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 u = 1,0 = 3, = 0.3. 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. Do you think this distribution with these parameters is appropriate to use? Why or why not? [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 u = 1,0 = 3, = 0.3. 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. Do you think this distribution with these parameters is appropriate to use? Why or why not? [3 marks]