Fit exponential or linear trends to exposures, premiums, and losses, and apply them over the correct trend periods.

Your loss data is two years stale before you file, and it must pay claims a year into the future. Trend is the bridge: fit a slope to the past, then walk it forward the exact right number of years.

Ratemaking uses old experience to set future rates. Between the middle of your data and the middle of the period the new rates cover, costs move. Trend adjusts each historical quantity to its expected future level. You trend three things: exposures (when the base is inflation-sensitive), premiums (for shifts in the mix of business, not rate changes), and losses (for frequency and severity change).

Every trend calculation has two parts. The trend factor is how fast the quantity changes per year. The trend period is how many years you move it. Get either wrong and the projected rate is wrong.

KEY: Exponential trend multiplies; linear trend adds. Exponential means a constant percentage change per year. Linear means a constant dollar change per year.

Common mistakes

• Using endpoint-to-endpoint instead of midpoint-to-midpoint. Measuring from the end of the data year to the effective date gives the wrong span. The correct loss trend runs from the experience occurrence midpoint (July 1 for a full accident year) to the future occurrence midpoint.
• Reading an accident-year midpoint on policy-year data. Policy-year losses center one full policy term after the policy-year start, not at the middle of the year. Use January 1 of the following year for annual policies, October 1 for six-month policies.
• Trending premium on data that is not on-level. A premium trend fit on data still carrying old rate levels double-counts the rate change that on-leveling already removed. Trend the on-level, per-exposure figure so only mix shift is captured.

Bottom line

• Trend projects a quantity to the future policy period; the two moving parts are the annual trend factor and the trend period (length in years).
• Exponential trend multiplies by $(1+r{)}^t$; linear trend adds slope times t. Losses and severity default to exponential because inflation compounds.
• Fit exponential by regressing $\ln (\text{value})$ on time (annual factor $e^b$); fit linear by ordinary least squares on the raw values.
• Select frequency and severity trends separately, then multiply them into the pure premium trend; a lone pure-premium fit hides offsetting shifts.

Exam shortcut

For any trend period, draw a timeline and mark two midpoints: the middle of the experience year and, for annual policies over a one-year rating period, one full year past the effective date. The gap between them in years is t. On policy-year data, shift the trend-from date to one full policy term after the policy-year start.

The full lesson (about 3,732 words, 25 min read) adds 4 worked examples, all 8 common mistakes, a self-check, free in the app.

Learning objectives

• A8

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