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
