Question 5 a Suppose that the profit of a portfolio of as.pdf

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Question 5 (a) Suppose that the profit of a portfolio of assets (X) has the probability mass function P(X = 10) = 0.1, P(X = 5) = 0.3, P(X = 2) = 0.4, P(X = 10) = 0.17, P(X = 20) = 0.03. (i) Write down the equation and plot the CDF of X. (ii) Calculate the 4% VaR of the profit X. (iii) Calculate the expected shortfall at 4% level of the profit X. (iv) Calculate the tail conditional expectation at 4% level of the profit X. (b) Suppose that the profit of a portfolio of assets (X) follows a uniform distribution over the interval (2, 2). (i) Write down the equation and plot the CDF of X. (ii) Calculate the 1% VaR of the profit X. (iii) Calculate the expected shortfall at 1% level of the profit X. (iv) Calculate the tail conditional expectation at 1% level of the profit X..

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