duration changes when interest rate changes

duration is measuring interest rate sensitivity of bond price. If duration is 2, when interest changes by 1%, bond price will change by 2%.

however, is duration going to change when interest rate changes? i vaguely remember so.

Correct. Do a calculation and you will see why.

remember that duration is sort of an “average time weighted maturity” of the CFs. if you have a high discount rate then the PV of the final coupon + principal payment (usually the largest CF) will be lower and thus there is less weight on this CF. If rates are lower then the PV of that final principal + coupon payment will be higher thus will carry a higher weight (i.e. more weight on that final period). It’s pretty mechanical.

With all due respect, you have this backwards.

(Macaulay) duration is not time-weighted cash flows; it’s cash-flow-weighted time. There’s a whacking big difference.

Although modified duration _ is not _ the slope of the price-yield curve (though some prep providers seem to claim that it is), nonetheless the price-yield curve provides a good visualization for the effect on modified duration of a change in yield. When yields are low, the price-yield curve is quite steep, and modified duration is high. When yields are high, the price-yield curve is quite flat, and modified duration is low.

Understood. Modified duration changes depending on the level of yield. Thank you.

the yield on yield curve is spot yield right?

Typically, when someone mentions _ the _ yield curve, they mean (or, at least, should mean) the spot yield curve.

However, depending on context, they may mean the _ par _ yield curve.

I wouldn’t worry about it for the exam. On the exam they’ll make it clear which yield curve (e.g., par curve, spot curve, forward curve) they mean for a given question.

My pleasure.

Please define more on when yields are low why modified duration is high and vice versa?

S200magician