Liabilities and Liability-Driven Investment (LDI) Strategy
The liabilities are classified into four types: Type I, Type II, Type III, and Type IV. Each type has unique characteristics and implications. We will focus on Type IV liabilities
Model Development for Type IV Liabilities
The model development process for Type IV liabilities involves two main steps. The first step is to establish the model assumptions. These assumptions form the foundation of the model and influence the model’s outcomes. Hence, it’s crucial to select realistic and appropriate assumptions.
The second step is to calculate future liabilities based on the model assumptions established in the first step. This calculation provides an estimate of the potential obligations that the organization may have to meet in the future.
Financial Modeling Assumptions in Pension Plans
The model assumes a typical employee who has been employed for G years and is projected to work for another T years before retiring and living for Z years. The retirement benefits are computed based on the final wage (W), a multiplier (m), and the total number of years worked (G + T).
There are two measures of retirement obligations: the accumulated benefit obligation (ABO) and the projected benefit obligation (PBO). The ABO is calculated based on the years worked and the current annual wage \(W_0\), even though the annuity paid in retirement is based on the final wage \(W_T\) and total years worked (G + T). The ABO represents the legal liability of the plan sponsor if the plan were to be closed or converted to another type of plan. The ABO is the present value of the projected annuity, discounted at an annual rate r on high-quality corporate bonds.
$$ABO = \frac{1}{(1 + r)^T} \left[ \frac{m \times G \times W_0}{1 + r} + \frac{m \times G \times W_0}{(1 + r)^2} + \ldots + \frac{m \times G \times W_0}{(1 + r)^Z} \right]$$
The PBO, on the other hand, uses the projected wage for year T instead of the current wage in the Z-year annuity. The PBO is the liability reported in financial statements and used to assess the plan’s funding status.
$$PBO = \frac{1}{(1 + r)^T} \left[ \frac{m \times G \times W_T}{1 + r} + \frac{m \times G \times W_T}{(1 + r)^2} + \ldots + \frac{m \times G \times W_T}{(1 + r)^Z} \right]$$
The relationship between \(W_0\) and \(W_T\) is given by \( W_T =W_0 \times (1 + w)^T\), where \(w\) is the average annual wage growth rate for the employee’s remaining work life of \(T\) years.
The PBO will always be larger than the ABO by the factor of \((1 + w)^T\), assuming positive wage growth in nominal terms.
The assumed post-retirement lifetime (Z years) is crucial. A higher value for Z increases both the ABO and PBO measures of liability. The pension plan faces longevity risk, which is the risk that employees live longer in their retirement years than assumed in the models.
Another significant assumption is the time until retirement (T years). In the ABO measure, increases in T reduce the liability. That result also holds for the PBO as long as wage growth (w) is lower than the discount rate (r). Assuming w is less than r is reasonable if it can be assumed that employees over time generally are compensated for price inflation and some part of real economic growth, as well as for seniority and productivity improvements.
Effective Duration and Basis Point Value
Effective duration is a key concept in financial analysis, especially when dealing with assets and liabilities. It is calculated by adjusting the yield curve in the valuation model and recalculating the present values. It is crucial in determining the potential risks and liabilities associated with different financial measures such as the Accumulated Benefit Obligation (ABO) and the Projected Benefit Obligation (PBO).
BPV helps in understanding the sensitivity of the assets and liabilities to changes in interest rates. For example, if the asset BPV is significantly lower than the liability BPV, the pension plan may face a deficit if all yields decrease by 10 bps.
Addressing the Duration Gap
The duration gap is the difference in the duration of assets and liabilities. A pension fund manager can reduce or even completely eliminate this gap using financial derivatives. The larger the duration gap, the more sensitive a firm is to changes in interest rates. One way to hedge against this risk is by using futures contracts.
For instance, consider the Ultra 10-year Treasury futures contract at the Chicago Mercantile Exchange. This contract has a Basis Point Value (BPV) of USD95.8909. The BPV is a measure of how much the price of a security will change if the interest rate changes by one basis point. The on-the-run T-note is the cheapest-to-deliver (CTD) security.
Hedging Interest Rate Risk
To fully hedge the interest rate risk created by the duration gap, a pension plan would need to buy, or go long, a certain number of contracts. This is calculated using the formula:
$$ N_f = \frac{\text{Liability portfolio BPV} – \text{Asset portfolio BPV}}{\text{Futures BPV}} $$
Where:
\(N_f\) = Number of contracts
Liability Portfolio BPV = BPV of the liability portfolio
Asset Portfolio BPV = BPV of the asset portfolio
Futures BPV = BPV of the futures contract
One concern with hedging with futures is the need for daily oversight of the positions. This is because futures contracts are marked to market and settled at the end of each trading day into the margin account.
Using Interest Rate Swaps to Reduce Duration Gap
An interest rate swap can be understood as a combination of two bond transactions from the perspective of a pension fund. This involves purchasing a long-term fixed-rate bond while simultaneously issuing a floating-rate note (FRN), effectively swapping fixed for floating interest payments.
