Life Insurance Source of Earnings

1
Life Insurance Source of Earnings

• Participating policies (mutual companies)
• Universal life type policies (SFAS 97)
• Amortization of DPAC gross profits
• Mortality, persistency, interest, expenses

2
Post Mortem Analysis

• causes of superior / inferior performance

3
Estimation Error - Process Error

• Estimation error difference between forecast and
  true expected value
• Process error difference between true expected
  value and realization

4
Workers Compensation

• Static vs dynamic DPAC amortization
• Charged, expected, and actual results
• Solicitation costs on not-taken policies

5
Analysis Levels

• Individual factor
• Policy year
• Policy cohort

6
Contribution Principle

• Policyholder dividends contribution to profits
• Three factor models

7
Persistency

• Increased withdrawals ?
• Increased current earnings
• Lower future earnings

8
Loss Cost Trend

• Fast track data to countrywide trends
• Countrywide trends to state trends
• State trends to predict loss cost changes

9
Estimation Error and Process Error
Estimated Fast Track Actual Fast Track Loss Cost Change
Loss Severity 7 8 5
Loss Frequency 1 2 4
10
Loss Trend Analysis (2)
Projection Projection Estimation Estimation Process Process
Date Initial Projection Implicit Profit Revised Estimate Estimation Error Actual Change Process Error Total Variance
12/02 7 0 8 -250K 5 750K 500K
12/03 7 0 8 -250K 6 500K 250K
11
Loss Trend Analysis (1)
Projection Projection Estimation Estimation Process Process
Date Initial Projection Implicit Profit Revised Estimate Estimation Error Actual Change Process Error Total Variance
12/02 7 0 8 -250K 5 750K 500K
12
Credibility

• Estimating past experience
• Removing sampling error

13
Interest Spread
Year Invested Funds Investment Yields Credited Interest Interest Spread Interest Margin Capital Gain/Loss PV of Margin
0 2,500 9.5 7 2.5 62,500 -50,000 12,500.00
1 3,500 10 7 3.0 105,000 0 93,750.00
2 3,000 10 7 3.0 90,000 0 71,747.45
3 2,000 10 7 3.0 60,000 0 42,706.81
4 1,000 10 7 3.0 30,000 0 19,065.54
Total 239,769.81
14
Retention Rates

• Historical 90 retention
• New policy year 80 retention
• Acquisition costs 20 new 5 renewal
• ELR 80 new 70 renewal
• Total new-renewal spread 25

15
Solicitation Costs
Assumptions Assumptions
Initial Revised
A. Premium 100 million 100 million
B. Excess acquisition costs 20 million 20 million
C. Not taken rate 20 60
D. Not taken premium A ? C/(1-C) 25 million 150 million
E. Not taken acquisition costs ½ ? D ? 20 2.50 million 15 million
F. Total acquisition costs B E 22.5 million 35 million
G. Average policy lifetime 8 years 5 years
H. Annual amortization F / G 2.81 million 7.00 million
16
Retrospectively Rated Policies

• High non-ratable losses
• Low investment income
• Excessive expenses
• High lapse rates or not-taken rates

17
Item Values

• Value in pricing analysis
• Expected cost at policy inception
• Actual (realized) cost

18
Ratable Losses
Date Insurance Charge Expected Non-ratable losses Expected Gain Actual Non-ratable losses Variance Actual Gain
1/2001 500,000 450,000 50,000 --- --- ---
12/2001 500,000 450,000 50,000 470,000 20,000 30,000
12/2002 500,000 500,000 50,000 515,000 65,000 15,000
19
Retro Source of Earnings
Valuation Date Non-ratable Losses Interest Earned Persis- tency Maintenance Expenses Explicit Profit Total Profit
1/1/2001 2,000 2,500 ?1,500 750 1,250 5,000
12/31/2001 1,400 3,400 ?2,500 750 1,100 4,150
12/31/2002 2,100 3,600 ?2,900 750 1,100 4,650
20
Pricing Paradigms

• Premium / loss paradigm
• Credit / charge paradigm