In six years, you will have to pay a single, deterministic liability for an amount of \(€ 30,000\). Consider a portfolio consisting of a zero maturing in eight years and a bond paying a single annual coupon with rate \(4 \%\), maturing in four years. The term structure is flat at a rate of \(3.5 \%\), with annual compounding. Assume a face value of \(€ 1000\) for both bonds.

- Build a first-order immunized portfolio and check its performance for an immediate shift of 50 basis points.

- Repeat the procedure, but now include another zero maturing in three years, in order to match both duration and convexity of the assets and the liability. Compare the performance against the previous portfolio.