An investment universe of the following risky assets with a dependence structure (correlation) is given. Use...

 

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An investment universe of the following risky assets with a dependence structure (correlation) is given. Use the ready appropriate formulae from Portfolio Optimisation Lecture. Asset A 0.02 0.05 1 0.3 0.3 0.3 0.3 1 0.6 0.6 B 0.07 0.12 W2 R = 0.3 0.6 C 0.15 0.17 W3 0.3 1 0.6 0.6 0.6 1 D 0.20 0.25 W4 Consider minimum variance portfolio with a target return m. 1 argmin w'Ew s.t. w'1 = 1, = w 2 w' = m w Formulate the Lagrangian function and give its partial derivatives. No further derivation required. Compute the allocations w* and portfolio risk = w'w, for m = 4.5%. Now, stress the correlation matrix: multiply all correlations by x1.25 and x1.5, and compute the respective optimal allocations and portfolio risk (the same m = 4.5%). An investment universe of the following risky assets with a dependence structure (correlation) is given. Use the ready appropriate formulae from Portfolio Optimisation Lecture. Asset A 0.02 0.05 1 0.3 0.3 0.3 0.3 1 0.6 0.6 B 0.07 0.12 W2 R = 0.3 0.6 C 0.15 0.17 W3 0.3 1 0.6 0.6 0.6 1 D 0.20 0.25 W4 Consider minimum variance portfolio with a target return m. 1 argmin w'Ew s.t. w'1 = 1, = w 2 w' = m w Formulate the Lagrangian function and give its partial derivatives. No further derivation required. Compute the allocations w* and portfolio risk = w'w, for m = 4.5%. Now, stress the correlation matrix: multiply all correlations by x1.25 and x1.5, and compute the respective optimal allocations and portfolio risk (the same m = 4.5%).