Calculate overall average rates and rate changes using the loss cost and loss ratio methods.

Two ratemaking methods, same target: a rate that pays losses, funds expenses, and earns the planned profit. Loss cost builds the rate from scratch. Loss ratio adjusts the rate already on the books.

Two routes to the same indication. The loss cost method (also called pure premium method) computes a rate per exposure unit from the ground up. The loss ratio method adjusts the current rate by a multiplicative factor. Choose the method that fits the data and the situation, not the result you want.

When to use loss cost. Pick the loss cost method when no current rate exists (new product), when the exposure base is changing, or when current premium is unreliable. You need a credible exposure count by class and reliable losses per exposure.

When to use loss ratio. Pick the loss ratio method when a current rate is in force, premium can be brought to current rate level, and management thinks in terms of "how much should we change rates." Most established personal and commercial lines use this method.

Common mistakes

• Putting fixed expenses in the denominator. They belong in the numerator; the denominator is $1-V-Q$.
• Using nominal historical premium instead of on-level premium. The loss ratio must use premium at current rate level.
• Forgetting to develop losses to ultimate or to trend them forward. The formula assumes both are already done.

Bottom line

• Loss cost method: indicated rate $R=(L+F)/(1-V-Q)$, where $L$ is pure premium, $F$ is fixed expense per exposure, $V$ is variable expense ratio, $Q$ is target profit.
• Loss ratio method: indicated change factor $\text{ICF}=(\text{LR}+F\%)/(1-V-Q)-1$, using on-level premium in the loss ratio.
• Permissible loss ratio $=1-V-Q$, the denominator in both formulas.
• Fixed expense sits in the numerator; variable expense sits in the denominator because it scales with premium while fixed expense does not.

Exam shortcut

Memorize the denominator pattern: $1-V-Q$. Whatever scales with premium (commission, premium tax, profit margin) goes here. For a loss ratio question, compute $(\text{LR}+F\%)/(1-V-Q)$ first, then subtract 1. Skipping the subtraction is the most common slip. If the problem gives both exposures and on-level premium, run loss cost and then cross-check with loss ratio. Matching answers confirms you did not double-count expenses.

The full lesson (about 5,048 words, 34 min read) adds 4 worked examples, all 10 common mistakes, a self-check, free in the app.

Learning objectives

• 6d

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