## **Learning Outcomes**

This article explains how defined benefit (DB) pension plan surplus is measured, interpreted, and managed as the core risk metric for plan sponsors and insurers. It clarifies the distinction between funded status, surplus, and the funded ratio, and analyzes the main drivers of surplus volatility, including asset returns, liability discount rates, demographic assumptions, and asset-liability covariance. The article outlines how sponsor objectives, risk tolerance, and plan maturity shape surplus management policies and contribution strategies. It explains the principles of liability‑driven investing (LDI) and asset‑liability management (ALM), contrasting them with traditional asset‑only approaches. It details the design and use of key LDI techniques—cash flow matching, duration matching, surplus optimization, and derivative overlays—to hedge interest rate, inflation, and longevity risk. The article also presents the construction and interaction of hedging and return‑seeking portfolios, including dynamic “glide path” de‑risking as funding levels improve. Finally, it reviews typical exam-style applications, enabling analysts to identify appropriate LDI responses to changes in funded status, sponsor strength, or regulatory regimes and to evaluate whether a proposed strategy primarily targets surplus risk reduction or return enhancement in typical exam-style scenarios.

## **CFA Level 3 Syllabus**

For the CFA Level 3 exam, you are expected to understand DB pension plan surplus management and liability-driven investing (LDI), with a focus on the following syllabus points:

- Recognise surplus as a key metric for DB plan risk and plan sponsor financial management
- Interpret the drivers and sources of surplus volatility in DB plans and insurers
- Evaluate risk considerations associated with funding status, sponsor strength, asset-liability covariance, and workforce demographics
- Compare and implement LDI strategies (e.g., cash flow matching, duration matching, surplus optimisation)
- Explain the objectives and regulatory context for surplus optimisation in institutional portfolios

## **Test Your Knowledge**

_Attempt these questions before reading this article. If you find some difficult or cannot remember the answers, remember to look more closely at that area during your revision._

1. What is the surplus of a defined benefit pension plan, and why does it matter to both the plan sponsor and beneficiaries?
2. How does liability-driven investing (LDI) differ from traditional asset-only investing?
3. Give two examples of strategies used to reduce surplus risk in a DB plan.
4. Why might a plan sponsor prefer to increase hedging of liabilities as the funded status of their DB plan rises?

## **Introduction**

Defined benefit (DB) pension plans and insurers face unique challenges in managing their financial position over time. Unlike defined contribution plans, DB plans promise set benefit payments, but must manage the investment and liability risks to ensure these obligations are met. The key financial metric for a DB plan is its **surplus**—the difference between the value of plan assets and the present value of projected liabilities. Surplus management, and the use of liability-driven investing (LDI), have become central to risk and funding decisions for pensions and insurers. This article explains the purpose and measurement of surplus, why and how it can be volatile, and how an LDI framework is used to structure and manage surplus risk over a changing time horizon.

> **Key Term: surplus**
> The excess (if positive) or deficit (if negative) of the fair value of plan assets over the present value of projected benefit obligations (liabilities) in a DB plan or insurer.
>
> **Key Term: liability-driven investing (LDI)**
> An investment approach where asset allocation is designed primarily to hedge the characteristics and risks of plan or insurer liabilities, rather than to target asset-only objectives.

## SURPLUS MEASUREMENT AND PLAN FUNDED STATUS

The surplus of a DB plan is calculated as:

$$
\text{Surplus} = \text{Fair value of plan assets} - \text{Present value of plan liabilities}
$$

A positive surplus indicates fully funded (or even overfunded) status; a negative surplus signals the plan is underfunded. The **funded ratio** gives a quick assessment:

$$
\text{Funded Ratio} = \frac{\text{Fair value of assets}}{\text{Present value of liabilities}}
$$

A funded ratio below 100% raises pressure on the sponsor to add contributions or reduce liabilities.

