Assume that on 1st January 2018, the following zero-coupon yield curve and Euro-denominated zero-coupon government bonds (AAA-rating) are available in the market:

Zero-coupon yield curve

Euro-denominated zero-coupon government bonds

Assume there are no default risk or liquidity premiums and that markets are efficient. As a fund manager specialized in the fixed-income assets, you hold 35 units of Bond A, 30 units of Bond B, 20 units Bond C and 25 units of Bond D.

Questions:

1. Calculate the 1-year forward rate from year 1 to year 2, 2 to 3 and 3 to 4.

2. What is the market value of your bonds and your bond portfolio?

3. Calculate the modified duration and convexity for each bond on 1st January 2018.

4. Calculate the modified duration and convexity of the portfolio on 1st January 2018.

5. You noticed a parallel shift in the yield curve that leads to the market interest rates in the yield curve to increase by 5 basis point on the same day. Calculate the change in the value of your bond portfolio based on this parallel shift.

Maturity 12 4 9 10 7 8 Yield 2,00% 2,50% 3,00% 3,30% 3,50% 3,60% 3,65% 3,68% 3,69% 3,70% Par value (in EUR) 1000 1000 1000 1000 Maturity (in years) Bond A Bond B Bond C Bond D 4 10 Maturity 12 4 9 10 7 8 Yield 2,00% 2,50% 3,00% 3,30% 3,50% 3,60% 3,65% 3,68% 3,69% 3,70% Par value (in EUR) 1000 1000 1000 1000 Maturity (in years) Bond A Bond B Bond C Bond D 4 10