Elena is an investment manager undertaking a risk analysis on her companys 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 = 0.8, = 2, = 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.

d) Calculate the 90th percentile for this distribution. Interpret what this value would mean in terms of the loss on the portfolio.