# Callable bonds outperformace

I got this question wrong from a Kaplan essay test, but I genuinely don’t understand their explanation… maybe someone can help.

Cooper suggests buying more callable bonds for the portfolio by stating, “Callable bonds can outperform non-callables after a bond bull market when interest rates start to increase. This is
due to their negative convexity.” State whether you agree or disagree with Cooper’s
statement and explain why.

Disagree: if interest rate rise, bonds with higher convexity will perform better, therefore callable bonds are not preferred in this scenario given their negative convexity

Agree: During a bull market, declining interest and negative convexity result in the duration of
callable bonds declining. That reduced duration is beneficial during a subsequent initial rise in
interest rates. The lower duration reduces the price decline as rates increase.

Callables are limited in their upside when interest rates are low. When interest rates start to rise, the callables will lose less value than their noncallable brethren.

Thanks @S2000magician.
I am still a bit confused, as I thought negative convexity was limiting the upside when interest rate fall but had limited effect when interest rate rise (somewhere in level I o II they say callable bonds behave like straight bond when rate rise). Therefore my point that higher convexity should be preferred anyway in this scenario.

Callable bonds behave like option free bonds when the yield rises above the level where the call option value is essentially zero.

Suppose that when the YTM is 1%, a straight bond has a price of \$1,475 while an otherwise identical callable bond has a price of \$1,015 because it’s callable at 102. Suppose that if interest rates rise to 6%, both bonds will sell at par. The callable bond has lost only \$15 (0.1478%) in value while the straight bond has lost \$475 (32.2034%) in value: the callable outperforms the straight bond.

Higher convexity is preferable for the same duration. The point here is that the callable bond has much shorter (effective) duration at very low yields than does the straight bond. Duration is a first-order effect, while convexity is a second-order effect. Put another way, duration trumps convexity.

I was not considering differences in duration, but I guess these are implicit in the question.
Thanks again, @S2000magician

My pleasure.

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