Bonds & Fixed Income· Lesson 4 of 8· 5 min

Duration and Interest Rate Risk

For the same 1% rise in rates, a 10-year bond falls far more than a 1-year bond. Duration measures exactly this sensitivity.

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Text version · Bonds & Fixed Income, lesson 4: “Duration and Interest Rate Risk”

For the same 1% rise in rates, a 10-year bond falls far more than a 1-year bond. Duration measures exactly this sensitivity.

Duration = sensitivity to rates

A bond with a duration of 8 falls about 8% in price for every 1% rise in rates. The longer the maturity and the lower the coupon, the bigger the duration.

Duration = the cash flows' center of gravity

Place each cash flow's present value on a timeline: the point where it balances is the duration (in years).

Convexity: gains more, loses less

Duration is a straight-line estimate, but the real price curve bends. This convexity means bonds rise more than estimated when rates fall and fall less than estimated when rates rise, and the bigger the move, the more noticeable it is.

Key takeaways

(Modified) duration ≈ the percentage price change for a 1% change in rates. Macaulay duration is the "center of gravity" of the cash flows, measured in years.
The longer the maturity and the lower the coupon, the higher the duration and the bigger the interest rate risk.
Price change ≈ −duration × change in rates.
Convexity makes real price changes "rise more, fall less". The bigger the rate move, the more the duration estimate is off.

Try it yourself

You can do these exercises in this lesson's interactive simulation:

Click “Example: rates up 1%”: roughly what's the 10-year bond's duration? What are the “Estimated change” and the “Actual change”?
Drag the rate change to +3%: which of the three bonds falls the most? How far apart are the dashed line (estimate) and the real bar?
Drag to −3%: how much does the 30-year zero rise? Why is the real gain even bigger than the estimate?
Switch through the three bonds and see which year the balance point (center of gravity) of the beam below lands on.

Quiz and explanations

1. A bond has a duration of 8 years and rates rise by 1%. Its price roughly…: Answer: Falls 8%.−8 × 1% = −8%.
2. Which bond is most sensitive to interest rates?: Answer: A 30-year zero-coupon bond.It has the longest maturity and no cash flows along the way, so its duration is the highest.
3. A bond priced at $1,000 has a modified duration of 6. Rates fall by 0.5%. Roughly what's its new price?: Answer: $1,030.−6 × (−0.5%) = +3%, and $1,000 × 1.03 = $1,030 (convexity makes it slightly more in reality).

Terms in this lesson

convexity (Convexity): How much the price-yield curve bends; convexity makes bonds gain more than duration predicts when rates fall and lose less when rates rise.
duration (Duration): How sensitive a bond's price is to interest rates: a 1% rate move changes the price by roughly “duration” percent.
present value (Present Value): What a future amount of money is worth today after discounting at an interest rate.