# Sample Exam # 3, Q14- Callable bonds

Why do they believe that callable bonds will outperform bullets when we have rising interest rates ??? Isn’t it’s true only if yields are lower than coupon rates ? But they didn’t gave any such details in the question. So in general I supposed we should consider such question from the interest rate level equal to coupon rate unless otherwise specified (decreasing interest rates – due to negative convexity callables’ll underperform bullets, rising interest rates – perfomance of callables’ ll be identical to bullets). That’s from level 1….

Price of a Callable Bond = price of Non-callable bond (such as a bullet) - Call Value In a rising interest rate environment, the value of the call option declines as it becomes more out of the money: eg: assume it’s callable at 100, the value of the call wouldn’t worth as much when the price of the bond is at 95 compared to when it’s at 98. Correct me if I am wrong…

You’d be outperforming vs a non-callable bond by the difference in the call value.

in general, there’s a spread between callable and bullet. with interest rate rising, the call becomes remote, the spread narrows. as a result, the value decline of callable is slower than its bullet countparty. of course, up to a point, the two converges.

this is probably way too simplistic (and maybe wrong), but, I think of it like this: you pay less for a callable bond due to the call feature. with rising interest rates the price approaches the bullet, hence the callable bond will outperform (return prespective) a bullet in rising interest rates.

They callable will outperform in a rising rate environment becasue their price is already not as high as the bullet due to the negative convexity. Therefore, when interest rates rise, they will fall by less than the bullets. But when rates get really high, the point is moot and bot perform poorly.

Guys, look at the graph for callable vs bullet: to the left of coupon rate there is negative convexity area (here I agree with CFA logic) but to the right perfomance is identical

Peter is right - The logic holds when the MBS is in the negative convexity region and therefore already at a discount to the bullett. When the rate go up, the prices of both will go down, but the MBS less so since it is already at a lower price.