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1

Measures of return (3)

(Robbin - IRR)

1. IRR on equity flows
2. Growth ROE model
3. PVI/PVE

2

Indicated premium

(Robbin - IRR)

premium where expected return = target return

3

Appropriateness of fixed vs. variable premium-to-surplus (P/S) ratio

(Robbin - IRR)

required surplus should vary with unpaid loss estimates

>> fixed P/S ratio is not appropriate, but used for simplicity

4

UW income

(Robbin - IRR)

UW income(j) = EP(j) - incurred loss(j) - GAAP incurred expense(j)

incurred expense includes fixed & variable expenses

5

Difference in GAAP equity and statutory (SAP) equity at time 0

(Robbin - IRR)

deferred acquisition costs (DAC)

6

Expenses in GAAP vs. statutory (SAP) accounting

(Robbin - IRR)

GAAP - expenses are incurred as premium is earned

SAP - expenses are incurred according to a fixed pattern

7

Deferred acquisition costs (DAC)

(Robbin - IRR)

DAC = statutory incurred expenses(0) - GAAP incurred expenses(0)

8

Relationship between GAAP equity and statutory (SAP) equity at each point in time

(Robbin - IRR)

time 0: GAAP equity = statutory equity + DAC

all other times: GAAP equity = statutory equity

time n: GAAP equity = statutory equity = 0

9

Total assets

(Robbin - IRR)

assets(j) = UEPR(j) + loss reserve(j) + statutory expense reserve(j) + statutory equity(j)

10

Unearned premium reserve (UEPR)

(Robbin - IRR)

UEPR = premium - EP to date

11

Loss reserve (LRSV)

(Robbin - IRR)

loss reserve = incurred losses to date - paid losses to date

initial loss reserve = 0

loss reserve may need to be discounted

12

Statutory expense reserve (XRSV)

(Robbin - IRR)

statutory expense reserve = statutory incurred expenses to date - paid expenses to date

13

Invested assets (IA)

(Robbin - IRR)

invested assets(j) = assets(j) - amounts receivable(j)

14

Amounts receivable (RECV)

(Robbin - IRR)

amounts receivable = premium - premium paid to date

15

Investment income (II)

(Robbin - IRR)

investment income(j) = investment rate * invested assets(j - 1)

16

Pre-tax income (INCPTX)

(Robbin - IRR)

pre-tax income(j) = UW income(j) + investment income(j)

17

Tax amount (TAX)

(Robbin - IRR)

tax(j) = UW tax rate * UW income + II tax rate * investment income

18

After-tax income (I)

(Robbin - IRR)

after-tax income(j) = pre-tax income(j) - tax(j)

19

More realistic tax assumptions (3)

(Robbin - IRR)

1. utilize carry-forwards & carry-backs
2. apply reserve discounting & unearned premium disallowance
3. deferred tax balance to reflect differences b/w tax basis & accounting basis income

20

Equity flows (definition) & signage

(Robbin - IRR)

flows of money b/w equity investor and company

negative CF = investor > company
positive CF = company > investor

21

Sources of equity flows (3)

(Robbin - IRR)

1. purchase of stock
2. payment of dividends
3. repurchase of stock

22

Equity flow formula

(Robbin - IRR)

equity flow = income - change in GAAP equity

initial equity flow = - initial equity (b/c initial income = 0)

23

Reasons that the initial equity flow is always negative (2)

(Robbin - IRR)

1. initial commitment of equity is needed to fund initial surplus
2. commitment of equity associated with DAC

24

IRR on equity flows

(Robbin - IRR)

rate (IRR or y) that makes the PV(equity flows) = 0

25

Assumption of the IRR on equity flow method

(Robbin - IRR)

assumes any capital shortfall will be corrected by equity capital

26

Objections to IRR analyses (2)

(Robbin - IRR)

1. may be multiple solutions to the IRR equation
2. implicit assumption that proceeds can be reinvested at the IRR (which may not be true)

