Reading 14 Linking Pension Liabilities to Assets

Question 1

Market Related Exposures

Answer 1

1. Inactive Participants

• These are the benefits attributable to participants currently receiving pension payments (retirees), or participants who are no longer working for the firm and are owed a benefit, but have not yet started receiving benefit payments (deferreds).
• Inactive benefit payments are fixed and hence the value of these benefit payments very “bond like” with the only market exposure being the exposure to the term structure.

2. Active Participants

We slice the estimated benefit payments into two components: benefits attributable to past service rendered and wages earned (accrued benefits) and benefits attributable to future service and wages (future benefits).

Future Benefits

• These benefits drive the evolution of the liability over the long term, but they will have very little impact on the pension plan’s overall liability in the short term.
• For frozen pension plans, the liability attributable to future benefits is zero and therefore doesn’t need to be considered.

3. Future Participants

Question 2

Linking Assets and Liabilities via Fundamental Factors

Answer 2

• If the plan provides for some inflation indexation, the liability has some similarity with real rate bonds and thus is exposed to changes in the real rate bond premium.
• In a first step to that end, we determine the factors involved - Real Rate, Inflation, Growth, Equity Premium, Nominal Bonds Premium, Real Bonds Premium.
• The next step in the process requires setting the sensitivities of assets and liabilities versus the factors. The sensitivities describe how much the value of the assets and liabilities move in response to a move in the corresponding factor.

Question 3

Value of a liability

Answer 3

As for assets, the value of a liability can be determined in two steps:

• estimating the expected benefit payments, i.e., the future cash outflows; and
• discounting them. That is:

V_L=∑_tB_t/(1+r_t)^t

Question 4

Designing Investment Policies Relative to Liabilities

Answer 4

However, by definition, investing in the liability mimicking portfolio will not provide an expected return in excess of the liability and therefore future service benefits and benefits earned by future participants would be defeased by future cash contributions.

The challenge is to find the most efficient way to allocate more assets to “higher returning” asset classes such as equities while minimizing the amount of unrewarded risk taken versus the liability. This can be approached in two steps.

1. Hedge the liability. Derivatives can be used to synthetically represent the market-related exposures of the liability mimicking asset portfolio. For example, interest rate derivatives can be used to mimic the term structure exposure of the liability—the liability’s largest risk factor. And, utilizing derivatives to hedge requires far less capital than cash investment, thus, freeing up capital to be invested in “higher returning” assets.
2. Focus the remaining capital on efficient return generation. This can be done within asset-only space because once the liability has been hedged assets should not be given “credit” for further hedging.

The traditional approach typically leads to 60%–70% equities with the remainder in short and immediate duration nominal bonds. The liability relative approach, on the other hand, leads to investing in long duration nominal bonds, real rate bonds, equities and derivatives to hedge the liability, with the remainder invested in well-diversified return focused component.

Question 5

How to Define Risk?

Answer 5

• If the plan sponsor defines risk as the risk that assets will not hedge the liability over the next year, then we must focus on short-term market-related liability exposures. This has been the focus of most advisors by using a portfolio of long duration bonds to proxy the liability. This approach captures the liability’s exposure to short-term changes of the term structure.
• In order to see the full picture of pension fund investment risk, one must also focus on the volatility of the estimated benefit payments themselves and how they change over time

Question 6

Market Related Exposures and Liability Mimicking Assets

Answer 6

• _Portion of the Investment Benchmark: _Inactive
• Market Related Exposures: Term structure
• Liability Mimicking Assets: Nominal bonds
• Portion of the Investment Benchmark:** Active—accrued**
• Market Related Exposures: Term structure
• Liability Mimicking Assets: Nominal bonds
• Portion of the Investment Benchmark: Active—future wage
• Market Related Exposures: Inflation, Growth, Term structure
• Liability Mimicking Assets: Real rate bonds, Equities. Nominal bonds,

Question 7

The greatest source of liability noise?

Answer 7

• Pensions are subject to non-markte exposures referred to as liability noise.
• Inactive participants can be divided into retirees and deferreds. The liability noise from either of these groups is less than that from active participants.

Question 8

Non-Market Related Exposures: Liability Noise

Answer 8

The uncertainty in benefit payments attributable to non-market related exposures “liability noise.” There are two components of liability noise:

• plan demographic experience differing from the actuary’s model given that the underlying probabilities are certain; and
• model uncertainty—the fact that the underlying probabilities are not certain (e.g., mortality rate change due to medical innovations).
• ! the larger a plan’s population, the more closely the plan’s experience will track the model. Thus, model uncertainty is reduced, which results in less liability noise.

Inactive Participants

For retirees, liability noise is attributable to one major source. Embedded within the actuarial projection of benefit payments is a mortality assumption about the length of people’s lives and hence the duration they will be receiving benefits.

Active Participants

In addition to a mortality assumption, active employees’ estimated benefit payments are embedded with assumptions of withdrawal, disability, and retirement, and therefore are embedded with a large amount of uncertainty, much more so than those of retirees or deferreds.

Question 9

Intrinsic value of future wage liability

Answer 9

In the case of s years till retirement, d years till demise and subsequent termination of the obligation, the intrinsic value of future wage liability is

V_L−FW=B/(r−g)∙[((1+g)^s−1)∙((1+r)^d−s−1)]/(1+r)^d

Question 10

Asset-Only and Liability-Relative Perspectives

Answer 10

Pension liabilities, representing the present value of deferred wages, by their very nature are driven by economics and have many market related exposures. Not integrating these exposures can result in inefficient investment policies when measured versus liabilities, as they may be exposed to excessive and unrewarded risk relative to liabilities.

Asset Only perspective

• Liability exposures: None
• Risk-free investment/Benchmark: Cash
• Low risk investments: Low correlation with assets

Liability Relative perspective

• Liability exposures: Term structure, inflation, growth
• Risk-free investment/Benchmark: Liability mimicking asset portfolio
• Low risk investments: High correlation with liability