# Spong - 2014 CFAI Mock (PM), Version A

Can anyone explain why callables would outperform bullets with a steepening of the yield curve? Is it because the embedded call option dminishes in value to the issuer, and that makes the bond more valuable to the holder? Confused…

“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.”

If interest rates increase, value of callable bond would not depreciate as much as price of non-callable would. this is because of negative convexity effect.

however if int rates fall, the value of callable bond would not appreciate as much as non callable bond; that’s why negative convexity bonds face int rate risk in the event of decrease in interest rates.

That makes sense, even more so when I draw it out on a graph. THANKS!

Here’s another way to look at it also:

Let’s say we’ve been in a period of declining rates. Everything else being equal, we know that our bullet bond has outperformed our callable bond. Beause the callable bond exhibits negative convexity its price has not appreciated as much as the bullet bond.

When interest rates rise the bullet bond will fall more in value versus the callable because it exhibits no convexity. In essence, the bullet bond’s price has a longer distance to drop when rates rise. Most call provisions in callable bonds are generally only 1-5% over par. Due to its negative convexity it can’t trade much higher than that.

The key thing to look out for on these types of questions is the interest rate environment.