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Elena is an investment manager undertaking a risk analysis on her company's portfolio. The portfolio size is $17 million. She wants to consider the potential impact of the worst-case scenario. She decides to measure the loss on the portfolio within the next year (measured in $ millions) using a Generalised Pareto distribution with y = 0.8,0 = 2,5 = 0.2. a) Calculate the mean and standard deviation of this distribution. [3 marks] b) Elena has left one important value out of her distribution assumptions above. Explain what the Generalised Pareto distribution measures, and what the purpose of this missing value is. [2 marks] c) Upon being informed of the above, Elena decides to use $8 million for the missing value in b). Under these assumptions, calculate the probability that the portfolio loses more than $16 million in the next year. [2 marks] d) Calculate the 90th percentile for this distribution. Interpret what this value would mean in terms of the loss on the portfolio. [3 marks] Elena is an investment manager undertaking a risk analysis on her company's portfolio. The portfolio size is $17 million. She wants to consider the potential impact of the worst-case scenario. She decides to measure the loss on the portfolio within the next year (measured in $ millions) using a Generalised Pareto distribution with y = 0.8,0 = 2,5 = 0.2. a) Calculate the mean and standard deviation of this distribution. [3 marks] b) Elena has left one important value out of her distribution assumptions above. Explain what the Generalised Pareto distribution measures, and what the purpose of this missing value is. [2 marks] c) Upon being informed of the above, Elena decides to use $8 million for the missing value in b). Under these assumptions, calculate the probability that the portfolio loses more than $16 million in the next year. [2 marks] d) Calculate the 90th percentile for this distribution. Interpret what this value would mean in terms of the loss on the portfolio. [3 marks]