Duration of a Bond Portfolio
Duration of a Bond Portfolio
A bond portfolio's duration is the weighted-average duration of all its holdings, weighted by market value (or, equivalently, proportion of portfolio). It represents the average time to repayment and the portfolio's overall interest rate sensitivity.
Key takeaways
- Portfolio duration = Σ(duration of bond i × weight of bond i)
- Larger positions pull portfolio duration toward their own duration
- Portfolio duration is used for risk management, benchmarking, and liability matching
- You can construct a portfolio with a specific target duration
- Duration matching aligns portfolios to investor time horizons and liability dates
The weighted-average calculation
Suppose you hold a bond portfolio with three positions:
| Bond | Market Value | Duration |
|---|---|---|
| Bond A | $2 million | 3 years |
| Bond B | $3 million | 5 years |
| Bond C | $5 million | 8 years |
| Total | $10 million | ? |
Portfolio duration: = ($2M / $10M × 3) + ($3M / $10M × 5) + ($5M / $10M × 8) = (0.20 × 3) + (0.30 × 5) + (0.50 × 8) = 0.6 + 1.5 + 4.0 = 6.1 years
The portfolio's duration is 6.1 years. The largest position (Bond C, 50% of portfolio) pulls the duration toward 8 years. The smaller positions (A and B) contribute less weight.
Practical interpretation
A portfolio duration of 6.1 years means:
- If yields rise 1%, the portfolio loses roughly 6.1%
- If yields fall 1%, the portfolio gains roughly 6.1%
- A 0.5% yield move costs or gains roughly 3.05%
For a $10 million portfolio:
- A 1% yield rise: $10M × 6.1% = $610,000 loss
- A 1% yield fall: $10M × 6.1% = $610,000 gain
- A 50 basis-point move: $305,000 impact
This is the core risk metric that portfolio managers track daily.
Duration and portfolio composition
Portfolio duration varies dramatically based on holdings:
Conservative, short-duration portfolio:
- Holdings: Treasury bills (0.5 years), short-term corporates (1.5 years), intermediate bonds (3 years)
- Portfolio duration: ≈1.5–2 years
- Interest rate risk: Low
- Example: A money market fund or short-duration bond fund like a 1–3 year bond fund
Moderate, intermediate-duration portfolio:
- Holdings: Mix of 5–10 year Treasuries, investment-grade corporates, bonds (various maturities)
- Portfolio duration: ≈4–6 years
- Interest rate risk: Moderate
- Example: BND (Vanguard Total Bond Market), AGG (iShares Aggregate Bond)
Aggressive, long-duration portfolio:
- Holdings: 20–30 year bonds, zero-coupon bonds, lower-coupon bonds
- Portfolio duration: ≈8–12+ years
- Interest rate risk: High
- Example: TLT (iShares 20+ Year Treasury ETF), or a long-duration active bond fund
Real-world examples
BND (Vanguard Total Bond Market ETF):
- Holds a broad mix of U.S. bonds: Treasuries, corporates, mortgages, municipals
- Average duration: ≈ 5.5 years
- Average maturity: ≈ 7.5 years
- A 1% yield rise costs ≈5.5% of NAV
AGG (iShares Core U.S. Aggregate Bond ETF):
- Similar composition to BND
- Average duration: ≈ 5.5 years
- Tracks the Bloomberg U.S. Aggregate Bond Index
TLT (iShares 20+ Year Treasury ETF):
- Holds only long-maturity (20+ years) U.S. Treasuries
- Average duration: ≈ 17–18 years
- A 1% yield rise costs ≈17–18% of NAV
- Much more volatile than BND or AGG
LQD (iShares Investment-Grade Corporate Bond ETF):
- Holds investment-grade corporate bonds
- Average duration: ≈ 7–8 years
- Slightly longer than broad bond index because corporate bonds are typically intermediate to long-duration
HYG (iShares High-Yield Corporate Bond ETF):
- Holds higher-yielding (riskier) corporates
- Average duration: ≈ 5–6 years (shorter than LQD because high-coupon bonds have shorter duration)
- More credit risk; less interest rate risk than LQD
BNDX (Vanguard International Bond ETF):
- Holds investment-grade bonds from developed and emerging markets
- Average duration: ≈ 5–6 years
- Mix of currencies; duration in portfolio's home currency
Duration matching and liability management
Pension funds and insurance companies use portfolio duration to match assets to liabilities.
