Duration & Rate Risk
Modified duration, why long bonds lose more when rates rise, and convexity simplified
In 2022, the Federal Reserve raised rates from near-zero to 4.50% — the most aggressive tightening cycle since Paul Volcker in the early 1980s. The Bloomberg U.
S. Aggregate Bond Index lost 13%. But that average masked enormous dispersion: short-term Treasury bills barely moved.
Intermediate bonds fell 10-15%. The iShares 20+ Year Treasury ETF (TLT) fell 31%. Same asset class, same rate environment, wildly different outcomes.
The variable that explains almost all of the difference is a single number: duration. Duration tells you exactly how much pain a rate change will inflict on your bond position — before it happens. Source: Bloomberg Index Services (Agg return); iShares TLT NAV total return 2022; FRED (Fed funds target range).
Duration answers a single question: if yields change by 1 percentage point, how much does my bond's price change? A bond with duration 5 loses approximately 5% if yields rise 1% and gains approximately 5% if yields fall 1%.
That is the opening. Finishing a lesson is where it stops being interesting and starts being useful: the full lesson runs to 7 sections and ends with 5 practice questions. A free account is what opens the rest, and the other 255 lessons in the Academy with it. No card.
What this lesson covers
- 1Duration: the interest-rate sensitivity number
- 2Modified duration — the practitioner's formula
- 3Duration by bond type — sensitivity ranges
- 4Applying duration to 2022: why TLT lost 31%
- 5Convexity: why duration is only an approximation
- 6The duration + convexity price change formula
- 7Where to see this on the platform