Werner01.Intro
Reading: BASIC RATEMAKING, Fifth Edition, May 2016, Geoff Werner, FCAS, MAAA & Claudine Modlin, FCAS, MAAA Willis Towers Watson
Chapter 1: Introduction
Contents
Pop Quiz
What colour T-shirt is Alice-the-Actuary wearing today? Click for Answer
Study Tips
VIDEO: W-01 (001) Introduction to Ratemaking → 5:00 Forum
This introductory chapter has some really great information to get you started on your pricing journey but you can cover it very quickly. I suggest spending 15-20 minutes scanning this wiki article then spending the rest of your time on the quiz questions, especially the 2 web-based practice problems. All of this introductory material will be reinforced in later chapters so your goal is to move on as quickly as possible.
Estimated study time: 1 hr (not including subsequent review time)
video_W-01_(001)_Intro_to_Ratemaking.mp4
BattleTable
Based on past exams, the main things you need to know (in rough order of importance) are:
- formulas for basic insurance ratios
- Fundamental Insurance Equation
reference part (a) part (b) part (c) part (d) E (2015.Fall #6) Combined Operating Ratio:
- calculate
In Plain English!
Intro
This morning Alice-the-Actuary bought her orange Lamborghini for a price of $200,000 from Danny-the-Dealer. The dealer's cost to obtain the Lamborghini from the manufacturer was $175,000. His profit was therefore $25,000.
price = cost + profit
Danny-the-Dealer charges everyone the same price and he knew his profit immediately after the transaction was completed. That's how profit and cost work if you're selling something like a car but it doesn't work that way with insurance.
The previous day, Alice bought insurance for her Lamborghini but the insurance company doesn't charge everyone the same price. Alice's driving record shows an arrest for drag-racing on the Ventura Freeway so she's a very high risk. Her insurer charged her $15,000 for a 1-year policy. That's the price in the equation above, but when the policy is sold nobody knows for certain the cost or the profit. If Alice has no claims in the coming year, the cost to the insurer is $0 and their profit is $15,000. If Alice however makes a claim for a fender-bender and it costs the insurer $25,000 in repairs then their profit is -$10,000. They lose money.
This is the reason ratemaking for insurance is so complex versus setting the price for a manufactured item like a car. With a car, you add up the costs of materials and labor, throw in a margin for profit, and that gives a reasonable price. The price, cost, and profit are the same for each individual sale and are known in advance. For auto insurance, the price, cost, and profit vary greatly across individuals. They are also not known in advance and this is why insurance ratemaking is called prospective. The actuary (that's you) does a statistical analysis to make sure the aggregate price across all customers will be greater than the aggregate future cost so that on average the insurer can still make a reasonable profit.
Take a quick look at SOP.Ratemaking. It's short and most of the content is covered later in Werner anyway. The main thing to memorize from it are the 4 principles of ratemaking.
Rating Manuals
According to Werner and Modlin:
- The rating manual is the document that contains the information necessary to appropriately classify each risk and calculate the premium associated with that risk. The final output of the ratemaking process is the information necessary to modify existing rating manuals or create new ones.
Rating manuals are discussed in Chapter 2 but this is not on the syllabus.
Basic Insurance Terms
There's a lot of overlap between the reserving and pricing material in the syllabus and the BattleActs program is organized assuming you cover the reserving material first. If you do intend to begin with pricing, please note that important background material necessary for both reserving and pricing is contained in the following wiki articles from reserving:
- Friedland01.Overview
- Friedland02.ClmsProcess
- Friedland03.Data
- Friedland04.Meetings
- Friedland05.Triangles
- Friedland06.Diagnostics
For chapter 7 of Friedland you would need to cover up through the Development Method to fully understand the pricing material. (The section on Influence of a Changing Environment could be covered when you study reserving.)
For chapters 14, 16, and 17 of Friedland, you really just need the definitions and a very basic understanding of the concepts of recoveries, ALAE, and UALE. You don't need to know the methods of estimating those quantities until you cover the reserving material.
Here are some brief explanations of the basic terms. Scan the definitions but don't spend a long time here because all of this is covered in much greater detail in subsequent chapters.
| Exposure is the basic measure of risk underlying the insurance premium. |
- If you purchase a 1-year auto policy for $1,200 then your insurer would record 1 written exposure unit and $1,200 of written premium. If your policy was for 6 months instead of a year, the number of written exposures would be 0.5 and the written premium would be $600. If you and 4 friends (5 people total) purchase 1-year policies, the insurer would record 5 written exposure units and 5 x $1,200 = $6,000 of written premium.
- But just because an insurer writes a policy for $1,200 doesn't mean they 'get' the full $1,200 of written premium right away. They have to earn the exposures and premiums over the policy term. Assuming a 1-year term, the earned exposure after one month would be 1/12 and the earned premium would be $1,200 x 1/12 = $100. That's because the insurer's service is provided evenly over the 1-year period and they must earn that premium as insurance coverage is provided.
- It's easy to see that for each individual policy, written exposure = earned exposure + unearned exposure. Same idea for written, earned, and unearned premium. (This equation is a little different for a calendar year aggregation of policies but we will cover that in a later chapter.)
- In-force exposures is the total number of risks for which coverage is being provided at any given point-in-time. In-force premium is the total written premium corresponding to in-force exposures.
| Claim is a demand for payment from the insurance company by the policyholder. |
- If Alice has a fender-bender with her Lamborghini on Jan 1 (great way to start the year!), the accident date or occurrence date is Jan 1. If she calls her insurance company the next day to officially make the claim we say the report date is Jan 2.
| Loss is the dollar amount of compensation paid or payable to the claimant under the terms of the insurance policy. |
- If the auto body shop charges Alice $4,500 for repairs and she is reimbursed by her insurer, then the insurer suffers a loss of $4,500.
