New on FinoLib · Volume III: Finance Encyclopedia
New on FinoLib, my finance education website: I have published an article called Global Recession Case Study: A Fully Traced Example, from Volume III: Finance Encyclopedia. Here is what the article explains, written as a short expert briefing; the full piece, with every worked example, is one click away.
The idea in plain words
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.
Key points
■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 closer look
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.
A worked example
Trace the Chain — Case One
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.
Decision rule
When rates are rising, measure surplus sensitivity, not asset losses. Compute the dollar durations D_A × A and D_L × L. If D_L × 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.
The costliest mistake
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.
Where Experts Disagree: Does an Inverted Yield Curve Still Predict Recession?
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…
Recap
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.
What the full article covers
The full article includes worked examples, a look under the hood at the mechanics, a clear decision rule, the one mistake that costs people the most, a recap, a reveal-on-click quiz and the official sources behind every figure.
Volume III: Finance Encyclopedia
Read the full article on FinoLib
The complete article, Global Recession Case Study: A Fully Traced Example, with every worked example, diagram, quiz and source, is free to read in Volume III, Finance Encyclopedia on finolib.com.
Explore the Finance Education Series: Vol. II — Capital Markets · Vol. I — Global Economy · Vol. III — Finance Encyclopedia · Vol. IV — Finance Careers · Vol. V — Personal Finance