Liability-driven investing and cash flow driven investing: covering liabilities with bonds

Advanced12 min read · updated 16 September 2026 · 12 sources

Pension funds and insurers measure their assets not against an index but against their liabilities. With liability-driven investing (LDI), they mainly hedge the interest rate and inflation risk of these liabilities, often with interest rate swaps and borrowed money. With cash flow driven investing (CDI), they buy bonds whose coupons and redemptions cover the payouts year by year. This article builds on asset-liability management with the hedge ratio, immunization, cash flow matching in figures and the lessons of the 2022 UK gilt crisis.

The starting point: present value, discount rate and funding ratio

A pension fund owes its members pensions over decades; a life insurer owes guaranteed benefits. These liabilities are valued as a present value: every future payment is discounted at the liability discount rate or, more precisely, with a discount curve that assigns each maturity its own rate. Accounting and regulatory rules determine which curve applies. Three metrics follow from this:

The crucial point is that the present value of the liabilities moves with interest rates. When rates fall, it rises (sharply, for long-dated pension promises). Equities and cash barely react to this, so the funding ratio fluctuates with every move in rates. How sensitive the present value is, is measured by duration; expressed in dollars, it is the basis point value (PV01): the change in present value when all rates rise by 0.01 percentage points. If you want to keep the funding ratio stable, you need the same basis point value on the asset side. That is the basic idea of LDI.

LDI: hedging interest rate and inflation risk

An LDI program splits the assets into two parts: the matching portfolio replicates the interest rate sensitivity of the liabilities, while the return-seeking portfolio, with equities, credit or real estate, is meant to close a deficit or grow the surplus. How much interest rate risk is hedged is given by the hedge ratio:

• Long-dated government bonds provide duration but tie up capital.
• Interest rate swaps: the fund receives fixed and pays floating. This provides duration with almost no capital outlay, but requires collateral as soon as the swap loses value.
• Inflation swaps and linkers hedge pensions that rise with prices. Waring (2004) stresses that such liabilities have two durations: one with respect to the real rate and one with respect to inflation.
• Repo transactions: the fund sells bonds with an agreement to repurchase them and uses the proceeds to buy more. This is duration on credit.
• Key rate matching: instead of hedging only the total duration, the basis point value is spread across maturity buckets, so that twists in the yield curve also move the surplus little.

Swaps and repo create leverage: it is the only way for a fund with a large return-seeking portfolio to achieve a high hedge ratio. The price is liquidity risk: when rates rise, the funding ratio does improve, but swaps and repo immediately call for collateral. This is what pushed many UK LDI funds into distress in 2022.

Many pension plans gradually shift assets from the return-seeking to the matching portfolio. This glide path can be tied to calendar years or to funding ratio thresholds. The guide by the UK pensions association gives as a traditional example a plan with a 90% funding ratio that holds 35% in equities and switches entirely into government bonds over twenty years (PLSA 2023).

CDI: covering payouts with coupons and redemptions

Cash flow driven investing takes a more concrete approach: the fund buys bonds whose payments line up in time with the payouts (cash flow matching or dedication). According to PLSA (2023), the core is a large holding of high-quality fixed income assets with contractually fixed payments and yields above government bonds. The foundation is usually investment-grade corporate bonds, held to maturity on a buy and maintain basis and only replaced if their credit quality threatens to deteriorate. Government bonds are added for the longest maturities.

CDI does not replace LDI. PLSA (2023) sees an integrated LDI solution as the foundation: it hedges interest rate, inflation and currency risks, bridges gaps between payment dates and holds liquidity for monthly payouts and collateral calls. The approach is mainly suitable for mature plans with a high funding ratio. In the process, the risks shift from interest rates to credit:

• Default and downgrade: if an issuer defaults, a payment is missing; you only earn the credit spread if you experience fewer defaults than were priced in.
• Reinvestment: surpluses between two payouts must be invested at the rates then prevailing. This is the reinvestment risk from bond mathematics.
• Liquidity: even if you hold bonds to maturity, you need cash for collateral calls. This is one of the lessons of 2022 (PLSA 2023).

Redington immunization or exact matching?

Redington (1952) formulated the principle of immunization for life insurers: the assets should be invested so that a small change in rates does not reduce the surplus. For a parallel shift of a flat curve, this leads to three conditions:

The first two conditions cancel out the effect of small rate changes on the surplus; the third ensures that it tends to rise rather than fall with larger moves. Immunization is cheap: two bonds are already enough. But it only holds for parallel shifts and must be readjusted continually, because the durations of the two sides change differently over time and with rates.

Exact cash flow matching, by contrast, covers every payment on its date and is immune to any curve movement, but costs more when suitable maturities are missing. In practice, the two are combined: short, predictable payments through matching, long ones through duration or key rate hedging.

Worked examples: five years of liabilities

A fund has to pay $10 million at the end of each year for five years. All rates are 3%, and the curve is flat. This is an example with round numbers.

Cash flow matching with three bonds

Three bonds with annual coupons, valued at 3%: A, one year, 2.5% coupon (price 99.51); B, three years, 3% (price 100.00); C, five years, 3.5% (price 102.29). The fund parks surpluses without interest until the next date. The calculation runs backwards:

Immunization with two bonds

Cheaper, but less robust: a one-year and an eight-year bond with a 3% coupon at par, mixed to match the present value and duration of the liabilities.

