UW Gains or Losses
Earn Premiums - Losses + Expenses
Measures: UW Performance
Loss Ratio
Incurred Losses / Earned Premiums
Measures: UW Performance
Expense Ratio
UW Expenses / Written Premiums
Measures: UW Performance
Combined Ratio (Trade Basis)
Loss Ratio + Expense Ratio
Measures: UW Performance
Investment Income Ratio
Net Investment Income / Earned Premiums
Measures:Overall Operating Performance
Overall Operating Ratio
Combined Ratio - Investment Income Ratio
Measures:Overall Operating Performance
Return on Equity Ratio (aka Policyholder Surplus)
(GAAP Basis) = Net Income / Average Owners’ Equity (SAP Basis) = Net Income / Average Policyholders Surplus
Measures:Overall Operating Performance
Chronology of a Rate Filing
See the following notecards
Year 1 - 1/1
Start of the Experience Period
Year 3 -12/31
End of Experience Period
Year 4 - 3/31
Start of data collection and analysis
Year 4 - 7/1
Rates filed with regualtors
Year 4 - 9/1
Approval of rates received
Year 5 - 1/1
New rates initially used
Year 5 - 12/31
Rates no longer used
Year 6 - 12/31
Last loss incurred under this rate filing
Policy Year Timeframe
1/1/x1 - Beginning of Policy Year
12/31/X1 - Last Policy Issued for this Policy Year
12/31/X2 - Policy issued 12/31/X1 Expire
Ratemaking Methods
- Pure Premium
- Loss Ratio
- Judgment Method
Pure Premium Method
Step 1: Incurred Losses/Total Unit Years ($40)
Step 2: Expenses / Total Unit Years (e.g. $17)
Step 3: Step 1 + Step 2 (e.g. 57) / 1- %PC (e.g. %5)
Answer = $60
Purpose: To develop rates from past experience (cannot be used without past experience)
Ratio Method
Actual Loss Step 1: Incurred Losses / Earned Premiums
Expected Loss Step 2: 100% - Expense Provision
Step 3: Actual Loss - Expected Loss / Expected Loss
Purpose: To modify existing rates (cannot be used without existing rates; cannot be used to determine rates for a new type of insurance).
Judgment Method
No Formula: Used in Ocean Marine, Inland Marine, Aviation
Purpose: To develop rates when data are limited (requires skilled judgment)
Surplus Share Reinsurance Loss Sharing
PI is responsible for a proportional amount (expressed in $ or %). If it retains a line (e.g.$25,000). It is responsible for loss < $25,000 and contributes $25,000 to a loss above that amount.
Example:
Line of $25,000: Loss of $100,000; PI pays $25,000; RI Pays $75,000
Retention of 25%: Loss of $150K; PI pays 25K, RI pays $112,500
Surplus Share Reinsurance Premium Sharing
Line (PI) $50k; Ceded (RI) $200k; for a total of $250k; PI would pay 20% ($50k / $250K) of Premiums and Losses. RI would pay 80% $200k / $250k)
Excess of Loss Reinsurance
$500,000 x $500,000
Translation: RI would indemnify PI for losses that exceeded $500,000 for losses up to $1,000,000 (500k+500k).
Co-Participation Provision
Purpose: To encourage PI to efficiently manage losses that exceed attachment point.Denoted as a % above the layer.
Example: If co-participation clause is 5%, the layer would be specified as 95% of 20,000,000 x 5,000,000 (RI’s responsiblity).
Per Risk Excess of Loss
The “in excess of” (x) amts apply to each risk (e.g. building).
Example:
$950k x $50k Coverage
Three buildings are damaged by tornadio with a RI payment of $1,400,000. RI pays it all because the three buildings each represent a risk. If a Per-Occurance limit applied, it would have only paid $1,000,000.
Per Policy Excess of Loss
The “in excess of” (x) amts apply to each policy.
Example:
$900k x $100k Coverage
Loss occured on three different policies with a RI payment of $1,100,000 total. RI pays it all because the excess of loss allows for up to a $1,000,000 RI payment for each policy.
Calculating net underwriting gain or loss
Earned premiums - (incurred losses + underwriting expenses)
Formula for overall gain or loss from operations
Net underwriting gain or loss + investment gain or loss
Lapse ratio
Number of policies that lapse during a period / total number of policies written at the beginning of that period.
Operating ratio
Combined ratio after dividends - net investment ratio
Combined ratio
Loss ratio + expense ratio
Expense ratio
Incurred underwriting expenses / written premiums
Combined ratio ( trade basis)
[Incurred losses including LAE/ earned premiums] + [incurred underwriting expenses/ written premiums]
Loss ratio
Incurred losses / earned premiums
Policyholder surplus
Total admitted assets minus total liabilities
Return on equity
Net income/ net worth (book value). Can be called shareholders equity, owners equity, policyholder surplus depending on context
Determining business income loss
Revenue - cost of goods sold - discontinued operating expenses
Or
Net profit (or loss) plus operating expenses that continue
Earned premiums
Written premiums for the year + the difference between unearned premiums at the beginning of the year and unearned premiums at the end of the year
Rate making using the pure premium method
Calculate pure premium
Estimate expenses per exposure unit based on insurer past expenses
Determine profit and contingencies factor
Add the pure premium and the expense provision and divide by 1 minus the profit and contingencies factor
Incurred losses
Losses paid during the year + difference between loss reserves at the end of the year and loss reserves at the beginning of the year