### Surplus Volatility: Causes and Consequences

Surplus is not static. Both assets and liabilities fluctuate with changes in markets, discount rates, demographic assumptions, or sponsor covenants. Even when assets and liabilities are well-matched, surplus can experience marked changes as assumptions shift:

- Investment returns (asset volatility)
- Changes in the discount rate (liability volatility)
- Correlation between assets and liabilities (asset-liability covariance)
- Demographic events (longevity, retirement patterns)

> **Key Term: surplus volatility**
> The variability in surplus over time, driven by the separate and combined movements in plan assets and liabilities, reflecting risk for the plan sponsor.

Surplus volatility matters because sudden deficits may force unplanned sponsor contributions, trigger benefit reductions, or even raise default risk in extreme cases.

### Sponsor Viewpoint

For DB pensions and insurers, surplus is central to financial management. The sponsor or owner wishes to:

- Avoid large, unpredictable contributions (budget risk)
- Minimize balance sheet volatility (especially for corporate sponsors)
- Satisfy regulatory funding requirements
- Retain flexibility in managing workforce and benefits

An underfunded plan brings sponsor risk, but large positive surpluses can also be problematic if overfunding cannot be efficiently extracted or used.

## PRINCIPLES OF LIABILITY-DRIVEN INVESTING (LDI)

Liability-driven investing (LDI) is based on the premise that the primary risk facing a DB plan is not asset volatility per se, but **surplus volatility**—the risk assets and liabilities move out of sync.

Unlike traditional asset-only investing, which seeks to optimise portfolio return and risk in isolation, LDI builds the asset allocation to hedge liability risk and secure benefit payments.

> **Key Term: asset-liability management (ALM)**
> The integrated management of a plan or insurer's assets and liabilities, aiming to control surplus risk and ensure payment of projected obligations.

### Drivers of LDI Adoption

- Regulatory emphasis on funding levels and solvency
- Shift from return-seeking to risk reduction as funding levels improve or plans mature
- The need to manage interest rate risk, longevity risk, and sponsor balance sheet impact

An LDI approach may be gradually adopted as a plan’s surplus rises, or as the plan’s duration shortens and benefit payments accelerate (plan maturation).

### Main LDI Strategies

A variety of techniques implement LDI, with the goal of minimizing surplus risk:

#### Cash Flow Matching

- Construct an asset portfolio whose expected cash flows match liability outflows (benefit payments)
- Most suited for plans with predictable, fixed benefit cash flows

#### Duration Matching

- Allocate assets so that asset duration equals liability duration (and present values match), making surplus less sensitive to changes in interest rates

> **Key Term: duration gap**
> The difference between the duration of plan assets and that of liabilities; a positive or negative gap exposes the surplus to interest rate risk.

#### Surplus Optimization

- Use quantitative models to optimize the allocation between a “hedging portfolio” targeting liability sensitivity and a “return-seeking portfolio” aiming to increase surplus
- Constraints include target funded status, contribution volatility, and permissible risk levels

#### Use of Derivatives (Overlay)

- Interest rate swaps, futures, and other derivatives are used to adjust portfolio duration or hedge specific liability risks (e.g., inflation, longevity) beyond the available bonds

### **Worked Example 1.1**

A corporate DB plan is 105% funded, with assets (market value) of \$210 million and present value of liabilities (projected benefit obligation) of \$200 million. The plan sponsor seeks to reduce surplus volatility with minimal impact on expected returns. They consider increasing the allocation to long-duration fixed income and using interest rate swaps to align asset duration with liability duration.

> **Answer:**
> The plan’s surplus is \$10 million. By increasing exposure to long-duration bonds and swaps, the plan reduces surplus sensitivity to interest rate moves. This limits the likelihood of an unexpected deficit if rates fall, meeting the sponsor’s risk preference.

## RISK CONSIDERATIONS FOR SURPLUS MANAGEMENT

Every DB plan sponsor must balance several factors:

- Funding status: Is the plan under-, fully-, or over-funded?
- Sponsor financial strength: Can the sponsor absorb asset/liability shocks if surplus falls?
- Correlation between sponsor core business and plan assets: Are pension/insurer risks linked to the sponsor’s main revenues?
- Plan maturity: What is the weighted average age and service tenure of the workforce? More mature plans need greater liquidity and lower risk.
- Regulatory and accounting regime: Do rules require mark-to-market of liabilities or fixed discounting?

