Couldn't get the intuitive meaning - Fixed income, negative meaning, relative, interest, interpret

draz

Please someone help with the intuitive meaning of negative convexity, yield curve related aspects.. and the callable bonds .. out/under perform related to interest rates..
I’m sure there must be threads on these topics.. but couldn’t find them..
How to interpret the below -
“
Early Retirement Provisions
Due to the negative convexity caused by the embedded option, callable bonds do the
following:
1. Underperform non-callables when interest rates fall (relative to the coupon rate)
due to their negative convexity.
2. Outperform non-callables in bear bond markets with rising rates as the
probability of call falls. (When the current rate is lower than the coupon rate,
their negative convexity makes callables respond less to increasing rates.)
3. When yields are very high, relative to coupon rates, the callable bond will
behave much the same as the non-callable (i.e., the call option has little or no
value)

adehbone

Draw the return profile of neg convexity out on an IR/ Price graph and compare the two.

MiniMe7

The call basically creates a cap. So that when rates fall, you don’t benefit from the price rise. everything goes from there. if yields are very high, well the senstivity will be the same as normal bonds cos it’s in the area of the return profile that isn’t altered by the call. it’s only in low rate area of the return proifile that it behaves differently. that’s point 3 dealt with.
point 2, well, if you imagine when the IR is less than the coupon, you must be in the lower end of the return profile, and normal bonds will have benefited from price rises, whereas our callable bond has not (because when rates fall, the likelihood is that the bond will be called to replace with cheaper borrowing, and you won’t benefit therefore from the price rise). so since our bond is worth less to start with, it has further to go (outperform) when prices rise!
point 1 is sort of covered in the brackets/parenthesis above. this results in the value not increasing as much as the non-callable when rates rise.
basically all this means is that you don’t buy callables when rates are falling. but you do buy then when rates are low and expected to rise, like in todays real markets!
god i’m good ;) here’s hoping we pass…