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Expenses & Profits

LAE

  • Selecting the ULAE factor…
    • ULAE Ratios:
      • CY 2016: 5%
      • CY 2017: 10%
      • CY 2018: 10%
      • CY 2019: 10%
    • The difference (5% in CY 2016) could be due to two reasons:
      • Operational change: 10% continues in the future
      • An anomaly: could potentially appear in the future
    • Assume Operational change and select 10%
    • Assume anomaly and account for the 5% by taking a volume weighted average.

UW Expenses

Flow

  • expenses as % of premium
  • Sum-product \(\to\) Fixed & Variable parts
\[ \text{Premium} = \dfrac{\text{Losses} + \text{LAE} + \text{Fixed Expenses}}{1- V - Q_{t}} \]

where,

  • \(Q_{t}:\) Target Profit as % of premium
  • \(V:\) Variable Expense rate as % of premium

This equation is basically telling us, if you remove the variable expenses and profit provision from premiums, you are left with a provision for losses, their adjustment expenses & fixed expenses required to keep the business running.

  • Indicated rate per unit of exposure = Indicated Average Premium. Given by,
\[ \text{Indicated Avg. Premium} = \dfrac{\text{Pure Premium incl. LAE} + \text{FE per exp}}{1 - V - Q_{t}} \]
  • Fixed expenses are assumed to be the same for every exposure regardless of the the premium size.
    • e.g. Insurer's home office's rent
  • Variable expenses are assumed to vary directly with the premiums.
    • e.g. Commissions paid as a % of premium
  • Why combining the expenses and premiums across years together is wrong.
    • Relating all expenses to earned premiums assumes the book is not changing in size (WP = EP)
    • If we observe that one of the expense categories (Oth Acq) is growing while the premiums are shrinking \(\implies\) the volume weighted average may not reflect expected

Methods for Pricing

  1. All Variable Expense Method
  2. Premium Based Projection Method
  3. Exposure/Policy-Based Projection Method

Details

  • (1), (2) & (3) \(\to\) \(\dfrac{\text{Variable Expenses}}{\text{Premiums}}\)
  • (1), (2) \(\to\) \(\dfrac{\text{Fixed Expenses}}{\text{Premiums}}\)
  • (3) \(\to\) \(\dfrac{\text{Fixed Expenses}}{\text{Exposures}}\)

How to choose which expenses, premiums or exposures (E/P/E) to use?

  • Expenses incurred at the start of policy terms \(\to\) Written E/P/E
    • Commissions & Brokerages
    • Other Acquisition
    • Taxes, Licenses & Fees
  • Expenses incurred throughout the policy terms \(\to\) Earned E/P/E
    • General Expenses

This Makes a difference if the company size is changing. Why?

State Level Country-wide Level
Taxes, Licenses & Fees CEO's Salary
General Expenses
Other Acquisition1
Commissions & Brokerages
(more often here)		 Commissions & Brokerages
  • Selected ratios should be best representative of the future expectation.

All Variable Expense Method

Method:
No fixed expenses, so take appropriate ratios (Expense / Premiums);
sum them to get the Variable Expense Ratio;
Use them in the FII to get the indicated rates.
  • Inaccurate if some expenses are truly fixed.
  • If so, it will undercharge risks with lower-than-average premium
    • Since it assumes all expenses are variable and are fully reduced with the lower average premium
  • It will also overcharge risks with higher-than-average premium
    • Since it bases expenses fully on the higher average premium

This distortion can be fixed using:

Finally,

  • No Expense trend needs to be applied to historical expenses
    • since all expenses are fully based on premium
    • They will adjust automatically, along with the premium changes.

Premium-Based Projection Method

Method:
Apply the variable expenses method to find the variable expenses and the fixed expenses,
with an additional piece of information: THE ASSUMED FIXED PERCENTAGE,

This biforcates the variable expenses and the fixed expenses,
though the process of calculation is the same for both.

