5. (20 pts) Consider two different bonds X and Y where we expect at most one of them to default. The face value of both bonds is 500 If a bond defaults, there are two possible outcomes with recovery values 350 and 450 as well as probabilities of 3% and 2%, respectively. All in all, the two bonds can have ve possibles outcomes, the rst being when bond X has a loss of 150 and bond Y has no losses. The probability of this outcome is 0.95 x 0.03 = 0.0285. The ve possible outcomes are: Outcome 1 2 3 4 5 X 350 450 500 500 500 Y X +Y Probability 500 500 350 450 500 850 950 850 950 1000 3% 2% 3% 2% 90% Further, assume that the initial value of each bond is the expected value of the payoff. {a} Calculate 5% Wait and ES for X, Y and X+Y. (b) Explain the properties of a coherent risk measure. 15 Will subadditive in this case? How about ES? .II