Question 1 (Sortino ratio, (12 marks)). Consider a portfolio selection problem where R is the target return rate on the expected return of the portfolio. The set of feasible portfolios is denoted by X C R" and it is to be assumed that this is a compact convex set. 1. Formulate an optimization problem for finding a feasible portfolio with the largest value of Sorting ratio. Also state, with justification, whether your objective function is convex or concave or neither. (5 marks) 2. Let STR* denote the maximum Sorting ratio obtained by solving the problem in the first part. Show how you can compute a value i 0 be any positive scalar and consider the following function , : RV(0) - R defined on the space RV (?) of random variables supported over some scenario set !, - log ( E ) 1. Check whether this function satisfies each of the four properties - monotonicity, translation equivariance, positive homogeneity, and subadditivety. (16 marks) 2. Conclude what you can say whether this function is a coherent risk measure or not. (2 marks)