Callable Bond vs Bulllet

CFA Level III Fixed Income
#1

CFAI Online assessment FIPM-Spong question no.5, which compares the performance of callable/puttable stuctures vs. bullet in a lower interest rate volatility and steepen yield curve environment. I don’t get the highlighted part. With high interest rates, call option value will decrease. Then how does this lead to the conclusion that callables will outperform bullets??

Solution says

Spong’s fourth statement indicates that Vertex expects a 25 bp rise in short-term rates and a 75 bp increase in long-term rates—that is, the yield curve is expected to steepen. In this environment callables and putables will outperform bullet structures. As rates rise, given low implied interest rate volatility, the probability of a call diminishes as does the value of the call option. Consequently, callables will outperform bullets. As rates rise the put option becomes more valuable, furthermore the put allows the investor to put the option back at par, thus avoiding losses. For these reasons, the value of the putable structure can be expected to increase. In contrast, the bullet structure will decline in value. Thus, putables also outperform bullets.

#2

Spoiler

In the question it is said that Vertex is evaluating total return and the question writer drops in that “…annual reinvestment rate [are] 2%”.

This is our cue that interests rates are low.

In low interest rate environment the price/yield relationship of a callable bond exhibits negative convexity i.e. the curve, which, in near-zero and rising interest rates would normally go down in an almost-straight line, is actually going sideways for for callable bonds.

So if we compare:

In low and rising yields

  • bullet structure: price goes down in almost-straight line;

  • call structure: price goes sideways hence these structures perform better than (i.e. returns are less negative than) bullet.

As the answer indicates this is due to the value of the call option that reduces interest rate sensitivity (bad for the bondholder if interests are falling but good if interests are rising).

Good luck, Carlo