Question

The value of outstanding bonds change whenever the going rate of interest changes. In general, short-term rates are more volatile than long-term rates. Therefore, short-term bond prices are more sensitive to interest rate changes than are long-term bond prices. Is this statement true or false? Make up a reasonable example using a short-term and a long-term bond to help answer the question.

Answer 1

The statement is False. Even though short term rates are more volatile than long term rates, prices of long term bonds are more sensitive to interest rate changes than short term bonds. The reason is that short term bonds have very few cash flows and the present value of those cash flows dont change much because they are in the short term. However, long term bonds have a lot of cash flows and their present value change very much with change in interest rates.

Lets say 10% annual payment bond with 2 years to maturity and 10 years to maturity. Both have par of 1000. Current yield is 10%

Case 1: Yield rises to 12%

Price of 2 year bond=10%*1000/12%*(1-1/1.12^2)+1000/1.12^2=966.20

Price of 10 year bond=10%*1000/12%*(1-1/1.12^10)+1000/1.12^10=887

Case 2: Yield falls to 8%

Price of 2 year bond=10%*1000/8%*(1-1/1.08^2)+1000/1.08^2=1035.67

Price of 10 year bond=10%*1000/8%*(1-1/1.08^10)+1000/1

08^10=1134.20

Thus we see long term bonds are more sensitive to interest rate changes than short term bonds