Immunization Principle

Interest Rate Immunization Principle

The principle of interest rate immunization is a strategic approach used in managing multiple liabilities, especially applicable to Type I cash flows. In this context, Type I cash flows refer to those with known scheduled amounts and payment dates, such as a series of fixed mortgage payments. This allows the asset manager to utilize specific portfolio statistics for effective management.

Liability Management Approaches

There are several strategies to manage these liabilities:

• Duration Matching: This strategy involves aligning the duration of the assets in the portfolio with the duration of the liabilities, thereby mitigating the risk of interest rate fluctuations. For instance, if a company has a 10-year loan, it might invest in 10-year bonds to match the duration.
• Derivatives Overlay: This approach involves using derivatives, such as futures contracts on government bonds, to adjust the risk profile of an investment portfolio without having to buy or sell the underlying assets.
• Contingent Immunization: This strategy allows for active bond portfolio management as long as the surplus is above a designated threshold. If the surplus falls below this level, the manager switches to a passive strategy to protect the portfolio from further losses.

Duration Matching

Duration matching is a financial strategy employed to immunize multiple liabilities. This strategy is grounded on the principles of aligning the portfolio Macaulay duration with the investment horizon and ensuring that the initial investment equals or surpasses the present value of the liability. These two conditions can be merged to dictate that the money duration of the immunizing portfolio aligns with the money duration of the debt liabilities.

Money Duration

Money duration, also referred to as “dollar duration,” is the product of the portfolio modified duration and the market value. The modified duration is the portfolio Macaulay duration divided by one plus the cash flow yield per period. This concept is especially beneficial when dealing with multiple liabilities, as the market values and cash flow yields of the assets and liabilities may not be equal.

The money duration for the debt liabilities can be calculated :

$$ \begin{align*} \text{Money Duration} & = \text{Portfolio MacD}_{\text{ur}} \times \text{PV of debt liabilities} \\ & \times \text{Annualized CF yield} [(1 + 2 )] \end{align*} $$

Where:

• Portfolio \(\text{MacD}_{\text{ur}}\) is the portfolio Macaulay duration,
• PV of debt liabilities is the present value of the debt liabilities, and
• Annualized CF yield is the annualized cash flow yield.

Basic point value

Another measure used for money duration is the basis point value (BPV), which is the money duration multiplied by 1 basis point (bp). The BPV is an approximation of the change in market value for each 1 bp change in the cash flow yield. However, it does not include convexity.

The present value of a basis point (PVBP), also known as the PV01 or DV01 in North America, is a closely related risk measure. The total cash outlay on a given date is the sum of the market values of the bonds in the portfolio.

Duration Matching and Immunization of Multiple Liabilities

The primary objective of this strategy is to ensure that the market value of the asset portfolio mirrors the changes in the debt liabilities, irrespective of the fluctuations in interest rates. This is achieved by allowing a parallel upward shift in the yield curve, which results in a decrease in the market value.

Steepening Twist Scenario

A steepening twist scenario occurs when short-term yields on high-quality bonds decrease while long-term yields increase. This results in a loss in the asset portfolio as the cash flow yield increases.

In practice, the manager likely waits until the mismatch is large enough to justify the transaction costs in selling some bonds and buying others. Another method to rebalance the portfolio is to use interest rate derivatives.

Interest Rate Derivatives

Interest rate derivatives are financial instruments that provide a cost-effective method for portfolio managers to maintain the target duration of an immunizing portfolio. This is particularly useful when the yield curve experiences shifts and twists over time. For instance, a significant instantaneous upward shift in the yield curve can decrease the portfolio duration statistics and market value. The Basis Point Value (BPV) of the immunizing asset portfolio also decreases. To close the money duration gap, the asset manager could sell some bonds and buy more of others. However, a more efficient and lower-cost rebalancing strategy is to buy, or go long, a few interest rate futures contracts to rebalance the portfolio.

Consider an asset manager in the United States who chooses to hold a portfolio of short-term bonds for reasons such as greater liquidity, perception of finer pricing in the short-term market, or regulatory requirements that necessitate holding these short-term bonds. In this case, a derivatives overlay strategy can be used to close the duration gap while keeping the underlying portfolio unchanged.

