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REV: SEPTEMBER 27, 2004
GEORGE CHACKO
PETER HECHT
VINCENT DESSAIN
ANDERS SJÖMAN
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Note on Duration and Convexity
When interest rates go up, bond prices fall.
All actors in the financial markets—money managers, traders, arbitrageurs—know this. But how
do they compare how much prices will change between various financial instruments, before interest
rates actually change? To inform their strategies, traders want to know, for instance, which bond will
lose more in price given that interest rates rise 100 basis points: a 6% coupon bond with a 15-year
maturity or one with a 30-year maturity—or maybe a 9% coupon bond with a 30-year maturity. To
help estimate price sensitivity between bonds of different maturities and coupon rates, two measures
are normally used: duration and convexity.
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As measures, however, duration and convexity are not just limited to bonds. They apply to all
financial instruments, fixed income and equity alike. They also measure price reaction to risk factors
other than just interest rates. Therefore, put more generally, duration and convexity take into account
any change for any risk factor affecting the price of any financial instrument. Although many
examples in this note will center on their use for bonds regarding yield and interest rate changes, this
larger application of duration and convexity should not be underrated.
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The main difference between the two concepts is that duration focuses on small changes in risk
factors, and convexity then builds on duration to adjust for larger changes. For bonds, for instance,
the basic price-yield relationship of an option-free bond—a bond without any embedded options,
such as being callable or putable—dictates that the bond price will change in the opposite direction of
the change in the required yield.1 (A more formal restatement of this note’s first sentence.) When
graphed, this correlation appears as a convex curve (see...