Other things equal, an increase in a bond\'s maturity will (usually) increase it

Question

Other things equal, an increase in a bond's maturity will (usually) increase its interest rate risk. The present values of payments made further in the future are more sensitive to changes in the discount rate used to calculate present value than are the present values of payments made sooner discount must say "usually" because there are instances where an increase in a coupon bond's maturity will decrease its Macaulay duration. For a discount bond, duration first increases with longer maturity and then decreases over a range of relatively long maturities until it approaches the duration of a perpetuity, which is YTM) / YTM We

Explanation / Answer

One rule to learn is maturity is directly proportional to duration.

So if maturity decreases thus thus you will receive initial investment faster and that's the definition of duration . Duration is the period in which you recover initial investment.

2nd way to understand is that duration also defined as sensitivity of percentage in bond price. Now for short term bonds , interest rate won't change a lot and thus their price won't change a lot , means duration is less as compared to scenario of a long term bond.

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