Study Notes and Published Refences - Note TSA XXXIX - PRICING IN A RETURN-ON-EQUITY ENVIRONMENT

Overview

ROE = GAAP Income / Prior YE GAAP equity
- corp profitability measure common in ins industry
relationship between pricing objective ROI and corp profit measure ROE
examing relationship between ROE and after-tax ROE
StatSurplus(t) = StatSurlus(t-1) + StatIncome(t) - Dividend(t)
GAAPEquity(t) = GAAPEquity(t-1) + GAAPIncome - Dividend(t)
StatIncome(t) = BookProfit(t) + i*(StatSurplus(t-1))
DAC(t) = DAC(t-1) - (DAC(0)*g*v^(w-t+1))/(1-v^w)
- v = 1/(1+g) where g = i from DAC amort sched and w is amort period
GAAPIncome(t) = StatIncome(t) - DAC(t-1) + DAC(t)
ROE = GAAP Income / GAAP Equity
example shows what happens if DAC < ROI adn i < ROI
since i < ROI, stat income invested @ lower rate, brings down ROE below ROI
DAC amortizes more at lower rate than ROI rate which brings down ROE in early years
- trend reverses in later years
can fix i < ROI problem by releasing Stat Income via divs to other LOB or to stockholders
ignoring taxes, 2 main reasons why ROI = ROE objective is prevented
- stat surplus not used to acq NB will hurt performance if surplus not earning an annual return equal to RO objective
- GAAP requires degree of conservatism.
  - Eliminates use of annual ROI pricing objective as inv earnings rate in development of DAC amort sched and benefit reserve
    - therefore earnings deferred to later years and result is non-leve (incr) emergence of ROE

Effect of FIT

ROI is minimally affected by FIT
intro of FIT dramatically changes relationship of ROI to ROE
1st yr ROE reduced by factor of (1-T) - since initial equity not affected by after-tax ROE
for ROE=ROI, GAAPEquity(t) = (1-T)DAC(t) w/ DAC amortized @ ROI
- and stat surplus = 0 or reinvested @ ROI/(1-t)
a company holding surplus, invested at rate < ROI/(1-T), en excess of that necessary to producce new business &/or producing new business cannot produce a compnay-wide after-tax ROE = ROI pricing objective
- unless it owns a block w/ an after-tax ROE > company-wide after-tax ROE objective
- This could occur
  - past business priced to produce ROI > current objective and pricng assumptions met
  - experience emerged more favorably than was anticipated in pricing
  - past accts practices were conservative and deferred earnings
Potential soln - price new products using ROI objective > corp after-tax ROE objective
- advantages
  - if corp after-tax ROE < ROI, will meet ROE goal quicker
  - in later years, renewal business ROE would = ROI which is > corp ROE goal which will offset negative effect that production of NB has on corp ROE
- if goal was to meet ROE goal in 1st year, ROI pricing objective = ROE/(1-T)
  - and renew ROE > corp ROE (approaches ROI) if suplus dividended out
  - GAAP won't allow ROI as amort schedule rate
- marketplace may not allow success of ins product w/ ROI that high
non-ins industries produce returns by leveraging equity w/ debt
stat acctg principle eliminate this option for LIC
- equity (not just current assets) needed to acq new life ins business
need to leverage new business w/ old
growth in ne production dictated by
- past and current acct practices
- reinvestment adn stockholder div practices
- age of existing blocks
- relative size of existing blocks vs NB
reinvestment and stock div practices must consider degree of risk assoc w/ existing block
stat surplus in excess of what is needed to produce NB must be maintained and amt ret depends on risk elements assoc w/ block
- therefore, get effect on after-tax ROE of maintainnig this surplus must be considered when detererming how much NB can be writeene w/in ROE constraints
Soln: calc ROI on new products on basis of stat "reserve" = reserve + add'l amt needed as risk surplus to ensure solvency of LOB (benchmark surplus)
ROE = ROI shoudl emerge even though sufficient assets avail to ensure solvency

Generalized Case

conclusions drawn from examples not dependent upon specific emergence of SAP profits assumed
- by def, Sum(PVProfit_SAP) = 0 @ ROI rate
- therefore sum(PVProfit_GAAP) = 0 @ ROI rate
if inv earning rate for GAAP = ROI and all other assumptions = pricing
- GAAP book profit each year (leveled as % prem) must = 0
ROE = ROI regardless of emergence of SAP profits if SAP-GAAP adjustments assume inv earning rate = ROI

Special Considerations

DEFRA mess w/ GAAP income and ROE b/c of "fresh start"
- need to be taken into consideration during corp planning process

Conclusions

Relationship between ROI and ROE dependent on # items
- past and current Acctg practices
- past and future reinsvestment and stockholder div practices
- risk assoc w/ existing block and stat suplus req'd to insure co's future solvency
- age of existing block of business
- relative size of existing block when compared to NB to be produced.

Copyright © 2004 Steve Welander.
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