Callable bond vs non-callable bond

So I know that callable bonds will underperform non-callable bonds when rates decline due to their negative convexity. However, do they underperform normal bonds when interest rates rise? I would assume they would because they get a discount due to call feature, but just wanted to check. At best I would think they would equal the performance of nomral bonds when interest rates rise, I see no reason why they would ever outperform non-callable bonds. I checked in the CFAI notes but couldn’t find it.

In fact, callable bonds (usually) will outperform non-collable bonds when interest rates rise CFAI Volume 4, Reading 30, p. 54 explains it Value of MBS = Value of Treasury - Value of pepayment option Lets look at it with an example: Value of MBS = 90 Value of Treasury = 100 Value of prepayment option = 10 90 = 100 - 10 Lets assume when interest goes down 100 bps, value of Treasury goes up by 5 and value of prepayment option goes up by 2, so we have: 93 = 105 - 12 Gain for Treasury is 5; gain for MBS is 3. MBS gain is partially offset by the gain on prepayment option. Treasury outperformed. Now lets assume when interest goes up by 100 bps, value of Treasury goes down by 5 and value of prepayment option goes down by 2, so we have: 87 = 95 - 8 Loss for Treasury is 5; loss for MBS is 3. MBS loss is partially offset by the loss on prepayment option. MBS outperformed.

Callables outperform noncallables when rates rise… as the call option is less valuable…

Thanks for the detailed response volkovv.