- If you haven't already, you need to read The Claims Process from the reserving material for more details on this and on important terms like case outstanding loss and IBNR.
| Expense is the dollar amount an insurer incurs while paying claims and otherwise running the business (salaries, rent, etc...). |
- Categories of expenses include:
- → Loss Adjustment Expenses or LAE are the costs of investigating and settling claims consisting of:
- ALAE or Allocated Loss Adjustment Expenses
- ULAE or Unallocated Loss Adjustment Expenses
- (See What is ALAE and ULAE? for more information.)
- → Loss Adjustment Expenses or LAE are the costs of investigating and settling claims consisting of:
- → Underwriting Expenses abbreviated as U/W Expenses are the costs of acquiring customers consisting of:
- Commission and Brokerage
- Other Acquisition Expenses
- General Expenses
- Taxes, Licenses, and Fees
- → Underwriting Expenses abbreviated as U/W Expenses are the costs of acquiring customers consisting of:
| Underwriting Profit is the dollar amount left over from premiums after losses and expenses have been paid. |
- You can also think of U/W profit (also called operating income) as the sum of the profits generated from individual policies.
Note that a company's total profit includes both U/W profit and investment income but the investment component is beyond the scope of the Werner text.
Fundamental Insurance Equation
Recall from earlier the basic formula price = cost + profit. We can make this specific to insurance using concepts from the previous section:
Fundamental Insurance Equation: premium = (Losses + LAE + U/W Expenses) + U/W profit
The premium corresponds to price in the basic formula. The U/W profit corresponds to profit. And the term in parentheses corresponds to cost. Learn this formula well. The principles of ratemaking specify that this equation should be balanced, both at the aggregate level (principle 2) and at the individual level (principle 3). In practice however, this equation rarely balances at the individual level for all policyholders. What we can realistically strive for is balance for relatively small segments of customers.
As a very simple example, suppose your total costs are $1,050 and you want $150 in U/W profit. To balance the FIE you would need to charge a premium of $1,050 + $150 = $1,200.
Basic Insurance Ratios
The source text provides a list of symbols used in the text. The link is Notation - Pricing and can also be accessed from anywhere in the wiki in the sidebar under Miscellaneous Battle Reports. I thought it was funny that the text didn't use any of this notation when introducing the basic insurance ratios. Ian-the-Intern kindly put together a formula sheet for the basic ratios which is also available in the sidebar. There are then 2 web-based practice problems to help you learn them.
Unfortunately, the pricing and reserving texts don't always use the same terms to refer to the same quantities. If an insurer receives reports of 5 different accidents, they would say the number of claims is 5. The reserving text would say the claims counts is 5. And common usage is to simply to say that counts = 5.
Terminology: number of claims = claim counts = counts
There is also an inconsistency in the terms for amounts. The pricing text uses losses to denote dollars of losses related to claims. The reserving text uses the term claims. Common usage has been to use the term losses because the term claims can easily be confused with counts. Anyway, just be aware of the following equivalence:
Terminology: losses = claims ← dollar amounts
The text covers 11 basic insurance ratios that I like to organize into 3 different groups:
Group 1: Frequency, Severity, Pure Premium
- The terms frequency and severity mean exactly what you'd think they mean. If an auto insurer has 10 claims for every 100 customers their frequency is 10/100 = 0.10. If those 10 claims cost the insurer $25,000 in total, their average loss or severity is $25,000/10 = $2,500. The pure premium is defined as $25,000/100 = $250 because this is the average premium the insurer needs to charge every customer to cover the $25,000 in losses. Pure premium is equivalent to frequency x severity. You can verify that using the formula sheet and (very) simple algebra.
Group 2: Loss Ratio, LAE Ratio, Loss & LAE Ratio, Underwriting Expense Ratio, Operating Expense Ratio, Combined Operating Ratio
- Okay, there's a lot there but these ratios are all indicators of profitability because they measuer losses or expenses (or both) against premium. When you practice the web-based problems in the next quiz, you'll get a sense for typical values for these ratios. In very rough terms, the Loss Ratio for an auto insurer might be around 70-75% and the various underwriting and loss adjustment expenses might be about 25%. These different loss and expense components sum to the Combined Operating Ratio (COR) which is the primary measure of profitability for an insurer. The goal is to keep it under 100%. If the COR = 95% then the remaining 5% is profit. Some insurers have a COR > 100% which means either they're losing money or they're making up the loss with investment income.
- Pay very close attention to the fact the Loss Ratio has a different denominator (premium) versus the LAE ratio where denominator is losses.
- Note also the 2 versions of the formula for Loss & LAE Ratio. (See the formula sheet). I point this out because you needed both those formulas to solve the following exam problem. It wasn't hard - just algebraic manipulation - but if you didn't remember both versions of the Loss & LAE Ratio formula, you wouldn't be able to do it.
- E (2015.Fall #6)
Group 3: Retention Ratio, Close Ratio
- These 2 ratios are of lesser importance for what we're going to be doing but you should know how to calculate them. The Retention Ratio measures customer loyalty and the Close Ratio measures the attractiveness of your product to a potential new customer.
Here are a couple of problems on calculating these basic insurance ratios along with detailed solutions. The quiz has a similar web-based problem and there you can generate an infinite number of practice problems until you get so good you can do them in your sleep.
Here are some interactive quiz problems...
POP QUIZ ANSWERS
- Alice (Her T-shirt is purple, her 2nd favourite colour after orange!)
