This case traces how a rise in interest rates travels through an insurer or a pension plan. A rate rise cuts the present value of both its bonds and its long-dated promises. When the promises’ dollar duration is larger than the bonds’, the surplus rises. That is what happened to most large US pension plans in 2022, and the IAIS saw the same effect on life insurers’ solvency. The real strains are about cash: policy surrenders and collateral calls on hedges, as the UK’s September 2022 LDI episode showed.
Why it matters: A rate shock can leave a firm better off on paper and still short of cash.
Summary: Rising rates lower the present value of an insurer’s or pension plan’s long-dated liabilities as well as its bonds, and when the liabilities’ dollar duration is larger, the surplus rises: that is what happened to most large US pension plans in 2022, and the IAIS noted the same effect on life insurers’ solvency. The real strains of a rate shock are liquidity strains — policy surrenders and cash collateral calls on hedges, as the UK’s September 2022 LDI episode showed.
- Compare dollar durations, not asset losses: Harbor Life’s liabilities (12 × $92bn) outweigh its bonds (8 × $100bn), so a 2-point rise adds $6.08 billion of surplus.
- The 100 largest US corporate pension plans lost 18.6% on assets in 2022, yet their funded ratio rose from 96.3% to 99.3% because obligations fell 28.2%.
- Surrenders and collateral calls need cash now; size liquidity, and hedge leverage, to the stress move, not the average day.
- Cap rates rise with interest rates and property values fall: $10 million of NOI is worth $200 million at 5% and $160 million at 6.25%.
- A property-casualty insurer with short claims sits on the other side and loses surplus when rates rise.
The situation: A central bank raises its policy rate fast to fight inflation, as the Federal Reserve did between March 2022 and July 2023, when it lifted the federal funds target range from 0–0.25% to 5.25–5.50% (Volume I §2.3). In this case, unlike the actual 2022–23 cycle, the economy tips into recession about eighteen months later. The decision belongs to the chief investment officer of a US life insurer — call it Harbor Life, an illustrative company — who must decide, as the hikes begin, what to do about the gap between the duration of the insurer’s assets and the duration of its liabilities.
Harbor Life’s balance sheet. Assets: $100 billion of bonds with a modified duration of 8. Liabilities: the present value of future policy payments, $92 billion, with a duration of 12, because life and annuity payments stretch decades out. Surplus: $100 billion − $92 billion = $8 billion. Duration (Volume II §3.2) says a value changes by about −duration × value × change in yield. That applies to the liabilities as much as to the bonds, because a liability’s value is also a present value: discount the same future payments at a higher rate and they are worth less today.
Take a 2-percentage-point rise in yields. Assets: ΔA ≈ −8 × $100bn × 0.02 = −$16.0 billion. Liabilities: ΔL ≈ −12 × $92bn × 0.02 = −$22.08 billion. Surplus change = ΔA − ΔL = −16.0 − (−22.08) = +$6.08 billion, so the surplus rises from $8.0 billion to $14.08 billion. The rule underneath is a comparison of dollar durations (duration × value): the liabilities’ 12 × 92 = 1,104 exceeds the assets’ 8 × 100 = 800, so higher rates shrink the liabilities by more than the bonds. These are first-order estimates; convexity makes both changes slightly smaller.
This is what happened in 2022. For the 100 largest US corporate pension plans, assets returned −18.6%, yet the discount rate rose from 2.73% to 5.18%, obligations fell 28.2% (from $1,848.3 billion to $1,327.5 billion), and the funded ratio rose from 96.3% to 99.3% (Milliman). The International Association of Insurance Supervisors (IAIS) said in December 2022 that for life insurers “rising interest rates can have positive effects on solvency positions,” and named the real dangers: liquidity risks “such as those arising from margin calls on interest rate hedges or mass policy surrenders.”
The real strain, part one: surrenders. Holders of fixed annuities crediting 3% can surrender and buy new ones paying more (lapse risk). If 15% of a $30 billion block surrenders, Harbor pays 0.15 × $30bn = $4.5 billion at book value for a liability (duration 7) now worth $4.5bn × (1 − 7 × 0.02) = $3.87 billion: an economic loss of $0.63 billion. Raising the cash by selling bonds priced at 1 − 8 × 0.02 = 84% of book means selling $4.5bn ÷ 0.84 = $5.36 billion of book value, a realized loss of $0.86 billion.
The real strain, part two: collateral. The textbook fix for a duration gap is to add duration with receive-fixed swaps or leveraged gilt or Treasury positions — the liability-driven investment (LDI) toolkit — whose losses are settled in cash at once. In September 2022 the UK’s 30-year gilt yield “rose by 160 basis points in just a few days,” with daily rises above 50 basis points against a largest daily rise of 29 in data back to 2000. With over £1 trillion in LDI strategies, funds sold gilts into a falling market to meet collateral calls, until the Bank of England bought £19.3 billion of gilts between September 28 and October 14. A fund with $10 billion of capital behind $40 billion of hedges at duration 20 is wiped out by a rise of $10bn ÷ (20 × $40bn) = 1.25 points.
