relationship between coupon rate/ market yield and interest rate risk

CFA Level I
#1

how does a lower coupon rate or a lower market yield imply a lower interest rate risk??

#2

it should be the other way round?? lower the coupon payment and lower the ytm greater the percent changes in market price of bond for a 1% change in interest rate!!

#3

yes. it is the other way round

#4

Lower coupon rate ==> higher duration: higher interest rate risk.

Lower YTM ==> higher duration: higher interest rate risk.