A pension fund does not exist to make money in the abstract. It exists to pay pensions. An insurance company does not invest to grow a pile of assets. It invests to pay claims. For these investors, the relevant measure of success is not whether assets grew but whether assets grew relative to the liabilities they must fund. Standard asset-only MVO misses this entirely. Liability-relative asset allocation does not.
Understanding What You Actually Owe
Liability: A legal or practical obligation to pay a specified sum at a future date. May be fixed or dependent on future events
Surplus: The market value of assets minus the present value of liabilities. A positive surplus means the investor is overfunded
Funding ratio: Assets divided by the present value of liabilities. Above 1 means overfunded. Below 1 means underfunded
Quasi-liability: An expected future cash outflow that is not a legal obligation but is essential to the investor's mission. A university endowment's spending commitment is a quasi-liability
Liabilities come in two varieties. Fixed liabilities have known amounts and dates set by contract. A frozen pension plan with no future benefit accruals is close to this: the payments are essentially known once the actuary models life expectancy. Contingent liabilities depend on uncertain future events. An active pension plan has contingent liabilities because payments depend on when employees retire, how long they live, and what future salary growth looks like.
The discount rate used to calculate the present value of liabilities matters enormously. A small change in discount rate produces a large change in the present value of long-dated obligations.
Company LOWTECH has a frozen defined benefit pension plan. Its future payment obligations total over 30 years. At a 4% discount rate (required by US pension regulations for high-quality corporate bonds), the present value of all liabilities is USD 2.26 billion. The plan's assets are worth USD 2.50 billion. Surplus = USD 0.24 billion. Funding ratio = 1.11. The plan is 11% overfunded. Now change the discount rate to 2% (the long-term government bond rate). The present value of liabilities rises to USD 3.04 billion. The plan swings from a USD 0.24 billion surplus to a USD 0.54 billion deficit. Funding ratio falls to 0.82. Nothing changed in the actual obligations. Only the discount rate changed. This shows why liability-relative investors watch interest rates so closely: a rate move simultaneously changes both asset values (especially bonds) and liability values.
Approach 1: Surplus Optimisation
The key shift in thinking: Instead of maximising risk-adjusted asset return, surplus optimisation maximises risk-adjusted surplus return. The liabilities are treated as a short position in the portfolio. An asset that moves in line with the liabilities reduces surplus volatility. An asset that moves independently of the liabilities increases surplus volatility.
Surplus return is defined as the change in asset value minus the change in liability value, expressed as a percentage of initial asset value. The optimiser maximises expected surplus return minus a penalty for surplus variance, with the same risk aversion coefficient framework as standard MVO.
What makes this different from asset-only MVO is the conservative end of the efficient frontier. In an asset-only world, the most conservative portfolio is mostly cash. In a surplus world, cash is useless as a hedge: it has no correlation with long-duration liabilities. The most conservative surplus portfolio is heavily weighted in assets whose returns are driven by the same factors that drive liabilities: long-duration bonds, specifically corporate bonds whose credit spread movement mirrors the pension liability discount rate.
For the LOWTECH pension plan, surplus optimisation produces a frontier where the lowest-risk portfolio holds approximately 60% corporate bonds. This cuts surplus volatility by roughly half compared to LOWTECH's current mix. The current portfolio sits below the surplus efficient frontier, meaning it takes on more surplus risk than necessary for the level of expected surplus return it delivers. Shifting toward more bonds simultaneously reduces risk and brings the portfolio onto the efficient frontier.
Approach 2: Hedging and Return-Seeking Portfolios
This approach is more intuitive than surplus optimisation. It divides all assets into two buckets. The first is the hedging portfolio, which holds assets designed to move in line with the liabilities as closely as possible. The second is the return-seeking portfolio, which is managed independently to grow the surplus.
For a frozen pension plan with fixed cash flows, the hedging portfolio is straightforward to construct. Long-duration bonds matched by maturity to each pension payment (cash-flow matching) or matched by duration (immunisation) will move in tandem with the pension obligations when interest rates change. As long as these bonds do not default, the liabilities are covered regardless of what markets do.
The surplus is then invested in the return-seeking portfolio using standard MVO or another approach. This is the part of the assets that the pension sponsor can afford to take risk with, because even if the return-seeking portfolio goes to zero, the hedging portfolio still covers the obligations.
LOWTECH has USD 2.50 billion in assets and USD 2.26 billion in pension liabilities at a 4% discount rate. Under the two-portfolio approach: USD 2.26 billion goes into a hedging portfolio of long-duration corporate bonds matched to the pension cash flows. The remaining USD 0.24 billion (the surplus) goes into a diversified return-seeking portfolio of global equities, real estate, and hedge funds. As long as the bonds do not default, the pension is fully funded regardless of equity market performance. The return-seeking portfolio gives LOWTECH a chance to grow the surplus over time without risking the fundamental promise to pensioners.
This approach only works when there is a positive surplus. An underfunded plan cannot fully hedge its liabilities because it does not have enough assets. Variants of the approach address this: a partial hedge that covers most but not all liabilities, combined with a glide path that increases the hedging allocation as the funding ratio improves over time.
Approach 3: Integrated Asset-Liability Management
For banks and insurance companies, asset and liability decisions cannot be separated at all. A bank's liabilities are its deposits and borrowings. Its assets are loans and securities. Changing the asset portfolio without considering the liability portfolio creates risk that is invisible to either side in isolation.
Integrated asset-liability management (ALM) models both sides simultaneously across many scenarios. It can incorporate multi-period decisions, transaction costs, capital adequacy requirements, and regulatory constraints. It answers the question that the other two approaches struggle with: what is the probability that we can meet all obligations under a wide range of economic conditions over the next 10 or 20 years?
Insurance companies use a version called dynamic financial analysis (DFA). Catastrophic risk insurers, for example, have liabilities that depend on rare events like earthquakes and hurricanes. The liabilities are not hedgeable through standard bond portfolios. Only an integrated multi-period simulation, incorporating scenarios for rare events on both sides of the balance sheet, can properly assess the capital needed.
Testing Robustness: Stress Tests and Scenario Analysis
Whatever liability-relative approach is chosen, it should be tested for robustness. Stress tests examine what happens to surplus under specific shocks: a 100 basis point parallel rise in the yield curve, a repeat of the 2008 financial crisis, a period of unexpected inflation. Each shock affects both assets and liabilities, and the analyst must be careful to apply the same economic assumptions to both sides.
More comprehensive robustness testing uses multi-period simulation. This generates probabilistic outcomes for both assets and liabilities across many scenarios, allowing the investor to estimate the probability of making future contributions, the probability of becoming underfunded, and the range of outcomes under good and bad conditions. Sensitivity analysis varying key assumptions (such as the expected return of equities or the future growth rate of pension liabilities) shows which inputs matter most and where estimation error is most dangerous.