Why does immunization against interest rate shocks using duration for fixed-income securities work?

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Question restatement: Why does immunization against interest rate shocks using duration for fixed-income securities work?

Option to evaluate: B. Because the gains or losses on reinvested cash flows that result from an interest rate change are exactly offset by losses or gains from the security when it is sold.

Analysis of Option B: This statement captures the core idea behind immunization with duration. When you immunize a portfolio, you typically align the portfolio’s duration with a investment horizon so that the sensitivity of the asset values to interest rate changes (price changes) is offset by the sensitivity of the cash flows (reinvested at new rates). If rates rise, the asset’s price typically falls, but the higher reinvestment rate on intermediate cash flows can compensate, while if rates fall, the asset’s price rises and reinvested cash flows come in at a lower rate. The net effect is that the gains or losses from changing reinvestment income balance the gains or losses from the market value change of the bonds when sold at the horizon. This alignment is the essence of duration-based immunization.

Reasoning about potential criticisms or nuances: In practice, exact offsetting holds approximately for small parallel shifts in the yield curve and assuming constant cash flow timing and no changes in convexity significant enough to break the balance. The statement focuses on the reinvestment risk offsetting the price risk at horizon, which is the intuitive mechanism behind duration immunization. It does not hinge on more complex effects like convexity, which can introduce residual mismatch.

Why conceptual alternatives (if any) would be flawed: Since no alternative options are provided in this input, there is nothing to contrast directly. However, if an option claimed immunization eliminates all risk or relied solely on price changes without considering reinvestment of cash flows, that would be inaccurate, because duration-based immunization relies on balancing price movements with reinvestment income to stabilize the portfolio's value at the horizon.

Summary takeaway: Option B correctly articulates the key mechanism of duration-based immunization—the offsetting relationship between reinvested cash flow gains/losses and changes in the value of the security when sold under interest rate changes.

FINS5530-Financial Institution Mgmt T1 2025

Why does immunization against interest rate shocks using duration for fixed-income securities work?

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