2. Suppose you are advised to use the following risk metric ye, which one may name Median Shortfall: P(Rt |Rt < VaR) = 0.5 1 a) Explicitly derive the expression for yo in case of Rt function of t, t and a ~ N(t, ) as a (6 points) b) What four features are necessary to ensure coherence of any risk-metric? Your answer should contain either formal representation or detailed ex- planation (4 points) c) Is this risk-metric coherent if R ~ N(t, )? If not, which features of a coherent risk metric are violated? Your answer should contain a robust proof or a counter-example. (5 points) d) Calculate or derive the value of yo as a approaches 0, i.e. lim va in case of rt ~N(t, ) as a function of t, t and a a0 (5 points)