Underwriting and Actuarial Decision Making
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Transcript of Underwriting and Actuarial Decision Making
September 22, 2004
Maine Event 2004Thinking about Decision Making
Rich Clement: Underwriting Decisions
Rick Leavitt: Actuarial Decisions- Issues- Simulation- Game Theory
September 22, 2004
Maine Event 2004
Underwriting Decisions
September 22, 2004
Maine Event 2004
Difficulties In Underwriting
Limited to poor information
Quick turnaround time
Competition – Acquisition/Irrational Pricing
Multiple Products
Tenure of underwriters – size of accounts
Economic conditions
Evaluation periods are too short
Most volatile time period
September 22, 2004
Maine Event 2004
Difficulties In Underwriting
Limited Tools/Consistently Changing Tools
Changing plan designs – move to employee contributions
New sales and underwriting territories
Aging workforce
Obesity – co-morbid conditions
Pressure on underwriting gain from poor investment income
Limitations to Home Office Partners
September 22, 2004
Maine Event 2004
Difficulties In Underwriting
Mind space for LTD
Increasing medical costs
Churning business
Employer’s “attitude” towards employee’s
Regulatory issues
Internal meetings
Profitable Growth Goals
September 22, 2004
Maine Event 2004
Traditional U/W Response
September 22, 2004
Maine Event 2004
Traditional U/W Response
Risk Analysis
Read and Understand the RFP
Why is case out to bid?
Who is the broker?
Partner with sales on strategy.
Who is employer? – Financial Underwriting
Manual rates
SIC, OCC, Area factors
September 22, 2004
Maine Event 2004
Traditional U/W Response
Risk Analysis (continued)
Plan design features
Experience evaluation
Cause and effect
Most recent period is volatile
Credibility
Other perspectives
Claims, actuarial, similar customers
trust yourself
September 22, 2004
Maine Event 2004
New Approaches
Track Decisions
Competitive advantage
Learn from your mistakes
Evaluate # of claims
Strategic direction
Understand where you make money
Maintain underwriting discipline – mistakes sell
“Hit them were they ain’t” – Ty Cobb
September 22, 2004
Maine Event 2004
Actuarial Decisions
…. Harder than I thought
“All you need in this life is ignorance and confidence; then success is sure”
- Mark Twain
“The greatest obstacle to discovery is not ignorance - it is the illusion of knowledge”
- Daniel Boorstein
September 22, 2004
Maine Event 2004
Actuarial Decision Making
1980’s actuary: Conduct an experience study and recommend rate modifications
21st Century Actuary: ???
“Actuaries are professionals who provide expert advice and relevant solutions for business and societal problems that involve economic risk” ….SOA Promotional Material
Given difficult business environment, it is not enough just to get the pricing right.
September 22, 2004
Maine Event 2004
2004 Disability Product Strategy
1. “Slow and Steady Wins the Race”
- Develop Appropriate Pricing and Stay the Course
- You might need investor and management education
*** Strategy Options ***
2. “Decisive and Aggressive”
- Identify Target Markets and Attack Aggressively
- Fix Mistakes as you Go
September 22, 2004
Maine Event 2004
2004 Disability Product Strategy
*** Strategy Options ***
3. Market Intelligence: “Hit ‘em where they ain’t”
-Exploit Undeveloped Market Niches
4. “Execution, execution, execution”
-Improve Distribution Efficiency/UW Decision Making
-Reduce Administrative Expenses and Cost of Capital
-Risk Evaluation Tools = Smart Decision Making
September 22, 2004
Maine Event 2004
Actuarial Decisions: LTD
Why is it so hard to get the pricing right?
1. Volatility of Loss
September 22, 2004
Maine Event 2004
Loss Volatility
Social Security Age-Gender Adjusted Incident Rates
0.300.350.400.450.500.550.600.650.700.75
1970 1975 1980 1985 1990 1995 2000
September 22, 2004
Maine Event 2004
Actuarial Decisions: LTD
Why is it so hard to get the pricing right?
1. Volatility of Loss – Random versus external impacts
2. Loss takes a long-time to develop
September 22, 2004
Maine Event 2004
LTD Components of Loss
0%
20%
40%
60%
80%
100%
120%
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15Duration in Years
DLR
IBNR
Payments
September 22, 2004
Maine Event 2004
Actuarial Decisions: LTD
Why is it so hard to get the pricing right?
