Robbin - IRR Flashcards
Measures of return (3)
Robbin - IRR
- IRR on equity flows
- Growth ROE model
- PVI/PVE
Indicated premium
Robbin - IRR
premium where expected return = target return
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
UW income
Robbin - IRR
UW income(j) = EP(j) - incurred loss(j) - GAAP incurred expense(j)
incurred expense includes fixed & variable expenses
Difference in GAAP equity and statutory (SAP) equity at time 0
(Robbin - IRR)
deferred acquisition costs (DAC)
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
Deferred acquisition costs (DAC)
Robbin - IRR
DAC = statutory incurred expenses(0) - GAAP incurred expenses(0)
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
Total assets
Robbin - IRR
assets(j) = UEPR(j) + loss reserve(j) + statutory expense reserve(j) + statutory equity(j)
Unearned premium reserve (UEPR)
Robbin - IRR
UEPR = premium - EP to date
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
Statutory expense reserve (XRSV)
Robbin - IRR
statutory expense reserve = statutory incurred expenses to date - paid expenses to date
Invested assets (IA)
Robbin - IRR
invested assets(j) = assets(j) - amounts receivable(j)
Amounts receivable (RECV)
Robbin - IRR
amounts receivable = premium - premium paid to date
Investment income (II)
Robbin - IRR
investment income(j) = investment rate * invested assets(j - 1)
Pre-tax income (INCPTX)
Robbin - IRR
pre-tax income(j) = UW income(j) + investment income(j)
Tax amount (TAX)
Robbin - IRR
tax(j) = UW tax rate * UW income + II tax rate * investment income
After-tax income (I)
Robbin - IRR
after-tax income(j) = pre-tax income(j) - tax(j)
More realistic tax assumptions (3)
Robbin - IRR
- utilize carry-forwards & carry-backs
- apply reserve discounting & unearned premium disallowance
- deferred tax balance to reflect differences b/w tax basis & accounting basis income
Equity flows (definition) & signage
Robbin - IRR
flows of money b/w equity investor and company
negative CF = investor > company
positive CF = company > investor
Sources of equity flows (3)
Robbin - IRR
- purchase of stock
- payment of dividends
- repurchase of stock
Equity flow formula
Robbin - IRR
equity flow = income - change in GAAP equity
initial equity flow = - initial equity (b/c initial income = 0)
Reasons that the initial equity flow is always negative (2)
Robbin - IRR
- initial commitment of equity is needed to fund initial surplus
- commitment of equity associated with DAC
IRR on equity flows
Robbin - IRR
rate (IRR or y) that makes the PV(equity flows) = 0
Assumption of the IRR on equity flow method
Robbin - IRR
assumes any capital shortfall will be corrected by equity capital
Objections to IRR analyses (2)
Robbin - IRR
- may be multiple solutions to the IRR equation
2. implicit assumption that proceeds can be reinvested at the IRR (which may not be true)
Situations when there will be multiple solutions to the IRR on equity flows (2)
(Robbin - IRR)
multiple equity flow sign changes, such as with:
- earning of investment income
- release of surplus
PVI / PVE measure of return
Robbin - IRR
measure of single policy ROE
Present value of income (PVI)
Robbin - IRR
PVI = (1 + income interest rate) * PV(income discounted at income interest rate)
**discounted to time 1
Present value of equity (PVE)
Robbin - IRR
PV(GAAP equity discounted at the equity discount rate)
** discounted to time 0
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
Condition when PVI / PVE = IRR on equity flows return measure
(Robbin - IRR)
when the discount rate used = IRR
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)
Growth ROE/book of business growth model
Robbin - IRR
models a book of single policy business where:
- new policy is written at the start of each accounting period
- each subsequent policy = scaled version of the prior policy (scaling = growth rate)
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
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
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
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
Relationship between discounted reserves & ROEs
Robbin - IRR
lower reserves increase income, which increases ROE
Relationship between growth rates and ROEs
Robbin - IRR
high growth rates lead to decreased ROE
Methods to account for quarterly equity flows in the PVI / PVE method (2)
(Robbin - IRR)
- calculate PVI / PVE at a quarterly level (quarterly effective returns)
- annualize return by dividing equity by 4
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
Sensitivity of profit provision to surplus
Robbin - IRR
higher surplus loading factors lead to higher profit provisions
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)
Sensitivity of profit provision to loss payment patterns/duration
(Robbin - IRR)
higher duration loss payment patterns lead to lower profit provisions
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)
- RA DCF finds fair premium directly rather than requiring target return on surplus
- RA DCF has no underlying corporate or accounting structure
- surplus does not play a major role in RA DCF
- different reflection of risk
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
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
