Hi, In the sept 2005 Q1, I am not clear s to how the part c and part d have been solved... Assistance required on the math behind it.
Hi Pratik In this question the return R = 300,000 - 500,000 U where U is uniform [0,1]. c) asks for the shortfall probability below 100,000. So we want P(R < 100,000) = P(300,000 - 500,000 U < 100,000) = P(U > 0.4) = 0.6 As U is uniform on [0,1] there is a 60% chance of being bigger than 0.4 and 40% chance of being lower. d) asks for the Value at Risk at the 5% level. We want the result for R that gives the bottom 5%. This is the same as the top 5% for U. As U is uniform, we just need U=0.95, which gives: R = 300,000 - 500,000 x 0.95 = 300,000 - 475,000 = -175,000. The Value at Risk is then 175,000, ie we could lose at least 175,000 with probability 5%. I hope this clarifies the solution. Best wishes Mark
