An immunized bond portfolio is a portfolio which, for a given fixed target date, gives the holder a fixed return no matter what happens to interest rates from the initial date and the future target date. Essentially, an immunized bond portfolio has the cash flow structure of a zero$-$coupon bond with maturity equal to the fixed target date.

Suppose you can only trade the following three bonds:

Bond A: maturity $2$ years, coupon rate $5\%,$ FV $1000,$ Price $964\mathrm{.}5$

Bond B: maturity $2$ years, coupon rate $10\%,$ FV $1000,$ Price $1055\mathrm{.}57$

Bond A: maturity $3$ years, coupon rate $15\%,$ FV $1000,$ Price $1186\mathrm{.}1$

Given the three bonds, the spot rates in this economy are: r$1=5\mathrm{.}5\%$ r$2=7\%$ r$3=8\%$

Suppose that you have $$1000$ and you want to construct an immunized portfolio with a target date of three years. In other words, you want to create a $($synthetic$)3-$year zero$-$coupon bond and invest in it your capital of $$1000.$ What annual return will you get?

The annual return on the immunized portfolio is:

What bonds would you buy or sell and in what amounts: