Consider a 3-asset portfolio worth $100M with the following 10-day return variance-covariance matrix and its corresponding correlation matrix Assuming return normality a) What is the 100-day 99% relative value at risk (VaR) assuming the following weights: Stock 140%, Stock 225%, Stock 3115% i.e w' =[0.4,0.25,1.15]. [2 marks] b) Interpret your VaR estimate in part a). [1 mark] c) What is the VaR diversification benefit for the portfolio in part a)? [2 marks] d) Recalculate the 100-day VaR and the VaR diversification benefit if the weight vector is changed to w=[0.5,0.25,0.25]. [1 mark] e) Explain how and why the change in weights in part d) has affected the VaR and the diversification benefit. [2 marks] Now assume normality is unreasonable due to the presence of fat tails in the return distributions f) For a given weight vector, outline how monte-carlo simulation can be used to calculate the 100 day VaR at 99% in the presence of fat tails. [4 marks] g) Is the simulated VaR in part f ) likely to be larger or smaller than the estimates assuming return normality? Why/why not? [2 marks] Consider a 3-asset portfolio worth $100M with the following 10-day return variance-covariance matrix and its corresponding correlation matrix Assuming return normality a) What is the 100-day 99% relative value at risk (VaR) assuming the following weights: Stock 140%, Stock 225%, Stock 3115% i.e w' =[0.4,0.25,1.15]. [2 marks] b) Interpret your VaR estimate in part a). [1 mark] c) What is the VaR diversification benefit for the portfolio in part a)? [2 marks] d) Recalculate the 100-day VaR and the VaR diversification benefit if the weight vector is changed to w=[0.5,0.25,0.25]. [1 mark] e) Explain how and why the change in weights in part d) has affected the VaR and the diversification benefit. [2 marks] Now assume normality is unreasonable due to the presence of fat tails in the return distributions f) For a given weight vector, outline how monte-carlo simulation can be used to calculate the 100 day VaR at 99% in the presence of fat tails. [4 marks] g) Is the simulated VaR in part f ) likely to be larger or smaller than the estimates assuming return normality? Why/why not? [2 marks]