第一个不对，你要是被call了 还有reinvest 风险，就算YTC大 那也只能到你被Call的那天，后面的呢~~

1. this is essentially about comparing bonds with different yield and maturity, so the usual assumption here is that u could realize or materialize a reinvest yield equal to the call yield (or even better), and under this assumption, call is always better than full maturity. but practically, as jessicagyh pointed out, that assumption may break, and the interest rate or yield risk in reinvestment is always present.

2. i think there is an implicit condition here that the bond is priced at par on issue. this has to do with the scenario or condition of the exercise of the call option embedded within the bond. when would the issuer of bond choose to call? only if it's beneficial to the issuer. now u've got the key that the call price Pc >= maturity price or par price P0, and call has a less life time than full maturity. therefore, if the issuer exercises the call, they'll end up paying more within a shorter time span. put it this way, which one would u choose? pay me $110 today? or pay me $100 in a year? sure u could issue a new bond and use the proceeds from new issue to pay me today, but the discount spot price implies u gotta face a steeper interest rate or yield (compared to issue), which would give u little incentive to exercise the call and refinance. so the only option the issuer has under this circumstance for call or refinancing is to wait til the bond price goes up to premium, or equivalently the interest rate or yield drops low enough. just remember, the callable bond gives issuer an option for later refinancing at beneficial conditions, and no matter how desperate he or she is, a debtor would never borrow another 10% loan to pay his or her current 8% debt. of course, as a bondholder, u may wish the bond call happens so u can materialize a high yield. but unfortunately the option privilege in callable bond belongs to issuer, so your wish would only stay up in the air unless your bond issuer is a total tosser.  back to your question, YTC is meaningless under this scenario because the refinancing environment is so bad that exercising the call would only make the issuer worse off.

我看书的时候也正好碰到了楼主的问题，了解2楼的意思了。YTC始终是根据n、FV(call price)、PV和PMT这几个值算出来的。当你确定了call date这天时，PV是根据spot rate计算的，n只到call date这天，FV也可以确定好，即使计算出的YTC>YTM,也只到当天的情况，也许之后PV和call date变化后，YTC和YTM之间的大小关系就不能确定了呢。因此不能说一时的YTC>YTM就能保证你买下来不会有call的风险。

Nice...