What it is
Duration is a measure of a bond's sensitivity to changes in interest rates. Specifically, modified duration tells you the approximate percentage change in a bond's price for a 1% change in interest rates. A bond with a duration of 10 will fall approximately 10% in price when interest rates rise by 1%.
Duration is fundamentally about time: cash flows received far in the future are worth much less when discounted at higher rates, so long-dated bonds are far more sensitive to rate changes than short-dated ones.
The intuition
Consider two bonds, each paying a 2% coupon, maturing in 2 years and 30 years respectively. When interest rates rise from 2% to 4%, the 2-year bond falls slightly — the coupon payments are unattractive, but you get your principal back in 2 years and can reinvest at higher rates. The 30-year bond falls dramatically — you are locked into a below-market 2% coupon for 30 years, and the distant principal repayment is worth much less at higher discount rates.
The approximate price impact formula for a rate change of Δr:
ΔP/P ≈ -Duration × Δr
For a 30-year bond with duration of roughly 18, a 2% rate rise produces approximately a 36% price decline.
Silicon Valley Bank 2023: the canonical modern example
SVB accumulated a large portfolio of long-dated US Treasury bonds and mortgage-backed securities between 2020 and 2022, when rates were near zero and yields were low. When the Federal Reserve raised the federal funds rate from 0.25% to 5.25% between 2022 and 2023 — the fastest rate-hiking cycle in 40 years — the market value of SVB's bond portfolio fell sharply.
SVB had not hedged this duration risk. The portfolio losses exceeded the bank's equity. When depositors became aware of the losses and began withdrawing funds, SVB was forced to sell the bonds at a loss to meet withdrawals, realizing losses that had previously been unrealized. The bank failed over a weekend in March 2023, the second-largest bank failure in US history by assets.
The duration risk was visible in SVB's balance sheet. Long-dated fixed-income assets with short-dated deposit liabilities is a classic duration mismatch — one of the basic risks that bank risk management exists to control. SVB's management chose not to hedge because it would have reduced reported income.
Convexity
Duration is a linear approximation. For small rate changes, it is accurate. For large rate changes, convexity becomes important.
Convexity measures the curvature of the price-yield relationship. Positive convexity means that price falls less than duration predicts when rates rise and price rises more than duration predicts when rates fall. Most standard bonds have positive convexity, which benefits holders in volatile rate environments.
Mortgage-backed securities (MBS) can exhibit negative convexity: when rates fall, homeowners refinance, shortening the expected duration of the security at exactly the moment when longer duration would be beneficial. SVB held significant MBS, compounding its duration risk.
One thing most people get wrong
Duration risk is linear in small rate moves but becomes nonlinear — and worse — for large moves. The 2022-2023 rate cycle was not small. Rates rose 500 basis points in 18 months. Over that range, the linear approximation breaks down significantly, and portfolios with high duration lost substantially more than simplified duration calculations predicted. The SVB failures were worse than linear models suggested precisely because the rate moves were so large. The lesson for risk management: stress-test interest rate exposure at rate moves of 3%, 5%, and 10% — not just 1% — to understand the nonlinear behavior at the tail.