Which of the following statements regarding immunization are true?

• If long-term interest rates are lower than short-term rates, the need for immunization is reduced.
• Either Macaulay or modified duration can be used to develop an immunization strategy.
• Both processes of matching the present values of the flows or the flows themselves will produce exact matching.

• I only
• II only
• III only
• I, II and III
• The correct answer is not given by (A), (B), (C), or (D).

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

Step 1: Understanding the Concept of Immunization

Immunization is a crucial strategy in financial risk management, aimed at protecting a portfolio's net worth or ensuring the ability to meet liabilities from adverse changes in interest rates. This question requires us to evaluate three distinct statements regarding the principles and application of immunization strategies. The statements are:

• Statement I: If long-term interest rates are lower than short-term rates, the need for immunization is reduced.
• Statement II: Either Macaulay or modified duration can be used to develop an immunization strategy.
• Statement III: Both processes of matching the present values of the flows or the flows themselves will produce exact matching.

Step 2: Evaluating Statement I

 Statement I: "If long-term interest rates are lower than short-term rates, the need for immunization is reduced."

This statement is False. The need for immunization arises from interest rate risk, which is the exposure of a financial institution's net worth (assets minus liabilities) to fluctuations in interest rates. This risk is primarily due to a mismatch in the duration of assets and liabilities. The shape of the yield curve—whether it is normal (long-term rates higher than short-term), inverted (long-term rates lower than short-term), or flat—describes the current term structure of interest rates. However, it does not diminish the fundamental underlying interest rate risk if an institution's assets and liabilities have different sensitivities to interest rate changes. Regardless of the yield curve's shape, if there is a duration mismatch, the institution remains exposed to interest rate risk, and thus, the need for immunization persists. The yield curve's shape might influence the *magnitude* or *type* of interest rate changes, but not the *necessity* of managing the inherent risk.

Step 3: Evaluating Statement II

 Statement II: "Either Macaulay or modified duration can be used to develop an immunization strategy."

This statement is True. Both Macaulay duration and modified duration are fundamental measures of interest rate sensitivity and are extensively used in constructing immunization strategies.

• Macaulay Duration: This metric represents the weighted average time until a bond's cash flows are received, effectively indicating the economic life of a fixed-income security. It is expressed in years.
• Modified Duration: This measure quantifies the percentage change in a bond's price for a given percentage point change in yield. It is directly related to Macaulay duration by the formula:

[[math]]D_{Mod} = \frac{D_{Mac}}{1+y}[[/math]]

where [math]D_{Mac}[/math] is the Macaulay duration and [math]y[/math] is the yield per period. In an immunization strategy, the primary goal is often to match the duration of assets to the duration of liabilities to protect against interest rate risk. Both Macaulay and modified duration provide valid means to achieve this duration matching. Modified duration is often preferred for its direct interpretation of price sensitivity, but Macaulay duration also plays a crucial role in understanding the effective maturity and reinvestment risk horizon. Therefore, either measure can be effectively employed in developing an immunization strategy.

Step 4: Evaluating Statement III

 Statement III: "Both processes of matching the present values of the flows or the flows themselves will produce exact matching."

This statement is False. It is crucial to differentiate between two distinct approaches to matching cash flows and their implications for immunization:

• Matching Present Values (Duration Matching): This approach typically involves matching the present value of assets to the present value of liabilities and, critically, matching their durations. While effective in immunizing a portfolio against small, parallel shifts in the yield curve, this strategy is an approximation. It does not guarantee that specific cash inflows will precisely offset specific cash outflows at every future payment date. It relies on the concept of convexity to provide a cushion against larger interest rate movements but is not considered "exact matching" as it doesn't eliminate all forms of interest rate risk, especially those arising from non-parallel shifts or large changes.
• Matching the Flows Themselves (Cash Flow Matching or Exact Matching): This is a more rigorous and robust immunization strategy. It requires structuring the asset portfolio such that the cash inflows from assets exactly meet or exceed the cash outflows required for liabilities on each and every future payment date. This method provides true "exact matching" because it inherently eliminates both price risk (the risk that the present value of liabilities changes) and reinvestment risk (the risk that cash flows cannot be reinvested at the expected rate). By ensuring cash is available precisely when needed, this strategy offers the highest degree of immunization against all types of interest rate changes (assuming no default risk).

Therefore, only "matching the flows themselves" (cash flow matching) leads to exact immunization. Matching present values (duration matching) provides a strong but approximate form of immunization.

Step 5: Conclusion

Based on the comprehensive evaluation of each statement:

• Statement I is False.
• Statement II is True.
• Statement III is False.

Consequently, only Statement II is true. The correct answer is B.

Key Insights

• The necessity of immunization stems from interest rate risk due to duration mismatches and is independent of the yield curve's shape (normal, inverted, or flat).
• Both Macaulay duration and Modified duration are valid and widely used metrics for quantifying interest rate sensitivity and implementing immunization strategies.
• Duration matching (matching present values and durations) offers an approximate form of immunization, primarily effective against small, parallel shifts in interest rates.
• Cash flow matching (matching the flows themselves) provides exact matching, eliminating both price risk and reinvestment risk by precisely aligning asset inflows with liability outflows at each payment date.

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Solution: B

I) False. The yield curve structure is not relevant.

II) True.

III) False. Matching the present values is not sufficient when interest rates change.

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