Duration

What Is Duration?

Duration is the most important single number in bond investing, it measures a bond's price sensitivity to changes in interest rates. In its most practical form (modified duration), it answers: "How much will this bond's price change for a 1% (100 basis point) move in yields?"

A bond with a modified duration of 7 will:

• Fall ~7% in price if yields rise by 100 bps
• Rise ~7% in price if yields fall by 100 bps

This simple approximation (which becomes less accurate for large yield moves, that's where convexity matters) is the foundation of all fixed-income risk management, portfolio construction, and trading. Every bond portfolio in the world is managed with duration as the primary risk metric.

Types of Duration

The Duration Spectrum

What Drives Duration

Three factors determine a bond's duration:

1. Maturity

Longer maturity = higher duration. A 30-year Treasury has roughly 8-9x the duration of a 2-year Treasury. This is intuitive: the longer you've committed money, the more sensitive your investment is to rate changes.

2. Coupon Rate

Lower coupon = higher duration. A zero-coupon bond has the maximum possible duration (equal to its maturity) because ALL cash flow arrives at the end. Higher-coupon bonds receive more of their cash flows earlier, reducing the weighted-average time and therefore the duration.

This explains a critical phenomenon in 2020-2021: when the Treasury issued enormous quantities of bonds at near-zero coupons (1-2%), these bonds had unusually high duration for their maturity. When rates subsequently surged in 2022, these low-coupon bonds experienced losses far beyond what investors accustomed to higher-coupon environments expected.

3. Yield Level

At lower yield levels, duration is higher, bonds become more interest-rate sensitive. This is a mathematical consequence of discounting: at low yields, a given change in rates represents a larger proportional change in the discount factor. The practical implication: duration risk was maximized in 2020-2021 when yields were near zero, making the subsequent rate-driven losses extraordinarily severe.

The 2022-2023 Duration Catastrophe

The period from January 2022 to October 2023 produced the worst bond bear market in modern history and the most vivid demonstration of duration risk:

The losses were devastating not because of credit defaults (these were all US government bonds) but purely because of duration. Investors who thought Treasuries were "safe" learned that safety from default risk does not mean safety from interest rate risk.

The Silicon Valley Bank Failure

SVB's collapse in March 2023 was duration risk personified. The bank held $91 billion in held-to-maturity (HTM) securities, mostly long-duration agency MBS and Treasuries purchased at near-zero yields in 2020-2021. As rates rose, these securities accumulated $15+ billion in unrealized losses, exceeding the bank's entire equity capital of $11.8 billion.

When depositors (primarily tech startups and VCs, concentrated and communicative) realized the bank was technically insolvent on a mark-to-market basis, they withdrew $42 billion in a single day, the fastest bank run in history. SVB was seized by regulators on March 10, 2023, followed by Signature Bank on March 12 and First Republic on May 1.

The entire crisis was a duration mismatch: long-duration assets funded by short-term deposits. When rates rose, the assets cratered while the cost of deposits (competing with 5%+ money market funds) soared. The banks were squeezed from both sides.

Duration and Equity Markets

Growth Stocks as Long-Duration Instruments

The concept of duration extends far beyond bonds. Growth stocks, companies whose value depends on cash flows expected 5-15+ years in the future, behave like long-duration bonds:

• A company trading at 50x earnings derives most of its value from distant future cash flows
• When discount rates rise (because interest rates increase), those distant cash flows are worth less today
• The higher the P/E ratio, the more "duration" the stock carries

This framework explains why the Nasdaq 100 (high P/E, growth-heavy) fell 33% in 2022 while the Dow Jones (lower P/E, value-heavy) fell only 9%. Both were responding to the same rate shock, but the Nasdaq carried more "duration."

The Duration Map of Equity Sectors

Convexity: Duration's Partner

Duration provides a linear approximation of price sensitivity, but the actual relationship between yields and prices is curved. Convexity measures this curvature.

Positive Convexity (Favorable)

Most Treasury bonds have positive convexity: prices rise more than duration predicts when yields fall, and fall less than duration predicts when yields rise. This asymmetry benefits the bondholder.

Price change formula: ΔP ≈ -(Duration × Δy) + ½(Convexity × Δy²)

For large yield moves, the convexity term becomes significant. A bond with duration 15 and convexity 200:

• If yields fall 200 bps: ΔP ≈ +30% + 4% = +34% (convexity adds 4%)
• If yields rise 200 bps: ΔP ≈ -30% + 4% = -26% (convexity reduces loss by 4%)

Negative Convexity (Dangerous)

Mortgage-backed securities (MBS) exhibit negative convexity: when rates fall, homeowners refinance, returning principal early and shortening the bond's effective duration. When rates rise, nobody refinances, extending duration. MBS holders get shorter duration when they want longer (rates falling, bond rallying) and longer duration when they want shorter (rates rising, bond falling).

This MBS negative convexity is a systemic risk: the $9+ trillion agency MBS market requires constant hedging by holders (primarily banks, the Fed, and Fannie/Freddie), and the hedging flows amplify rate moves. When rates rise, MBS holders must sell Treasuries to reduce duration (extending their hedge), pushing yields even higher, a pro-cyclical feedback loop.

Portfolio Duration Management

For Bond Portfolios

Active bond managers express their rate view through duration positioning:

• Overweight duration (long duration): Bet that yields will fall, profit from rate cuts
• Underweight duration (short duration): Bet that yields will rise, protect against rate hikes
• Duration-neutral: No rate bet, focus on credit selection or curve trades

The typical duration decision range is ±2 years around the benchmark index duration. A portfolio manager with a benchmark duration of 6 years might run 4-8 years depending on their rate view.

For Multi-Asset Portfolios

The 60/40 portfolio's duration has become a critical consideration. With the Bloomberg Agg at ~6.5 years duration, a 40% bond allocation contributes ~2.6 years of duration to the total portfolio. In a rising-rate environment, this "safe" allocation can drag total portfolio returns significantly, as 2022 painfully demonstrated.

Duration Hedging

Institutions hedge unwanted duration exposure through:

1. Treasury futures: Short ZN (10-year) or ZB (30-year) futures to reduce duration
2. Interest rate swaps: Pay fixed / receive floating to reduce duration
3. Options: Buy puts on TLT or buy payer swaptions for asymmetric protection
4. Inverse bond ETFs: TBT (2x inverse 20+ year) for simpler hedging

Key Takeaways for Traders

1. Duration is the primary risk in "safe" bonds, 2022 proved that a AAA-rated bond can lose 40% purely from rate moves
2. Low-coupon bonds carry extra duration risk, the 2020-2021 vintage of near-zero-coupon Treasuries was uniquely vulnerable
3. Growth stocks ARE long-duration instruments, trade them with the same rate sensitivity framework as bonds
4. Duration risk is maximized at low yield levels, the same 100 bps rate increase hurts much more when starting from 1% than from 5%
5. The convexity of MBS creates systemic feedback loops, large rate moves are amplified by MBS hedging flows