Real-Life Examples Section
Example scenario:
Current bond price (P₀): $1,025
Price if yield increases 50 bps (P₊): $985
Price if yield decreases 50 bps (P₋): $1,058
Current yield: 5.5%
Yield change (Δy): 0.005 (50 bps)
Calculations:
Effective duration: ($1,058 – $985) ÷ (2 × $1,025 × 0.005) = 7.12 years
Dollar duration: 7.12 × $1,025 = $7,298
Basis point value: $7,298 × 0.0001 = $0.73 per bp
Interest rate sensitivity: High (7-12 range)
FAQs
1. What is effective duration?
Effective duration measures a bond’s price sensitivity to changes in benchmark interest rates, accounting for embedded options. It uses actual price changes when yields shift, making it accurate for callable, putable, and mortgage-backed securities.
2. How is effective duration calculated?
Effective Duration = (P₋ – P₊) ÷ (2 × P₀ × Δy), where P₋ is price if yield decreases, P₊ is price if yield increases, P₀ is current price, and Δy is yield change.
3. What is the difference between effective duration and modified duration?
Modified duration assumes fixed cash flows and applies to option-free bonds. Effective duration uses actual price changes and accounts for embedded options, making it accurate for callable and putable bonds.
4. What is a good effective duration?
A good effective duration depends on your risk tolerance and investment horizon. Lower duration (0-3) means lower interest rate risk. Higher duration (7+) means higher risk and higher potential return.
5. Why is effective duration important for callable bonds?
Callable bonds have negative convexity and their duration changes when rates move. Effective duration captures this dynamic, providing a more accurate measure of interest rate risk than modified duration.
6. How does effective duration apply to mortgage-backed securities?
MBS have prepayment risk that changes with interest rates. Effective duration captures how prepayments affect price sensitivity, making it the preferred measure for MBS.
7. What is the difference between effective duration and Macaulay duration?
Macaulay duration is the weighted average time to receive cash flows. Effective duration measures price sensitivity to yield changes. They measure different aspects of bond risk.
8. What is dollar duration?
Dollar duration = Effective Duration × Bond Price. It measures the dollar change in bond price for a 1% change in yield. It helps quantify total price impact.
