Bond Risk Measures and Immunization › Limitations and Practical Considerations

Duration and convexity are powerful tools, but they rest on assumptions that may not hold in practice. Understanding these limitations helps practitioners apply these measures appropriately and recognize when more sophisticated analysis is required.

Common-factor scenario limitation: An individual bond's own-YTM modified duration is a local price sensitivity; it does not assume that all benchmark-curve yields move together. The portfolio and immunization scenarios in this chapter use a common yield change, so a single matched scalar exposure does not describe arbitrary curve-shape changes. In reality, short rates and long rates often move differently. The curve can steepen, flatten, or twist in ways that a single scalar exposure cannot capture. For example, if short-term yields rise while long-term yields stay fixed on an initially upward-sloping curve, the long-minus-short spread narrows: the curve flattens over those maturities. A single common-factor duration approximation would not fully describe portfolio performance in such a scenario. Key rate durations address this limitation by measuring sensitivity to changes at specific maturities, such as the 2-year, 5-year, 10-year, and 30-year points. However, they add complexity to the analysis.

Instantaneous shift assumption: Duration is a local price derivative at a fixed valuation time. Calendar passage changes remaining cash-flow dates, and coupon payments can cause jumps in the measured duration. A previous asset-liability match can therefore drift and require rebalancing; duration need not decrease smoothly or monotonically along every coupon-bond path.

Yield level dependency: Both duration and convexity change as yields change. A portfolio immunized at 5% yields will have different risk characteristics at 3% yields. Large rate movements can materially alter a portfolio's risk profile. The duration and convexity calculated before a rate move may not accurately describe the portfolio's behavior after the move.

Credit and liquidity risks: Duration addresses interest rate risk only. Corporate bonds face additional risks from credit spread changes, defaults, and liquidity conditions that duration does not capture. Spread duration measures sensitivity to credit spread changes and should be considered alongside interest rate duration for corporate bond portfolios. Default and liquidity risks require separate analysis entirely.

Embedded options: Callable bonds and mortgage-backed securities contain embedded options that create negative convexity in certain yield ranges. When rates fall, callable bonds may be redeemed by the issuer, limiting the investor's upside. Standard duration measures can be misleading for these instruments because the cash flow pattern depends on the path of interest rates. Effective duration, which uses scenario-based revaluation to account for how embedded-option cash flows change with rates, is an appropriate sensitivity measure for these securities, alongside full scenario repricing.

Reinvestment assumptions: Immunization assumes coupons can be reinvested at prevailing rates. In practice, transaction costs, minimum investment sizes, and market liquidity affect actual reinvestment rates. An investor receiving a small coupon payment may not be able to reinvest at the quoted market rate due to bid-ask spreads or minimum trade sizes.

Despite these limitations, duration and convexity remain foundational risk measures. They provide a common language for discussing interest rate exposure, enable rapid approximate calculations for portfolio analysis, and form the building blocks for more sophisticated risk management systems. Practitioners who understand both the power and the limitations of these tools can apply them effectively while recognizing situations that require additional analysis.