Jon Moshier / Notes / Liability Matching draft
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Liability Matching

Why pensions, insurers, and retirees buy bonds to cover known future bills regardless of whether equities return more, and how matching duration can blow up when you add leverage.

Not all money has the same job. Some money is free to grow on any timeline. Some money has to pay a specific bill on a specific date, and for that money a higher expected return is worthless if it might not be there when the bill comes due. Liability matching is the discipline of investing the second kind against the obligation it has to cover, and it explains why trillions of dollars sit in bonds that “underperform” stocks.

Two jobs for money

A defined-benefit pension has promised retiree Jane $4,000 a month for life. An insurer owes a death benefit whenever a policyholder dies. These are obligations with known size and roughly known timing. The institution’s job is not to maximize return. It is to be solvent on the date each payment falls due.

Equities have the higher long-run expected return, but the return arrives on no schedule and with deep drawdowns. The S&P 500 fell 57% peak to trough in 2007-2009. A pension that funded Jane’s checks with stocks and hit that drawdown the year she retired would be selling at the bottom to pay her, or failing to pay. So the institution buys a bond that returns a known amount on a known date that matches the obligation. It accepts a lower return to remove the timing risk. This is liability-driven investing, and a majority of UK defined-benefit schemes (around 60% by the Chicago Fed’s account) run some version of it.

This is also exactly who buys TIPS. A pension paying cost-of-living-adjusted benefits owes more dollars when inflation is high. An inflation-linked bond pays more in exactly that case. The match neutralizes inflation risk rather than betting on it.

How the match actually works

Two methods, increasing in sophistication.

Cash-flow matching is literal. You owe $1M in 2031, so you buy a bond that pays $1M in 2031. Stack enough of these and every obligation has a dedicated bond maturing to meet it. No guessing, no reinvestment risk. Expensive and rigid, because you need an instrument for every payment date.

Immunization is cleverer and rests on duration, the weighted-average time to receive a bond’s cash flows, measured in years. The British actuary Frank Redington coined the term in 1952. The insight: when interest rates rise, two things happen to a bond portfolio that cancel. Bond prices fall (a capital loss), but the coupons you reinvest now earn more (a reinvestment gain). At a holding horizon equal to the portfolio’s [private link], those two effects offset to a first approximation for a parallel shift in rates, and your realized return is locked in. Match the duration of your assets to the duration of your liabilities and a rate shock moves both sides by roughly the same amount. Your funding gap stays put.

Duration matching is cheaper than cash-flow matching because you are matching one number, not every date. The cost is that it only protects against small, parallel rate moves and has to be rebalanced as durations drift.

The trap: matching with borrowed money

Here is where the sound idea turns dangerous. Pension liabilities are very long, often 20-plus years of duration. To match that with bonds, a fund would need to hold mostly long-dated gilts and leave little for growth assets. So UK pensions used leveraged LDI: derivatives and repo to get the duration exposure of far more bonds than they actually bought, freeing cash to hold equities on the side. Efficient, until rates move fast.

In September 2022, the UK chancellor’s mini-budget spooked the gilt market and 30-year gilt yields rose more than 1.6 percentage points in three days. Rising yields mean falling bond prices, which triggered margin calls on the leveraged positions. To post collateral, funds had to sell gilts. Their selling pushed gilt prices down further, triggering more margin calls. A liability-matching strategy designed to remove risk had become a forced-seller feedback loop. The Bank of England said some funds were hours from collapse and stepped in with emergency long-dated bond purchases to stop the spiral. The lesson is precise: the matching was not the problem. The leverage layered on top of it made an otherwise stabilizing strategy reflexive. See Systems Thinking on how feedback and delay turn a control mechanism into an oscillator.

For individuals

The same logic scales down. The “money has a job” idea is [private link], usually treated as a bias, here used deliberately: split retirement savings into a floor and an upside. Cover essential, non-negotiable spending (the part you cannot let the market vote on) with safe matched assets, and let the rest ride in equities.

The clean tool is a TIPS ladder: buy inflation-protected Treasuries maturing in each year of retirement, each rung sized to that year’s spending. It delivers a known, inflation-adjusted cash flow with no sequence-of-returns risk, because you are not selling anything into a down market; you are holding to maturity. Morningstar and the bogleheads community treat a TIPS ladder as the individual’s version of cash-flow matching. The tradeoff is the same as the institution’s: you give up equity upside on the matched portion to remove timing risk from the spending you can’t defer.

The leverage trap scales down too. A “matched” floor stops being matched if there is borrowing on the other side of the household balance sheet. A retiree holding a bond ladder while carrying a mortgage, or borrowing against the portfolio, has reintroduced exactly the reflexivity that broke the UK pensions: the gross position is larger than the net, and a rate move hits the financing before it helps the bonds. Matching only immunizes the obligation it is actually set against.

Try it

Build a cash-flow-matched ladder on paper (1-2 hours, spreadsheet). List your next 10 years of a known recurring obligation (rent, tuition, retirement spending), one row per year. For each, find a Treasury or TIPS maturing that year and size a position so its maturity value covers the obligation. Sum the cost today — that is the present value of the liability, and the yield curve does the discounting for you. Then stress it: rerun assuming rates jump 2%. The ladder’s cost-to-build drops, but your already-bought rungs still pay their face value on schedule. That invariance, payments unaffected by the rate move, is immunization you can see. Compare against funding the same spending from an S&P 500 position and applying a 2008-style 50% drawdown in year one.

See also

Sources

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