Harbor’s dollar-duration gap is 1,104 − 800 = 304 ($ billion × years). Each choice is judged at a 2-point rise, with the 15% surrender wave above.
| Choice | Surplus change from rates | Cash collateral to post | Surrender loss | Net economic effect |
|---|---|---|---|---|
| 1. Leave the gap open (asset duration 8) | +$6.08bn | $0 | −$0.63bn | +$5.45bn |
| 2. Close it with receive-fixed swaps (304 ÷ 8.5 ≈ $35.8bn notional of 10-year swaps, assumed duration 8.5) | $0 (swap loss of $6.08bn offsets the gain) | $6.08bn | −$0.63bn | −$0.63bn, plus a $6.08bn liquidity call |
| 3. Close it with physical bonds (sell shorter bonds, buy longer; duration 11.04) | $0 | $0 | −$0.63bn | −$0.63bn |
The flip point. Surplus is unaffected by rates when the asset duration equals DL × L ÷ A = 12 × 92 ÷ 100 = 11.04. Below 11.04, rising rates add surplus; above it, they cost surplus. A property-casualty insurer sits on the other side: with $100 billion of assets at duration 5 and $70 billion of claims reserves at duration 3, its flip is 3 × 70 ÷ 100 = 2.1, and the same 2-point rise changes its surplus by ΔA − ΔL = (−5 × 100 × 0.02) − (−3 × 70 × 0.02) = −10.0 + 4.2 = −$5.8 billion.
The decision and the outcome. Harbor’s CIO keeps the gap open (choice 1) and arranges a $5 billion committed repo facility against its Treasuries. At +200 basis points the surplus rises by $6.08 billion, surrenders cost $0.63 billion, and the $4.5 billion of surrender cash is borrowed, not raised by sales, so the $0.86 billion realized loss never occurs. A pension sponsor that prizes a stable funded ratio would choose differently: choice 3, or choice 2 with collateral that survives a move larger than 2022’s.
The rest of the chain. The curve (Volume II §3.5): the hikes lift short yields faster than long ones and invert the curve (see the box below). Commercial real estate (Part 2.2: Cap Rates and Property Valuation): cap rates rise with interest rates, so values fall. A building with $10 million of net operating income is worth $10m ÷ 0.05 = $200 million at a 5.0% cap rate and $10m ÷ 0.0625 = $160 million at 6.25%. With a $130 million loan, equity falls from $70 million to $30 million (−57%), and a lender capping refinancing at 65% loan-to-value lends only 0.65 × $160m = $104 million: a $26 million gap at maturity. Government finances (Part 3.4 and 3.7): in the recession automatic stabilizers widen the primary deficit with no new law, and the debt ratio follows dnext = d × (1 + r) ÷ (1 + g) + primary deficit. At d = 80% of GDP, r = 3%, g = 5% and a 0.5% deficit: 80 × 1.03 ÷ 1.05 + 0.5 = 78.98%. At r = 4%, g = 1% and a 3.5% deficit: 80 × 1.04 ÷ 1.01 + 3.5 = 85.88%, up 5.9 points in a year.
The case’s first link — hikes invert the curve, and inversion forecasts the slowdown (Volume II §3.5) — rests on strong evidence. Estrella and Mishkin (1996, Federal Reserve Bank of New York) found that the 10-year minus 3-month Treasury spread “significantly outperforms other financial and macroeconomic indicators in predicting recessions two to six quarters ahead.” The 2022–24 cycle then produced the awkward test: the 10-year minus 3-month spread was inverted every trading day from October 25, 2022, to December 12, 2024, and the 10-year minus 2-year spread from July 6, 2022, to August 26, 2024, yet as of October 2026 the NBER lists no business-cycle peak after February 2020.
Engstrom and Sharpe (2018, Federal Reserve Board) argue that the signal lives in the near-term forward spread — the forward Treasury bill rate six quarters ahead minus today’s 3-month yield, a gauge of expected policy — and that once it is included the long-term spread’s effect is “economically small and not statistically different from zero.” Others treat 2022–24 as one miss in a short record of recessions. Open question: how far years of central-bank bond buying changed what the curve’s shape means. Treat inversion as one input to a probability, not a forecast of a date.
