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

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:

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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 divided by total 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 the risk. In a bad year they would make less than 5%; in a good year, more. Over a longer time period, it should average out to 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.

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