Robbin: UW Profit Provision

Question 1

Five types of underwriting profit

Answer 1

Provision included in manual rates

Corporate target UW profit provision

Breakeven UW profit provision

Charged UW profit provision

Actual UW profit

Question 2

Corporate target UW profit provision

Answer 2

Should be sufficient to generate expected return similar to that provided by investments with similar risk

Question 3

Breakeven UW profit provision

Answer 3

Provides rate of return equal to rate of return on risk free investments

Question 4

CY investment income offset procedure

Answer 4

U = U⁰ - i_AFIT * PHSF

Question 5

Advantages of using CY data for investment income offset

Answer 5

Data from Annual Statement

Since the figures are in filed reports, moral hazard of pessimistic projections lessened

CY investment portfolio yields are relatively stable

Question 6

Disadvantages of using CY data for investment income offset

Answer 6

Since CY results are retrospective, not totally applicable to ratemaking

Question 7

Advantages of CY investment income offset procedure

Answer 7

Easy to get numbers

Calculation straight forward

Question 8

Disadvantages to CY investment income offset procedure

Answer 8

Lack of economic theory

Results distorted if large change in volume or reserve adequacy

Question 9

Steps to CY investment income offset

Answer 9

1. Average portfolio balance due to UEPR = average direct UEPR * (1 - expense ratio) - average premiums receivable
2. Reserves relative to premiums = PLR * Loss reserves / Loss incurred
3. Add (1) and (2), multiply by after tax portfolio yield
4. Traditional UW profit provision - (3) = final UW profit provision

Question 10

Robbin PV offset method

Answer 10

Applies offset based on difference between PV of losses for short tail reference line and line under review

Question 11

Options to discount losses, Robbin PV offset method

Answer 11

Portfolio yield from recent year

Estimated portfolio yield for effective year

New money yield (more suited, prospective)

Question 12

Advantages to PV offset method

Answer 12

Accounts for II in simple manner

Not distorted by rapid growth/decline

No need to select target return or allocate surplus

Question 13

PV cash flow return model

Answer 13

Selects UW profit provision necessary to produce PV of total cash flow (discounted at investment ROR) equal to PV of changes in equity (discounted at target ROR)

Question 14

PV cash flow return model, procedure

Answer 14

Cash flow = UW Cash flow + investment income - tax

UW Cash flow = premium - loss - expense

Question 15

PV cash flow return model, discounts

Answer 15

Discount equity at target ROR

Discount cash flows at investment ROR

Question 16

Risk adjusted discounted cash flow model

Answer 16

Discount losses using CAPM:

i_r = i_f + ß(i_m - i_f)

Discount all others at risk free rate

Assumes income is earned at the end of the year

Question 17

Advantages of risk adjusted discounted cash flow model

Answer 17

Great intuitive appeal

Grounded in modern financial theory

Not necessary to determine target ROR

Question 18

Disadvantage of risk adjusted discounted cash flow model

Answer 18

Hard to determine beta

Question 19

Model construction questions

Answer 19

Should surplus be included?

How should surplus requirement be determined?

How should risk be incorporated into the model?

Is it better to use cash flows or income flows?

How to reflect income taxes?

Question 20

Parameter selection questions

Answer 20

What discount rate should be used?

What is the right target ROR?

Question 21

Premium, Robbin

Answer 21

P = PV_losses + P*(FR + VR + U⁰) + L(1 - PV_x⁰)

Question 22

Two reasons to support discounting of policyholder supplied funds at risk free rate

Answer 22

Insured is not bearing risk of insurer’s investments

Profit greater than risk free rate should belong to owners of insurer as reward for bearing such risk

Question 23

Two reasons to support the exclusion of investment income on surplus in ratemaking process

Answer 23

Surplus belongs to owners, so policyholder should not receive credit for them

Insurer with greater surplus would be penalized as it would receive greater investment income –> charging lower rates