Robbin - IRR

Question 1

Measures of return (3)

Robbin - IRR

Answer 1

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

Question 2

Indicated premium

Robbin - IRR

Answer 2

premium where expected return = target return

Question 3

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

(Robbin - IRR)

Answer 3

required surplus should vary with unpaid loss estimates

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

Question 4

UW income

Robbin - IRR

Answer 4

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

incurred expense includes fixed & variable expenses

Question 5

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

(Robbin - IRR)

Answer 5

deferred acquisition costs (DAC)

Question 6

Expenses in GAAP vs. statutory (SAP) accounting

Robbin - IRR

Answer 6

GAAP - expenses are incurred as premium is earned

SAP - expenses are incurred according to a fixed pattern

Question 7

Deferred acquisition costs (DAC)

Robbin - IRR

Answer 7

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

Question 8

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

(Robbin - IRR)

Answer 8

time 0: GAAP equity = statutory equity + DAC

all other times: GAAP equity = statutory equity

time n: GAAP equity = statutory equity = 0

Question 9

Total assets

Robbin - IRR

Answer 9

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

Question 10

Unearned premium reserve (UEPR)

Robbin - IRR

Answer 10

UEPR = premium - EP to date

Question 11

Loss reserve (LRSV)

Robbin - IRR

Answer 11

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

initial loss reserve = 0

loss reserve may need to be discounted

Question 12

Statutory expense reserve (XRSV)

Robbin - IRR

Answer 12

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

Question 13

Invested assets (IA)

Robbin - IRR

Answer 13

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

Question 14

Amounts receivable (RECV)

Robbin - IRR

Answer 14

amounts receivable = premium - premium paid to date

Question 15

Investment income (II)

Robbin - IRR

Answer 15

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

Question 16

Pre-tax income (INCPTX)

Robbin - IRR

Answer 16

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

Question 17

Tax amount (TAX)

Robbin - IRR

Answer 17

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

Question 18

After-tax income (I)

Robbin - IRR

Answer 18

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

Question 19

More realistic tax assumptions (3)

Robbin - IRR

Answer 19

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

Question 20

Equity flows (definition) & signage

Robbin - IRR

Answer 20

flows of money b/w equity investor and company

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

Question 21

Sources of equity flows (3)

Robbin - IRR

Answer 21

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

Question 22

Equity flow formula

Robbin - IRR

Answer 22

equity flow = income - change in GAAP equity

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

Question 23

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

Robbin - IRR

Answer 23

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

Question 24

IRR on equity flows

Robbin - IRR

Answer 24

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

Question 25

Assumption of the IRR on equity flow method | Robbin - IRR

Answer 25

assumes any capital shortfall will be corrected by equity capital

Question 26

Objections to IRR analyses (2) | Robbin - IRR

Answer 26

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)

Question 27

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

Answer 27

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

Question 28

PVI / PVE measure of return | Robbin - IRR

Answer 28

measure of single policy ROE

Question 29

Present value of income (PVI) | Robbin - IRR

Answer 29

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

Question 30

Present value of equity (PVE) | Robbin - IRR

Answer 30

PV(GAAP equity discounted at the equity discount rate) ** discounted to time 0

Question 31

Appropriate interest rate for discounting income & equity in the PVI / PVE measure of return & justification (Robbin - IRR)

Answer 31

cost of capital justification: rate the company is able to borrow at

Question 32

Condition when PVI / PVE = IRR on equity flows return measure (Robbin - IRR)

Answer 32

when the discount rate used = IRR

Question 33

Interpretation of IRR when PVI / PVE = IRR | Robbin - IRR

Answer 33

IRR is a PVI / PVE measure where the discount rate changes with profitability (inconsistent with PVI / PVE method, which assumes a fixed discount rate)

Question 34

Growth ROE/book of business growth model | Robbin - IRR

Answer 34

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)

Question 35

ROE for the growth ROE/book of business growth model and trend over time (Robbin - IRR)

Answer 35

ROE = EOY income / BOY GAAP equity eventually stabilize at the equilibrium growth ROE

Question 36

Point in time when ROEs stabilize for the growth ROE/book of business growth model (Robbin - IRR)

Answer 36

reached after all losses are paid for the single policy

Question 37

Condition when growth ROE = IRR on equity flows return measure & IRR interpretation (Robbin - IRR)

Answer 37

g = IRR on equity flows IRR interpretation: maximum self-sustaining growth rate

Question 38

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

Answer 38

eventually stabilize when final single policy loss is paid

Question 39

Relationship between discounted reserves & ROEs | Robbin - IRR

Answer 39

lower reserves increase income, which increases ROE

Question 40

Relationship between growth rates and ROEs | Robbin - IRR

Answer 40

high growth rates lead to decreased ROE

Question 41

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

Answer 41

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

Question 42

Indicated premium and profit provision | Robbin - IRR

Answer 42

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

Question 43

Sensitivity of profit provision to surplus | Robbin - IRR

Answer 43

higher surplus loading factors lead to higher profit provisions

Question 44

Sensitivity of profit provision to interest rates | Robbin - IRR

Answer 44

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

Question 45

Sensitivity of profit provision to loss payment patterns/duration (Robbin - IRR)

Answer 45

higher duration loss payment patterns lead to lower profit provisions

Question 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)

Answer 46

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

Question 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)

Answer 47

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

Question 48

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

Answer 48

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