!!!provide the answers rounded to the nearest ten-thousandth

(all explanations are needed)

2. An investor invested $20 million in the following portfolio:

20% invested in 3-year zero coupon bond

40% invested in 2.25-year T-note paying 5% coupon

40% invested in 3.5-year floating rate bond with 20 basis point spread with annual payments (Assume that the yield curve has not changed for the last 6 months.) Answer the following questions using the semi-annually compounded yield curve in the Appendix: (2-a) Calculate the durations of the securities in the portfolio above.

(2-b) Compute the duration of the portfolio.

(2-c) Compute the dollar duration of the portfolio

(2-d) Calculate 95% ES (Expected Shortfall) of the portfolio. Assume that has the following distribution:

dr~N(0.003, 0.01^2)

(2-e) You decide to hedge your portfolio with a 2-year coupon bond paying 2% on a quarterly basis. How much should you go short/long on this bond in order to make it immune to interest rate changes?

Appendix: (semi-annually compounded) Yield Curve Yield Maturity (years) 0.25 1.78% 0.5 0.75 1 2.10% 2.25% 2.38% 1.25 1.5 1.75 2 2.25 2.5 2.75 3 2.55% 2.71% 2.83% 2.99% 3.09% 3.15% 3.25% 3.30% 3.33% 3.35% 3.38% 3.40% 3.42% ( ) 3.44% ( ) 3.25 3.5 3.75 4 4.25 4.5 4.75 5 Appendix: (semi-annually compounded) Yield Curve Yield Maturity (years) 0.25 1.78% 0.5 0.75 1 2.10% 2.25% 2.38% 1.25 1.5 1.75 2 2.25 2.5 2.75 3 2.55% 2.71% 2.83% 2.99% 3.09% 3.15% 3.25% 3.30% 3.33% 3.35% 3.38% 3.40% 3.42% ( ) 3.44% ( ) 3.25 3.5 3.75 4 4.25 4.5 4.75 5