Pension funds · RiskAtoms Academy

By the end you will be able to

1Tell defined benefit pensions apart from defined contribution pensions, and say who bears which risk.
2Explain the funding ratio and why falling interest rates raise the value of pension promises.
3Explain liability-driven investing, and how leverage made it fragile in 2022.

Why it matters

In late September 2022, UK government bond prices fell so fast that the Bank of England stepped in to buy them. The fire spread not through banks but through pension schemes, the most cautious investors in the country.

Core explanation

Promises that last for decades

A pension turns today's pay into income in old age. Workers and employers put money aside for forty years or so; it is then paid out for twenty or thirty more. A pension fund holds and invests that money in between. Pension funds are among the largest investors in the world, from Japan's Government Pension Investment Fund to Dutch, Canadian and Australian funds.

There are two basic designs, and the difference is who carries the risk.

Defined benefit (DB)

The income is promised

The pension is a formula: for example, 1/60 of final salary for each year worked. The sponsoring employer must pay in whatever it takes. If investments disappoint or members live longer, the employer pays more.

Defined contribution (DC)

The contributions are set

Employer and worker pay a set percentage of salary into a personal pot, such as a US 401(k) or an Australian superannuation account. The income depends on how the pot grows, so the member carries the investment and longevity risk.

Many private employers in the US, UK and elsewhere have closed their DB schemes to new members and moved to DC, because DB promises proved expensive and volatile. Public-sector schemes are more often still DB. Some countries use mixes: the Netherlands is moving its large collective schemes to a new contribution-based system that still shares risk across members.

Sort itDB or DC?

The employer must pay more if investments do badly.
Your statement shows a pot of money with your name on it.
Your pension is 1/60 of final salary for each year of service.
If you live to 100, you may run out of money unless you buy an annuity.
The scheme reports a funding ratio and may run a deficit.

Measuring a DB promise. A DB scheme owes a stream of pension payments far into the future. To compare that with its assets, it turns the stream into one value today, using a discount rate based on bond yields. Here is the key point: when interest rates fall, the value of the promises rises. With lower rates, the scheme needs more money today to grow into the same future payments. Assets divided by that value is the funding ratio.

Liability-driven investing. A scheme holding mostly shares can see its funding ratio swing wildly: shares fall, rates fall, liabilities rise, all at once. In liability-driven investing (LDI) the scheme buys long-dated bonds, often inflation-linked, and interest rate swaps, so that its assets rise when its liabilities rise. The share of the liabilities matched is the hedge ratio.

A scheme that is short of money still wants growth from shares. So many UK schemes used leverage: they borrowed against their gilts (through repo, L1.6.04) or used swaps, to hedge more than their bond holdings alone could. The hedge worked when rates fell. But if rates rose sharply, the hedge lost value and lenders demanded collateral in cash, within days. That is what happened in 2022.

TimelineThe UK gilt and LDI crisis, 2022

1 / 5

23 Sep

A fiscal statement shocks the market

The UK government announces large unfunded tax cuts. Investors demand higher yields on gilts, and long-dated yields jump.

The formal version

The funding ratio is a simple division. The value of the liabilities builds on compounding from L1.2.04, run backwards. A payment $B$ due in $t$ years is worth today the amount that would grow into it at rate $y$ :

V_0 \times (1 + y)^t = B \quad \Longrightarrow \quad V_0 = \frac{B}{(1 + y)^t}

Add this up over every future pension payment to get the value of the liabilities:

L = \sum_{t=1}^{T} \frac{B_t}{(1 + y)^t}

And compare it with the assets:

\text{Funding ratio} = \frac{\text{assets}}{L}

Because $y$ is in the denominator, a lower $y$ makes $L$ bigger. Discounting is covered fully in L1.3.03.

Try it

A scheme owes £10m a year for 25 years and starts 95% funded. Half of its liabilities are hedged. At the starting settings rates fall by one point: the liabilities rise from £148.3m to £164.8m, and the funding ratio slips to 90.5%. Raise the hedge ratio to 95% and the ratio stops moving. Then push the hedge above 95% (it now needs borrowing) and move rates up.

Try itKeep a pension scheme funded

Change in long-term interest rates-1.00 pts

Hedge ratio (share of liabilities matched)50%

Change in share prices0%

Funding ratio today95.0%

Funding ratio after90.5%

Liabilities after£164.8m

Assets after£149.1m

Deficit£15.7m

The hedge gains £8.3m.

