Term
| CY investment offset description |
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Definition
| Adjust traditional UW profit by investment income |
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Term
Method #1 Calendar Year Investment offset Procedure
Formula |
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Definition
U = U0 - iafit * PHSF
U0 traditional UW provision
PHSF = Policy Holder Surplus Funds |
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Term
(3) Advantages of
Calendar Year Approaches |
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Definition
1) Data is easily obtained and verified from Annual Statement
2) Filed Figures more likely to be accurate (no pessimistic estimates
3) Calendar Year investment Portfolio yield is relatively stable |
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Term
Disadvantage (1)
Calendar Year Approaches |
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Definition
| 1) Calendar Year results are retrospective may not be applicable to prospective ratemaking |
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Term
Policy Holder Surplus Funds
Equation
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Definition
PHSF=LR/INC *Permissible LR +
(UNPR *( 1-PPACQ) - PRECV)
Reserves/Premium + UNPR % |
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Term
| (2) Disadvantages of Calendar Year Investment Offset method |
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Definition
1) Lack of Economic Theory supporting
2) Results are distorted if change in reserve adequacy |
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Term
| (2) Advantages of Calendar Year Investment Offset method |
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Definition
1) Figures are easy to get from filed documents
2) Calculation is straightforward |
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Term
| Method #2: Present Value Offset Method |
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Definition
Adjusts the traditional UW provision for investment income by the
PV(losses) from reference line and
PV(losses) from actual line |
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Term
| (3) options of yield rates for PV Offset Method |
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Definition
1) New Money Yield
2) Portfolio yield from recent year
3) Estimated portfolio yield for when rates will be in effect |
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Term
| Formula for PV Offset Method |
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Definition
U =
U0 - PLR * (PV[Ref line] -
PV[New Line]) |
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Term
| (3) Advantages of PV Offset Method |
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Definition
1) Accounts for Investment Income in simple manner
2) Not distorted by rapid growth/decline
3) No need to select target return or allocate surplus |
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Term
| PV Offset Method Fundamental Formula |
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Definition
P = L * PV(X) + EXP + Uo*(P) +
L*[ 1- PV(Xo)] |
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Term
| Method #3: Calendar Year ROE |
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Definition
| This method selects an UW profit provision necessary to acheive the target ROE |
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Term
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Definition
ROE = [U*P + II - FIT ]/
GAAP EQ
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Term
| CY ROE detailed Formula for U |
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Definition
U = 1/(1-tu) * [r *QSR/PSR -
Iafit * ( PHSF + 1/PSR)]
- QSR = Equity Surplus Ratio
- PSR = Premium Surplus Ratio
- r = target return on equity
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Term
| (2) Advantages CY ROE Method |
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Definition
1) Figures are easy to verify
2) Produces an ROE similar to GAAP ROE |
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Term
| (3) Disadvantage of CY ROE Method |
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Definition
1) Since it is CY method, distorted by large growth or reserve changes
2) Need to select a Target Return
3) Need to select a Leverage Ratio |
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Term
| Method #4 PVI/PVE Method Description |
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Definition
| Selects a UW profit provision necessary to achieve a target present value return (income over equity) |
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Term
| Average Equity Balance EQBi |
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Definition
Σj=1(EQB)*vj-1/Σj=1vj-1
Use to turn quarterly balances into annual
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Term
| PVI/PVE method Discount rates |
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Definition
| Can use target rate of return or rf |
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Term
| PVI/PVE method Advantages (1) |
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Definition
| Measure is comparable to GAAP ROE |
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Term
| PVI/PVE Disadvantages (2) |
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Definition
- Need to Select a discount rate
- Need to Select a target rate of return
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Term
| Method 5: PV of Cashflow Return Model description |
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Definition
Select an UW profit provision necessary to produce a PV of total cash flow (discounted at Investment RoR) = PV of Changes in equity (discounted at target
RoR) |
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Term
| PV Cashflow Return Formula |
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Definition
| PV(Δ Equity;target {r}) = PV(total cashflow; investment {i}) |
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Term
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Definition
| Cashflow for a single policy: UW Income + Investment Income - Tax |
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Term
| PV Cashflow method Advantages (1) |
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Definition
| PV of underwriting cashflows are what most people think conceive as UW profit |
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Term
| PV Cashflow method Disadvantages (1) |
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Definition
| Unclear exactly what type of profit is being measured. Different timing than GAAP. |
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Term
| Method 6: Risk Adjusted Discounted Cash Flow Model |
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Definition
| This method calculates a fair premium, and derives the Profit Provision Fair premium = Risk adjusted present value of UW cash flows + PV(taxes) taxes. |
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Term
| Risk Adjusted Discount rate is calculated using |
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Definition
ß=cov(market return, return of the item being valued)
Ir = if + ß(im - if )
Difficult for liabilities
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Term
| Discount rates for Risk Adjusted |
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Definition
| Losses discount at Risk Adjusted rate, other CF as Rf Discount to time zero |
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Term
Risk Adjusted Discount Cashflow Model
Advantages (3) |
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Definition
- Great Intuitive appeal
- Grounded in modern financial theory
- Not Necessary to determine a target rate of return
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Term
Risk Adjusted Discount Cashflow Model
Advantages (1) |
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Definition
| Not easy to determine Beta |
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Term
| Risk Adjusted Discounting CF formula |
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Definition
PV(P;if)=PV(L:ir)+PV(FX;if)+PV(FIT;if)
PV(FIT) = PV(TUW) +PV(TII)
PV(TUW) = [(P-E)/(1+rf)-L/(1+ra)]*tu
PV(TII) = (P-E+S)*rf*ti /(1+rf) |
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Term
| Risk Adjusted Discount ALT Formula |
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Definition
PV(P;if)=PV(L;ir)+PV(FX;if)+
t * PV(II on Surplus)/(1-t) |
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Term
Beta in Risk Adjusted CF
ß |
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Definition
| Note the stock beta of invested asset portfolio must equal the weighted average of liability beta and firm's equity |
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Term
| Insurance premium discount factor |
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Definition
| Should be below the risk free rate, since risk is being passed off by policyholder, implying lower return |
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Term
| Method 7: Internal Rate of Return Model description |
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Definition
| select a premium that achieves a specified target return on equity flows between company and shareholders |
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Term
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Definition
Equity Flow = Income - Chg in Stat Surplus
use single policy |
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Term
| IRR method advantages (2) |
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Definition
1) Return to Stockholders is similar to rate on a loan
2) Reflects the accounting rules via CF impacts |
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Term
| IRR method disadvantages (2) |
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Definition
1) Necessary to select a target return
2) Necessary to select a surplus requirement |
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Term
| Model Construction questions (5) |
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Definition
| 1) Should surplus be included in the model 2) How should surplus requirement be determined? 3) how should risk be included the model? 4) is it better to use cash flows or income flows? 5) how to reflect income taxes? |
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Term
| Parameter Selection questions (2) |
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Definition
| 1) what discount rate should be used? 2) What is the right target return? |
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Term
| (2) regulation approaches |
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Definition
1)Rate of return approach
2)Constrained market theory |
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Term
| PV Offset formula if UPP for reviewed line is known |
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Definition
P = (L + FX)/(1 - VX - U)
Note that losses are undiscounted! Discount is included in U. |
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Term
| CAPM method equity vs liability discounting equation |
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Definition
PV(LR)(rf -in) = equity(R - rf)
R = return on equity
PV(LR) = discounted loss reserves
in =discount on reserves
R = return on equity
in words, what ever points you lose on reserves, you make up for in equity |
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