Consider bonds A and B with similar maturities but where bond A is more convex than bond B$.$ Which ONE of the following statements is correct?

$($a$)$ If bond yields decrease by $100$ basis points, the price of A will increase more than that of B$.$

$($b$)$ If bond yields rise, the duration of bond B will decrease at a faster rate than that of bond A$.$

$($c $)$ If bond yields change by $100$ basis points, applying the modified duration rule will give a better estimate of the new price for bond A than for bond B$.$

$($d $)$ Investors will prefer bond B to bond A$.$

$($e$)$ None of the above