Components of an Interest Rate Swap
- Fixed-Rate Bond Purchase: The pension fund buys a fixed-rate bond from the swap dealer, which, for example, could be a 30-year bond with a fixed interest rate of 4.16%.
- Floating-Rate Note Issuance: To finance this purchase, the pension fund issues a floating-rate note that pays interest based on a short-term market reference rate, such as the three-month MRR (Market Reference Rate).
Calculating the Notional Principal for Duration Gap Closure
The objective of using an interest rate swap is often to close the duration gap between assets and liabilities, stabilizing the fund’s financial position against interest rate fluctuations. The calculation for determining the required notional principal (NP) to achieve this is given by :
$$\text{Asset BPV} + \left(\frac{\text{NP} \times \text{Swap BPV}}{100}\right) = \text{Liability BPV}$$
- Asset BPV: This is the basis point value (BPV) of the assets, which measures the assets’ price sensitivity to a 1 basis point change in interest rates.
- Liability BPV: Similarly, this is the BPV of the liabilities, representing their sensitivity to interest rate movements.
- Swap BPV: The BPV specific to the swap arrangement, which in this scenario, is noted as a numerical value (e.g., 0.1673).
Strategic Application
The notional principal amount derived from the equation facilitates effective risk management by matching the duration of the pension fund’s assets and liabilities, ensuring that the fund’s financial exposure to interest rate movements is minimized. This strategy is crucial for maintaining financial stability and fulfilling long-term financial obligations.
Hedging Ratio
The hedging ratio can vary from 0% to 100%. A 0% hedging ratio implies no hedging, leaving the pension plan exposed to a significant negative duration gap and the risk of lower corporate bond yields if it does not hedge. A 100% hedging ratio indicates an attempt to fully balance, or immunize, the assets and liabilities. However, in reality, partial hedges are common and the manager’s task is to select the hedging ratio between 0% and 100%.
Stakeholders and Hedging Strategy
All stakeholders of the retirement plan, including the plan sponsor, the regulatory authorities, the auditors, the employees covered by the plan, and potentially the employees’ union representatives, should understand the hedging strategy. If swap rates increase, the value of the receive-fixed swap becomes negative, necessitating an explanation of those losses to stakeholders. If the contract is collateralized, the pension fund will have to post cash or marketable securities with the swap dealer.
Strategic Hedging
The plan manager might opt for a partial hedge, known as “strategic hedging”, instead of trying to reduce the duration gap to zero. The plan sponsor may allow the manager some flexibility in selecting the hedging ratio, for example, to stay within a range of 25% to 75%. The performance of the strategic hedging decisions can be measured against a strategy of maintaining a preset hedging ratio, such as 50%.
Duration Gap Management Using Options
Portfolio managers often employ derivative overlay strategies to manage the duration gap in their portfolios. One such strategy involves the purchase of a specific type of option known as a receiver swaption . This option grants the holder the right to enter into a receive-fixed interest rate swap. The cost of this swaption, known as the swaption premium, is a fixed amount paid upfront.
Receiver Swaption
Imagine a company, ABC Inc., that holds a receiver swaption. This contract gives ABC Inc. the right, but not the obligation, to enter into a receive-fixed interest rate swap. The swaption’s strike rate is predetermined. If the current swap fixed rate is higher than this strike rate, the swaption is considered out of the money. However, if the swap rate falls below the strike rate, the swaption gains intrinsic value.
Swaption Premium and Execution
The swaption premium, or the cost of purchasing the swaption, is determined by the level of interest rate volatility and the time to expiration. It is calculated as a percentage of the notional principal and paid upfront. If the swap rate falls below the strike rate, ABC Inc. can choose to either take delivery of the swap and receive the above-market fixed rate or close out the swap with the counterparty to capture the present value of the annuity.
Swaption Collar
A swaption collar is a type of derivatives overlay strategy used in financial markets. It involves the purchase of a receiver swaption and the writing of a payer swaption, often referred to as a “zero-cost” collar due to the absence of initial expense. For instance, a pension plan might use this strategy to hedge against interest rate fluctuations.
Potential Losses
Potential losses on the receive-fixed swap and swaption collar are time-deferred and rate-contingent, making them uncertain. This means that the losses depend on the time and the rate at which the swap is exercised.
In the Field of financial management, hedging strategies play a crucial role in mitigating risks associated with derivatives. The success of a plan manager is often gauged by their ability to navigate sudden changes in yields. This can be achieved through various strategies such as entering the receive-fixed swap, buying the receiver swaption, or entering the swaption collar.
For instance, consider a scenario where a plan manager is managing a portfolio of USD497 million. If the market rates fall, the value of the receiver swaption would increase, leading to potential gains. However, if yields unexpectedly increase, it could lead to significant losses on the hedge, which could be perceived as a managerial mistake.
The irony of interest rate risk management is that the view on rates is part of decision making even when uncertainty about future rates is the motive for hedging. The notional principal is assumed to be USD497 million, which is a 50% hedging ratio. There are gains if rates on comparable 30-year swaps are below 4.16% and losses if rates are above 4.16%. The payoff line is not linear.
