Question 4 Assume that daily returns are conditionally normally distributed and given by Pt+1 = x +0z+10+1, 4+1 N(0,1), where the time increment between t and t +1 is one day, w is constant, and 04+1 denotes an estimate as of time t for the conditional standard deviation one day ahead. (a) The 1-day Value-at-Risk at the critical level a, VaR +1, is defined as Pr[rt+1 SVaR +1] = a. (1) Show that the exact formula for VaR at the a critical level and 1-day horizon is given by VaR_1 = +04+10-(a), (2) where o is the standard normal cumulative density function. Note: The definition in equation (1) follows the notation of the subject guide. Using an alternative definition based on losses leads to a different VaR formula, which is also accepted if correct. (c) The expected shortfall ES-1 at the critical level a and 1-day horizon can be defined as ES +1 = Ex["2+1|rt+1