Robbin: IRR, ROE, and PVI/PVE

Question 1

Growth model calendar year ROE

Answer 1

ROE earned by business if growing at constant rate

Question 2

Robbin’s goals for prices

Answer 2

Should be consistent and sensitive to risk

Should reflect management’s risk return preferences (based on theoretical surplus as opposed to actual)

Question 3

Equation for underwriting income during j^th accounting period

Answer 3

U_j = EP_j - IL_j - IX_j

Question 4

Deriving GAAP equity from required surplus

Answer 4

Q₀ = S₀ + DAC

Q_j = S_j for j > 1

Question 5

Equation for Assets

Answer 5

A_j = UEPR_j + XRSV_j + LRSV_j + S_j

XRSV = Stat Expense Reserve

Question 6

Equation for invested assets

Answer 6

Invested assets = SAP reserves + Surplus - receivables

Should be INITIAL amounts

Question 7

PVI/PVE

Answer 7

Question 8

Advantage of PVI/PVE over IRR approach

Answer 8

Market based rate is used as the reinvestment rate

Question 9

IRR on equity flows procedure

Answer 9

Question 10

Equation for GBBOP_k and GBEOP_k

Question 11

Formula for end of period income, GIEOP_k

Answer 11

Question 12

Equilibrium growth phase

Answer 12

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

Question 13

ROE based on discounted reserves

Answer 13

Higher during the initial years, but over time converges with undiscounted

Question 14

While insurer is still growing

Answer 14

Growth reduces ROE; can be countered by discounting reserves

Question 15

Indicated premium sensitivity to changes in surplus

Answer 15

Higher surplus loading factors produce higher required profit provisions

Question 16

Indicated premium sensitivity to changes in interest rates

Answer 16

Raising interest rates reduces required profit provision (higher II would mean less UW income required to hit target)

Question 17

Indicated premium sensitivity to changes in loss payout pattern

Answer 17

Increasing duration reduces required profit provision

Question 18

Comparing RA DCF

Answer 18

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

Question 19

Robbin setup

Answer 19

1. UW Income
2. Investable assets
3. Investment income
4. Total income
5. Equity flows

Question 21

Objective of PVI/PVE method

Answer 21

Determine UW profit provision such that PVI/PVE = target ROR