Derivatives Overlay

A derivatives overlay transforms some aspect of the underlying portfolio. In this context, interest rate derivatives are used to change the interest rate risk profile, increasing the portfolio BPV.

Synthetic Barbell Strategy

The asset manager has established a synthetic “barbell” strategy: having positions in the short-term and longer-term segments of the yield curve. The term “synthetic” means “created with derivatives.” The underlying asset portfolio is concentrated in the short-term market. The derivatives portfolio is either at the 6.5-year or 10-year segment of the yield curve. CME Group also has actively traded two-year and five-year Treasury futures contracts. Therefore, the asset manager could choose to spread out the futures contracts across other segments of the yield curve. That diversification reduces the structural risk to the immunization strategy arising from non-parallel shifts and twists to the curve.

The required number of futures contracts to close or reduce a duration gap can be calculated using the following formulas:

$$
N_f = \frac{\text{Liability portfolio BPV} – \text{Asset portfolio BPV}}{\text{Futures BPV}}
$$

Where:

• \(N_f\) is the required number of futures contracts.
• Liability portfolio BPV is the BPV of the liability portfolio.
• Asset portfolio BPV is the BPV of the asset portfolio.
• Futures BPV is the BPV of the futures contract.

$$ \text{Futures }BPV \approx \frac{BPV_{CTD}}{CF_{CTD}}$$

Where:

• Futures BPV is the BPV of the futures contract.
• \(BPV_{CTD}\) is the BPV of the cheapest-to-deliver (CTD) security.
• \(CF_{CTD}\) is the conversion factor for the CTD security.

Contingent Immunization

Contingent immunization combines active and passive investment strategies to manage interest rate risk while aiming to protect against downside risks. This strategy is particularly useful in situations where the initial market value of the asset portfolio is greater than the liabilities, creating a surplus that can be strategically employed.

Key Components of Contingent Immunization

• Surplus Utilization: The surplus, the difference between the market value of the assets and liabilities, provides a cushion that allows asset managers to pursue higher-yield, potentially higher-risk investment strategies. This surplus acts as a buffer that can absorb potential losses from these active strategies without jeopardizing the core goal of meeting liabilities.
• Active and Passive Management Balance: In contingent immunization, the asset manager initially engages in active management strategies. If these strategies prove unsuccessful and the surplus diminishes, the management approach automatically reverts to a purely passive strategy focused on duration matching to ensure liabilities are covered.
• Flexibility in Asset Allocation: With a sufficient surplus, managers can increase portfolio risk by investing in various asset categories, such as equities, fixed income, and alternatives. They can also engage in derivative transactions like buying commodity options or credit default swaps, aiming to maximize returns while maintaining a safety net.
• Liquidity Consideration: Since positions may need to be quickly unwound if losses approach the critical threshold, liquidity remains a crucial criterion in selecting investments under this strategy.

Application in Fixed-Income Derivatives

In fixed-income markets, especially in scenarios involving futures contracts like T-note futures, contingent immunization can be particularly effective. Asset managers may choose to over-hedge or under-hedge based on their expectations of interest rate movements, adjusting the number of futures contracts held accordingly. This approach allows the manager to potentially reduce costs or capture gains based on accurate market forecasts.

Risk Management and Strategy Adjustment

The ability to adjust the hedge—either over-hedging when a decrease in yields is anticipated or under-hedging when an increase is expected—provides a dynamic tool for managing interest rate risk. This flexibility is a core advantage of the contingent immunization strategy, allowing managers to adapt to market conditions to optimize the cost of retiring debt liabilities while maintaining a focus on the primary objective of meeting the underlying financial obligations.

Practice Questions

Question 1: A portfolio manager is considering using a strategy that involves using futures contracts on government bonds to adjust the risk profile of an investment portfolio, without having to buy or sell the underlying assets. This strategy is being considered in the context of managing a portfolio with a present value of corporate debt liabilities of EUR200,052,250, a cash flow yield of 3.76%, a Macaulay duration of 6.00, and a convexity of 45.54. Which of the following strategies is the manager considering?

1. Duration matching
2. Contingent immunization
3. Derivatives overlay

Answer: Choice C is correct.

