Work out a callable or putable bond's effective duration and explain what it means
The idea
Effective duration measures sensitivity to a parallel shift in the benchmark curve, allowing the cash flows to change with rates. It is (PV₋ − PV₊) ÷ (2 × ΔCurve × PV₀), where PV₋ and PV₊ are values after the curve moves down and up by ΔCurve. For a bond with options, obtain each value by shifting the curve, recalibrating the tree and revaluing with the OAS held constant. It is the right measure whenever cash flows depend on rates, since modified duration assumes fixed cash flows. Interpret it as the approximate percentage change in value for a 1 percentage point shift. Forgetting the factor of 2 doubles the answer.
In the app: 2 practice questions on this outcome, a narrated walkthrough with diagrams, spaced review that brings it back before you forget it.
Take the free diagnostic →More in Valuation and Analysis of Bonds with Embedded Options
- Explain bonds and other debt securities that contain embedded options
- Explain how a callable or putable bond's value links to the value of its embedded option and of the equivalent straight bond
- Explain how to apply the arbitrage-free approach when valuing a bond that contains embedded options
- Explain the effect of interest rate volatility on what a callable or putable bond is worth
- Explain the effect of shifts in the yield curve's level and shape on what a callable or putable bond is worth
- Use an interest rate tree to work out what a callable or putable bond is worth
- Explain how option-adjusted spreads are computed and what they are used for
- Explain the effect of interest rate volatility on option-adjusted spreads
- Contrast the effective durations of straight, callable and putable bonds
- Explain how one-sided and key rate durations help assess the rate sensitivity of bonds that contain embedded options
- Contrast the effective convexities of straight, callable and putable bonds
- Work out what a floating-rate bond with a cap or a floor is worth
- Set out the key characteristics of a convertible bond
- Work out the parts that make up a convertible bond's value and explain what they mean
- Explain how to value a convertible bond within an arbitrage-free framework
- Weigh the risk and return profile of a convertible bond against the profiles of a straight bond and the underlying common shares