Difference between Macaulay duration and modified duration?

Question

I'm studying finance and am struggling to find the difference between the macaulay duration and the modified duration?

I believe the Macaulay duration is the effective time a bond is due to be repaid in years using a weighted average of future coupons/cashflows.

The bit I'm struggling with is what the modified duration really shows (I think it somehow relates to interest rates and sensitivity).

Using an example in the picture below with a 2 year bond that has a face value of £1000 and 2 annual coupons, I understand that the bond will effectively repay its face value in 1.92 years (Macaulay duration). But what does the modified duration tell me? How does 1.89 relate to interest rate and price sensitivity?

Answer 1

Modified duration is mathematically the derivative of the price of the bond with respect to its yield (or interest rates). A modified duration of 1.89 means that for every 1% change in yield, the price of the bond changes by -1.89%. So if the price of a bond is 102%, and the yield of the bond goes from 5% to 6%, the price of the bond will drop to 100.11% (since price is inversely related to interest rates).

So they are related (and similarly named) measurements but have different applications.