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?