Data, Profit, and Background

Question 1

3 criteria for good exposure based

Answer 1

1. Proportional to expected loss: EB chosen for LOB should be risk char. that exhibit most directly proportional relationship to losses
2. Practical: EB should be objective, and easy & inexpensive to obtain and verify
3. Considerate to historical precedence: it is very costly for industry to change an existing exposure base
   - can result in large premium swings for individual insureds
   - requires changing the rating algorithm, which can be costly from IT standpoint
   - will require significant adjs for future RM analyses

Question 2

Common exposure bases

Answer 2

Personal Auto: car-years

Homeowners: house-years

WC: payroll

CGL: sales revenue, payroll, square footage, # of units

CProp: amount of insurance coverage

PL: # of professionals

MedMal: # of physician years

Personal Articles: value of item

Question 3

4 common ways to measure exposures or premium

Answer 3

1. WE/WP: total exposures coming from policies issued during given time period as of certain point in time
2. EE/EP: portion of written exposures for which coverage has been provided as of certain point in time
3. UE/UP: portion for which coverage has not been provided
4. IFE/IFP: # of insured units for all policies exposed to loss at given point in time

Question 4

2 common ways to aggregate WE, EE, and UE

Answer 4

1. CY: considers all policies during year regardless of policy effective dates; metrics are FIXED once year is over
2. PY: considers all policies with effective dates during the year; metrics can still change after year is over

WP = EP+change in UP

-starting amounts will always be 0 on PY basis so

PY WP=PY EP + PYUP

Question 5

4 common ways to aggregate over time:

Answer 5

1. CY: considers all transactions with transactions dates during the year
2. AY: all transactions as of given valuation date on claims with an AD during the year
3. RY: all transactions as of given valuation date on claims with RD during the year
4. PY: all transactions as of give valuation date on claims coming from policies with policy effective date during the year

Question 6

2 common loss statistics

Answer 6

1. Paid losses: summation of paid loss amounts across transactions and claims
2. Reported losses: case incurred loss

reported loss = paid loss + change in case reserves

starting case reserves for AY, RY, or PY are always = 0

Question 7

why is it hard to determine price of insurance product?

Answer 7

in insurance, cost of policy being sold may not be known until many years after the policy is sold as there is uncertainty in how many claims occur, when those claims will be reported and settled, and how much the claims will cost the insurer

Question 8

Actuaries used methods to estimate cost of insurance policies in 2 ways

Answer 8

1. RM estimate costs of policies before they are sold and add a target profit in order to set prices

price = estimated cost + target profit

2. Reserving estimate cost of policies after they are sold so that those costs can be subtract from revenue to measure profit

estimated profit = price - estimated cost

Question 9

fundamental insurance equation

Answer 9

prem = loss + LAE + UW exp + UW profit

Question 10

how does insure set UW profit target

Answer 10

-insurer may set UW profit target depending on how well its investments are performing -> higher investment returns, may be willing to write policies with negative UW profit margin b/c can still achieve positive total profit

Question 11

Ultimate losses have 3 components

Answer 11

1. Reported losses
2. INBR reserve = amount estimated to ultimately settle claims that have occurred but have not yet been reported to insurer -> pure IBNR
3. IBNER reserve=estimate of development of reported losses for claims that have been reported to the insurer -> development on known claims
   - premium and LAE may also develop over time and may need to be estimated in advance

Question 12

ultimate loss

Answer 12

ultimate loss=final amount required to close and settle a claim or group of claims

Question 13

granularity of RM equations

Answer 13

RM: equation should be balanced at aggregate level across all policies that insurer sells so that insurer stands to make its overall target UW profit

eqn should be balanced at smallest level of granularity that is stat. reliable to ensure rates are fair for diff customers

Question 14

granularity of reserving eqns

Answer 14

Reserving: eqn must be used to measure profit at level needed for financial reporting which is generally @ LOB by AY level

eqn can be used to measure profit at any other levels of granularity for which insurer wishes to make business decisions

Question 15

how can you make estimates of losses more accurate?

Answer 15

by subdividing data into groups of policies/claims that exhibit similar characteristics

Question 16

how should you group data

Answer 16

generally group data to level that best balances homogeneity of data and credibility of data while considering resources available to complete analysis in timely manner

Question 17

3 main considerations in deciding what time method to use in grouping data

Answer 17

1. Accurately matching premiums and exposures to losses
2. Using the most recent data available AKA using most responsive data
3. Minimizing cost of data collection and retrieval

Question 18

Time Methods in Analyses

Answer 18

1. CY: considers all policies and loss transactions during the yr; no development so results are final immediately after year is over; data readily available since required for financial reporting; provides poor match in timing between premium and losses
2. C/AY: combines CY prem and AY claims data; most commonly used method in RM and reserving analyses; better match than 1; future development must be estimated since AY losses can develop over time
3. AY: premium audits taking place after CY is over are incorporated into prem data; prem and loss is subject to development; truer match
4. PY: considers all prem and loss from policies with effective dates during the year; provides true match; PY data takes longer to develop than AY data
5. RY: groups loss data based on date claims are reported; primarily used for claims-made policies; # of claims is known at end of year; RY is useful in estimating IBNER but not IBNR

Question 19

Different methods work better in diff situations

Answer 19

• AY loss data when want to isolate major claim events
• PY data when want to isolate policy or UW changes
• RY data when want to isolate changes in claims practices
• quarterly data when BOB is growing or shrinking rapidly

Question 20

LAE ratio

Answer 20

LAE/loss

Question 21

UW expense ratio

Answer 21

UW exp/prem = exp incd @ start/WP + gen exp/EP

Question 22

operating expense ratio

Answer 22

UW expense ratio + LAE/EP

Question 23

combined ratio

Answer 23

LR + LAE/EP + UW exp/WP = LR + operating exp ratio

Most common measure of overall UW profit for insurers