Expenses and Profit Loading in Ratemaking

Two insurers have identical expected losses of $400 per car-year and no fixed expenses. Company A has a 28% variable expense ratio and a 5% profit target, requiring a rate of $597.01. Company B has a 35% variable expense ratio and the same profit target, requiring $666.67. Expenses and profit are percentages of the final premium, so the rate must cover them after funding the losses.

Ratemaking must also provide for contingencies: uncertainty in the projected losses and expenses. When the stated profit and contingencies loading is a percentage of gross premium, include the full percentage in the target loading before calculating the permissible loss ratio.

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: Add fixed expenses per exposure to the pure premium before dividing by the permissible loss ratio.

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.
• Adding fixed expenses after the gross-up. That leaves variable expenses and profit unfunded on the fixed-expense portion of premium. Add the fixed dollar cost to pure premium in the numerator, then divide the whole amount by the permissible loss ratio.
• 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 + Fixed Expenses per exposure) / (1 - V - Q)
• 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 + Fixed) / (1 - V - Q). 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 1,596 words, 11 min read) adds 2 worked examples, all 5 common mistakes, a self-check, free in the app.

Learning objectives

• 5d

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