a) A company has a position in bonds worth $6 million. The modified duration of the portfolio is 5.2 years. Assume that the standard deviation of the daily yield change (when yield is measured in percent) is 0.09 . Estimate a 20-day 90% Value-at-risk for the portfolio. Note that - P(Z>1.282)=0.1, where Zn(0,1). - PMDPy, where P is the value of the portfolio. [9 marks] Consider a position consisting of a $300,000 investment in gold and a $500,000 investment in silver. Suppose that the daily volatility of these two assets are 1.8% and 1.2% respectively, and that the coefficient of correlation between their returns is 0.6 . What is the 10 -day 97.5% Valueat-risk for the portfolio? By how much does diversification reduce the value-at-risk? Note that - P(Z>1.96)=0.025, where Zn(0,1). - Cov(X+Y)=Var(X)+Var(Y)+2Corr(X,Y)Var(X)Var(Y)