Werner07.OtherExpenses

Reading: BASIC RATEMAKING, Fifth Edition, May 2016, Geoff Werner, FCAS, MAAA & Claudine Modlin, FCAS, MAAA Willis Towers Watson

Chapter 7: Other Expenses and Profit

Study Tips

Werner is well-written but I found chapter 7 to be a little wordy. There 3 types of expense ratio methods you have to learn. In the previous chapter we looked at LAE (Loss Adjustment Expenses) and in this chapter we look at underwriting expenses. The goal here is to project an underwriting expense ratio for use in a ratemaking analysis. Depending on the method, the expense ratio may be split between fixed and variable expenses.

• Method 1: All Variable Expense Method
• Method 2: Premium-Based Projection Method   ← this is the most frequently asked method
• Method 3: Exposure-Based (Policy-Based) Projection Method

(I find these easier than trending and on-leveling problems from previous chapters.)

There is also has an brief introduction to calculating a premium rate, a topic that's covered in detail in Pricing - Chapter 8. Aside from the mechanics of each method, you also need to know their advantages and disadvantages.

Estimated study time: 3 days (not including subsequent review time)

BattleTable

Based on past exams, the main things you need to know (in rough order of importance) are:

• fact A...
• fact B...

reference	part (a)	part (b)	part (c)	part (d)
E (2019.Fall #6)	Werner06.LossLAE	profit provision - investment income	trending - necessary when...
E (2019.Spring #6)	total expense ratio - all expenses variable	variable permissible LR: - calculate	distortions - due to expense ratio	variable permissible LR: - calculate
E (2018.Fall #6)	premium-based method - versus exposure-based	premium-based method - versus exposure-based
E (2018.Spring #7)	Excel Practice Problems
E (2017.Fall #7)	premium-based method - U/W expense ratio	premium-based method - operating expense ratio	total permissible LR - calculate	Werner08.Indication 1
E (2017.Spring #2)	Werner05.Premium	variable expense ratio - for U/W profit 5%	Werner05.Premium	Werner05.Premium
E (2017.Spring #4)	expense ratio - C&B, general	permissible LR - calculate	U/W profit provision < 0 - is profit possible?	U/W profit expectations - met / not met
E (2016.Fall #6)	expense provision - actuary's approach	expense provision - alternative approach
E (2016.Spring #7)	premium-based method - indicated average rate	achieve target profit - without changing rates?
E (2014.Fall #6)	variable expense method - indicated average rate	premium-based method - indicated average rate	excessive or inadequate - indicated average rate
E (2013.Fall #7)	premium-based method - versus exposure-based	premium-based method - versus exposure-based
E (2013.Fall #12)	pricing strategy - evaluate
E (2013.Spring #9)	Werner08.Indication 1	expense provision - fixed vs variable	expense provision - fixed vs variable

¹ For this problem you need the indicated rate change formula from chapter 8:

Full BattleQuiz

In Plain English!

Intro

Recall the Fundamental Insurance Equation:

premium    =    (Losses   +   LAE   +   U/W Expenses)   +   U/W profit

Our goal in a ratemaking analysis is to estimate each of these components for the period when the proposed rates will be in effect. We learned how to do this for premium in Chapter 5 and for losses and LAE in Chapter 6. In this chapter, we're going to do the same thing for U/W Expenses and U/W profit. (We'll also take another quick look at how reinsurance fits into the big picture.)

A Simple Example

Click Notation - Pricing for a full list of the notation used in Werner. This example looks more complicated than it really is because of all the notation but once you get past that, it's just simple algebra. The notation we need in this section is as follows. Note that total exposures is denoted by X:

• P, P → Premium, Average premium (P divided by X)
• L, L → Losses, Pure Premium (L divided by X)
• E_L, E_L → Loss Adjustment Expense (LAE), Average LAE per exposure (E_L divided by X)
• E_F, E_F → Fixed underwriting expenses, Average underwriting expense per exposure (E_F divided by X)

For the above variables, the total dollar amount is listed first and the average dollar amount is listed second. The average amount equals the total amount divided by exposures X.

• V → Variable expense provision (E_V divided by P)
• Q_T → Target profit percentage

This is going to be your very first rate indication. Use the Fundamental Insurance Equation to calculate the average premium the insurer must charge.

• L + E_L = $180 (average Loss + LAE)
• E_F = $20 (fixed U/W expenses)
• V = 15% (includes premium taxes and other things)
• Q_T = 5% (target profit percentage)

The target profit percentage is the compensation an insurer receives for taking on risk. In a bad year they would make less than 5%; in a good year, more. Over a longer time period, the average should be roughly 5%. (This doesn't include investment income.) We're going write the Fundamental Insurance Equation using this notation then solve for P. Note that in the last step, we divide both sides by X to switch from total dollar amounts to average dollar amounts.

Now just substitute the given values into the final formula:

P   =   ($180 + $20) / (1.0 - 0.15 - 0.05)   =   $250

You can practice a slightly harder variation of this problem in the quiz.

mini BattleQuiz 1

Underwriting Expense Categories

Underwriting expenses are expenses incurred in the acquisition and servicing of policies. They are also referred to as operational and administrative expenses.

Question: what are the 4 categories of U/W expenses

Commissions & Brokerage: payment to agents or brokers for generating business

Other Acquisition: expenses for generating business, other Commissions and Brokerage

Taxes, Licenses & Fees: all taxes and fees excluding federal income tax (Ex: premium taxes)

General: all remaining expenses (Ex: building maintenance, salaries)

These expense categories can be further split into fixed expenses and variable expenses. Fixed expenses are the same for each risk. An simple example is the cost of an auto insurance policy form. It doesn't matter whether the premium is $300 or $800, the cost of the printed form is the same. Variable expenses are different for each risk and are expressed as a percentage of premium. An example is agents' commission which is typically 10-15% of written premium.

We're going to cover 3 methods for calculating the U/W expense term in the Fundamental Insurance Equation. The premium-based projection method appears most often on past exams.

METHOD 1: All Variable Expense Method

This first method assumes all 4 categories of expenses are variable. That means the amounts vary with premium. In the example below, you're given the expense ratios for calendar years 2023 and 2024 and the dollar amounts for 2025. You have to calculate the ratios for 2025 then use information from all 3 years to select an appropriate total expense ratio for a ratemaking analysis.

For example, the Commissions and Brokerage ratio for 2025 is 963/DWP = 963/9000 = 10.7%. It's an easy calculation but you have to be careful whether to use written or earned premium in the denominator. Commissions and brokerage expenses are incurred when the policy is written so it's logical to express them as a percentage of written premium. General expenses however (like building maintenance and salaries) are incurred over the policy term so we match them to premium earnings over that same time frame. Note that Other Acquisition and TLF are incurred at policy inception so we use written premium for those as shown in the solution below.

Here are 2 practice problems on this method:

Practice: 2 Expense Ratio Problems (like 2019.Spring #6a)

METHOD 2: Premium-Based Projection Method

The premium-based projection method is similar to the method 1 but with one extra step. As before, divide the dollar amounts for each category by written or earned premium as appropriate to get the total expense ratios. Then separate those ratios into their fixed and variable components using the % fixed values that are given. (These percentages would have been produced by a separate study, although the % fixed for commissions is virtually always 0%.) For me, the key to solving it correctly is being extra careful about organizing my table. There are a lot of percentages floating around and it's easy to get mixed up. Every exam problem is a little different but insofar as is possible try to organize your solution essentially the same way every time.

Here are 2 practice problems:

Practice: 2 Premium-Based Projection Method problems (like 2017.Fall #7a)