When is portfolio convexity minimized?

The minimization of portfolio convexity occurs when the Macaulay duration of assets equals the Macaulay duration of liabilities. When the durations are matched, it means that the timing of the cash flows from the assets closely aligns with the timing of the cash flows required for the liabilities. This balance reduces the impact of interest rate changes on the overall portfolio and stabilizes its value.

In this scenario, the convexity of the portfolio is minimized because the symmetrical cash flows from the assets reduce the portfolio's exposure to interest rate risk. A portfolio with equal durations is less sensitive to changes in interest rates; hence, it exhibits more stable value changes in response to shifts in yields. Convexity, which represents the second derivative of price with respect to yield, would be influenced negatively if there were mismatches in durations, ultimately leading to greater sensitivity to interest rate fluctuations.

While options regarding the present value of assets and liabilities or equal asset maturities may affect other aspects like credit risk or liquidity, they do not directly address the minimization of convexity in relation to matching durations.