Round your answers to two decimal points, and don$$t round intermediate calculations.

Problem $1.$

Suppose that you have decided to fund a three$-$year liability with a portfolio consisting of positions in a twoyear zero$-$coupon bond $(2$YR$)$ and a four$-$year zero$-$coupon bond $(4$YR$).$ The current interest rate level is $10\%.$

a$)$ Compute the price of both bonds.

b$)$ Since our liability is a three$-$year liability, we want to immunize our portfolio by duration matching.

Set up the portfolio, describing how many dollars you have to invest into each bond.

c$)$ Immediately after you make your initial purchases, rates fall to $8\%.$ If you do not rebalance your

portfolio, what is your realized yield after three years?

d$)$ What is the duration of the portfolio after the drop in interest rates without rebalancing?

e$)$ How would you have to rebalance your portfolio?