The strategy that the portfolio manager is considering is called a Derivatives Overlay. A derivatives overlay strategy involves the use of derivatives, in this case futures contracts on government bonds, to adjust the risk profile of an investment portfolio without having to buy or sell the underlying assets. This strategy is often used by portfolio managers to manage interest rate risk, credit risk, or other types of risk in a portfolio. In this case, the manager is considering using futures contracts to adjust the duration and convexity of the portfolio to match the characteristics of the corporate debt liabilities. This can help to reduce the risk of changes in interest rates affecting the value of the portfolio relative to the liabilities. The use of derivatives in this way can provide a cost-effective and flexible way to manage portfolio risk, without the need to trade large volumes of the underlying assets.

Choice A is incorrect. Duration matching is a strategy used to manage interest rate risk by matching the duration of assets and liabilities. While the manager is considering adjusting the duration of the portfolio, the use of futures contracts to do this is more characteristic of a derivatives overlay strategy.

Choice B is incorrect. Contingent immunization is a strategy that involves investing in risky assets while also maintaining a risk-free investment that can be used to meet liabilities if the risky investment performs poorly. This strategy is not being considered by the manager in this case, as there is no mention of a risk-free investment or of investing in risky assets.

Question 2: A portfolio manager is considering a strategy that combines active and passive management for a portfolio with a present value of corporate debt liabilities of EUR200,052,250, a cash flow yield of 3.76%, a Macaulay duration of 6.00, and a convexity of 45.54. The manager actively seeks to increase returns when the portfolio’s surplus is above a certain level. If the surplus falls below this level, the manager switches to a passive strategy to protect the portfolio from further losses. Which of the following strategies is the manager considering?

1. Duration matching
2. Derivatives overlay
3. Contingent immunization

Answer: Choice C is correct.

The strategy that the portfolio manager is considering is called Contingent Immunization. Contingent immunization is a strategy that combines active and passive management. It allows the portfolio manager to actively manage the portfolio to seek higher returns when the portfolio’s surplus, which is the excess of the portfolio’s value over the present value of the liabilities, is above a certain level. If the surplus falls below this level, the manager switches to a passive strategy, specifically immunization, to protect the portfolio from further losses. Immunization is a strategy that matches the duration of assets and liabilities to minimize the impact of interest rate changes. In this case, the manager would adjust the portfolio to match the Macaulay duration of the liabilities, thereby immunizing the portfolio against interest rate risk. This strategy provides a safety net that guarantees a minimum return, while still allowing the potential for higher returns when conditions are favorable.

Choice A is incorrect. Duration matching is a passive strategy that involves adjusting the duration of a portfolio to match the duration of its liabilities. While this strategy is used in contingent immunization when the surplus falls below a certain level, it does not involve any active management component and therefore does not fully describe the strategy the manager is considering.

Choice B is incorrect. A derivatives overlay strategy involves using derivatives to alter the risk profile of a portfolio. While this strategy can be used in conjunction with other strategies, it does not involve switching between active and passive management based on the level of the portfolio’s surplus, and therefore does not describe the strategy the manager is considering.

Glossary

• Contingent Immunization: A strategy that allows for active bond portfolio management as long as the surplus is above a designated threshold.
• Macaulay Duration: A measure of the weighted average time until a bond’s fixed cash flows are received.
• Duration Matching: A strategy used to immunize multiple liabilities.
• Money Duration: The portfolio modified duration multiplied by the market value.
• Bond Price Volatility (BPVs): The rate at which the price of a bond increases or decreases for a set of yields.
• Interest Rate Derivatives: Financial instruments that derive their value from the underlying interest rate.
• Immunizing Portfolio: A portfolio strategy used to manage risk where the duration of assets and liabilities are matched.
• Yield Curve: A line that plots the interest rates of bonds having equal credit quality but differing maturity dates.
• Derivatives Overlay: A strategy that uses derivatives to achieve a desired risk and return profile without changing the underlying portfolio.
• Synthetic Barbell Strategy: A strategy that involves taking positions in both short-term and long-term bonds, using derivatives to create the long-term position.

Portfolio Management Pathway Volume 1: Learning Module 4: Liability-Driven and Index-Based Strategies.

LOS 4(b): Compare strategies for a single liability and for multiple liabilities, including alternative means of implementation.