Welcome to the World of Rate-Making!

Hello there! If you are studying for Exam FAM, you have reached a core part of the "Short-Term Insurance" section. In this chapter, we are looking at a fundamental question: How do insurance companies decide how much to charge?

Whether it’s car insurance or home insurance, companies need to ensure they collect enough money to pay for claims (losses), cover their running costs (expenses), and make a small profit. We will explore two primary ways to calculate these rates: the Loss Cost (Pure Premium) Method and the Loss Ratio Method. Don't worry if this seems like a lot of math right now—we will break it down step-by-step!

The Goal: The Indicated Rate

Before we dive into the methods, let's understand what we are looking for. An Indicated Rate is the "suggested" price the actuary calculates based on data. It represents the amount of money needed to cover all future costs perfectly. Think of it like a recipe: if you know the cost of ingredients and your time, you know exactly what to charge for a cake to avoid losing money.


1. The Loss Cost (Pure Premium) Method

The Loss Cost Method (often called the Pure Premium Method) focuses on how much each "unit" of insurance costs in terms of claims. This method is typically used when you are starting a new line of business or when you have reliable data on the number of units (exposures) but perhaps not on the historical premiums.

The Formula

To find the Indicated Rate (\(R\)), we use this formula:

\( R = \frac{L + F}{E \times (1 - V - Q)} \)

Where:

  • \(L\) = Expected Losses and Loss Adjustment Expenses (LAE).
  • \(F\) = Total Fixed Expenses (costs that don't change with the size of the premium, like rent).
  • \(E\) = Number of Earned Exposures (the "units" of insurance, like "car-years").
  • \(V\) = Variable Expense Provision (as a percentage of premium, like commissions).
  • \(Q\) = Profit and Contingencies Provision (as a percentage of premium).

An Everyday Analogy

Imagine you are running a pizza delivery service.
- Losses (\(L\)): The cost of the ingredients.
- Fixed Expenses (\(F\)): The monthly rent for your kitchen.
- Exposures (\(E\)): The number of pizzas you expect to sell.
- Variable Expenses (\(V\)): The 10% commission you pay the delivery app.
- Profit (\(Q\)): The 5% profit you want to keep.
To find the price per pizza, you add the ingredients and rent, then divide by the number of pizzas, while adjusting for the app commission and your profit margin.

Quick Review: Pure Premium

The Pure Premium (\(P\)) is simply \(\frac{L}{E}\). It is the average loss per exposure. If you know the Pure Premium, the formula becomes even simpler:
\( R = \frac{P + (F/E)}{1 - V - Q} \)

Key Takeaway: Use the Loss Cost Method when you want to calculate the dollar amount of the rate per exposure.


2. The Loss Ratio Method

The Loss Ratio Method is used when you already have an existing business and you want to know if your current rates need to go up or down. Instead of calculating a dollar amount, this method calculates a percentage change.

The Formula

The Indicated Rate Change (\(IC\)) is calculated as:

\( IC = \frac{LR + FE}{1 - V - Q} - 1 \)

Where:

  • \(LR\) = The Experience Loss Ratio. This is \(\frac{\text{Projected Losses}}{\text{Earned Premium at Current Rate Level}}\).
  • \(FE\) = The Fixed Expense Ratio. This is \(\frac{\text{Fixed Expenses}}{\text{Earned Premium at Current Rate Level}}\).
  • \(V\) = Variable Expense Provision (%).
  • \(Q\) = Profit and Contingencies Provision (%).

Wait, what is "Earned Premium at Current Rate Level"?

This is a common "trick" in FAM! To compare apples to apples, we must act as if the premiums we collected in the past were collected using the rates we are currently charging today. If we raised rates last month, our old data doesn't reflect that yet, so we have to "on-level" the premium.

Did you know?

If the result of the formula is positive (e.g., +0.05), you need a 5% rate increase. If it’s negative (e.g., -0.02), you need a 2% rate decrease.

Key Takeaway: Use the Loss Ratio Method when you want to find the percentage change to apply to existing rates.


3. Comparing the Two Methods

It is important to remember that if you use the same data and assumptions, both methods will give you the exact same result! The choice depends on what information you have available.

Use Loss Cost (Pure Premium) when:
1. You are pricing a new line of business.
2. Current premiums are not available or are unreliable.
3. You want the rate in dollars (e.g., "\$500 per car").

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Use Loss Ratio when:\n
1. You are reviewing an existing line of business.\n
2. You want to know the percentage adjustment (e.g., "Increase all rates by 4%").

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4. Components of the Rate: A Closer Look

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To succeed on the exam, you need to be very comfortable with the components that go into these formulas.

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Losses and LAE (\(L\))

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We don't just use "raw" historical losses. Actuaries adjust them for:\n
- Loss Development: Estimating how much claims will grow as they get older.\n
- Loss Trending: Adjusting for inflation (e.g., car repairs cost more in 2025 than in 2023).

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Expenses

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This is where many students get tripped up. You must distinguish between Fixed and Variable:

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  • Fixed Expenses: These are dollar amounts that don't care how big the premium is. Examples: Building rent, salaries of the IT department.
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  • Variable Expenses: These are percentages of the premium. Examples: Premium taxes (the government takes a %), commissions (the agent takes a %).
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Common Mistake Alert!
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In the Loss Ratio Method, make sure you convert the dollar amount of fixed expenses into a ratio by dividing by the premium. In the Loss Cost Method, you keep them as dollars or divide them by exposures.

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5. Step-by-Step Calculation Example

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Scenario: An insurance company has a Pure Premium of \$200. Fixed expenses are \$20 per exposure. Variable expenses are 10% and the target profit is 5%.

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Step 1: Identify the method. We have "per exposure" data, so let's use the Loss Cost Method.

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Step 2: Plug in the values.\n
- \(P = 200\)\n
- \(F/E = 20\)\n
- \(V = 0.10\)\n
- \(Q = 0.05\)

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Step 3: Solve the formula.\n
\( R = \frac{200 + 20}{1 - 0.10 - 0.05} \)\n
\( R = \frac{220}{0.85} \)\n
\( R = 258.82 \)

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The indicated rate is \$258.82.


Summary Checklist for Success

  • Loss Cost Method: Target = Dollar Rate. Formula uses \(L, F, E, V, Q\).
  • Loss Ratio Method: Target = % Change. Formula uses \(LR, FE, V, Q\).
  • On-Leveling: Always ensure premiums are adjusted to the current rate level.
  • Fixed vs. Variable: Don't mix them up! Variable and Profit provisions belong in the denominator as \((1 - V - Q)\).
  • Rounding: In FAM, pay close attention to whether the question asks for a rate per unit or a total premium.

Keep practicing these formulas until they feel like second nature. You've got this!