a) In the solution for Charlie, where did the expected shortfall for risk free asset is 2 x 1 = 2 come from? b) Can expected shortfall be <0 ?
Expected shortfall a) Charlie's benchmark return is 2% and the risk-free earns 0% so by investing in this Charlie would "expect" (in actual fact, definitely receive) a shortfall of 2%. I'm not particularly clear why we've then multiplied 2% by 1 (prob of return is certain, ie 1?) but it's always good fun to multiply things by 1 if you've got a bit of spare time on your hands. b) No, you only integrate over the range where there is a shortfall. Value at Risk on the other hand, apparently can be negative! Though I don't anticipate this being in the exam, as many people (including myself) might well sensibly assume that VaR = max (what you get when you do the maths, 0). John
Thanks John Correct me if i'm wrong: a) does this means the expected shortfall of a risk free asset is max(L,0) ? b) i was told that in capital calculations (DFA modelling), the VaR capital is never negative (not sure how do i relate this to this subject) c) can i say that the expected shortfall is the expected loss given the benchmark level? if so, how do i explain why is the expected shortfall of charlie's risk free asset is 2, assuming that negative benchmarks = losses and positive = gain? d) For Adam, where did the average shortfall will be 1 1/2% come from? Is it {-2 - (-3) } /2 = 1.5%? sorry for the many questions.
