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.
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.
Study This Term In
Related Terms
Interest Rate Risk
SecuritiesInterest 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
SecuritiesA bond is a fixed-income debt security where the issuer owes the holder a debt and pays interest (coupon) plus principal at maturity.
Yield
SecuritiesYield is the income return on an investment, expressed as a percentage, including interest or dividends received.