New on FinoLib · Volume III: Finance Encyclopedia
My latest article is now live on FinoLib, the free finance library I write: Types of Insurance and Why Insurance Exists Explained, from Volume III: Finance Encyclopedia. Read the summary below for the substance of the topic, then continue to FinoLib for the complete treatment.
1.1 Why Insurance Exists — Risk Pooling and the Law of Large Numbers
The idea in plain words
Insurance turns a loss you can’t predict into a small fee you can. Imagine a thousand neighbors who each fear a house fire: none knows whose house will burn, but together they can predict roughly how many fires will happen, so each pays a little into a shared pot. The law of large numbers says the more policies in the pool, the steadier the claim rate becomes. But losses that hit many people at once, like a hurricane, don’t average out. Those must be carried by capital, reinsurance or catastrophe bonds.
Key points
■With a 2% claim probability, the claim rate’s standard deviation is 0.14 percentage points for 10,000 policies and 0.014 for 1,000,000.
■A hundredfold larger pool cuts relative uncertainty only tenfold (1 ÷ √n).
■A pairwise correlation of just 0.01 sets a floor of 70% relative uncertainty, however large the pool.
A closer look
Insurance exists to convert an individually unpredictable, potentially catastrophic loss into a small, predictable, affordable cost. It works through risk pooling: a large number of people face similar risks (a house fire, a car accident, a death), each individually unlikely, and each pays a small premium into a shared pool; the pool pays out to the smaller number who actually experience a loss in any given period.
Decision rule
If losses are independent, measurable and individually small relative to capital, then pool them and price on expected loss plus a loading; scale cuts relative volatility by 1 ÷ √n. Once the correlation between policies exceeds roughly 1 ÷ n (the point where the correlated term overtakes the independent one in the formula above), size capital and reinsurance from the modeled catastrophe tail, not from the policy count. For a 100,000-policy regional property book that threshold is a correlation of only 0.00001.
The costliest mistake
Capitalizing a concentrated book as if its risks were independent. For 1,000,000 homes with a 2% claim probability and a $15,000 average claim, expected claims are 1,000,000 × 2% × $15,000 = $300 million. A three-standard-deviation buffer is 3 × 0.014% × 1,000,000 × $15,000 = $6.3 million if claims are independent, but 3 × 1.40% × 1,000,000 × $15,000 ≈ $630 million at a correlation of 0.01, a hundred times more.
1.2 Types of Insurance
The idea in plain words
There are three big families of insurance, and each behaves differently. Life insurance makes promises that can last decades and depends on how long people live and whether they keep their policies. Property and casualty insurance, covering things like homes and cars, depends on how often claims happen, how big they are and on catastrophes. Health insurance depends mainly on rising medical costs. Because their risks differ, you need different measures to tell whether each line is healthy.
Key points
■One year of $1,000,000 coverage costs $3,115 in expected claims for a US man of 40 and $16,455 at 65 (SSA 2023 period table).
■Level premiums overcharge early and build a reserve that pays for the costlier later years.
■Two extra years of annuitant life raise an annuity’s value by 7.4% in the worked example.
A closer look
India’s unit-linked insurance plan (ULIP) is the counterpart of variable universal life; its lock-in rules sit in the India Lens at the end of this Part.
Decision rule
A reading rule for any insurer: classify each line by tail length and correlation, then watch the matching metric. If the line is short-tailed with largely independent claims (personal auto, most health), judge it on the combined ratio (Part 1.3: The Actuarial Function — Pricing Risk Before It Happens).
The costliest mistake
Underestimating longevity on a block of annuities. With the simplified annuity values above, pricing 18 years of payments for annuitants who live 20 makes the liability 13.590 ÷ 12.659 − 1 = 7.4% larger than priced: about $74 million on a $1 billion block, surfacing year by year long after the premiums were collected. Annuity writers defend themselves with mortality tables that assume continuing improvement, regular checks of their own experience against the table, and longevity reinsurance.
Recap
Life, property-casualty and health insurance differ in the length of their promises and the correlation of their losses: life books run on mortality, longevity and lapse, P&C books on frequency, severity and catastrophes. Read each line with its matching metric: combined ratio for short-tailed lines, reserve adequacy and rate sensitivity for long-dated ones, modeled tail loss for catastrophe lines.
What the full article covers
In the full article I take you through these sections:
■1.1 Why Insurance Exists — Risk Pooling and the Law of Large Numbers
■1.2 Types of Insurance
It includes 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, Types of Insurance and Why Insurance Exists Explained, with every worked example, diagram, quiz and source, is free to read in Volume III, Finance Encyclopedia on finolib.com.
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