Answer: If a consol (perpetual) bond with a $100 face value pays a 3.0% coupon in perpetuity and the yield is 5.0%, the consol's price is $60 and its modified duration is 20 years.

For a consol (perpetuity) with annual coupon \(C\) and yield \(y\): \[ P = \frac{C}{y} \] Here, \(C = 3\) and \(y = 5\%\), so: \[ P = \frac{3}{0.05} = 60 \] For a perpetuity, the **modified duration** is: \[ D_{mod} = \frac{1}{y} = \frac{1}{0.05} = 20 \] So **A** is true. Why the others are false: - **B**: Higher convexity does not guarantee superior performance; return also depends on carry, yield curve shifts, and financing effects. - **C**: Duration and convexity generally rise with maturity, but DV01 is not a universal monotonic rule in all settings. - **D**: Portfolio convexity is also value-weighted across component bonds, so this statement is false.

Author: Manit Arora