Key Rate Duration

Key rate duration (or partial duration) is a good measure of a bond’s sensitivity to a change in the benchmark yield curve for a specific maturity segment. Unlike effective duration, key rate durations help identify “shaping risk” for a bond; in other words, a bond’s sensitivity to changes in the shape of the benchmark yield curve (i.e. the yield curve becoming steeper or flatter).

A financial analyst may want to know how the price of the callable bond is expected to change if benchmark rates at short maturities shift by a specific bps but longer maturity benchmark rates remain constant. This case would represent a flattening of the yield curve, given that the yield curve is upward sloping.

For parallel shifts in the benchmark yield curve, key rate durations could indicate the same interest rate sensitivity as effective duration.

Duration is a basic measure of interest rate risk on a fixed-rate bond. As time passes, the Macaulay duration declines smoothly and then jumps upward after the coupon is paid. The relationship between the Macaulay duration and the time-to-maturity for a zero-coupon bond is the 45-degree line. Therefore, Macaulay duration of a zero-coupon bond is its time-to-maturity.

A perpetuity or perpetual bond or “consol” is a bond that does not mature as there is no principal to redeem. The investor receives a fixed coupon payment forever.

Question

Which is a bond that does not mature?

A. Perpetual bond or “consol”

B. A zero-coupon bond with 45-degree line against Macaulay duration

C. A callable bond with a flat yield curve

Solution

The correct answer is A.

A perpetuity or perpetual bond or “consol” is a bond that does not mature as there is no principal to redeem. The investor receives a fixed coupon payment forever.

 

Reading 55 LOS 55d:

Define key rate duration and describe the use of key rate durations in measuring the sensitivity of bonds to changes in the shape of the benchmark yield curve

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