1. Consider the following bonds:

1. 3-year zero coupon bond with a face value of 100 (Bond A),
2. a semi-annual 6% coupon bond with a face value of 100 and a maturity of 4 years (Bond B)

3. a semi-annual 5% bond with a maturity of 2 years and a face value of 100 (Bond C).

Assume that the required yield is 4% per annum across all maturities.

1. Calculate the prices of all three bonds.
2. Calculate the duration of all three bonds.
3. Calculate the convexity of all three bonds.
4. If an investor owns one thousand of the 3-year zero coupon bonds, calculate how much of each of the other bonds should be held to make the portfolio immune to small parallel shifts in required yields using the durations and convexities of the bonds.