Question

Explain intuitively why bonds with longer maturities are more sensitive to changes in interest rates?

Answer 1

Bond price is output of present value of future cash flows. The cash flows of the bonds are discounted by the yield or interest rate depending on tenor. As cash flows are discounted for the overall tenor of the bond, higher the bond term more the discounting opportunity and this makes long term bond sensitive to the interest rate.

Bonds bears fixed rate which remains static whereas the interest rate scenarios keep fluctuating and brings opportunity and risk. If interest rate is higher than the bond coupon then that will make a bond cheaper and if interest rate is lower than bond coupon then bond will sell at premium.

The bond holders holding long term bonds bear more price risk as the bond assures a static cash flow and market yield may be more than the coupon interest rates that bond holders get hence bond price become low when market yields are high and bondholders holding bond for longer duration have to suffer against such fluctuations.

Mathematically, cashflow is part of numerator and interest rate settles in denominator applying the time (Year) as its power e.g Formula: CF_n / (1+R)^Year. This sensitizes the cash flows; higher the interest rate lower the bond value lower the interest rate higher the bond value. As tenor or term or year is factored in denominator it mathematically impacts the price of the bond. So, if we go on increasing the tenor of the bond the price of the bond will be impacted more (please look at formula). As time factor is applied in denominator while discounting the cash flow hence it is makes price of the bond more sensitive.