Consider a portfolio currently worth $10,000,000. Suppose that a historical simulation of the portfolio's losses based...

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Consider a portfolio currently worth $10,000,000. 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 (in $000s) from this historical simulation: Rank 14 24 34 4€ 54 6 74 8 9 10 Loss Rank Loss Rank 378.5 24.0 251.6 19.8 70.5 19.3¹ 46.8 17.9 46.5¹ 17.8 38.9 17.1 34.2 16.7 29.9 14.5 29.8 14.4 25.0¹ 13.9 114 124 134 14 15 16 174 18 19 20 214 224 234 24 25€ 26 27 28 29 30 Loss Rank Loss Rank Loss 13.3 314 9.8 991¹ 12.8¹ 32 9.2¹ 992 12.7 33 993 12.7< 34 994 12.6 35€ 995 12.3¹ 36 10.6 374 10.5 38 10.3 9.9¹ 39 40€ 7.9 7.8 7.7 7.6 7.5 7.5 -42.5 € -47.3 -57.3 -79.9 -112.7¹ -113.4 -144.2 € -146.7 996 997 998 6.9¹ 999 -302.1 6.8 1000 -774.7 a) Estimate the one-day 99% VaR and the one-day 99% ES directly from the simulation data.< (5 marks) b) Suppose that an EVT model fitted to the losses from the historical simulation that exceed $7,000 yields the following estimates for the generalised Pareto distribution's parameters: The shape parameter is estimated as 0.75, while the scale parameter is estimated as 8.24. Calculate the one-day 99% VaR and the one-day 99% ES based on the estimated EVT model. (5 marks) c) Use the EVT model to evaluate the unconditional probability that the one-day loss will be more than 1% of the current portfolio worth. < (5 marks) Consider a portfolio currently worth $10,000,000. 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 (in $000s) from this historical simulation: Rank 14 24 34 4€ 54 6 74 8 9 10 Loss Rank Loss Rank 378.5 24.0 251.6 19.8 70.5 19.3¹ 46.8 17.9 46.5¹ 17.8 38.9 17.1 34.2 16.7 29.9 14.5 29.8 14.4 25.0¹ 13.9 114 124 134 14 15 16 174 18 19 20 214 224 234 24 25€ 26 27 28 29 30 Loss Rank Loss Rank Loss 13.3 314 9.8 991¹ 12.8¹ 32 9.2¹ 992 12.7 33 993 12.7< 34 994 12.6 35€ 995 12.3¹ 36 10.6 374 10.5 38 10.3 9.9¹ 39 40€ 7.9 7.8 7.7 7.6 7.5 7.5 -42.5 € -47.3 -57.3 -79.9 -112.7¹ -113.4 -144.2 € -146.7 996 997 998 6.9¹ 999 -302.1 6.8 1000 -774.7 a) Estimate the one-day 99% VaR and the one-day 99% ES directly from the simulation data.< (5 marks) b) Suppose that an EVT model fitted to the losses from the historical simulation that exceed $7,000 yields the following estimates for the generalised Pareto distribution's parameters: The shape parameter is estimated as 0.75, while the scale parameter is estimated as 8.24. Calculate the one-day 99% VaR and the one-day 99% ES based on the estimated EVT model. (5 marks) c) Use the EVT model to evaluate the unconditional probability that the one-day loss will be more than 1% of the current portfolio worth. < (5 marks)

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a To estimate the oneday 99 VaR Value at Risk directly from the simulation data we need to find the ... View the full answer