Portfolio duration and convexity

In short

• Two methods: (1) treat the portfolio's aggregate cash flows as one bond and use their weighted-average time to receipt; (2) take the weighted average of the individual bonds' durations and convexities.
• Method 1 is theoretically correct but hard to use in practice. Method 2 is what portfolio managers commonly use.
• Weights are each bond's share of total market value (full value), not par value.
• Plug portfolio duration and convexity into the same estimate: $-D_P \Delta y + \tfrac{1}{2} C_P (\Delta y)^2$.
• The weighted-average approach implicitly assumes a parallel shift: every bond's yield moves by the same amount. Real curves often steepen, flatten or twist.
• It is more accurate when the bonds' yields are close to each other and the yield curve is flat.