4. Consider a pension fund that pays $100M in 15 years. The current market interest rate is 6% at all maturities. The pension fund wants to invest in 1-year and 30-year zero-coupon bonds (assets) with face values of $100. 1 a. How would you do a portfolio immunization using the two zero-coupon bonds? How many securities should the fund buy? And, what is the new present value of the fund's assets when the interest rate rises to 7%? b. Suppose you are given with a security that has zero duration and zero convexity. How would you match both duration and convexity of liability? What is the percentage change in the fund's assets implied from duration and convexity when the interest rate rises to 7%? 4. Consider a pension fund that pays $100M in 15 years. The current market interest rate is 6% at all maturities. The pension fund wants to invest in 1-year and 30-year zero-coupon bonds (assets) with face values of $100. 1 a. How would you do a portfolio immunization using the two zero-coupon bonds? How many securities should the fund buy? And, what is the new present value of the fund's assets when the interest rate rises to 7%? b. Suppose you are given with a security that has zero duration and zero convexity. How would you match both duration and convexity of liability? What is the percentage change in the fund's assets implied from duration and convexity when the interest rate rises to 7%