Your portfolio is 5 million euros invested in bonds. The interest rate (market rate) is 6%. The horizon of portfolio management is 4 years (in 4 years you will sell all the bonds of the portfolio). Given the structure of the portfolio: 2 bonds with the following characteristics:

Bond	Maturity	Face value	Nominal rate
1	2 years	2000	8%
2	6 years	3000	5%

a. Compute the price, duration, sensitivity, and convexity of the 2 bonds. Suppose that 2 bonds are annual-coupon-payment bond

b. You invest all your wealth in bond 2, then compute the loss on your portfolio if the market rate increases to 8% using duration, convexity, and the exact variation. What do you observe?

c. Compute the number of each bond if portfolio sensitivity to interest rate becomes 0.