Example: A pension fund has promised payments:
- $10M due in 5 years
- $15M due in 10 years
- $20M due in 15 years
The fund calculates the duration of these liabilities (weighted-average payout date) and buys bond portfolios with matching duration.
If the liability duration is 10 years, the fund buys bonds with roughly 10-year duration. Interest rate changes now affect assets and liabilities similarly:
- Rates fall → both asset values and liability values rise
- Rates rise → both asset values and liability values fall
The fund is hedged against interest rate moves.
Without duration matching, a pension fund is exposed to "mismatch risk"—assets and liabilities moving in different directions if rates change.
Building a portfolio to a target duration
Asset managers construct portfolios with specific duration targets. If a manager wants a 6-year duration portfolio from available bonds with durations 2, 5, 8, and 10 years:
One possible mix:
- 20% in 2-year bonds
- 40% in 5-year bonds
- 30% in 8-year bonds
- 10% in 10-year bonds
Portfolio duration: = 0.20 × 2 + 0.40 × 5 + 0.30 × 8 + 0.10 × 10 = 0.4 + 2.0 + 2.4 + 1.0 = 5.8 years
Close to 6 years (refinement of weights gets even closer).
Duration rebalancing
As time passes, portfolio duration changes. A bond held for one year is now one year closer to maturity, so its duration decreases by roughly one year.
If a 10-year bond is held for one year, its duration drops from 7.5 years to 6.5 years (approximately). If you wanted to maintain 7.5-year portfolio duration, you'd need to buy longer-duration bonds to offset.
Large bond funds rebalance quarterly or annually to maintain their target duration.
Duration in different market environments
In a falling-rate environment (2019–2020):
- Longer-duration funds (TLT, LQD) soared (gains amplified)
- Shorter-duration funds (short-term corporates, money market) had modest gains
- Portfolio managers who overweight long duration benefit
In a rising-rate environment (2022–2023):
- Long-duration funds (TLT) suffered severe losses (declines amplified)
- Short-duration funds (short-term Treasuries, corporates) had smaller losses
- Portfolio managers who underweight long duration or reduce duration benefit
In a stable-rate environment:
- Duration is less critical; credit spreads matter more
- Portfolio manager skill in picking individual bonds rises in importance
Duration gap analysis
Large institutional portfolios often report "duration gap" or "key rate duration" tables that show:
- Current portfolio duration vs. benchmark duration
- If a manager's portfolio duration is 6.5 and the benchmark is 5.5, the portfolio is "long duration" by 1 year
- This means the portfolio outperforms if rates fall, underperforms if rates rise
Duration gap is a key risk metric for active managers.
Portfolio duration workflow
Simplification: duration as portfolio risk
For most bond investors, portfolio duration is the single most important risk metric.
A portfolio with 4-year duration is half as volatile (in percentage terms) as a portfolio with 8-year duration. If you're uncomfortable with large portfolio swings, you want short duration. If you're prepared for volatility (or expect rates to fall), longer duration is acceptable.
Duration also matters for returns. In a low-rate environment, longer duration amplifies modest rate declines into meaningful gains. In a high-rate environment, shorter duration limits losses if rates rise further.
Next
Portfolio duration tells you the aggregate interest rate sensitivity of your holdings. But individual bonds and portfolios don't move in perfect lockstep with yields. Convexity—the curvature in the price–yield relationship—explains why longer-duration bonds benefit asymmetrically from falling rates. That's our introduction to convexity, the final major topic in this chapter.