2. (35pts) Consider a portfolio which consists of two assets, Si and S2 The returns of the assets are normally distributed: Si N(0.175,0.067) and S2 N (0.055, 0.013). Si and S are corre- lated. Correlation coefficient is given by r12= -0.164. Determine the values of shares xi and x2 which make the Value at Risk (VaR) of the portfolio minimum. The value of portfolio today is $200 million. a) What is the probability that the end of month portfolio value is less than $50 million? b) What is the probability that the end of the month gain is more than $20 million? c) Calculate Value at Risk (VaR) with 3% probability. HINT: r12=cov (82,52) 2. (35pts) Consider a portfolio which consists of two assets, Si and S2 The returns of the assets are normally distributed: Si N(0.175,0.067) and S2 N (0.055, 0.013). Si and S are corre- lated. Correlation coefficient is given by r12= -0.164. Determine the values of shares xi and x2 which make the Value at Risk (VaR) of the portfolio minimum. The value of portfolio today is $200 million. a) What is the probability that the end of month portfolio value is less than $50 million? b) What is the probability that the end of the month gain is more than $20 million? c) Calculate Value at Risk (VaR) with 3% probability. HINT: r12=cov (82,52) 2. (35pts) Consider a portfolio which consists of two assets, Si and S2 The returns of the assets are normally distributed: Si N(0.175,0.067) and S2 N (0.055, 0.013). Si and S are corre- lated. Correlation coefficient is given by r12= -0.164. Determine the values of shares xi and x2 which make the Value at Risk (VaR) of the portfolio minimum. The value of portfolio today is $200 million. a) What is the probability that the end of month portfolio value is less than $50 million? b) What is the probability that the end of the month gain is more than $20 million? c) Calculate Value at Risk (VaR) with 3% probability. HINT: r12=cov (82,52) 2. (35pts) Consider a portfolio which consists of two assets, Si and S2 The returns of the assets are normally distributed: Si N(0.175,0.067) and S2 N (0.055, 0.013). Si and S are corre- lated. Correlation coefficient is given by r12= -0.164. Determine the values of shares xi and x2 which make the Value at Risk (VaR) of the portfolio minimum. The value of portfolio today is $200 million. a) What is the probability that the end of month portfolio value is less than $50 million? b) What is the probability that the end of the month gain is more than $20 million? c) Calculate Value at Risk (VaR) with 3% probability. HINT: r12=cov (82,52)