Suppose you are advised to use the following risk metric V, which one may name Median...

 

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Suppose you are advised to use the following risk metric V, which one may name Median Shortfall: P(R₂ ≤ -Vª|R₂ <-VaR) = 0.5 1 a) Explicitly derive the expression for in case of R₁~ N(μ, o) as a function of t, ot and 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(, o)? 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 Vaas a approaches 0, i.e. lim Vin case of rt~ N(t,0) as a function of t, ot and a a-0 (5 points) Suppose you are advised to use the following risk metric V, which one may name Median Shortfall: P(R₂ ≤ -Vª|R₂ <-VaR) = 0.5 1 a) Explicitly derive the expression for in case of R₁~ N(μ, o) as a function of t, ot and 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(, o)? 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 Vaas a approaches 0, i.e. lim Vin case of rt~ N(t,0) as a function of t, ot and a a-0 (5 points)

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a To derive the expression for Median Shortfall PRR VaR when R follows a normal distribution R N we need to find the threshold value VaR such that PR ... View the full answer