1. Volatility of Loss – Random versus external impacts
2. Loss takes a long-time to develop
3. Product Complexity
September 22, 2004
Maine Event 2004
LTD Product Complexity
Risk Drivers are Correlated (Isolation of Risk is Impossible)
Age Elimination Period Work-Place EnvironmentGender Definition of Disability Societal AttitudesOccupation Replacement Percent Health TrendsSalary Maximum Benefit Local and National EconomyIndustry Definition of Earnings Financial Health of EmployerRegion Pre-ExCase-Size M&N Limit
LTD Components of Risk
September 22, 2004
Maine Event 2004Example of Risk Dependence
Distribution of Ages by Occupational Group
8%
9%10%
11%
12%
13%14%
15%
16%17%
18%
30 35 40 45 50 55
Executives
Other
Blue-Collar
September 22, 2004
Maine Event 2004
Actual Manual Rates
A B CMax Rate / Min Rate
Base Rates 0.57 0.64 0.64 113% Age 0.57 0.65 0.61 Gender 1.05 1.04 1.00 Elim 0.77 0.78 0.92 Benefit Dur 0.98 0.97 0.99 SS Credit 0.70 0.67 0.71Rate 1 0.18 0.22 0.25 137%
Companies
September 22, 2004
Maine Event 2004
Actual Manual Rates (Cont)
A B CMax Rate / Min Rate
Rate 1 0.18 0.22 0.25Salary 0.96 1.00 1.00Occupation 1.31 1.25 1.73Industry 0.75 1.16 0.87Area 0.90 1.00 1.00Size Lives 1.00 1.00 1.27Rate 2 0.16 0.32 0.47 306.0%
September 22, 2004
Maine Event 2004
Actual Manual Rates (Cont)
A B CMax Rate / Min Rate
Rate 2 0.16 0.32 0.47Plan Provisions 1.40 1.08 0.96Net Rate 0.22 0.34 0.46 210.2%
Expenses 45.0% 44.0% 45.8%
Final Rate 0.39 0.61 0.84 213.3%
September 22, 2004
Maine Event 2004
Manual Rate Volatility
0
0.5
1
1.5
2
2.5
0 0.5 1 1.5 2 2.5Average Rate
Car
rier
Rat
e
September 22, 2004
Maine Event 2004
Actuarial Decision Making
So Let’s see….
Disability Rates are all over the place
Trends are hard to predict and hard to track
Some Carriers are buying Market share
Some Carriers are behaving, uh, irrationally
Investors want short-term results on a long-term product
What is an actuary to do??
September 22, 2004
Maine Event 2004
One Approach: Simulation
Simulate Reality and Test Various Strategies
But….
Need to simplify may eliminate key dynamics
Be careful not to assume your outcomes
Test outcomes and relationships for “Reasonability”
(Need Reality Check)
September 22, 2004
Maine Event 2004Example: Sales/Profit Model
Assumptions:
All Carriers have identical expertise
Average Rate = Best Estimate of Cost
Sale depends on Rate (5% Threshold)
Incumbent has rate advantage on renewal
Some Cases will take almost any rate increase
Some Cases will leave regardless of renewal action
September 22, 2004
Maine Event 2004
New Sales Price ElasticityMaximum Discount 20%Std Dev of Rates 10%
Manual Rate
MarginClose Ratio
Sold Discount
Sold Rate
Margin
15% 2.7% 11.0% 0.3%13% 3.2% 10.5% -1.4%10% 3.8% 10.0% -3.3%8% 4.4% 9.2% -4.7%5% 4.9% 8.7% -6.3%2% 5.6% 8.0% -8.1%0% 6.2% 7.2% -10.0%-3% 6.9% 6.8% -12.0%-5% 7.8% 5.8% -14.5%-8% 8.6% 5.2% -16.5%-10% 9.6% 4.4% -19.0%-13% 10.8% 3.8% -21.8%-15% 12.0% 3.2% -24.1%
-25.0%
-20.0%
-15.0%
-10.0%
-5.0%
0.0%
5.0%
10.0%
15.0%
-15% -10% -5% 0% 5% 10% 15%
Manual Rate Margin
Close Ratio
Sold Discount
Sold Rate Margin
September 22, 2004
Maine Event 2004
Persistency Model
IncreasePct Not Shopped
Shopped Persist
Total Persist
0% 100% 53% 93%
5% 100% 25% 93%
10% 86% 24% 83%
15% 76% 25% 78%
20% 67% 27% 73%
25% 58% 28% 68%
30% 40% 27% 58%
0%
20%
40%
60%
80%
100%
120%
0% 5% 10% 15% 20% 25% 30%
Increase
Percent not Shopped
Persistency on Shopped Cases
Total Persistency
September 22, 2004
