convertible bond: conversion premium and perform

for a convertible bond, why bond will underperform because of the conversion premium of the bond? I thought the less premium over straight value of the bond, the less attractive the convertible bond. but it is not correct. why? Thanks.

ok when you buy something for 95, which is worth 100, you already profited 5 -thatz discount. Premium is that you are over paying right… so for you to recoup that extra, you should forgo some of the coupon that you get initally, and the time time it takes for you to recoup this premium (partly) is the “Premium payback period” ok now, be careful…I saw a question on this topic, something to do with price and “bid” was in the question - what they implied was which is profitable for you to sell to a dealer - and they showed the dealers bid price, in this case reverse willbe true, more premium the better for you to sell…and lower it is the better for you to buy.