Does the magnitude and direction of the interest-rate change matter for Macaulay duration i.e. will it remain the same for a given coupon paying bond and YTM no matter what the one-time interest rate change actually is?
It’s linear so it will remain the same.
But the larger the interest rate change, the less good the approximation.
If you have larger changes, add the convexity adjustment
If you expand the value as a Taylor series in the change in the interest rate,
V(r+\Delta r)=V(r)+V'(r)\Delta r+V''(r)\frac{(\Delta r)^2}{2!}+V'''(r)\frac{(\Delta r)^3}{3!}+\cdots,
so at leading order \Delta V\approx V'(r)\Delta r
If you add in the convexity, you keep another term, so \Delta V\approx V'(r)\Delta r+V''(r)\frac{(\Delta r)^2}{2!}
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