Explanation
Macaulay duration is the weighted average of the present value of payments received on a bond, weighted by the year in which the payments are received. If the yield curve changes shape, it will change the present values of the coupons and therefore also the Macaulay duration. Statement I is therefore not correct. However, if the bond were to be a zero-coupon bond, changes in the curve will not affect its duration so long as the interest rate at maturity stays constant.
Modified duration = Macaulay Duration/(1 + rate/compounding frequency). Therefore modified duration will change if the compounding frequency changes, assuming the nominal rate of interest for the coupons are identical. Therefore statement II is correct.When rates are expressed as continuously compounded rates, modified duration and Macaulay duration will be identical. This intuitively follows from the formula for modified duration: Modified duration = Macaulay Duration/(1 + rate/compounding frequency). For continuously compounded rates, the compounding frequency approaches infinity, so the denominator approaches 1, leaving modified duration equal to the Macaulay duration. Therefore statement III is correct.
Convexity is higher for a bond that has its payments spread out compared to a bond that has its payments concentrated at a single point in time. For a bond with a higher coupon, the higher coupons have the effect of spreading the present value of the bond over a longer period, when compared to a bond with lower coupons where the payment is comparatively more concentrated at the maturity. Therefore Convexity is higher for a bond with a lower coupon when compared to a similar bond with a higher coupon. Statement IV is not correct.