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For risky bonds, duration is defined as

sensitivity of price due to change in underlying yield

while spread duration is

sensitivity of price due to change in the 'spread in yields to the risk free curve'.

If we consider 'yield' to be yield of risk free curve + a spread. Then why do we care what contributed to a change to that yield? The price sensitivty should be the same regardless?

Any one can illustrate why that is NOT the case?

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Adding to the answer of Tim:

If you consider a fixed-rate bond then IR-duration and spread-duration have the same effect on the bond.

For a floating-rate bond, on the other side, you have IR-risk only until the next reset of the floating rate and thus very small IR-duration. The credit risk, however, is much higher than IR-risk and you can measure this using spread-duration.

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Practitioners care about the difference between spread risk and sensitivity to the risk free curve because it enables them to hedge the risk for the bond separately. Those two elements combine to determine the risk of the bond, and can be hedged using different instruments in the marketplace.

So, for example, an investor can hedge the risk-free element of the bond using government bonds, or they can hedge the spread element using a Credit Default Swap (CDS). If the investor knows what the spread duration is, then it helps them to determine a CDS trade to hedge that component of risk.

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