Question

Longer term bonds are risker than shorter-term bonds. Explain.

Answer 1

Longer term bonds are more riskier than shorter term bond because the Longer term bonds carries two risk 1) Inflation risk and 2) Interest rate risk. Inflation risk means risk that inflation will increase in future and inestor will end up with no real return i.e Nominal rate of return - Inflation rate and Interest rate risk referes to risk that market interest rate may go up in future making coupon payments worth less in compared to other investment opportunities.

Lets understand with example . let say that there are two bond. Bond A and Bond B. Bond A has 10% coupon rate with maturity of 5 years . while Bond B has 10% coupon rate with maturity of 10 years. These bonds are selling at par i.e 1000$ only means market interest rate is also 10%. No assume if market interest rate increase to 15%, effect on bonds prices will be as follow

Bond A  

Here face value = $1000 ,
Interest = face value x coupon rate
= 1000 x 10%
= 100$
n = no of coupon payments= 5
YTM = 15%
Value of bond = Interest x PVIFA(YTM%,n) + redemption value x PVIF(YTM%,n)
PVIFA(YTM%,n) = [1-(1/(1+r)^n / r ]
PVIFA(15%,5) = [1-(1/(1+15%)^5 / 15%]
=[1-(1/(1+0.15)^5 / 0.15]
=[1-(1/(1.15)^5 / 0.15]
=[1-0.4971767 / 0.15]
=0.502823/0.15
=3.352155
PVIF(15%,5) = 1/(1+15%)^5
=1/(1.15)^5
= 0.497176
Value of bond = 100 x 3.352155 + 1000 x 0.497176
=335.22 + 497.18
= 832.40 $

Thus bond price has change from 1000$ to 832.40$

% change = 1000-832.40 /1000

=167.60/1000

=0.16760

i.e 16.76%

Bond B

Here face value = $1000 ,
Interest = face value x coupon rate
= 1000 x 10%
= 100$
n = no of coupon payments= 10
YTM = 15%
Value of bond = Interest x PVIFA(YTM%,n) + redemption value x PVIF(YTM%,n)
PVIFA(YTM%,n) = [1-(1/(1+r)^n / r ]
PVIFA(15%,10) = [1-(1/(1+15%)^10 / 15%]
=[1-(1/(1+0.15)^10 / 0.15]
=[1-(1/(1.15)^10 / 0.15]
=[1-0.247184 / 0.15]
=0.0.752815/0.15
=5.018768
PVIF(15%,10) = 1/(1+15%)^10
=1/(1.15)^10
= 0.247185
Value of bond = 100 x 5.01876 + 1000 x 0.247185
=501.8768 + 247.1847
= 749.06 $

Thus bond price has change from 1000$ to 749.06$

% change = 1000-749.06 /1000

=250.94/1000

=0.25094

i.e 25.09%

Thus Loner term bonds are risker than shorter term bonds