Robbin: IRR, ROE, and PVI/PVE Flashcards
Growth model calendar year ROE
ROE earned by business if growing at constant rate
Robbin’s goals for prices
Should be consistent and sensitive to risk
Should reflect management’s risk return preferences (based on theoretical surplus as opposed to actual)
Equation for underwriting income during jth accounting period
Uj = EPj - ILj - IXj
Deriving GAAP equity from required surplus
Q0 = S0 + DAC
Qj = Sj for j > 1
Equation for Assets
Aj = UEPRj + XRSVj + LRSVj + Sj
XRSV = Stat Expense Reserve
Equation for invested assets
Invested assets = SAP reserves + Surplus - receivables
Should be INITIAL amounts
PVI/PVE
Advantage of PVI/PVE over IRR approach
Market based rate is used as the reinvestment rate
IRR on equity flows procedure
Equation for GBBOPk and GBEOPk
Formula for end of period income, GIEOPk
Equilibrium growth phase
Where income statement and balance sheet accounts will be increasing at the growth rate
ROE would equal growth rate
Self-sustaining: no more capital required once this growth rate is reached
ROE based on discounted reserves
Higher during the initial years, but over time converges with undiscounted
While insurer is still growing
Growth reduces ROE; can be countered by discounting reserves
Indicated premium sensitivity to changes in surplus
Higher surplus loading factors produce higher required profit provisions
Indicated premium sensitivity to changes in interest rates
Raising interest rates reduces required profit provision (higher II would mean less UW income required to hit target)
Indicated premium sensitivity to changes in loss payout pattern
Increasing duration reduces required profit provision
Comparing RA DCF
Not based on particular accounting structure – no way to reflect treatment of expenses in SAP accounting, nor reserve discounting
Surplus does not have a large impact on premium
Robbin setup
- UW Income
- Investable assets
- Investment income
- Total income
- Equity flows
Objective of PVI/PVE method
Determine UW profit provision such that PVI/PVE = target ROR