Expenses and Profit Loading in Ratemaking

Two insurers have identical loss costs of $400 per car-year. Company A: 28% expenses, 5% profit target. Company B: 35% expenses, 5% profit target. Both try to charge $540, but that rate is only adequate for Company A. Company B needs $615. The difference is the expense loading formula: variable expenses scale with premium, creating a circular reference resolved by division, not multiplication.

HIGH-FREQUENCY: The PLR formula and the fixed/variable expense distinction appear on most FAM ratemaking problems.

$$\text{PLR}=1-V-Q_T$$

Variable expenses ($V$): commissions, premium taxes, acquisition costs, all stated as % of premium.

Fixed expenses: general admin per exposure, dollar amounts.

TRAP: Fixed expenses per exposure are added after dividing by PLR, not included in $V$. Including them in $V$ creates circularity and gives a slightly wrong rate.

$$\text{Gross Rate}=\frac{\text{Pure Premium (L + LAE)}}{1-V-Q_T}+F_{\text{per exposure}}$$

When all expenses are variable (no fixed):

Common mistakes

• Multiplying PP by the expense ratio instead of dividing by 1 - V - Q. PP = $400, total loading 35%: wrong gives $400\times 1.35=540$; correct gives $400/0.65=615.38$. Trap: $540 is always too low.
• Including fixed expenses in the PLR denominator. Fixed expenses per exposure are added after dividing by PLR, not mixed into $V$. Adding them to $V$ creates circularity. Trap: a slightly lower rate.
• Confusing the total expense ratio with $V$. The financial statement expense ratio includes all expenses (fixed + variable) as a fraction of premium. $V$ is variable only. Using total as $V$ overstates the loading. Trap: an inflated rate.

Bottom line

• Gross Rate = Pure Premium / (1 - V - Q) + Fixed Expenses per exposure
• PLR (Permissible Loss Ratio) = 1 - V - Q, the fraction of each premium dollar available for losses
• Variable expenses (commission, premium tax, acquisition) scale as a % of premium; fixed expenses (admin) are per exposure
• Divide, don't multiply: variable expenses are a % of the final rate, so gross up by dividing, not by multiplying pure premium

Exam shortcut

Immediately separate expenses into two piles: variable (% of premium) and fixed ($ per exposure). Sum variables into $V$. Write: Rate = PP / (1 - V - Q) + Fixed. The most common error is treating a variable expense as fixed or vice versa. Test: "Does it scale with the premium dollar? Variable. Does it exist regardless? Fixed." Remember: "Divide, Don't Multiply", the cardinal rule of expense loading.

The full lesson (about 1,531 words, 10 min read) adds 2 worked examples, all 5 common mistakes, a self-check, free in the app.

Learning objectives

• 5d

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