CPCU 520: All Formulas

Question 1

UW Gains or Losses

Answer 1

Earn Premiums - Losses + Expenses

Measures: UW Performance

Question 2

Loss Ratio

Answer 2

Incurred Losses / Earned Premiums

Measures: UW Performance

Question 3

Expense Ratio

Answer 3

UW Expenses / Written Premiums

Measures: UW Performance

Question 4

Combined Ratio (Trade Basis)

Answer 4

Loss Ratio + Expense Ratio

Measures: UW Performance

Question 5

Investment Income Ratio

Answer 5

Net Investment Income / Earned Premiums

Measures:Overall Operating Performance

Question 6

Overall Operating Ratio

Answer 6

Combined Ratio - Investment Income Ratio

Measures:Overall Operating Performance

Question 7

Return on Equity Ratio (aka Policyholder Surplus)

Answer 7

(GAAP Basis) = Net Income / Average Owners’ Equity (SAP Basis) = Net Income / Average Policyholders Surplus
Measures:Overall Operating Performance

Question 8

Chronology of a Rate Filing

Answer 8

See the following notecards

Question 9

Year 1 - 1/1

Answer 9

Start of the Experience Period

Question 10

Year 3 -12/31

Answer 10

End of Experience Period

Question 11

Year 4 - 3/31

Answer 11

Start of data collection and analysis

Question 12

Year 4 - 7/1

Answer 12

Rates filed with regualtors

Question 13

Year 4 - 9/1

Answer 13

Approval of rates received

Question 14

Year 5 - 1/1

Answer 14

New rates initially used

Question 15

Year 5 - 12/31

Answer 15

Rates no longer used

Question 16

Year 6 - 12/31

Answer 16

Last loss incurred under this rate filing

Question 17

Policy Year Timeframe

Answer 17

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

Question 18

Ratemaking Methods

Answer 18

1. Pure Premium
2. Loss Ratio
3. Judgment Method

Question 19

Pure Premium Method

Answer 19

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)

Question 20

Ratio Method

Answer 20

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).

Question 21

Judgment Method

Answer 21

No Formula: Used in Ocean Marine, Inland Marine, Aviation

Purpose: To develop rates when data are limited (requires skilled judgment)

Question 22

Surplus Share Reinsurance Loss Sharing

Answer 22

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

Question 23

Surplus Share Reinsurance Premium Sharing

Answer 23

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)

Question 24

Excess of Loss Reinsurance

Answer 24

$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).

Question 25

Co-Participation Provision

Answer 25

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).

Question 26

Per Risk Excess of Loss

Answer 26

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.

Question 27

Per Policy Excess of Loss

Answer 27

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.

Question 28

Calculating net underwriting gain or loss

Answer 28

Earned premiums - (incurred losses + underwriting expenses)

Question 29

Formula for overall gain or loss from operations

Answer 29

Net underwriting gain or loss + investment gain or loss

Question 30

Lapse ratio

Answer 30

Number of policies that lapse during a period / total number of policies written at the beginning of that period.

Question 31

Operating ratio

Answer 31

Combined ratio after dividends - net investment ratio

Question 32

Combined ratio

Answer 32

Loss ratio + expense ratio

Question 33

Expense ratio

Answer 33

Incurred underwriting expenses / written premiums

Question 34

Combined ratio ( trade basis)

Answer 34

[Incurred losses including LAE/ earned premiums] + [incurred underwriting expenses/ written premiums]

Question 35

Loss ratio

Answer 35

Incurred losses / earned premiums

Question 36

Policyholder surplus

Answer 36

Total admitted assets minus total liabilities

Question 37

Return on equity

Answer 37

Net income/ net worth (book value). Can be called shareholders equity, owners equity, policyholder surplus depending on context

Question 38

Determining business income loss

Answer 38

Revenue - cost of goods sold - discontinued operating expenses

Or

Net profit (or loss) plus operating expenses that continue

Question 39

Earned premiums

Answer 39

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

Question 40

Rate making using the pure premium method

Answer 40

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

Question 41

Incurred losses

Answer 41

Losses paid during the year + difference between loss reserves at the end of the year and loss reserves at the beginning of the year