3. (35pts) Consider a portfolio which consists of two assets. The returns of the assets are normally distributed with N(0.12,70.15) and N(0.1, 0.25). The value of portfolio today is $110 million. Sup- pose the time horizon is 15 days and the covariance matrices are given by 0.15 0.2 0.15 0.0 Sl= 1 and s2= 0.2 0.25 1 0.0 0.25 a) Let the shares of assets be: 11=0.55, 12=0.45 calculate VaR at 2% probability and for si? Show your calculations explicitly. b) Let the shares of assets be: 11=0.55, 12=0.45 calculate the Value at Risk (VaR) at 1% probability for S. c) Let the shares of assets be: x1=0.45, 22=0.55 calculate VaR at 2% probability and for sid) Let the shares of assets be: 11=0.45, 12=0.55 calculate the Value at Risk (VaR) at 1% probability for $? e) Let the shares of assets be: 21=0.55, 22=0.45 what is the probability that the end of year loss is more than $10 million for Sl? f) Let the shares of assets be: 11=0.45, 12=0.55 what is the probability that the end of year loss is more than $10 million for S2? 3. (35pts) Consider a portfolio which consists of two assets. The returns of the assets are normally distributed with N(0.12,70.15) and N(0.1, 0.25). The value of portfolio today is $110 million. Sup- pose the time horizon is 15 days and the covariance matrices are given by 0.15 0.2 0.15 0.0 Sl= 1 and s2= 0.2 0.25 1 0.0 0.25 a) Let the shares of assets be: 11=0.55, 12=0.45 calculate VaR at 2% probability and for si? Show your calculations explicitly. b) Let the shares of assets be: 11=0.55, 12=0.45 calculate the Value at Risk (VaR) at 1% probability for S. c) Let the shares of assets be: x1=0.45, 22=0.55 calculate VaR at 2% probability and for sid) Let the shares of assets be: 11=0.45, 12=0.55 calculate the Value at Risk (VaR) at 1% probability for $? e) Let the shares of assets be: 21=0.55, 22=0.45 what is the probability that the end of year loss is more than $10 million for Sl? f) Let the shares of assets be: 11=0.45, 12=0.55 what is the probability that the end of year loss is more than $10 million for S2