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Flashcards in Robbin - UW Deck (50)
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1

Total profit (general form)

(Robbin - UW)

total profit = UW gains + investment gains - income taxes

2

Sources of funding that generates investment income (2)

(Robbin - UW)

1. PH supplied funds
2. stockholder supplied funds

3

Types of investment income (4)

(Robbin - UW)

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

4

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

5

Types of UW profit (5)

(Robbin - UW)

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

6

Approaches for regulating insurance profit loads (2)

(Robbin - UW)

1. rate of return regulation
2. constrained free market theory

7

Rate of return regulation

(Robbin - UW)

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

8

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

9

Premium (general formula)

(Robbin - UW)

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

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

10

Combined ratio (general formula)

(Robbin - UW)

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

where c = expenses proportional to loss

11

Relationship between UW profit provision and the CR

(Robbin - UW)

U = 1 - CR

where U = UW profit provision

12

Methods to determine the UW profit provision (4)

(Robbin - UW)

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

13

CY investment income offset procedure (description)

(Robbin - UW)

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

14

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

15

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

(Robbin - UW)

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

16

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

17

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

18

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

(Robbin - UW)

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

19

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

20

Sensitivity of PHSF funds associated with loss reserves (3)

(Robbin - UW)

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

21

Advantages of the CY investment income offset method (2)

(Robbin - UW)

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

22

Disadvantages of the CY investment income offset method (2)

(Robbin - UW)

1. lacks underlying economic theory
2. subject to distortion from: rapid growth and changes in loss volume or reserve adequacy

23

Present value offset method (description)

(Robbin - UW)

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

UW profit provision using the PV offset method

(Robbin - UW)

U = U(0) - DELPVLR

where U(0) = traditional UW profit provision

25

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

26

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

27

Critical assumption for the PV offset method

(Robbin - UW)

interest rate used

28

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

29

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

30

Accounting for taxes in the PV offset method

(Robbin - UW)

use an after-tax interest rate for discounting

31

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

32

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

33

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)

34

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

35

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)

36

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)

37

Advantage of the PV CF return model

(Robbin - UW)

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

38

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)

39

Risk-adjusted discounted CF model (description)

(Robbin - UW)

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

40

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

41

Investment income assumption for the risk-adjusted discounted CF model

(Robbin - UW)

assume investment income is earned quarterly

42

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

43

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

44

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

45

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

46

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

47

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

48

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

(Robbin - UW)

only recognizes systematic risk

49

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

50

Investment income for the risk-adjusted discounted CF method

(Robbin - UW)

investment income = surplus * risk-free rate