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What Is Effective Duration?
Effective duration is a duration calculation for bonds that have embedded options. It is used to measure the risk that expected cash flows will fluctuate as interest rates change.
Effective duration can be estimated using modified duration if a bond with embedded options behaves like an option-free bond.
Key Takeaways
- Effective duration shows how sensitive bonds with embedded options are to changes in interest rates.
- It accounts for fluctuating expected cash flows due to changing interest rates, providing a risk measure.
- Effective duration estimates a bond’s price decline when interest rates increase by 1%.
- A bond behaves like an option-free bond if exercising its embedded option offers no benefit.
- Effective duration is lower than the bond’s maturity, indicating how price sensitivity decreases over time.
How Effective Duration Impacts Bond Pricing
A bond that has an embedded feature increases the uncertainty of cash flows, thus making it hard for an investor to determine the rate of return of a bond. The effective duration helps calculate the volatility of interest rates in relation to the yield curve and, therefore, the expected cash flows from the bond. Effective duration calculates the expected price decline of a bond when interest rates rise by 1%. The value of the effective duration will always be lower than the maturity of the bond.
A bond with embedded options acts like an option-free bond if exercising the option doesn’t benefit the investor. As such, the security’s cash flows can’t be expected to change given a change in yield. For instance, if interest rates are 10% and a callable bond pays a 6% coupon, the bond behaves like an option-free bond. The company wouldn’t benefit from calling and reissuing it at a higher rate.
Important
The longer a bond’s maturity, the greater its effective duration.
Calculating Effective Duration: A Step-by-Step Guide
The formula for effective duration contains four variables. They are:
- P(0) = the bond’s original price per $100 worth of par value
- P(1) = the price of the bond if the yield were to decrease by Y percent
- P(2) = the price of the bond if the yield were to increase by Y percent
- Y = the estimated change in yield used to calculate P(1) and P(2)
The full formula for effective duration is:
Effective duration = (P(1) – P(2)) / (2 × P(0) × Y)
Example of Effective Duration
As an example, assume that an investor purchases a bond for 100% par and that the bond is currently yielding 6%. Using a 10 basis-point change in yield (0.1%), it is calculated that with a yield decrease of that amount, the bond is priced at $101. Increasing the yield by 10 basis points is expected to lower the bond’s price to $99.25. Given this information, the effective duration would be calculated as:
Effective duration = ($101 – $99.25) / (2 × $100 × 0.001) = $1.75 / $0.20 = 8.75
The effective duration of 8.75 means that if there were to be a change in yield of 100 basis points, or 1%, then the bond’s price would be expected to change by 8.75%. This is an approximation. The estimate can be made more accurate by factoring in the bond’s effective convexity.
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