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CAS Exam 9 > Robbin - UW > Flashcards

Robbin - UW Flashcards

1
Q

Total profit (general form)

Robbin - UW

A

total profit = UW gains + investment gains - income taxes

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2
Q

Sources of funding that generates investment income (2)

Robbin - UW

A
  1. PH supplied funds

2. stockholder supplied funds

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3
Q

Types of investment income (4)

Robbin - UW

A
  1. interest
  2. dividends
  3. real estate income
  4. realized capital gains
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4
Q

Problem with total return approach to developing an UW profit provision

(Robbin - UW)

A

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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5
Q

Types of UW profit (5)

Robbin - UW

A
  1. UW profit provisions included in manual rates
  2. corporate target UW profit provisions (target returns)
  3. breakeven US profit provisions that generate expected returns = risk-free return
  4. charged UW profit provisions (after experience/schedule modifications)
  5. actual UW profits
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6
Q

Approaches for regulating insurance profit loads (2)

Robbin - UW

A
  1. rate of return regulation

2. constrained free market theory

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7
Q

Rate of return regulation

Robbin - UW

A

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

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8
Q

Constrained free market theory regulation

Robbin - UW

A

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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9
Q

Premium (general formula)

Robbin - UW

A

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

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

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10
Q

Combined ratio (general formula)

Robbin - UW

A

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

where c = expenses proportional to loss

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11
Q

Relationship between UW profit provision and the CR

Robbin - UW

A

U = 1 - CR

where U = UW profit provision

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12
Q

Methods to determine the UW profit provision (4)

Robbin - UW

A
  1. CY investment income offset
  2. PV offset
  3. PV CF return model
  4. risk-adjusted discounted CF model
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13
Q

CY investment income offset procedure (description)

Robbin - UW

A

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

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14
Q

UW profit provision using the CY investment income offset method

(Robbin - UW)

A

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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15
Q

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

(Robbin - UW)

A
  1. exclude all capital gains
  2. include only realized capital gains
  3. include realized & unrealized capital gains
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16
Q

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

(Robbin - UW)

A

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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17
Q

PHSF % for the CY investment income offset method

Robbin - UW

A

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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18
Q

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

(Robbin - UW)

A

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

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19
Q

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)

A

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

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20
Q

Sensitivity of PHSF funds associated with loss reserves (3)

Robbin - UW

A

can be distorted by:

  1. rapid growth
  2. change in loss volume
  3. changes in reserve adequacy

best to use a multi-yr average ratio for stability

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21
Q

Advantages of the CY investment income offset method (2)

Robbin - UW

A
  1. calculations are easily obtained & verified (b/c CY data is used)
  2. CY investment portfolio yields tend to be stable
22
Q

Disadvantages of the CY investment income offset method (2)

Robbin - UW

A
  1. lacks underlying economic theory

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

23
Q

Present value offset method (description)

Robbin - UW

A

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

24
Q

UW profit provision using the PV offset method

Robbin - UW

A

U = U(0) - DELPVLR

where U(0) = traditional UW profit provision

25
Q

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

(Robbin - UW)

A

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

PLR = permissible loss ratio

26
Q

Premium formula for the PV offset method

Robbin - UW

A

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

27
Q

Critical assumption for the PV offset method

Robbin - UW

A

interest rate used

28
Q

Choices of interest rate for the PV offset method (3)

Robbin - UW

A
  1. portfolio yield from a recent yr or an estimate for prospective period
  2. current embedded portfolio yield
  3. new money yield
29
Q

Portfolio yields vs. new money rates for the PV offset method

(Robbin - UW)

A

portfolio yields - more stable & easily verifiable

new money rates - consistent with ratemaking’s prospective view

30
Q

Accounting for taxes in the PV offset method

Robbin - UW

A

use an after-tax interest rate for discounting

31
Q

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

(Robbin - UW)

A
  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
32
Q

Advantages of the PV offset method (2)

Robbin - UW

A
  1. not distorted by rapid growth or changes in loss volume or reserve adequacy
  2. does not require a target ROR or required surplus
33
Q

Present value CF return model (description)

Robbin - UW

A

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)

34
Q

Iteration for the CY investment income offset method

Robbin - UW

A

iterate until PLR and offset are consistent

use PLR(new) = PLR(old) - change in U 
repeat until change in U = 0
35
Q

After-tax Total CF formula for the PV CF return model

Robbin - UW

A

total CF(t) = (prem(t) - loss(t) - expense(t) + invest. income(t)) * (1 - tax %)

(based on general form of profit formula)

36
Q

Rates of return used in the PV CF return model

Robbin - UW

A

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

37
Q

Advantage of the PV CF return model

Robbin - UW

A

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

38
Q

Disadvantage of the PV CF return model

Robbin - UW

A

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

39
Q

Risk-adjusted discounted CF model (description)

Robbin - UW

A

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

40
Q

Fair premium in the risk-adjusted discounted CF model

Robbin - UW

A

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

41
Q

Investment income assumption for the risk-adjusted discounted CF model

(Robbin - UW)

A

assume investment income is earned quarterly

42
Q

Beta used for the risk-adjusted discount rate for the risk-adjusted discounted CF model

(Robbin - UW)

A

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

** liability beta can be negative

43
Q

Method to estimate a liability beta for the risk-adjusted discounted CF model

(Robbin - UW)

A

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

44
Q

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

Robbin - UW

A
  1. intuitive appeal
  2. based on modern financial theory (CAPM)
  3. does not require a target ROR
  4. does not rely on CY data
45
Q

Disadvantage of the risk-adjusted discounted CF model

Robbin - UW

A

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

46
Q

Comparison of reflection of risk b/w UW profit provision methods

(Robbin - UW)

A

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

47
Q

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

Robbin - UW

A
  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
48
Q

Criticism of using CAPM to determine the risk-adjusted discount rate

(Robbin - UW)

A

only recognizes systematic risk

49
Q

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

(Robbin - UW)

A

PV(income tax) = PV(CFs) * tax %

where CF = premium - loss - expense + investment income & PV is discounted at the appropriate rates for each item

50
Q

Investment income for the risk-adjusted discounted CF method

Robbin - UW

A

investment income = surplus * risk-free rate

CAS Exam 9 (26 decks)

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