Fixed Income Callable Bonds Question

Schweser Constructed Response Question:

B. 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.

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.

My response was: Disagree. Callable bonds can outperform non-callabes in a rising rate environment if the higher yield earned from holding callable bonds is higher than the yield on the same bond without the embedded call. However, this is not due to negative convexity. Negative convexity is always a negative to a bondholder, and will not cause them to outperform.

Essentially, all-else equal, callable bonds should not perform during rising rate environment explicitly due to negative convexity. I don’t know how we are supposed to assume that in this case the bond was held during the bull market, duration declined, and then that resulted in the callable bond outperforming… It seemed to me that the question was asking specifically whether or not negative convexity can cause bonds to outperform during rising rates, and that answer is a definitive NO.

Any help? Am I looking at this wrong?

I disagree and the provided answer is correct. The callable will outperform due to lower duration at lower yields (hence after a bull market) which is a consequence of its negative convexity. Just plot the pice-yield curve for a callable against a non-callable and it’s quite obvious. The slope of the curve is the (negative) dollar duration of the bond and it’s less negative for the callable when yields are close to zero.

Yes, you are wrong - the official answer is right!

Negative covx does not always underperform the non-optional 1. The traditional curves plot (you are probably referring to) lines up the callable and non-callable based on current par value not on current par yield, which is higher for mbs due to the call option

Rising yields will lower probability of option itm so the value attributed to the yield component, which is higher, outperforms