We consider a bond, paying every period a coupon c (expressed as a percentage of the principal), and at the last payment date a principal M. The first coupon is paid in exactly 1 period(s) and there are T payments. The interest rate is r.

1. Express the price of the bond, as well as its duration with the previous notations. Give an interpretation of both quantities, and their relationship to the stream of bond cash.

The period coupon payment is 6 months. The periodic interest rate expressed on an annual basis is 1%.

The three following bonds are traded on the market:

Bond | Coupon | Maturity (in years)

A 1.00% 2.5

B 0.00% 3.5

C 2.00% 4.5

2. Compute the prices of bonds A, B and C.

3. Compute the durations of bonds A, B and C.

4. You want to invest 100k Euros in a portfolio with a duration of 3.5 years. What are the two possible portfolios (explicit the amount you have to invest for each portfolio)?

Hint: We will cover this aspect in the next lecture. Simply know that if you purchase xA bonds A of price PA and duration DA and xC bonds C of price PC and duration DC , the duration of the portfolio is xaPaDa+xcPcDc+xaPa+xcPc