Then use the on-level premium x fixed expense ratio = Fixed expense.

So, you derive both:

  • Variable Expense Ratio
  • Fixed Expense Ratio

\(\text{VE Ratio}+ \text{FE Ratio} = \text{All Variable Expense Ratio}\)

We (implicitly) assume,

We (implicitly) assume

Fixed expenses are trending at the same rate as the premiums.

E.g.

  • Projected avg premium at present rates = $500
  • Fixed Expense ratio = 12.5%
  • Fixed Expense per exposure = \(\$500 \times 12.5 \% = \$62.5\)
  • \(Q_{T}\) = 5%
  • Projected Pure premium (incl. LAE) = $250

Then, the indicated avg premium =

\[ \text{Ind. Avg Premium} = \dfrac{250+62.5}{1 - 12.5\% - 5\%} = 429.26 \]

Three potential Issues:

  1. One-time changes: hist. expense ratios differ
    • Sol: On-level before expense ratio calculation
  2. Premium and/or expense trends: impact expense ratios
    • Sol: Trend all premiums and expenses to future levels before calc expense ratio.
    • BUT this is not required in the exam, as we assume that they are trending at the same rate.
  3. Inequitable rates across states for multi-state insurers when countrywide fixed expenses are allocated to the state level
    • States with higher than average premiums will get a higher allocation of fixed expenses, may not be fair
    • \(\implies\) Calculate FE ratios by state.
    • Wording: allocating FE to the state on a variable basis result in average fixed expenses that are higher than the countrywide average

Exposure/Policy-Based Projection Method

Use the all variable method to find the variable expenses.

Consider the TREND for the fixed expense.

- Trend WRITTEN Fixed expenses (Avg Writ -> Avg Writ)
- Trend EARNED Fixed expenses (Avg Erd -> Avg Erd)
  • Calculate Variable Expense ratios based on premiums
  • Calculate Fixed Expense per exposure and trend them.

  • Indicated rate change

    • Loss ratio method: Find FE ratio… \(\dfrac{\text{FE per exposure}}{\text{Avg Premium}}\)
    • Pure premium method: Directly use the FE per exposure.

  • Shortcoming:

    • existing of an economies of scale in a changing book
    • may lead to increasing or decreasing projected average fixed expenses.

Reinsurance Costs

  • 2 common ways to incorporate reinsurance costs in ratemaking
    1. Restate all premium and loss data to be net of reinsurance costs
    2. Calculate net cost of reinsurance and treat it as a fixed expense

Permissible Loss Ratio

  1. Variable Permissible Loss Ratio
    • Portion of each dollar of the indicated premium that is "permitted" to be spent on Losses, LAE and Fixed expenses.
    • \(\text{Var PLR} = 1 - \text{VE}\% - Q_{t}\)

  2. Total Permissible Loss Ratio

    • Portion… "permitted" to be spent on Losses & LAE (& no FE).
    • \(\text{Var PLR} = 1 - \text{VE}\% - \text{FE}\% - Q_{t}\)
    • \(\text{Var PLR} = 1 - \text{Total Expense}\% - Q_{t}\)

  3. For Indicated average premium, we can just \(\dfrac{\text{Loss + LAE}}{\text{Total PLR}}\). How convenient!

Misc

Profit Provision

  1. Investment income
  2. Aggressive profit
  3. Profit as a Lifetime Value Perspective
  4. More reinsurance provision, would tolerate a lower profit margin
  5. One company might be more conservative in the estimation of the contingency piece of the profit provision

PY

  • PY not fixed even after its over?
    • Premium audits completing after the end of the policy year?
    • Retrospective rate adjustments

Some expenses

RISK CONTROL SERVICES

  • Before finalizing the rates the underwriter makes use of additional information to ensure he is not excessively charging.

  1. Because you benefit from the international presence of the company. Brand value, that is why Apple can setup their stores just about anywhere and get sales, without needing to advertise their product. ↩