Determine which of the following statements regarding asset-liability management techniques is true.

• Redington immunization requires that the convexity of the liabilities is greater than the convexity of the assets.
• An advantage of the Redington immunization technique over the cash-flow matching technique is that the portfolio manager has more investment choices available.
• Both Redington immunization and full immunization are based on the assumption that the yield curve has higher yields for longer term investments.
• A fully immunized portfolio ensures that the present value of assets will exceed the present value of liabilities with non-parallel shifts in the yield curve.
• A cash-flow matched portfolio requires less rebalancing than a Redington immunized portfolio, but more rebalancing than a fully immunized portfolio.

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

Step 1: Understanding the Problem and Asset-Liability Management Techniques

The question asks us to identify the true statement among the given options regarding various asset-liability management techniques. We need to evaluate each statement based on the principles of Redington immunization, full immunization, and cash-flow matching.

Step 2: Evaluating Option A - Redington Immunization and Convexity

Redington immunization aims to protect a portfolio from small, parallel shifts in the yield curve. It requires three conditions to be met at the current interest rate [math]i[/math]:

• The present value of assets must equal the present value of liabilities: [math]PV_A = PV_L[/math]
• The Macaulay duration of assets must equal the Macaulay duration of liabilities: [math]Dur_A = Dur_L[/math]
• The convexity of assets must be greater than or equal to the convexity of liabilities: [math]Con_A \ge Con_L[/math]

The third condition, [math]Con_A \ge Con_L[/math], ensures that if interest rates change (even slightly), the present value of assets will increase more than or decrease less than the present value of liabilities, thus maintaining a surplus or at least preventing a deficit. Therefore, the statement "Redington immunization requires that the convexity of the liabilities is greater than the convexity of the assets" is false. It should be the opposite: asset convexity must be greater than or equal to liability convexity.

Step 3: Evaluating Option B - Investment Choices in Redington Immunization vs. Cash-Flow Matching

Let's compare the flexibility in investment choices offered by Redington immunization and cash-flow matching:

• Cash-Flow Matching: This technique requires matching specific cash inflows from assets to specific cash outflows for liabilities precisely in terms of timing and amount. For example, if a liability of $1,000 is due at [math]t=5[/math], a cash-flow matched portfolio would ideally have an asset maturing for exactly $1,000 at [math]t=5[/math]. This approach completely eliminates interest rate risk. However, it is highly restrictive because it requires finding assets with very specific cash flow patterns and timings, severely limiting the available investment universe.
• Redington Immunization: This technique requires matching aggregate portfolio characteristics (present value, duration, and convexity) rather than individual cash flows. As long as these aggregate conditions are met, there is significant flexibility in selecting individual assets. For instance, a portfolio manager can combine various bonds with different maturities and coupon structures to achieve the desired overall duration and convexity, rather than being restricted to assets that mature on specific liability dates.

Given the above, Redington immunization provides a portfolio manager with a much broader range of investment choices compared to the stringent requirements of cash-flow matching. Therefore, the statement "An advantage of the Redington immunization technique over the cash-flow matching technique is that the portfolio manager has more investment choices available" is true.

Step 4: Evaluating Option C - Immunization and Yield Curve Assumptions

Both Redington immunization and full immunization are strategies to manage interest rate risk. They are designed to protect a portfolio's surplus or ensure liabilities can be met despite changes in interest rates.

• Redington Immunization primarily protects against small, parallel shifts in the yield curve.
• Full Immunization offers stronger protection, often by cash-flow matching or by ensuring assets mature precisely when liabilities are due, making it more robust against a wider range of yield curve shifts.

Neither of these techniques inherently assumes that "the yield curve has higher yields for longer term investments" (i.e., an upward-sloping yield curve). While an upward-sloping yield curve is a common observation, immunization strategies are designed to work regardless of the initial shape of the yield curve, by managing the portfolio's sensitivity to interest rate changes. Their effectiveness depends on the nature of the yield curve shifts (parallel, non-parallel) and the matching conditions, not on a specific initial shape. Therefore, the statement "Both Redington immunization and full immunization are based on the assumption that the yield curve has higher yields for longer term investments" is false.