Markets (Part 5.3: Market Makers and the Bid-Ask Spread, 6.5 and 6.7): when volatility jumps, market makers widen spreads because inventory is riskier and the next order more likely comes from someone better informed (adverse selection). Selling $200 million of stock across a 1 basis point half-spread costs $200m × 0.0001 = $20,000; at 7.5 basis points, $150,000 (illustrative). Herding speeds the fall, and the disposition effect — documented by Odean (1998) in 10,000 discount-brokerage accounts over 1987–1993 — leads investors to sell winners and hold losers. Operations (Part 8: Operational Risk Governance & Reconciliation): each 2022 collateral call had to be agreed with the counterparty the same day; a call not agreed is a reconciliation break, and in a fast market a break that ages a day is a liquidity shortfall (Part 8.5: Aged Breaks — The Audit and Risk Flag). Collateral processing is the kind of important business service that operational resilience rules ask a firm to keep within an impact tolerance (Part 8.7: Important Business Services and Impact Tolerances). And when a recession breaks a broker, whether clients get their money back turns on segregation and daily client-money reconciliation (Part 8.1: Reconciliation as a Regulatory Control, Not Just Operational Hygiene): the CFTC charged MF Global, bankrupt in October 2011, with misusing nearly $1 billion of customer funds. Ideas (Part 9.5: Keynes and the Keynesian Revolution): automatic stabilizers are the built-in form of the countercyclical fiscal argument Keynes made in the 1930s.
“Rising rates help long-liability institutions” holds for the Harbor Life balance sheet. These are the situations where it does not, or not in the same way.
| Situation | What changes | Why |
|---|---|---|
| Property-casualty insurer with short-tail claims | Surplus falls when rates rise (−$5.8bn in the example) | Assets’ dollar duration (5 × 100 = 500) exceeds the liabilities’ (3 × 70 = 210) |
| Pension plan hedged with leveraged LDI | Funded ratio stays stable, but cash collateral calls arrive | Hedge losses settle in cash; capital is wiped out at a move of capital ÷ (duration × exposure) |
| Rates rise alongside wider credit spreads (recession) | Corporate-bond assets fall more than liabilities | Where liabilities are discounted on a risk-free curve, the assets’ spread widening has no liability offset |
| Inflation-linked pensions | Liabilities may barely fall | If nominal yields rise because expected inflation rose, the real yield that discounts indexed benefits may hardly move |
| Accounting view rather than economic view | Reported equity can fall even as economic surplus rises | Some accounting and statutory bases mark bonds to market but discount liabilities at locked-in rates |
When the recession arrives, the risk changes character: rates fall back, part of the surplus gain reverses, and credit losses on Harbor’s corporate bonds have no liability offset. The decision that survives both phases is the one that sized liquidity for the stress, not the average day.
Before reading further: name the concept, and the volume it comes from, that explains why Harbor Life’s surplus rose even though its bonds lost $16 billion. Answer: dollar duration. The liabilities are present values too, and at a duration of 12 on $92 billion they fell by $22.08 billion, more than the assets did. That joins this volume’s Part 1: Insurance & Actuarial Finance to Volume II §3.2. If you answered that the liabilities were unaffected by rates, reread the Under the Hood box: only a liability measured at a fixed, never-updated discount rate behaves that way, and economically none does.
When rates are rising, measure surplus sensitivity, not asset losses. Compute the dollar durations DA × A and DL × L. If DL × L is larger, rising rates add surplus: protect liquidity (surrenders, collateral) rather than selling assets to “cut risk.” If you close the gap with derivatives, hold collateral that survives a yield move at least as large as the worst on record in your market — about 1.6 points in a few days for long UK gilts in 2022 — plus a margin. Ignore this rule when liabilities are inflation-linked or carried at a locked-in rate, because their economic duration is then not the one in the accounts.
Sizing hedge collateral to normal days. The illustrative LDI fund above runs 4× leverage: $40 billion of exposure on $10 billion of capital, at a duration of 20. A 1.6-point rise costs 20 × $40bn × 0.016 = $12.8 billion — $2.8 billion more than its capital — so positions are closed at the worst prices, and when yields fall back the losses stay locked in. At 2× leverage ($20 billion of exposure) the same move costs 20 × $20bn × 0.016 = $6.4 billion and the fund survives with $3.6 billion. The cost of the mistake is the difference between a hedge that rides out the spike and one that is forced to sell at the bottom. Avoid it by setting leverage from the stress move, not from average volatility.
Do rising interest rates hurt insurance companies?
Usually not their solvency, if their liabilities are long. A higher discount rate lowers the present value of future claims, and for life insurers and pension plans that fall is usually larger than the fall in their bonds. Property-casualty insurers with short-tail claims can lose surplus. The real strains are liquidity: policy surrenders and collateral calls on hedges.
Why did UK pension funds get into trouble in 2022 if higher yields improved their funding?
