You have been hired by a small pension fund to help them design a bong 610 million obligation that will come due in 4 years. The managers of the run 2 year zero coupon bond along with their existing bond portfolio A that includes to zero coupon bonds with the corresponding portfolio weight: (7 points) Security 5 year zeros 7 year zeros Portfolio weight 25% 25% Suppose that the yield to maturity on all bonds is 5% (in other words, the yield Ip them design a bond portfolio to fund a ne managers of the fund would like to use portfolio A that includes following three pints) 7 year zeros 10 year zeros 50% (in other words, the yield curve is flat at 5%). a) What are the durations of current existing bond portfolio A and the obligation (auc b) How would you structure your holdings of the 2 year zero coupon bond and their existing portfolio A so that you are protected against the risk of interest rate fluctuations? Please indicate the dollar amount you would invest in each security