Sample Questions
Question 1
Easy
A callable bond exhibits negative convexity when:
Solution
B is correct.
A callable bond exhibits negative convexity when interest rates are low and the call option is near or in the money. In this region, as rates fall further, the issuer becomes increasingly likely to call the bond, limiting the bond's price appreciation. The price-yield curve bends downward (concave shape) rather than upward (convex shape), creating negative convexity. The price is compressed near the call price.
A callable bond exhibits negative convexity when interest rates are low and the call option is near or in the money. In this region, as rates fall further, the issuer becomes increasingly likely to call the bond, limiting the bond's price appreciation. The price-yield curve bends downward (concave shape) rather than upward (convex shape), creating negative convexity. The price is compressed near the call price.
Question 2
Medium
The bootstrapping method is used to derive:
Solution
C is correct.
Bootstrapping is a method for deriving the spot rate (zero-coupon) curve from the yields of coupon-paying bonds. The process works iteratively: starting with the shortest maturity bond (which gives the first spot rate directly), each subsequent bond's coupon payments are discounted using previously derived spot rates, and the final spot rate is solved for. This produces a complete spot rate curve from observed par bond yields.
Bootstrapping is a method for deriving the spot rate (zero-coupon) curve from the yields of coupon-paying bonds. The process works iteratively: starting with the shortest maturity bond (which gives the first spot rate directly), each subsequent bond's coupon payments are discounted using previously derived spot rates, and the final spot rate is solved for. This produces a complete spot rate curve from observed par bond yields.
Question 3
Hard
A callable bond will most likely have a higher option-adjusted spread (OAS) than an otherwise identical non-callable bond when:
Solution
C is correct.
The OAS measures the spread after removing the effect of the embedded option. If a callable bond has a higher OAS than an otherwise identical non-callable bond, the callable bond is offering additional compensation beyond what its credit risk warrants, meaning it is underpriced (cheap) relative to the non-callable bond.
The OAS measures the spread after removing the effect of the embedded option. If a callable bond has a higher OAS than an otherwise identical non-callable bond, the callable bond is offering additional compensation beyond what its credit risk warrants, meaning it is underpriced (cheap) relative to the non-callable bond.
