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

False . Long Terms are more senitive to interest rate changes than short term bonds because of the added maturity risk.

Following are comparison of 2 bonds with same coupon rate and par value but different maturities.

Coupon = 14%*1000 = 140
Maturity = 6 years

a. PV of Bond A at 11% required rate = PV of Coupons + PV of Par value = 140*(1-(1+11%)^-6 )/11% + 1000/(1+11%)⁶ = 1126.92
PV of Bond A at 14% required rate = PV of Coupons + PV of Par value = 140*(1-(1+14%)^-6 )/14% + 1000/(1+14%)⁶ = 1000
PV of Bond A at 17% required rate = PV of Coupons + PV of Par value = 140*(1-(1+17%)^-6 )/17% + 1000/(1+17%)⁶ = 892.32

b. Maturity = 16
PV of Bond B at 11% required rate = PV of Coupons + PV of Par value = 140*(1-(1+11%)^-16 )/11% + 1000/(1+11%)¹⁶ = 1221.37
PV of Bond B at 14% required rate = PV of Coupons + PV of Par value = 140*(1-(1+14%)^-16 )/14% + 1000/(1+14%)¹⁶ = 1000
PV of Bond B at 17% required rate = PV of Coupons + PV of Par value = 140*(1-(1+17%)^-16 )/17% + 1000/(1+17%)¹⁶ = 837.84

The greater the length more is the responsiveness

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