Question

5. Assume you want to invest some money in the bond market for one year. If you expect that the interest rates will decline, what kind of bond that you would rather to invest, long-term bonds or short term bonds? Support your conclusion with numerical evidence. (Assume that all the 1-year, 2-years, 5-years, 10-years, and 20-years bonds have 10% coupon, annual coupon payment, for all of them current market price is 1000, and the interest rate will    drop from 10% to 5%). Which type of bond has greater interest-rate risk?

Answer 1

If rates decline, price of bonds increase so one would invest in bind whose price increases the highest. We know price increases highest for highest duration bonds and duration is directly proportional to maturity. Hence, we will invest in 20 year bonds because they have greatest interest rate risk.

Price of 1 year bond 1 year later=1000

Price of 2 year bond 1 year later=100/5%*(1-1/1.05)+1000/1.05=1047.619048

Price of 5 year bond 1 year later=100/5%*(1-1/1.05^4)+1000/1.05^4=1177.297525

Price of 10 year bond 1 year later=100/5%*(1-1/1.05^9)+1000/1.05^9=1355.391084

Price of 20 year bond 1 year later=100/5%*(1-1/1.05^19)+1000/1.05^19=1604.266043