C.W.K.
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Lesson 04 of 07 · published

Duration — how much a bond moves per 1% rate change

~30 min · duration

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How much does the price move when rates move?

From last lesson: bond prices change inversely with rates. Now the natural question: by how much? If yields rise 1%, does the bond's price drop 1%? 5%? 30%? The answer is duration.

Duration measures the bond's price sensitivity to a 1% change in yield. Roughly:

So a bond with duration 7 will drop about 7% in price when yields rise 1 percentage point (and rise about 7% when yields fall 1 percentage point). Same number, both directions.

That's the practical formula. Don't worry about the precise definition — the math is "weighted average time to receive cash flows" which is conceptually clean but rarely needed for retail use. Just know: duration is the price-sensitivity-per-1%-yield-change number.

Rough duration ranges by bond type

  • Cash / money market: duration ~0 (no rate sensitivity)
  • Short-term Treasury (1-3 year): duration ~1-3
  • Intermediate Treasury (5-10 year): duration ~4-8
  • Long-term Treasury (20-30 year): duration ~12-20
  • Zero-coupon bonds: duration ≈ years to maturity (the longest possible)

Longer maturity → larger duration → more price sensitivity. Higher coupon → shorter duration (more cash returned earlier). Zero-coupon bonds have duration equal to maturity because all cash returns at the end.

Why long bonds got murdered in 2022

The 10-year US Treasury yield went from about 1.5% in early 2022 to about 4.5% by late 2022 — roughly a 3-percentage-point rise. With duration around 8-9 for the 10-year, the price math is:

%ΔP ≈ −8.5 × 3.0 = −25.5%

So the 10-year Treasury dropped about 25% in price during 2022. Long-duration funds (like TLT, the 20+ year Treasury ETF) had duration around 17-18, so the math gave:

%ΔP ≈ −17.5 × 3.0 = −52.5%

TLT dropped about 30%+ in 2022 — actually less than the linear approximation predicted, because of convexity (next lesson). Still, "safe" Treasury bonds had stock-like losses for the year. Lesson 7-7 returns to this carnage.

Practical use

If you hold a bond fund and worry about rates rising, the fund's weighted-average duration tells you the expected price impact. A bond fund with duration 7 will lose about 7% per 1% rise in yields. Want less rate sensitivity? Choose lower-duration funds (short-term bond funds) or floating-rate instruments.

Conversely, if you expect rates to fall, longer duration amplifies your gains. Some bond traders deliberately load up on long-duration bonds when they think a rate-cutting cycle is coming.

The takeaway

Duration = price sensitivity to a 1% yield change. %ΔP ≈ −Duration × Δr. Longer-maturity bonds have higher duration → more price movement. Zero-coupon bonds have the highest duration (= years to maturity). Duration explains why long Treasuries crashed in 2022 even though credit risk hadn't changed. Convexity (next lesson) is the second-order correction.

Exercise

  1. A bond fund has duration 5. Yields rise 1.5 percentage points. Approximate % change in fund price?
  2. Same fund, yields fall 0.5 percentage points. Approximate % change?
  3. If you wanted to hedge a 1% rate rise on a portfolio of 10-year Treasuries (duration ~9), and you could short shorter-maturity bonds with duration ~3, roughly how much do you need to short relative to your long position?
  4. Why does a zero-coupon bond have higher duration than a same-maturity coupon bond?

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