27

Situations when there will be multiple solutions to the IRR on equity flows (2)

(Robbin - IRR)

multiple equity flow sign changes, such as with:
1. earning of investment income
2. release of surplus

28

PVI / PVE measure of return

(Robbin - IRR)

measure of single policy ROE

29

Present value of income (PVI)

(Robbin - IRR)

PVI = (1 + income interest rate) * PV(income discounted at income interest rate)

**discounted to time 1

30

Present value of equity (PVE)

(Robbin - IRR)

PV(GAAP equity discounted at the equity discount rate)

** discounted to time 0

31

Appropriate interest rate for discounting income & equity in the PVI / PVE measure of return & justification

(Robbin - IRR)

cost of capital

justification: rate the company is able to borrow at

32

Condition when PVI / PVE = IRR on equity flows return measure

(Robbin - IRR)

when the discount rate used = IRR

33

Interpretation of IRR when PVI / PVE = IRR

(Robbin - IRR)

IRR is a PVI / PVE measure where the discount rate changes with profitability

(inconsistent with PVI / PVE method, which assumes a fixed discount rate)

34

Growth ROE/book of business growth model

(Robbin - IRR)

models a book of single policy business where:
1. new policy is written at the start of each accounting period
2. each subsequent policy = scaled version of the prior policy (scaling = growth rate)

35

ROE for the growth ROE/book of business growth model and trend over time

(Robbin - IRR)

ROE = EOY income / BOY GAAP equity

eventually stabilize at the equilibrium growth ROE

36

Point in time when ROEs stabilize for the growth ROE/book of business growth model

(Robbin - IRR)

reached after all losses are paid for the single policy

37

Condition when growth ROE = IRR on equity flows return measure & IRR interpretation

(Robbin - IRR)

g = IRR on equity flows

IRR interpretation: maximum self-sustaining growth rate

38

Premium-to-surplus (P / S) ratios for the growth ROE/book of business growth model

(Robbin - IRR)

eventually stabilize when final single policy loss is paid

39

Relationship between discounted reserves & ROEs

(Robbin - IRR)

lower reserves increase income, which increases ROE

40

Relationship between growth rates and ROEs

(Robbin - IRR)

high growth rates lead to decreased ROE

41

Methods to account for quarterly equity flows in the PVI / PVE method (2)

(Robbin - IRR)

1. calculate PVI / PVE at a quarterly level (quarterly effective returns)
2. annualize return by dividing equity by 4

42

Indicated premium and profit provision

(Robbin - IRR)

solve for the indicated premium that yields selected return, then solve for the indicated profit provision using indicated premium

43

Sensitivity of profit provision to surplus

(Robbin - IRR)

higher surplus loading factors lead to higher profit provisions

44

Sensitivity of profit provision to interest rates

(Robbin - IRR)

higher interest rates/investment yields lead to lower profit provisions (b/c less UW income is needed)

45

Sensitivity of profit provision to loss payment patterns/duration

(Robbin - IRR)

higher duration loss payment patterns lead to lower profit provisions

46

Differences between the risk-adjusted discounted CF method (RA DCF) for determining the UW profit provision and the return measures in the IRR paper (4)

(Robbin - IRR)

1. RA DCF finds fair premium directly rather than requiring target return on surplus
2. RA DCF has no underlying corporate or accounting structure
3. surplus does not play a major role in RA DCF
4. different reflection of risk

47

Differences in reflection of risk in the risk-adjusted discounted CF method (RA DCF) for determining the UW profit provision and the return measures in the IRR paper

(Robbin - IRR)

RA DCF reflects risk through beta in the risk-adjusted rate (systematic risk only)

return measure methods reflect risk through required surplus and spread b/w target return & after-tax investment yields

48

Pricing perspectives of the risk-adjusted discounted CF method (RA DCF) vs. return measures in the IRR paper

(Robbin - IRR)

management & equity investors are more interested in determining indicated premium than fair premium

PH & regulators are more interested in determining fair premium than indicated premium