Step 5: Evaluating Option D - Full Immunization and Non-Parallel Shifts

A fully immunized portfolio generally provides a high degree of protection against interest rate risk. One common way to achieve full immunization is through exact cash-flow matching, where assets are purchased to provide cash flows that exactly offset liability outflows at each point in time. If structured perfectly, this approach eliminates interest rate risk. However, the statement claims that a fully immunized portfolio "ensures that the present value of assets will exceed the present value of liabilities with non-parallel shifts in the yield curve." While full immunization offers robust protection, especially against a wider range of yield curve shifts than Redington immunization, stating it "ensures" a surplus for all possible non-parallel shifts might be an overstatement. Large, complex, or unusual non-parallel shifts could still potentially impact the surplus, depending on the specific construction of the "fully immunized" portfolio. A truly "fully immunized" portfolio achieved through exact cash flow matching would be robust to any yield curve shift because cash flows are matched regardless of interest rates. Therefore, this statement is generally considered false in the context of what a typical "fully immunized" portfolio (not necessarily exact cash flow matching) can guarantee against all non-parallel shifts. A cash-flow matched portfolio, a specific form of full immunization, would be the only one to perfectly guarantee this.

Step 6: Evaluating Option E - Rebalancing Requirements

Let's compare the rebalancing requirements for each technique:

• Cash-Flow Matched Portfolio: Once established, a perfectly cash-flow matched portfolio generally requires the least rebalancing related to interest rate changes. The assets' cash flows are designed to match liabilities' cash flows irrespective of interest rate movements. Rebalancing would only be needed if the liabilities change, assets default, or other unexpected events occur, not due to interest rate fluctuations.
• Redington Immunized Portfolio: This technique requires periodic rebalancing. As time passes, the durations of assets and liabilities change, and interest rates may shift, causing the duration match and convexity condition to drift. To maintain the immunized state, the portfolio must be rebalanced.
• Fully Immunized Portfolio: If "full immunization" implies a strategy that eliminates interest rate risk across all possible yield curve shifts (e.g., through exact cash-flow matching or by having assets mature precisely at liability payment dates), it would require very little to no rebalancing related to interest rate changes, similar to cash-flow matching.

The statement says: "A cash-flow matched portfolio requires less rebalancing than a Redington immunized portfolio, but more rebalancing than a fully immunized portfolio."

• "less rebalancing than a Redington immunized portfolio" is true.
• "but more rebalancing than a fully immunized portfolio" is generally false. A cash-flow matched portfolio is often considered the gold standard for minimal rebalancing due to interest rate changes. If a "fully immunized portfolio" refers to exact cash-flow matching, then the rebalancing needs are identical. If it refers to other forms of full immunization, cash-flow matching typically still requires less.

Therefore, the entire statement is false because the second part is incorrect.

Step 7: Conclusion

Based on the evaluation of each statement, only Option B is true. The final answer is B.

Key Insights

• Redington Immunization Conditions: For protection against small, parallel yield curve shifts, a Redington immunized portfolio must satisfy [math]PV_A = PV_L[/math], [math]Dur_A = Dur_L[/math], and [math]Con_A \ge Con_L[/math].
• Investment Flexibility: Cash-flow matching is highly restrictive in asset selection due to its requirement for precise timing and amount of cash flow matches. Redington immunization, by contrast, offers greater investment flexibility because it only requires matching aggregate portfolio characteristics (PV, duration, convexity), not individual cash flows.
• Rebalancing Requirements: Cash-flow matched portfolios typically require the least rebalancing due to interest rate changes, as cash flows are naturally aligned. Redington immunized portfolios require periodic rebalancing to maintain the duration and convexity conditions as time passes and interest rates fluctuate.
• Yield Curve Assumptions: Immunization techniques are designed to manage interest rate risk regardless of the initial shape of the yield curve. They protect against changes in rates, not an assumption about the yield curve's slope.
• Robustness of Full Immunization: While full immunization provides strong protection against interest rate risk, especially if achieved through exact cash-flow matching, claiming it "ensures" a surplus for all non-parallel shifts can be an overstatement depending on how "full immunization" is implemented. Exact cash-flow matching is the most robust form.

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Solution: B

Cash-flow matching limits the number of investment choices available to the portfolio manager to a subset of the choices available for immunization.

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