Robbin - UW Flashcards by Kate Vista

Total profit (general form)

Robbin - UW

total profit = UW gains + investment gains - income taxes

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Sources of funding that generates investment income (2)

Robbin - UW

PH supplied funds

2. stockholder supplied funds

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Types of investment income (4)

Robbin - UW

interest
dividends
real estate income
realized capital gains

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Problem with total return approach to developing an UW profit provision

(Robbin - UW)

total returns are measured on a CY basis, which includes impacts from prior year policy writings, vs. ratemaking which uses a prospective PY basis

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Types of UW profit (5)

Robbin - UW

UW profit provisions included in manual rates
corporate target UW profit provisions (target returns)
breakeven US profit provisions that generate expected returns = risk-free return
charged UW profit provisions (after experience/schedule modifications)
actual UW profits

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Approaches for regulating insurance profit loads (2)

Robbin - UW

rate of return regulation

2. constrained free market theory

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Rate of return regulation

Robbin - UW

regulates rates so that insurers receive adequate, but not excessive, total returns

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Constrained free market theory regulation

Robbin - UW

assuming the manual rate is adequate & there is flexibility to deviate from the manual rate, the competitive market should force insurance prices to an optimal level

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Premium (general formula)

Robbin - UW

P = [(1 + c) * L + FX] / [1 - VR - U]

where c = expenses proportional to loss
U = UW profit provision

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Combined ratio (general formula)

Robbin - UW

CR = VR + [(1 + c) * L + FX] / P

where c = expenses proportional to loss

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Relationship between UW profit provision and the CR

Robbin - UW

U = 1 - CR

where U = UW profit provision

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Methods to determine the UW profit provision (4)

Robbin - UW

CY investment income offset
PV offset
PV CF return model
risk-adjusted discounted CF model

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CY investment income offset procedure (description)

Robbin - UW

applies an offset to the traditional UW profit provision for investment income as a % of premium

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UW profit provision using the CY investment income offset method

(Robbin - UW)

U = U(0) - after-tax portfolio yield * PHSF %

where U(0) = traditional UW profit provision 
and PHSF % = PH supplied funds as a % of premium

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Choices for handling capital gains for the after-tax portfolio yield in the CY investment income offset method (3)

(Robbin - UW)

exclude all capital gains
include only realized capital gains
include realized & unrealized capital gains

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After-tax portfolio yield for the CY investment income offset method

(Robbin - UW)

start with ratio of pre-tax investment income / avg. invested assets & apply appropriate tax rates by investment class

select a multi-yr rolling average to increase stability

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PHSF % for the CY investment income offset method

Robbin - UW

PHSF % = PHSF % associated with UPR + PHSF % associated with loss reserves

PHSF % = [UPR * (1 - prepaid acq. %) - prem. reserve] / EP + [PLR * (CY loss reserve / CY incurred losses)]

where UPR = avg. direct UPR
prem reserve = avg. premium receivable
EP = direct EP

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Prepaid acquisition costs for the PHSF % for the CY investment income offset method

(Robbin - UW)

prepaid acquisition % = commission % + premium tax % + other acquisition % + overhead %

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Reason that the premium reserve & prepaid acquisition costs are removed from the PHSF associated with UPR for the CY investment income offset method

(Robbin - UW)

these represent funds paid up front/otherwise not available to be invested

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Sensitivity of PHSF funds associated with loss reserves (3)

Robbin - UW

can be distorted by:

rapid growth
change in loss volume
changes in reserve adequacy

best to use a multi-yr average ratio for stability

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Advantages of the CY investment income offset method (2)

Robbin - UW

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calculations are easily obtained & verified (b/c CY data is used)
CY investment portfolio yields tend to be stable

Disadvantages of the CY investment income offset method (2)

Robbin - UW

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lacks underlying economic theory

2. subject to distortion from: rapid growth and changes in loss volume or reserve adequacy

Present value offset method (description)

Robbin - UW

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applies an offset to the traditional UW profit provision for the difference b/w PV(loss payment pattern) for a short-tailed reference line & PV(loss payment pattern) for LOB under review

UW profit provision using the PV offset method

Robbin - UW

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U = U(0) - DELPVLR

where U(0) = traditional UW profit provision

Difference b/w PV(losses) for the reference line & line under review (DELPVLR) (Robbin - UW)

DELPVLR = PLR * (PV(loss payment pattern for reference line) - PV(loss payment pattern for LOB)) PLR = permissible loss ratio

