You have a liability (obligation) with one payment of $7,000 due in 9 years. Use Bonds 1, 3 and 4 below to immunize the portfolio "completely", i.e., matching the duration AND the convexity of a bond portfolio with the duration of the liability. Show that if the interest rate changes by 4% (large swing immediately after you buy the bonds) your portfolio terminal value still remains almost unchanged. (whereas the terminal values for all individual Bonds depart much more significantly from it). Show clearly what weights you obtain for Bond 1, 3 and 4. The ongoing rate (YTM) is 3%, so the rate could jump to 7%.

Before starting to compute portfolio weights, first verify that when the interest rate DOESN'T change (i.e. stays at 3%) you do have terminal values of exactly $7,000 for all Bonds. This will assure that you have the correct percentage of face value bought. Only then can you start the duration/convexity matching (by computing the weights needed), and only then can you check whether the terminal value stays constant for your portfolio (weighted average of Bond 1, Bond 3 and Bond 4) while it does not for the individual Bonds.

Compute the terminal values of both Bond 2 and the Portfolio (made up of Bonds 1, 3 and 4) as a function of the interest rate (let r go from 0 to 10%)

Plot your results graphically to show that even though Bond 2 performs well in the region nearby 3%, it is no match for the portfolio if rates swing wildly.

Yield to maturity 3% Current Date 6/6/2021 Present Value of Future Obligation:

Bond 1 Bond 2 Bond 3 Bond 4 Coupon rate 9.00% 7.50% 7.00% 5.00%

Maturity 6/6/2051 6/6/2033 6/6/2030 6/6/2034

Face value 1,000 1,000 1,000 1,000