# The back-of-envelope math insurers do daily
An underwriter at a regional carrier gets a renewal file: $2.4 million in premium, $1.9 million in incurred losses last year, $600,000 in expenses. She has thirty seconds before the next call to decide if this account is worth keeping. No spreadsheet, no actuary on the line. Just five ratios she can run in her head. This lesson teaches you those same five.
Insurance runs on ratios more than raw dollars, because scale varies wildly (a $50,000 policy and a $50 million policy get judged the same way: did the math work?). The US property and casualty (P&C) industry alone wrote roughly $900 billion in net premium in 2023 (estimate, per NAIC data), and Europe's non-life market is estimated around €500 billion in gross written premium (Insurance Europe, most recent estimate). At that scale, nobody is opening Excel to sanity-check a renewal in a live meeting. You use ratios.
Loss ratio = incurred losses ÷ earned premium.
Take our underwriter's file: $1.9 million losses ÷ $2.4 million premium = 79%.
That means 79 cents of every premium dollar goes to paying claims, before any expenses. A loss ratio consistently above 60-65% in commercial lines usually signals a pricing problem or an adverse book of business. Personal auto in the US has run loss ratios in the 65-75% range in recent years (estimate, varies by state and year, per III.org industry data).
Combined ratio = loss ratio + expense ratio.
Add our underwriter's expenses: $600,000 ÷ $2.4 million = 25% expense ratio.
Combined ratio = 79% + 25% = 104%.
Anything over 100% means the insurer is losing money on underwriting alone, before investment income. The US P&C industry combined ratio has hovered around 100-103% in recent years (estimate, AM Best and III), meaning insurers often rely on investment returns to stay profitable overall. A combined ratio near 95% is considered strong; above 110% is a red flag for that line of business.
This is the single most quoted number in the industry. When a CEO says "we improved our combined ratio by 3 points," that is real money: 3% of premium flowing straight to the bottom line.
Premium-to-surplus = net written premium ÷ policyholder surplus (surplus being an insurer's assets minus liabilities, its cushion for paying unexpected claims).
If a carrier writes $300 million in premium and holds $150 million in surplus, that is a 2:1 ratio. Regulators and rating agencies like AM Best watch this closely: a ratio above roughly 3:1 suggests the insurer may be writing more business than its capital base can safely support. Most well-run US P&C insurers sit between 1:1 and 2:1 (industry benchmark, varies by line).
Quick gut check: a smaller ratio means more cushion per dollar of premium. It is the insurance version of asking "how much skin does this company have in the game relative to what it has promised to pay out?"
Retention rate = policies (or premium) renewed ÷ policies (or premium) up for renewal.
If an agency had 500 policies up for renewal last quarter and 430 renewed, retention = 430 ÷ 500 = 86%.
Retention is the insurance equivalent of a subscription business's churn metric. Personal lines carriers typically target 85-90% retention; commercial lines, especially small business, often run lower (75-85%, estimate) because of more frequent shopping and price sensitivity. A sudden 10-point drop in retention is usually the first sign of a rate increase that went too far, or a competitor undercutting aggressively.
This is the one brokers and underwriters use constantly when a rate filing goes through.
New premium = old premium × (1 + rate change %).
Say a state regulator approves an 8% rate increase on homeowners policies. A policyholder paying $1,800 annually now pays:
$1,800 × 1.08 = $1,944
Scale that up: if a carrier has 200,000 policies averaging $1,800, and it pushes an 8% rate increase but expects to lose 5% of policyholders to non-renewal, the net premium effect is:
Compare that to the pre-increase baseline of 200,000 × $1,800 = $360 million. Net gain: about $9.4 million, not the naive $28.8 million the rate increase alone would suggest. This is why actuaries build "elasticity" assumptions into every rate filing: the increase has to outrun the customers it pushes away.
Knowledge check
1. Why do insurers rely on ratios like the loss ratio and combined ratio rather than raw dollar figures when evaluating accounts?
2. An underwriter reviews a book of commercial accounts and finds a loss ratio of 68%. What does this most likely signal, based on the lesson's benchmark?
3. A combined ratio of 104% most directly indicates that:
4. Select ALL correct answers about the loss ratio calculation.
Select all the correct answers.
5. Select ALL correct answers about the combined ratio.
Select all the correct answers.
These five calculations are also your first due-diligence pass when evaluating an insurer as a partner, employer, or investment angle (not investment advice, just sector literacy):
For a live view of these figures, the NAIC's Insurance Statistics reports and Insurance Europe's annual Statistics publication are free and update annually.
How Insurance Companies Make Money
The mechanics are identical, but regulatory framing differs. In the US, each state regulates rates and solvency separately (no single federal insurance regulator). In Europe, Solvency II (the EU-wide prudential regulation framework effective since 2016) sets harmonized capital requirements, so the premium-to-surplus logic shows up there as the "Solvency Capital Requirement (SCR) ratio," conceptually similar but calculated under a different formula. Don't assume the exact thresholds transfer across the Atlantic, the concept does, the numbers don't.