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Fixed Expenses
- Expenses assumed to be the same for each risk, regardless of amount of premium
- E.g., overhead costs associated with the home office
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Variable Expenses
- Expenses vary directly with premium (i.e., constant percentage of premium)
- E.g., premium taxes and commissions
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All Variable Expense Method
- Does not diff erentiate between fixed and variable
- Expenses assumed to be a constant percentage of premium
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Relate historical expenses to either historical written or earned
- Use written if believe expense generally incurred at onset of policy
- Use earned if believe expense generally incurred throughout the policy
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Selection of expense provision
- Based on latest year or multi-year average
- Also use management input, prior expense loads, and judgment
- Expense load should reflect expectations in the future
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If non-recurring expense items during the historical period, the actuary should:
- Examine the materiality and nature of the expense to determine how/if should be incorporated
- May choose to spread out over several years or not include at all
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Potential Distortions of all variable method:
- Assumes all expenses vary directly with premium
- However, portion may be fi xed
- Understates premium need for small premium risks
- Overstates premium for large premium risks
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Options for companies using the All Variable Expense method to deal with distortion
- Premium discount to reduce expense loadings for larger premium polices
- Expense constants to handle expenses such as policy issuance and auditing
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What are the steps in the Premium-Based Projection Method?
- 1. Determine percentage of premium attributable to expenses for each of the expense categories
- 2. Divide ratio into fi xed and variable ratios: Ideally split based on detailed company data; Without needed data, make reasonable assumptions
- 3. Sum expense ratios across categories to determine fi xed and variable provisions
- 4. Note: this gives you the fi xed expense ratio, which is a ratio to premium - this is used with the loss ratio approach (Ch. 8)
- If using the pure premium approach, convert to fixed expense per exposure: Fixed per Exposure = Fixed Expense Ratio * Projected Average Premium
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Potential Distortions of premium based projection
- 1. Rate changes can impact the historical expense ratios and lead to an excessive or inadequate overall rate indication
- 2. Signifi cant premium trend between the historical experience period and the projected period can lead to an excessive or inadequate overall rate indication
- 3. Can create inequitable rates for regional or nationwide carriers because it uses countrywide expense ratios and applies them to state projected premiums to determine the expected fi xed expenses
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What are the steps in the Exposure/Policy-Based Projection Method?
- 1. Divide expenses into fi xed and variable amounts
- 2. Divide fi xed expenses by corresponding exposures (written/earned, countrywide/state)
- 3. Divide variable expenses by corresponding premium
- 4. Note: this gives you the fi xed expense per exposure - this is used with the pure premium approach
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Selecting projected average expense per exposure in the Exposure/Policy-Based Projection Method
- Similar expense ratios over several years implies expenses and exposures are increasing or decreasing proportionately
- Must consider impact of economies of scale given expected growth
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Other Considerations / Future Enhancements in the Exposure/Policy-Based Projection Method
- 1. The actuary splits expenses into fixed and variable
- 2. Allocates countrywide fi xed expenses to each state based on exposures
- 3. Some expenses considered fi xed vary by other characteristics
- 4. Existence of economies of scale in a changing book
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Trending Expenses
- Premium-based Projection Method
- If average expenses and average premium changing at same rate
- If assume average fi xed expenses changing at diff erent rate than average premium
- Exposure-based Projection Method
- If inflation sensitive exposure base used
- If non-inflation sensitive base or policy counts
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What are two ways to consider Reinsurance Costs in ratemaking analysis
- Reduce projected losses for reinsurance recoveries and premiums for cost of reinsurance
- Net cost of non-proportional reinsurance may be included as an expense item: i.e., cost of reinsurance minus expected recoveries
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Total Pro fit
Investment Income + UW Pro fit
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Two major sources of investment income
- Investment income on capital
- Capital belongs to owners of the company
- Substantial disagreement whether this investment income should be included in ratemaking
- Investment income earned on policyholder-supplied funds
- Two types - unearned premium reserves and loss reserves
- Longer the tail of the line, the longer opportunity for investment
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Underwriting Pro fit
Sum of pro fits generated from insurance policies
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Variable Permissible Loss Ratio
- VPLR = 1.0 - Variable Expense % - Target Profi t % = 1.0- V - Q
- Portion of each dollar of premium to be spent on Projected Loss, LAE & Fixed Expense
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Total Permissible Loss Ratio
- PLR = 1.0 - Total Expense % - Target Profi t % = 1.0 - F -V - Q
- Portion of each dollar of premium to be spent on Projected Loss & LAE
- If all expenses treated as variable, VPLR = PLR
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