Produce an indicated overall rate change two ways, once with the pure premium approach and once with the loss ratio approach.

Two actuaries analyze the same book and reach the same answer by different roads. One prices the coverage from scratch in dollars; the other adjusts the rate already on file by a percentage. Master both, because the exam asks you to move between them.

Both methods answer "what should we charge?" but they hand you different outputs. The pure premium method builds a rate from the ground up. The loss ratio method measures how far the current rate is from adequate and returns a change factor.

The pure premium is the loss cost per exposure.

$$PP = \frac{L + E_L}{X}$$

Load it for expenses and profit to get the indicated rate.

$$\text{Rate} = \frac{PP + F_{X}}{1 - V - Q}$$

Here $F_X$ is fixed expense per exposure, $V$ is the variable expense ratio, and $Q$ is the profit and contingencies provision. The denominator $1 - V - Q$ is the variable permissible loss ratio (VPLR), the share of each premium dollar available for losses and fixed expenses.

Common mistakes

• Using premium not at current rate level. Feeding collected premium of $3,600,000 into the loss ratio method instead of the on-level $4,000,000 overstates the loss ratio and the indicated change.
• Treating the loss ratio output as a dollar rate. The loss ratio method yields a factor like 1.1404, not $433. Forgetting to subtract 1 reports a "+114%" change.
• Mixing fixed expense forms. Fixed expense enters the pure premium method as $ per exposure and the loss ratio method as a ratio to premium. Plugging $25 into the loss ratio numerator instead of 0.0658 breaks it.

Bottom line

• The pure premium method produces an indicated rate in dollars per exposure; the loss ratio method produces an indicated rate change as a percentage of current rates.
• Pure premium rate equals (pure premium + fixed expense per exposure) divided by (1 − variable expense % − profit %).
• Loss ratio change factor equals (loss and LAE ratio + fixed expense ratio) divided by (1 − variable expense % − profit %); subtract 1 for the percent change.
• The denominator 1 − V − Q is the variable permissible loss ratio (VPLR), shared by both methods.

Exam shortcut

Compute the variable permissible loss ratio 1 − V − Q first; it is the shared denominator for both methods, so you only build it once. To cross-check, take the pure premium indicated rate and divide by the current average premium. That quotient must equal the loss ratio change factor. If it does not, hunt for an on-leveling error.

The full lesson (about 2,262 words, 15 min read) adds 4 worked examples, all 6 common mistakes, a self-check, free in the app.

Learning objectives

• A11

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