Determine which of the following statements is false with respect to Redington immunization

• Modified duration may change at different rates for each of the assets and liabilities a time goes by.
• Redington immunization requires infrequent rebalancing to keep modified duration ofassets equal to modified duration of liabilities.
• This technique is designed to work only for small changes in the interest rate.
• The yield curve is assumed to be flat.
• The yield curve shifts in parallel when the interest rate changes.

Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.

Step 1: Understanding Redington Immunization

Redington immunization is a strategy used in finance to protect a portfolio (typically an insurance company's assets and liabilities) from the impact of interest rate changes. The goal is to ensure that the surplus (Assets - Liabilities) remains stable even when interest rates fluctuate. This technique relies on satisfying three main conditions:

• Present Value Condition: The present value of assets must equal the present value of liabilities. This ensures that the portfolio is solvent at the initial interest rate.

[[math]]PV_{Assets} = PV_{Liabilities}[[/math]]

• Duration Matching Condition: The modified duration of assets must equal the modified duration of liabilities. This condition protects against small, parallel shifts in the yield curve, as it ensures that the present values of assets and liabilities change by approximately the same amount.

[[math]]ModDur_{Assets} = ModDur_{Liabilities}[[/math]]

• Convexity Condition: For a single liability, the convexity of assets must be greater than the convexity of liabilities. This condition provides protection against larger interest rate shifts and ensures that the surplus remains positive after interest rate changes.

[[math]]Convexity_{Assets} \gt Convexity_{Liabilities}[[/math]]

Step 2: Evaluating Each Statement

We will now analyze each statement provided in the question to determine its accuracy in the context of Redington immunization.

Statement A: Modified duration may change at different rates for each of the assets and liabilities as time goes by. This statement is True. Modified duration is a measure of interest rate sensitivity that changes as time passes and as interest rates change. Assets and liabilities typically have different cash flow patterns and maturities. Consequently, their modified durations will evolve differently over time, requiring adjustments to maintain the immunization conditions.

Statement B: Redington immunization requires infrequent rebalancing to keep modified duration of assets equal to modified duration of liabilities. This statement is False. As discussed in Statement A, modified durations of assets and liabilities change over time due to the passage of time, changes in the yield curve, and cash flows. To maintain the duration matching condition necessary for immunization, the portfolio must be frequently rebalanced. Infrequent rebalancing would expose the portfolio to interest rate risk.

Statement C: This technique is designed to work only for small changes in the interest rate. This statement is True. Redington immunization relies on duration and convexity, which are essentially first and second-order approximations of how present values change with interest rates. These approximations are most accurate for small, incremental changes in interest rates. For large interest rate shifts, these approximations become less reliable, and the portfolio may no longer be immunized.

Statement D: The yield curve is assumed to be flat. This statement is True in the context of how Redington immunization is often applied and simplified. While the core theory of Redington immunization primarily assumes parallel shifts in the yield curve, many practical applications and problem-solving scenarios simplify by assuming a flat yield curve where a single interest rate is used for discounting all cash flows. This simplification allows for easier calculation of duration and convexity.

Statement E: The yield curve shifts in parallel when the interest rate changes. This statement is True. This is a fundamental assumption of Redington immunization. The theory postulates that when interest rates change, all interest rates across the entire yield curve (for all maturities) shift up or down by the same amount. This parallel shift assumption simplifies the analysis and allows duration to be an effective measure of interest rate sensitivity across all maturities.

Step 3: Identifying the False Statement

Based on the analysis in Step 2, the only statement that is false is Statement B. Redington immunization requires frequent rebalancing, not infrequent rebalancing, to maintain its effectiveness. The final answer is B.

Key Insights

• Redington immunization aims to protect a portfolio from interest rate risk by ensuring the present value of assets equals liabilities, and their modified durations are matched.
• A key assumption of Redington immunization is that interest rate changes cause parallel shifts in the yield curve.
• The effectiveness of Redington immunization is primarily for small changes in interest rates, as it relies on Taylor series approximations (duration and convexity).
• Modified durations of assets and liabilities are dynamic; they change over time and with interest rate movements. Therefore, frequent rebalancing is essential to maintain the immunized position.

This article was generated by AI and may contain errors. If permitted, please edit the article to improve it.

Solution: B

All are true except B. Immunization requires frequent rebalancing.

Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.