Decision Making and Breakeven Numbers
Decision making is facilitated by breakeven numbers. It is easier to ask “do we expect the rate to be above or below a certain number” than to state a well-articulated probability distribution for the future rate. If the plan manager expects the swap rate to be at or below 4.16%, the receive-fixed swap is preferred. Its gains are higher than the other two derivatives overlays. If the manager expects the swap rate to be above 4.16%, however, the swaption collar is attractive because the swap would be incurring a loss.
Practice Questions
Question 1: In the realm of financial management, different types of liabilities present unique challenges and require specific strategies for effective management. One such type of liability is Type IV, which is exemplified by Defined Benefit (DB) pension plan obligations. These liabilities are characterized by their uncertain aggregate amounts and dates. To manage these effectively, an entity may adopt a certain investment strategy. This strategy involves the development of a model for these liabilities, which includes establishing model assumptions and calculating future liabilities. What is the name of this investment strategy used to manage Type IV liabilities effectively?
- Asset-Driven Investment strategy
- Liability-Driven Investment strategy
- Risk-Driven Investment strategy
Answer: Choice B is correct.
The investment strategy used to manage Type IV liabilities effectively is called the Liability-Driven Investment (LDI) strategy. This strategy is designed to focus on the liabilities of an entity, such as a pension fund, rather than on the returns of its assets. The main goal of LDI is to ensure that the entity has enough assets to meet its liabilities, regardless of the market conditions. This is achieved by matching the cash flows from the assets with the expected cash flows from the liabilities. The LDI strategy involves the development of a model for these liabilities, which includes establishing model assumptions and calculating future liabilities. This strategy is particularly useful for managing liabilities that have uncertain aggregate amounts and dates, such as Defined Benefit (DB) pension plan obligations. By focusing on the liabilities, the LDI strategy helps to reduce the risk of a funding shortfall and ensures that the entity can meet its obligations as they come due.
Choice A is incorrect. The Asset-Driven Investment strategy focuses on maximizing the returns on the assets, without taking into account the liabilities. This strategy may not be effective for managing Type IV liabilities, as it does not ensure that the entity will have enough assets to meet its obligations.
Choice C is incorrect. The Risk-Driven Investment strategy focuses on managing the risks associated with the investments, rather than on the liabilities. While this strategy can help to reduce the risk of losses, it does not ensure that the entity will have enough assets to meet its obligations. Therefore, it may not be effective for managing Type IV liabilities.
Question 2: The process of developing a model for Type IV liabilities, such as Defined Benefit (DB) pension plan obligations, involves two main steps. The first step is crucial as it forms the basis of the model and influences the outcomes. This step involves the establishment of certain parameters that are used in the model. The second step involves a calculation based on the parameters established in the first step. This calculation provides an estimate of the potential obligations that the entity may have to meet in the future. What is the first step in the model development process for Type IV liabilities?
- Calculating future liabilities
- Establishing the model assumptions
- Assessing the risk factors
Answer: Choice B is correct.
The first step in the model development process for Type IV liabilities, such as Defined Benefit (DB) pension plan obligations, is establishing the model assumptions. These assumptions form the basis of the model and influence the outcomes. They include parameters such as the expected rate of return on plan assets, the discount rate used to calculate the present value of future obligations, the rate of salary increase, and the mortality rate of plan participants. These assumptions are crucial as they determine the estimated value of the future obligations that the entity may have to meet. The assumptions need to be realistic and based on the best available information. They should also be reviewed and updated regularly to ensure that they remain relevant and accurate. The establishment of these assumptions is a critical step in the model development process as it sets the foundation for the subsequent calculation of the potential obligations.
Choice A is incorrect. Calculating future liabilities is the second step in the model development process for Type IV liabilities, not the first. This step involves a calculation based on the parameters established in the first step. It provides an estimate of the potential obligations that the entity may have to meet in the future.
Choice C is incorrect. Assessing the risk factors is an important part of the model development process, but it is not the first step. The risk factors are typically considered as part of the establishment of the model assumptions. They can influence the assumptions and hence the estimated value of the future obligations. However, the first step is the establishment of the model assumptions, not the assessment of the risk factors.
Glossary
- Liability-Driven Investment (LDI) strategy: An investment approach focusing on matching assets to the cash flows needed to fund liabilities.
- Projected Benefit Obligation (PBO): The present value of the retirement benefits an employee has earned up to now, calculated with expected salary increases.
- Longevity Risk: The financial risk of outliving one’s retirement resources.
- Effective Duration: A metric that measures a bond’s price sensitivity to interest rate changes.
- Basis Point Value (BPV): Indicates the financial impact on a security for every one basis point change in interest rates.
- Interest Rate Swap: A derivative where two parties exchange interest rate cash flows, based on a specified principal amount.
- Swaption: An option that allows the holder to enter into a swap as either the fixed rate payer or receiver.
- Derivatives: Financial instruments whose value is derived from other underlying assets.
- Hedging: A strategy used to offset potential losses in investments by taking an opposite position in a related asset.
Portfolio Management Pathway Volume 1: Learning Module 4: Liability-Driven and Index-Based Strategies .
LOS 4(c): Evaluate liability-based strategies under various interest rate scenarios and select a strategy to achieve a portfolio’s objectives