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想詢問這個該如何證明？

of duration relat-
ing to the maturity, yield, and coupon interest of the security being analyzed.
Duration and Maturity
A comparison of Tables 9-6, 9-3, and 9-7 indicates that duration increases with the
maturity of a fixed-income asset or liability, but at a decreasing rate:4
OD
OM
> 0
d²D
dM²
<0
To see this, look at Figure 9-4, where we plot duration against maturity for
a three-year, a two-year, and a one-year U.S. Treasury bond using the same yield of
4 This is the case for the vast majority of securities. It needs to be noted, however, that for bonds selling
below par, duration increases at a decreasing rate up to a point. At long maturities (e.g., 50 years) dura-
tion starts to decline. Few bonds in the market have a maturity long enough to see this decline.