What Is Effective Duration?
Let me explain effective duration to you—it's a way to measure how sensitive bonds with embedded options are to changes in interest rates. This calculation considers that expected cash flows can shift as rates move, making it a solid indicator of risk.
You can estimate effective duration using modified duration if the bond acts like one without options.
Key Takeaways
- Effective duration is a duration calculation for bonds that have embedded options.
- Cash flows are uncertain in bonds with embedded options, making it difficult to know the rate of return.
- The impact on cash flows as interest rates change is measured by effective duration.
- Effective duration calculates the expected price decline of a bond when interest rates rise by 1%.
Understanding Effective Duration
When a bond has an embedded feature, it adds uncertainty to the cash flows, which complicates figuring out the bond's rate of return for you as an investor. Effective duration steps in here to help you calculate how volatile interest rates are in relation to the yield curve, and thus the expected cash flows from the bond.
Specifically, effective duration tells you the expected price drop of a bond if interest rates go up by 1%. Remember, the effective duration value will always be less than the bond's maturity.
A bond with embedded options will behave just like an option-free bond if exercising the option doesn't benefit the investor. In that case, the cash flows won't change with yield shifts. For instance, if current rates are 10% and a callable bond pays a 6% coupon, the company won't call it and reissue at higher rates, so it acts like a non-callable bond.
Here's something important: the longer a bond's maturity, the larger its effective duration.
Effective Duration Calculation
To calculate effective duration, you need four variables: P(0) is the bond’s original price per $100 of par value, P(1) is the price if the yield decreases by Y percent, P(2) is the price if the yield increases by Y percent, and Y is the estimated yield change used for P(1) and P(2).
The full formula is: Effective duration = (P(1) - P(2)) / (2 × P(0) × Y).
Example of Effective Duration
Suppose you buy a bond at 100% par with a current yield of 6%. Using a 10 basis-point yield change (0.1%), if the yield drops by that, the bond prices at $101. If it rises by 10 basis points, the price is $99.25.
Plugging in: Effective duration = ($101 - $99.25) / (2 × $100 × 0.001) = $1.75 / $0.20 = 8.75.
This 8.75 means that for a 1% yield change (100 basis points), the bond’s price would change by about 8.75%. It's an approximation, and you can make it more precise by including the bond’s effective convexity.
