Overall Average Rates and Rate Changes

The actuary has two paths to the indicated rate change: build the rate from scratch (loss cost method) or compare actual to expected ratios (loss ratio method). Both should produce the same answer. If they don't, there's an error. The exam tests both and expects you to reconcile them.

HIGH-FREQUENCY: Both methods are tested on nearly every FAM ratemaking problem set.

Step 1. Indicated PP:

$$\text{Indicated PP}=\frac{\text{Developed, Trended L+LAE}}{\text{Earned Exposures}}$$

Step 2. Indicated Rate:

$$\text{Indicated Rate}=\frac{\text{Indicated PP}}{1-V-Q_T}+F$$

Step 3. Rate Change:

$$\text{Rate Change}=\frac{\text{Indicated Rate}}{\text{Current Average Rate}}-1$$

Current average rate = On-Level EP / Earned Exposures.

KEY: Both the loss cost method and loss ratio method are algebraically equivalent from the same data. If they give different answers, there is an error in the calculation.

Step 1. Adjusted LR:

$$\text{Adjusted LR}=\frac{\text{Developed, Trended L+LAE}}{\text{On-Level EP}}$$

Step 2. Rate Change:

Common mistakes

• Dividing by the adjusted LR instead of the target LR. Formula: Adjusted LR / Target LR - 1, not Target LR / Adjusted LR - 1. If adjusted = 80% and target = 65%: correct = +23.1%, reversed = -18.75%. Trap: a rate decrease when an increase is needed.
• Using unadjusted data in the loss ratio method. The numerator requires developed, trended losses. The denominator requires on-level premium. Using raw data produces a meaningless ratio. Trap: an adjusted LR that is wildly off.
• Forgetting to use on-level premium for the current average rate. In the loss cost method, current rate = on-level EP / exposures. Using historical (not on-leveled) premium understates the current rate and shrinks the indicated change. Trap: an indicated change that is too small.

Bottom line

• Loss cost method: Indicated Rate = Indicated PP / PLR. Rate Change = Indicated Rate / Current Rate - 1.
• Loss ratio method: Rate Change = Adjusted LR / Target LR - 1.
• Both methods are algebraically equivalent from the same adjusted data, differing only in framing.
• LCM (Loss Cost Multiplier) = 1 / PLR = 1 / (1 - V - Q); it converts an advisory loss cost into the insurer's rate.

Exam shortcut

Read the problem to pick your method. Given exposures and per-exposure data: loss cost method. Given aggregate premium and loss data with no exposure detail: loss ratio method. Either way, compute PLR first. If the problem gives you both the adjusted LR and the target LR, go directly to Change = Adjusted / Target - 1. Remember: "Loss Ratio Over Target Minus One", the loss ratio method in seven words.

The full lesson (about 1,897 words, 13 min read) adds 3 worked examples, all 5 common mistakes, a self-check, free in the app.

Learning objectives

• 5e

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