Because their hedges needed cash before the funding gain could help. Leveraged LDI funds lost money on their hedges as 30-year gilt yields rose 160 basis points in a few days, and had to post collateral at once. Selling gilts to raise it pushed yields higher still, until the Bank of England bought £19.3 billion of gilts to break the spiral.
Do higher interest rates raise or lower cap rates?
They tend to raise cap rates, which lowers property values. Value equals net operating income divided by the cap rate, so a building earning $10 million is worth $200 million at 5% and $160 million at 6.25%. Cap rates usually lag rate moves and depend on rent growth expectations too, but the direction follows the discount rate (Part 2.2: Cap Rates and Property Valuation).
Higher discount rates shrink long-dated liabilities as well as bonds, so a life insurer or pension plan whose liabilities carry the larger dollar duration gains surplus when rates rise, as most large US pension plans did in 2022. The dangers are liquidity — surrenders and cash collateral calls on hedges, which forced UK LDI funds to sell gilts until the Bank of England stepped in — and, once recession arrives, credit losses with no liability offset. Elsewhere in the chain, cap rates rise and property values fall, automatic stabilizers push the debt ratio up, and spreads widen as volatility rises.
Six questions on this chapter. Decide on your answer first, then click “Reveal Answer.”
1. An insurer holds $50 billion of bonds with a duration of 6 against $45 billion of liabilities with a duration of 10. Yields rise one percentage point. To a first approximation, what happens to its surplus?
- It rises by about $1.5 billion
- It rises by about $4.5 billion
- It falls by about $1.5 billion
- It falls by about $3.0 billion
Reveal Answer
Answer: A. ΔA = −6 × 50 × 0.01 = −$3.0bn and ΔL = −10 × 45 × 0.01 = −$4.5bn, so surplus changes by −3.0 − (−4.5) = +$1.5bn. The liabilities’ dollar duration (450) exceeds the assets’ (300).
2. When rates rose fast in 2022, which risks did the IAIS name as the real dangers for life insurers?
- Higher reserve requirements caused by longer life expectancy
- Margin calls on interest rate hedges and mass policy surrenders
- Falling solvency ratios caused by sharply lower discount rates
- Rising present values of long-dated policy liabilities overall
Reveal Answer
Answer: B. The IAIS said rising rates can improve life insurers’ solvency and named liquidity risks from hedge margin calls and mass surrenders. Higher discount rates lower, not raise, liability values.
3. A pension plan has $100 billion of assets and $80 billion of liabilities with a duration of 10. At what asset duration is its surplus roughly unaffected by a small change in rates?
- 6.4
- 12.5
- 10.0
- 8.0
Reveal Answer
Answer: D. Surplus is immune when DA × A = DL × L, so DA = 10 × 80 ÷ 100 = 8.0. Matching durations (10.0) ignores that assets exceed liabilities.
4. A building earns $6 million of net operating income. Interest rates rise and its cap rate moves from 5% to 6%. What happens to its value?
- It rises from $100 million to $120 million
- It falls from $120 million to $114 million
- It falls from $120 million to $100 million
- It stays at $120 million because income is unchanged
Reveal Answer
Answer: C. Value = NOI ÷ cap rate: 6 ÷ 0.05 = $120 million and 6 ÷ 0.06 = $100 million, a 16.7% fall. Cap rates rise with interest rates, so values fall.
5. Worked problem: A life insurer has bonds of $100bn with duration 8 and liabilities of $92bn with duration 12. Rates rise 2 points. What happens to assets and liabilities?
Reveal Answer
Answer: Assets fall 8 × $100bn × 2% = $16bn. Liabilities fall 12 × $92bn × 2% = $22.08bn.
6. Worked problem: What is the change in surplus?
Reveal Answer
Answer: Surplus rises by $22.08bn − $16bn = $6.08bn.
- Federal Reserve, Open Market Operations (federal funds target range history) — 2022–23 hikes from 0–0.25% to 5.25–5.50% (Part 10.2)
- CFTC press release 6626-13 (MF Global), June 27, 2013 — Misuse of nearly $1 billion of customer funds (Part 10.2)
- Estrella and Mishkin, “The Yield Curve as a Predictor of U.S. Recessions,” FRBNY Current Issues, 1996 — Yield-curve recession evidence (Part 10.2)
- Engstrom and Sharpe, “(Don’t Fear) The Yield Curve,” FEDS Notes, 2018 — Near-term forward spread (Part 10.2)
- Bank of England, letter from Jon Cunliffe on LDI, October 5, 2022 — 30-year gilt move, LDI size, collateral calls (Part 10.2)
- Bank of England, completion of the financial-stability gilt purchase unwind, January 2023 — £19.3 billion of purchases, September 28 to October 14, 2022 (Part 10.2)