> **Key Term: plan maturity**
> The proportion of plan liabilities associated with retirees versus active workers, influencing liquidity and risk tolerance of the plan.
>
> **Key Term: de-risking**
> The process of reducing plan investment risk, often by increased liability hedging, as a plan's funded status or maturation rises.

Surplus risk increases with:

- Higher asset-liability duration mismatch (duration gap)
- Weak sponsor financial position
- Greater plan maturity (high retiree ratio)
- Overexposure to return-seeking assets when liabilities are near (liquidity risk)

### **Worked Example 1.2**

A university endowment has shifted from a 60/40 equity/bond allocation to include 20% hedge funds and 10% real estate, reducing both asset and surplus volatility. Is this LDI or asset-only investing?

> **Answer:**
> Unless the new allocation is directly tied to liability sensitivity (e.g., duration, inflation link), it is traditional asset-only investing. LDI requires asset allocation based on liability characteristics, not just overall risk/return.

## IMPLEMENTATION: SURPLUS OPTIMISATION AND HEDGING PORTFOLIOS

LDI often structures the portfolio in two parts:

1. **Hedging Portfolio (HP):** Investments (usually long-duration bonds, inflation-linked bonds, and derivatives) chosen to closely track the liability sensitivities (interest rate duration, inflation).
2. **Return-Seeking Portfolio (RP):** Growth assets, such as equities and alternatives, designed to increase surplus and allow for lower sponsor contributions.

> **Key Term: surplus optimisation**
> The use of quantitative modelling to set asset allocation that maximizes expected surplus (or minimizes shortfall/contribution risk) for a given surplus risk level.

The split between the HP and RP is often dynamic, changing as the plan’s funded status or regulator requirements shift.

Plan sponsors may pursue so-called "glide paths," increasing the allocation to the HP as funded status or plan maturity improves.

### **Worked Example 1.3**

An insurer's liabilities have a duration of 12, and its asset portfolio duration is 8. The insurer is concerned about surplus volatility due to interest rate moves. What steps can be taken to align the portfolio with LDI objectives?

> **Answer:**
> The insurer should increase its allocation to long-duration fixed income and may employ interest rate swaps or futures to raise asset duration as needed, reducing the duration gap to zero and managing surplus volatility in line with liabilities.

### **Exam Warning**

> A common exam error is to focus solely on matching asset-liability values, while ignoring duration or cash flow timing. Effective surplus management requires attention to both present value and duration matching.

## SUMMARY

Effective surplus management for DB plans and insurers centers on mitigating surplus volatility and funding risk using a liability-driven framework. LDI organizes asset allocation policies and hedging strategies around the characteristics and risks of liabilities, using tools such as duration matching, cash flow matching, surplus optimization, and derivatives overlays. The role of the sponsor, plan maturity, regulatory regime, and balance between growth and hedging portfolios must all be considered.

## **Key Point Checklist**

_This article has covered the following key knowledge points:_

- Surplus is the excess (or deficit) of plan assets over liability present value in DB plans/insurers
- Surplus volatility is a key risk for sponsors—resulting from both asset and liability movements
- Liability-driven investing (LDI) structures assets to hedge liability risks, not just maximize return
- Main LDI strategies: cash flow matching, duration matching, surplus optimisation with hedging and return portfolios
- Key considerations for surplus management: plan status, sponsor strength, duration gap, asset-liability covariance, plan maturity, regulatory regime
- Surplus risk can be managed by increasing hedging as funded status rises or as a plan matures
- Overlay strategies using derivatives align asset duration to liability duration when direct cash flow matching isn't feasible

## **Key Terms and Concepts**

- surplus
- liability-driven investing (LDI)
- surplus volatility
- asset-liability management (ALM)
- duration gap
- plan maturity
- de-risking
- surplus optimisation

Pension plans and insurers - DB plan surplus management and LDI