Premium formula for the PV offset method | Robbin - UW

P = [L * PV(loss payment pattern for LOB) + FX + L * (1 - PV(loss payment pattern for reference line))] / (1 - VER - U(0)) ** uses traditional UW profit provision

Critical assumption for the PV offset method | Robbin - UW

interest rate used

Choices of interest rate for the PV offset method (3) | Robbin - UW

1. portfolio yield from a recent yr or an estimate for prospective period 2. current embedded portfolio yield 3. new money yield

Portfolio yields vs. new money rates for the PV offset method (Robbin - UW)

portfolio yields - more stable & easily verifiable | new money rates - consistent with ratemaking's prospective view

Accounting for taxes in the PV offset method | Robbin - UW

use an after-tax interest rate for discounting

Approaches for determining the after-tax interest rate for discounting (2) (Robbin - UW)

1. prospective approach - use assumed asset mix to weight appropriate prospective tax rates applied to pre-tax yields by investment type 2. retrospective approach - use actual prior yr income tax rate

Advantages of the PV offset method (2) | Robbin - UW

1. not distorted by rapid growth or changes in loss volume or reserve adequacy 2. does not require a target ROR or required surplus

Present value CF return model (description) | Robbin - UW

UW profit provision is set so that the PV(total CF discounted using investment rate of return) = PV(changes in equity discounted using target rate of return)

Iteration for the CY investment income offset method | Robbin - UW

iterate until PLR and offset are consistent ``` use PLR(new) = PLR(old) - change in U repeat until change in U = 0 ```

After-tax Total CF formula for the PV CF return model | Robbin - UW

total CF(t) = (prem(t) - loss(t) - expense(t) + invest. income(t)) * (1 - tax %) (based on general form of profit formula)

Rates of return used in the PV CF return model | Robbin - UW

use investment rate of return to calculate PV(total CF) and target rate of return to calculate PV(changes in equity)

Advantage of the PV CF return model | Robbin - UW

PV(UW CFs) is what people think of when measuring UW profit

Disadvantage of the PV CF return model | Robbin - UW

unclear what sort of profit is being measured (b/c the timing of UW CFs <> timing of GAAP UW income)

Risk-adjusted discounted CF model (description) | Robbin - UW

calculates a "fair premium" and then backs into an UW profit provision

Fair premium in the risk-adjusted discounted CF model | Robbin - UW

fair premium = risk-adjusted PV(UW CFs) + PV(income taxes) PV(premium) = PV(loss) + PV(expense) + PV(income tax) **all discounted to t=1 PV(loss) is discounted using a risk-adjusted discount rate and everything else is discounted using the risk-free rate

Investment income assumption for the risk-adjusted discounted CF model (Robbin - UW)

assume investment income is earned quarterly

Beta used for the risk-adjusted discount rate for the risk-adjusted discounted CF model (Robbin - UW)

liability beta (b/c the rate is being applied to loss liabilities) = covariance of insurance losses with market returns ** liability beta can be negative

Method to estimate a liability beta for the risk-adjusted discounted CF model (Robbin - UW)

calculate beta for a group of insurers calculate beta for the investment portfolios held by those insurers difference b/w market value of stocks & market value of investment portfolios = implicit market valuation of insurer liabilities, which informs the liability beta

Advantages of the risk-adjusted discounted CF model (4) | Robbin - UW

1. intuitive appeal 2. based on modern financial theory (CAPM) 3. does not require a target ROR 4. does not rely on CY data

Disadvantage of the risk-adjusted discounted CF model | Robbin - UW

difficult to estimate the liability beta since there is no open market for loss reserves

Comparison of reflection of risk b/w UW profit provision methods (Robbin - UW)

CY investment income offset and PV loss offset methods do not reflect risk PV CF return model reflects risk in selection of required surplus & target return risk-adjusted discounted CF model reflects risk using the risk-adjusted return to discount losses

Methods to determine the risk-adjusted discount rate (2) | Robbin - UW

1. view risk adjustment as a form of compensation to the insurer for placing its capital at risk in the insurance contract 2. derive risk-adjustment using CAPM

Criticism of using CAPM to determine the risk-adjusted discount rate (Robbin - UW)

only recognizes systematic risk

PV(income tax) calculation for the risk-adjusted discounted CF method (Robbin - UW)

PV(income tax) = PV(CFs) * tax % where CF = premium - loss - expense + investment income & PV is discounted at the appropriate rates for each item

Investment income for the risk-adjusted discounted CF method | Robbin - UW

investment income = surplus * risk-free rate

Robbin - UW Flashcards

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