Assets against liabilities hedge assets growth assets liabilities

The scheme pays £10m a year for 25 years, valued at a 4.5% discount rate today. Assets start at 95% of liabilities. Amounts in £ millions.

Worked example

Two retirements, one market fall

Maria works for a Canadian employer with a DB scheme. Ken, in Australia, has a DC superannuation pot. Both retire in the same year, just after share prices fall 20%.

Who feels the fall?

Step 1 of 5

1
Maria's DB pension
Final salary C$90,000, 35 years of service, accrual 1/60: 35/60 × C$90,000 = C$52,500 a year, often with some protection against inflation.

Regulatory lens

United States: private pensions fall under ERISA (1974). The Pension Benefit Guaranty Corporation (PBGC) insures DB pensions, up to limits, if the employer fails.
United Kingdom: The Pensions Regulator oversees workplace schemes, and the Pension Protection Fund pays compensation if a DB sponsor goes bust. After 2022, the Bank of England's Financial Policy Committee set a minimum level of resilience for LDI funds.
European Union: the IORP II Directive sets rules for workplace pension funds, and EIOPA runs EU-wide stress tests. In the Netherlands, De Nederlandsche Bank supervises pension funds.
Asia-Pacific: Australia's APRA supervises superannuation funds, and employers must pay a set share of salary into them. In Japan, the GPIF invests the national pension reserve under rules set by the government.
Accounting: companies that sponsor DB schemes report the deficit on their own balance sheet under IAS 19 (or US GAAP), discounting at high-quality corporate bond yields.

Looking ahead: pension risk and LDI leverage return in later levels on market and liquidity risk, and in the study of non-bank finance.

Sparks

SparkThe first state pension

Germany under Otto von Bismarck introduced old-age and disability insurance in 1889, one of the first state pension systems. It paid from age 70, which few workers then reached.

SparkThe pension fund that is not a pension fund

Norway's Government Pension Fund Global is one of the world's largest investors, owning a small slice of most listed companies on earth. Despite its name, it pays no pensions: it is a sovereign wealth fund that saves the country's oil revenue.

Key takeaways

Defined benefit promises an income, so the employer carries the risk; defined contribution sets the contributions, so the member does.
A DB scheme values its promises by discounting them; when rates fall, the liabilities rise.
Funding ratio = assets ÷ liabilities. Below 100% is a deficit the sponsor must fill.
Liability-driven investing matches assets to liabilities so the funding ratio moves less.
Leverage in LDI adds a liquidity risk: rising rates bring collateral calls, as in the UK in 2022.

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Glossary

Defined benefit (DB): A pension that promises a set income, usually based on salary and years of service. The employer must make up any shortfall.
Defined contribution (DC): A pension where contributions go into a personal pot. The retirement income depends on how the pot grows; the member bears the risk.
Sponsor: The employer that runs a defined benefit scheme and stands behind its promises.
Accrual rate: The share of salary a member earns as pension for each year of service, such as 1/60.
Discount rate: The interest rate used to turn future pension payments into a value today.
Funding ratio: Pension assets divided by the value of the pensions promised. Below 100% means a deficit.
LDI: Liability-driven investing: choosing assets so that their value moves with the pension liabilities, especially when interest rates change.
Hedge ratio: The share of the liabilities' sensitivity to interest rates that the assets match.
Collateral: Cash or bonds handed over to cover losses on a derivative or loan. A collateral call demands more of it.
Longevity risk: The risk that people live longer than expected, so pensions are paid for longer.

Deep Dives & Origins

Deep Dives

OECD, Pensions at a Glance (published every two years), for how pension systems compare across countries. Beginner.
Bank of England, Financial Stability Report, December 2022, on the LDI episode. Intermediate.
Hull, Risk Management and Financial Institutions (Wiley), the chapter on insurance companies and pension plans. Intermediate.

Origins

Bank of England, market notices of 28 September and 14 October 2022 on temporary gilt purchases.
Bank of England Financial Policy Committee, records of 2023 on LDI resilience.
Employee Retirement Income Security Act of 1974 (United States); PBGC.
Directive (EU) 2016/2341 (IORP II).
IASB, IAS 19 Employee Benefits.

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