Duration
Duration is a measure of a bond's price sensitivity to interest rate changes, expressed in years. A higher duration means greater price volatility when interest rates change.
🎬 Video Explanation
Exam Tip
Duration = interest rate sensitivity. Higher duration = more risk. Zero coupon: duration = maturity. Rates up 1% = price down by duration %.
What is Duration?
Duration measures how sensitive a bond's price is to changes in interest rates. It represents the weighted average time until a bondholder receives all cash flows (interest and principal). Higher duration = more interest rate risk.
Types of Duration
| Type | Description |
|---|---|
| Macaulay Duration | Weighted average time to receive cash flows |
| Modified Duration | Price sensitivity measure (most commonly used) |
| Effective Duration | Accounts for embedded options (calls, puts) |
Duration as Price Sensitivity
Approximate Price Change = -Duration × Change in Yield
Example:
- Duration: 5 years
- Interest rate increase: 1%
- Price change: -5 × 1% = -5% decline
Duration vs. Maturity
| Factor | Duration | Maturity |
|---|---|---|
| Definition | Weighted average of cash flows | Time until principal repayment |
| Considers Coupons | Yes | No |
| Risk Measure | Yes | Partial |
Factors Affecting Duration
| Factor | Effect on Duration |
|---|---|
| Longer Maturity | Increases duration |
| Lower Coupon | Increases duration |
| Lower Yield | Increases duration |
| Zero Coupon | Duration = Maturity |
Duration Examples
| Bond Type | Typical Duration |
|---|---|
| Money Market | Very low (< 1 year) |
| Short-Term Bond | 1-3 years |
| Intermediate Bond | 4-6 years |
| Long-Term Bond | 7-12+ years |
| Zero Coupon (30-yr) | 30 years |
Duration and Portfolio Management
| Interest Rate Outlook | Duration Strategy |
|---|---|
| Rates Rising | Shorten duration (reduce sensitivity) |
| Rates Falling | Lengthen duration (increase sensitivity) |
| Uncertain | Match duration to investment horizon |
Duration Calculation (Simplified)
For a rough estimate:
- Duration is typically lower than maturity
- Zero coupon bond: Duration = Maturity
- Higher coupon = Lower duration (more early cash flows)
Limitations of Duration
| Limitation | Explanation |
|---|---|
| Linear Estimate | Only accurate for small rate changes |
| Assumes Parallel Shift | Doesn't account for yield curve twists |
| Ignores Convexity | Convexity measures the curve in price/yield relationship |
Convexity
Convexity is the second-order measure that adjusts duration for the curvature in the price/yield relationship. Positive convexity benefits bondholders (price rises more than duration predicts when rates fall).
Exam Alert
Duration measures interest rate sensitivity. Higher duration = more price volatility. Zero coupon bonds have duration = maturity. When rates rise 1%, bond price falls approximately by its duration percentage.
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Related Terms
Interest Rate Risk
Interest rate risk is the potential for investment losses due to changes in interest rates, particularly affecting fixed-income securities like bonds whose prices fall when rates rise.
Bond
A bond is a fixed-income debt security where the issuer owes the holder a debt and pays interest (coupon) plus principal at maturity.
Yield
Yield is the income return on an investment, expressed as a percentage, including interest or dividends received.
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