Hedge ratio of a partially hedged pension fund

The 2022 gilt crisis: when the hedge demands cash

According to the Bank of England, more than £1 trillion was invested in LDI strategies in the United Kingdom. Smaller plans use pooled LDI funds, which are harder to rebalance because many investors are involved (Cunliffe 2022). At the end of September 2022, the yield on 30-year government bonds (gilts) rose by 160 basis points within a few days; previously, the largest daily rise since 2000 had been 29 basis points. For the leveraged LDI funds, this was a liquidity shock: their net asset value collapsed, counterparties demanded more collateral, and the funds had to sell gilts into an illiquid market. Based on market intelligence, the Bank expected at least £50 billion of additional sales, against recent average trading volume of £12 billion a day (Cunliffe 2022).

On September 28, the Bank announced that it would buy long-dated gilts on every working day until October 14; on the same day, the 30-year yield fell by more than 100 basis points (Cunliffe 2022). At their peak, the purchases amounted to £19.3 billion, of which £12.1 billion was in long-dated conventional gilts and £7.2 billion in index-linked gilts. From November 29, the Bank sold them again; by January 2023, the holdings had been unwound (Bank of England, APF 2023).

According to transaction data from the gilt, repo and swap markets analyzed by Pinter (2023), pension and insurance investors with larger repo and swap positions before the crisis sold more gilts. Trading costs rose within days, most sharply for small orders and for investors outside the LDI sector, and the dispersion of transaction prices more than doubled. The illiquidity spread to other market participants. As a lesson, the Bank's Financial Policy Committee recommended to the UK Pensions Regulator in March 2023 that LDI funds and mandates should be able to withstand a rise in yields of at least about 250 basis points; in the Bank's illustrative calibration, around 80 basis points relate to idiosyncratic risks and 170 to market-wide risks (Bank of England 2023).

Advanced: surplus risk, curves and optimization

• Leverage of the surplus: in the hedge ratio example, the surplus has a basis point value of 0.90 − 1.50 = −$0.60 million per basis point. A fall of 100 basis points widens the deficit from $100 million to $160 million, i.e. by 60%.
• Curve risk: against twists in the curve, only a hedge at each maturity point with key rate durations according to Ho (1992) helps.
• Basis risk: if liabilities are valued with a corporate bond curve but hedged with government bonds or swaps, the spread between the curves remains unhedged.
• Surplus optimization: Leibowitz and Henriksson (1988) apply Markowitz optimization to the surplus by treating the liabilities as a short position. The risk-free asset is then not cash but an immunized bond fund, and the optimal mix can differ drastically from the one without liabilities.

What research shows

• Redington (1952) established immunization for insurers; Fisher and Weil (1971) confirmed with US bond data that duration, not maturity, is the right yardstick.
• Leibowitz and Henriksson (1988) and Sharpe and Tint (1990) shifted portfolio theory from the assets to the surplus; Waring (2004) built an efficient frontier for the surplus on this basis.
• Martellini and Milhau (2012) derive optimal allocations for inflation-linked liabilities subject to floors on the funding ratio. These resemble portfolio insurance such as CPPI: the closer the floor, the smaller the return-seeking portfolio. In tests, their benefits prove relatively robust.
• Pinter (2023) documents forced selling by LDI investors in the 2022 gilt crisis, rising trading costs and contagion through illiquidity; the Bank of England then recommended buffers for about 250 basis points (Bank of England 2023).

Limitations and common mistakes

• Hedge ratio without a liquidity plan: leverage through swaps and repo is only as safe as the collateral you can deliver within hours. Before 2022, stress tests and risk management had assumed at most 100 basis points over a short period (Cunliffe 2022).
• Longevity: neither LDI nor CDI hedges the risk that pensioners live longer than assumed (PLSA 2023).
• Underestimating credit risk in CDI: a spread is not a return until defaults and downgrades have been deducted; downgraded bonds (fallen angels) can often only be sold at a discount.
• Private investors: the logic also helps on a small scale, but without leverage, for example with bonds or fixed-term deposits whose maturities match fixed expenses. This is not investment advice.

How Portfolio Lab calculates

The ALM page calculates, for a payment schedule, the present value of the liabilities at a fixed discount rate (discounted monthly), the Macaulay duration and the modified duration, the basis point value (“1 bp” = present value × modified duration × 0.0001) and the funding ratio. The interest rate risk table revalues the liabilities exactly at ±0.5 and ±1 percentage point and shows the corresponding funding ratio. The page does not calculate a hedge ratio directly: to get one, divide the basis point value of your bond holdings (market value × modified duration × 0.0001) by the displayed basis point value of the liabilities.

The page uses only a single rate: no yield curve, no swaps and no cash flow matching; in the simulation, the discount rate stays fixed. Under Financial goals, you can set a glide path between two portfolios, for example from an equity portfolio to a bond portfolio. The switch is time-driven between two years, not driven by the funding ratio. You will find long-dated government bonds and linkers under Asset classes. More on the calculation in the ALM methodology.

This article explains a method; it is not investment or tax advice. Worked examples are simplified and rounded. All terms in the glossary.