in $000s), estimate the one-day 99% VaR and the one- day 99% ES based on the EVT model. c) (5%) Use the EVT model to estimate the unconditional probability that the one-day loss will be (i) more than 5% of the current portfolio value, and (ii) more than 3.5% of the current portfolio value. Finally, what is the EVT model's estimate of the unconditional probability that the one-day loss is more than 1% of the current portfolio value? (d) (10%) The loss distribution from the historical simulation had a mean of -1.524 and a standard deviation of 128.4763 (both in $000s). Estimate the standard error of the historical simulation's 99% one-day VaR when the tail of the loss distribution is approximated using a generalised Pareto distribution.