Ratemaking basics

Why it matters

Ratemaking is how property and casualty insurers decide what to charge. Too low, and the company loses money and may not be able to pay claims; too high, and customers leave and regulators object. Pricing actuaries produce a rate indication: the percentage change to current rates that the data supports. Most US states require insurers to file rates and justify them, so the indication is also a regulatory document. The CAS covers ratemaking in its upper-level exams, and its principles are in the CAS "Statement of Principles Regarding Property and Casualty Insurance Ratemaking".

The fundamental insurance equation

premium = losses + loss adjustment expenses (LAE) + underwriting expenses + profit

A rate is "adequate" when expected premium covers expected losses, the costs of settling them (LAE), other expenses and a reasonable profit.

Preparing the data

Raw data cannot be used as is. Before computing anything, the actuary:

1. Brings premium to current rate level ("on-leveling"): past premium was collected at older rates, so restate it as if today's rates had applied.
2. Develops losses to ultimate: recent accident years still have open claims; loss development factors (module 4) estimate their final cost.
3. Trends losses and premium to the future period the new rates will apply to (inflation in repair and medical costs, changes in exposure).

In this lesson's activity those steps are already done, so the table holds earned premium at current rates and ultimate trended losses and LAE.

The loss ratio method

The experience loss ratio is losses (including LAE) divided by premium at current rates. The permissible loss ratio is the share of premium available for losses and LAE once expenses and profit are taken out:

permissible loss ratio = 1 - variable expense ratio - profit provision      (ignoring fixed expenses)
indicated rate change  = experience loss ratio / permissible loss ratio - 1

Worked example

Auto line, three accident years, all adjusted:

experience loss ratio = 2,159,000 / 3,300,000 = 0.6542
variable expenses 25%, profit 5%  ->  permissible loss ratio = 0.70
indicated change = 0.6542 / 0.70 - 1 = -0.0654   (a 6.5% decrease)

Notice the experience loss ratio uses totals, not the average of the yearly ratios. Summing premium and losses first weights each year by its size. Many companies also weight years differently or use five years of data.

With fixed expenses (costs that do not scale with premium, such as a policy-issuance cost), the formula becomes (loss ratio + fixed expense ratio) / (1 - variable expense ratio - profit) - 1.

The pure premium method

The alternative works per unit of exposure (a car-year, a house-year) rather than per dollar of premium:

indicated rate = (pure premium + fixed expense per exposure) / (1 - variable expense ratio - profit)
pure premium   = losses and LAE / exposures

It gives an indicated rate rather than a change, and it is used for new lines where there is no current rate to change. Both methods give the same answer when applied consistently.

Doing it in SQL

Pricing data usually lives in a database. A grouped query computes the indications for every line at once:

SELECT e.line,
       ROUND(SUM(e.losses) * 1.0 / SUM(e.earned_premium), 4) AS loss_ratio
FROM experience AS e
GROUP BY e.line;

Multiplying by 1.0 forces real (not integer) division in SQLite.

After the indication

The indication is a starting point. The actuary credibility-weights it (module 3, lesson 2) when data is thin, considers competition, regulatory caps and customer retention, and then distributes the overall change across rating variables (age, territory, vehicle) with methods such as generalized linear models (GLMs). Rate filings are reviewed by state regulators, who check that rates are not excessive, inadequate or unfairly discriminatory.

Common mistakes

• Averaging yearly loss ratios instead of dividing total losses by total premium.
• Using premium at historical rates. Without on-leveling, past rate changes distort the loss ratio.
• Forgetting LAE or mixing it into expenses twice.
• Integer division in SQL. SUM(a) / SUM(b) on integers returns 0 in SQLite.

Quick recap

• Premium = losses + LAE + expenses + profit.
• Adjust data first: on-level premium, develop and trend losses.
• Loss ratio method: indicated change = experience loss ratio / permissible loss ratio - 1.
• Pure premium method: rate = (pure premium + fixed expense) / (1 - V - Q).

Try it

In the Do tab, write one SQL query that computes the loss ratio and the indicated rate change for each line of business.