Robbin: UW Profit Provision Flashcards
Five types of underwriting profit
Provision included in manual rates
Corporate target UW profit provision
Breakeven UW profit provision
Charged UW profit provision
Actual UW profit
Corporate target UW profit provision
Should be sufficient to generate expected return similar to that provided by investments with similar risk
Breakeven UW profit provision
Provides rate of return equal to rate of return on risk free investments
CY investment income offset procedure
U = U0 - iAFIT * PHSF
Advantages of using CY data for investment income offset
Data from Annual Statement
Since the figures are in filed reports, moral hazard of pessimistic projections lessened
CY investment portfolio yields are relatively stable
Disadvantages of using CY data for investment income offset
Since CY results are retrospective, not totally applicable to ratemaking
Advantages of CY investment income offset procedure
Easy to get numbers
Calculation straight forward
Disadvantages to CY investment income offset procedure
Lack of economic theory
Results distorted if large change in volume or reserve adequacy
Steps to CY investment income offset
- Average portfolio balance due to UEPR = average direct UEPR * (1 - expense ratio) - average premiums receivable
- Reserves relative to premiums = PLR * Loss reserves / Loss incurred
- Add (1) and (2), multiply by after tax portfolio yield
- Traditional UW profit provision - (3) = final UW profit provision
Robbin PV offset method
Applies offset based on difference between PV of losses for short tail reference line and line under review
Options to discount losses, Robbin PV offset method
Portfolio yield from recent year
Estimated portfolio yield for effective year
New money yield (more suited, prospective)
Advantages to PV offset method
Accounts for II in simple manner
Not distorted by rapid growth/decline
No need to select target return or allocate surplus
PV cash flow return model
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)
PV cash flow return model, procedure
Cash flow = UW Cash flow + investment income - tax
UW Cash flow = premium - loss - expense
PV cash flow return model, discounts
Discount equity at target ROR
Discount cash flows at investment ROR
Risk adjusted discounted cash flow model
Discount losses using CAPM:
ir = if + ß(im - if)
Discount all others at risk free rate
Assumes income is earned at the end of the year
Advantages of risk adjusted discounted cash flow model
Great intuitive appeal
Grounded in modern financial theory
Not necessary to determine target ROR
Disadvantage of risk adjusted discounted cash flow model
Hard to determine beta
Model construction questions
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?
Parameter selection questions
What discount rate should be used?
What is the right target ROR?
Premium, Robbin
P = PVlosses + P*(FR + VR + U0) + L(1 - PVx0)
Two reasons to support discounting of policyholder supplied funds at risk free rate
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
Two reasons to support the exclusion of investment income on surplus in ratemaking process
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
