By modelling duration and modified duration in Excel, I found that modified duration approximates bond price change well when there is a 1% increase in yield, while duration is a good approximation when there is a 1% decrease in yield. I checked this with about 10-15 couples of coupon rates and YTM, and it seems it works always. Is this true? If yes, what is the reason behind it?
By duration I mean Macaulay duration; by modified duration I mean duration / (1+yield)