CFA Practice Question
Which of the following statements is (are) true with respect to the price behavior of callable bonds and prepayable securities?
II. At very low levels of interest rates, the call embedded in the bond will have a very low value.
III. Negative convexity will begin to appear for a callable bond at very low yield levels.
IV. At low yield levels, modified duration will overestimate the expected bond price for a given unit change in yield.
I. At very high levels of interest rates, the price of a callable bond will be very close to that of an equivalent non-callable bond.
II. At very low levels of interest rates, the call embedded in the bond will have a very low value.
III. Negative convexity will begin to appear for a callable bond at very low yield levels.
IV. At low yield levels, modified duration will overestimate the expected bond price for a given unit change in yield.
A. I and III
B. I, III, and IV
C. II and III
Explanation: II is incorrect because at very low levels of interest rates, the issuer has a tremendous incentive to call in the bonds and reissue them at a lower coupon rate. Thus, the call embedded in the bond will have a very high value.
User Contributed Comments 10
| User | Comment |
|---|---|
| unpredictor | I thought that duration consistently underestimated bond prices. That's why adding the convexity measure improved the estimate. Hence IV is wrong, no? |
| aggabad | but not in case of callable instruments because callable bond is cheaper that non-callable and at low levels of interest rates it's going to be called most likely |
| motoloco | Modified duration will overestimate, but effective will not. |
| surob | motoloco, you are right. Effective duration wouldn't overestimate b/c it takes into account embedded option of the bond. |
| something | In case of callable bond, convexity is negative, duration as a tangent would be above the actual price, therefore it'll overestimate the price, needs downward correction due to convexity. In case of noncallable bond, convexity is positive, a duration tangent will be below the curve, and actual price, therefore would require positive convexity adjustment to the duration adjusted price. |
| Lambo83 | I'm tired of needing to verify about 20% of the answers (and explanations) on Google. After my research I am confident that IV is incorrect. Modified Duration underestimates at low yields. |
| Lambo83 | In fact I didn't even need to dig deep because any price yield convexity graph will prove the answer here is wrong |
| myron | @Lambo83: Your comment would be correct for non-callable bonds. The question asks about callable bonds and yes, at low yield levels, modified duration consistently overestimate (not underestimate) the expected bond price. Check the graph in the notes and textbook, for CALLABLE bond. |
| editor | hi Lambo83: please comment on specific questions only and avoid stating/implying that you would need to verify "20% of questions/explanations", which is unrelated to this questions. thanks. |
| dbalakos | Very nice question although it should be specified in IV that we are talking about a callable bond as in the previous statements |