LM12: yield-based bond convexity and portfolio properties

convexity

• indicates the change in the modified duration of a bond as its YTM changes

• it accounts for the second-order effect of yield changes on a bond

money convexity

expresses convexity in terms of currency units

fixed rate bond will have greater convexity

the longer its time to maturity, the lower its coupon rate, the lower its YTM

for two bonds with the same duration

the one with the greater dispersion of cash flows has greater convexity

convexity is always positive

for an option free fixed rate bond

a more convex bond outperforms a less convex bond

in both falling and rising yield environments

portfolio duration and convexity

• can be calculated using the weighted average of time to receipt of the aggregate cash flows

• this method is the theoretically correct approach, but it is difficult to use in practice

• can also be calculated using the weighted averages of the durations and convexities of the individual bonds that make up the portfolio

• this method is commonly used, but it implicitly assumes parallel shifts in the yield curve, which are rare