- CFA Exams
- 2023 Level II
- Topic 6. Fixed Income
- Learning Module 30. Valuation and Analysis of Bonds with Embedded Options
- Subject 6. Effective Convexity
Seeing is believing!
Before you order, simply sign up for a free user account and in seconds you'll be experiencing the best in CFA exam preparation.
Subject 6. Effective Convexity PDF Download
Effective duration and effective convexity describe the interest rate risk of bonds with embedded options.
Effective Convexity = (PV- + PV+ - 2 x PV0)/[(ΔCurve)2 x PV0]
Since these measures are "effective" they must recognize that a shift in interest rates may bring about a change in cash flows, because embedded options may be exercised. In contrast, modified duration and convexity do not allow for the fact that the cash flows for a bond with an embedded option may change due to the exercise of the option.
In order to calculate effective duration and convexity, we use the binomial model to find both V -and V+. An important assumption is that OAS stays constant when interest rates shift.
Effective convexity includes the effects of yield changes on the cash flows. Effective convexity requires an adjustment in the estimated bond values (V-, V+) to reflect any change in estimated cash flows due to the presence of embedded options. When bonds include embedded options, effective convexity may even be negative. This is in fact just what investors need if they are constructing an estimate that falls within a region of positive convexity, as may be the case with callable bonds for example.
- When the call option is out of money, the callable bond has positive convexity.
- When the call option is near the money, the effective convexity becomes negative. This is because the callable bond is capped by the price of the call option.
- Putable bonds always have positive convexity.
Learning Outcome Statementscompare effective convexities of callable, putable, and straight bonds;
CFA® 2023 Level II Curriculum, Volume 4, Module 30
User Contributed Comments 2
|davidt876||OAS stays constant when interest rate shifts but changes when volatility increases/decreases|
|davidt87||nvm me that's just an assumption necessary to calculate duration/convexity for option embedded bonds|
I am happy to say that I passed! Your study notes certainly helped prepare me for what was the most difficult exam I had ever taken.
My Own Flashcard
No flashcard found. Add a private flashcard for the subject.