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3 categories of methods for determining UW PM
- Investment Income offset: start w/ U0, adjust to account for investment income
- Target Total return income: seek to ensure that the pricing will lead to a target expected total SH return
- Cash Flow methods: relies on actual premium, losses, expenses, and tax cash flows
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7 methods for determining UW PM
- Calendar Year Investment offset
- Present Value offset
- Calendar year ROE
- IRR on equity flow
- PVI / PVE
- PV Cash flow return
- Risk-adjusted discounted cash flow
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UW PM: Calendar Year investment income offset
- U = U0 - iAT(PHSF)
- PHSF = UEPR + L&LAE reserves
- UEPR = UEPR net of prepaid exp - P receivables
- L&LAE reserves = LR * (Loss reserves/Inc loss)
- + simple to implement using readily available data; results are relatively stable
- - stability issue when rapid growth or decline in vol
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UW PM: Present Value offset
- P = [L + EXP - L{PV(X0) - PV(X)}] / (1 - U0)
- U = U0 - PLR[PV(X0) - PV(X)]
- + simple, does not rely on historical ratio, avoids having to select a target return
- - stability issue when rapid growth or decline in vol
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UW PM: Calendar Year ROE
- ROE = (U - P + II - FIT) / EQ
- Set target and solve for U
- + most of the input is readily obtained from rptd financial statments
- - subject to distortion during periods of growth; requires a target ROE and a P/S ratio
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UW PM: IRR on Equity Flow
- Track the equity flow that would occur had we set up a company to write a single policy, and set it equal to initial investment
- 0 = ∑ [INCj + SCHNGj] / (1 + IRR)j
- + simple to interpret; captures impact of accounting rules on SH
- - need assumption about surplus; target IRR required
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UW PM: PVI / PVE
- Ratio is interpreted as rate of return and used to compare against target
- PVI = (1 + i)∑j=0 (INCj)vj
- PVE = ∑j-1 (EQBj)vj-1 / ∑j=1 vj-1
- + not distorted by historical; balance sheet growth rates; somewhat comparable to GAAP ROE
- - requires a selection of discount rates
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UW PM: PV Cash Flow return
- PV(∆EQ; r) = PV(TCF; i)
- + appealing focus on PV(UW CF)
- - no easy way to reconcile to a GAAP ROE measure
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UW PM: Risk-adjusted discounted CF Method
- PV(P; if) = PV(L; ir) + PV(FX; if) + t * PV(Inv Inc on surplus) * (1 - t)-1
- ir = if + β(im - if)
- + somewhat solid theoretical foundation; don't need target return
- - uncertainty in estimating liability β
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