Maine Event 2004
Scenario 1: On Target Pricing No Rate Increase on Renewal
YearClose Ratio Persist Gain
Inforce Premium
InforceGrowth 1-Persistency
1 4.1% 9.7% 120,952K2 3.7% 97.6% 9.7% 122,626K 0.8% 2.4%3 3.6% 95.9% 9.9% 129,439K 1.4% 4.1%4 3.7% 93.2% 10.0% 138,579K 5.6% 6.8%5 3.7% 96.0% 9.9% 151,229K 7.1% 4.0%6 3.5% 94.7% 10.0% 161,662K 9.1% 5.3%7 3.7% 94.2% 10.0% 175,382K 6.9% 5.8%8 3.8% 95.3% 10.0% 189,274K 8.5% 4.7%9 3.8% 95.2% 10.0% 207,111K 7.9% 4.8%10 3.7% 94.2% 9.9% 219,888K 9.4% 5.8%
Average Growth Gain
Year 1-5 4.7% 9.9%Year 6-10 7.8% 10.0%Years 1-10 6.2% 10.0%
0%
2%
4%
6%
8%
10%
12%
1 2 3 4 5 6 7 8 9 10
Year
0M
50M
100M
150M
200M
250M
Close Ratio1-PersistencyGainInforceGrowthInforce Premium
September 22, 2004
Maine Event 2004Scenario 2: Modest Acquisition:Break-even Pricing, 10% Increase on Renewal
YearClose Ratio Persist Gain
Inforce Premium
InforceGrowth 1-Persistency
1 7.9% -0.9% 132,193K2 7.3% 91.7% 1.9% 144,582K 10.2% 8.3%3 7.3% 83.7% 4.3% 156,896K 9.4% 16.3%4 7.5% 86.4% 6.6% 177,806K 8.5% 13.6%5 7.5% 81.4% 7.9% 181,538K 13.3% 18.6%6 7.6% 79.1% 8.0% 188,833K 2.1% 20.9%7 7.4% 77.9% 8.3% 187,089K 4.0% 22.1%8 7.4% 75.4% 7.7% 187,088K -0.9% 24.6%9 7.4% 80.7% 7.9% 197,112K 0.0% 19.3%10 7.6% 81.5% 8.1% 201,981K 5.4% 18.5%
Average Growth Gain
Year 1-5 8.6% 5.3%Year 6-10 2.2% 8.0%Years 1-10 5.3% 7.1%
-5%
0%
5%
10%
15%
20%
25%
30%
1 2 3 4 5 6 7 8 9 10
Year
0M
50M
100M
150M
200M
250M
Close Ratio1-PersistencyGainInforceGrowthInforce Premium
September 22, 2004
Maine Event 2004Scenario 3: Aggressive Acquisition:Priced at a Loss, 20% Increase on Renewal
YearClose Ratio Persist Gain
Inforce Premium
InforceGrowth 1-Persistency
1 10.4% -5.7% 141,580K2 10.1% 85.6% -2.2% 158,711K 18.0% 14.4%3 10.2% 74.2% 0.4% 169,974K 12.1% 25.8%4 10.2% 73.3% 2.1% 181,380K 7.1% 26.7%5 9.8% 69.3% 2.6% 176,732K 6.7% 30.7%6 10.2% 72.8% 2.9% 178,114K -2.6% 27.2%7 10.0% 71.5% 3.1% 183,033K 0.8% 28.5%8 10.2% 70.1% 2.3% 183,227K 2.8% 29.9%9 10.2% 70.9% 1.9% 184,402K 0.1% 29.1%10 10.0% 72.0% 1.5% 189,517K 0.6% 28.0%
Average Growth Gain
Year 1-5 8.1% 0.5%Year 6-10 1.4% 2.3%Years 1-10 4.7% 1.6%
-10%
-5%
0%
5%
10%
15%
20%
25%
30%
35%
1 2 3 4 5 6 7 8 9 10
Year
0M
50M
100M
150M
200M
250M
Close Ratio1-PersistencyGainInforceGrowthInforce Premium
September 22, 2004
Maine Event 2004
Scenario 4: Light Acquisition:Two Renewal Increases limited to 5%
YearClose Ratio Persist Gain
Inforce Premium
InforceGrowth 1-Persistency
1 7.0% 2.3% 131,330K2 6.5% 94.9% 3.7% 142,877K 9.4% 5.1%3 6.6% 93.5% 5.0% 162,392K 8.8% 6.5%4 6.3% 88.8% 6.3% 181,092K 13.7% 11.2%5 6.5% 90.9% 7.3% 194,838K 11.5% 9.1%6 5.6% 88.9% 8.5% 205,957K 7.6% 11.1%7 5.0% 86.5% 9.3% 210,020K 5.7% 13.5%8 5.2% 88.4% 9.9% 219,274K 2.0% 11.6%9 5.2% 86.6% 10.4% 226,125K 4.4% 13.4%10 5.0% 89.0% 10.8% 235,147K 3.1% 11.0%
Average Growth Gain
Year 1-5 10.2% 5.7%Year 6-10 3.8% 9.9%Years 1-10 7.0% 8.5%
-1%
1%
3%
5%
7%
9%
11%
13%
15%
1 2 3 4 5 6 7 8 9 10
Year
0M
50M
100M
150M
200M
250M
Close Ratio1-PersistencyGainInforceGrowthInforce Premium
September 22, 2004
Maine Event 2004
Scenario 5: Classic Underwriting Cycle
YearClose Ratio Persist Gain
Inforce Premium
InforceGrowth 1-Persistency
1 10.4% -5.1% 140,374K2 10.0% 94.1% -5.9% 158,514K 17.0% 5.9%3 9.9% 95.5% -3.5% 187,305K 12.9% 4.5%4 3.3% 87.3% 5.8% 177,076K 18.2% 12.7%5 3.2% 76.1% 12.2% 153,933K -5.5% 23.9%6 3.3% 72.7% 14.9% 132,051K -13.1% 27.3%7 8.7% 75.2% 7.0% 144,912K -14.2% 24.8%8 8.6% 85.3% 4.4% 171,704K 9.7% 14.7%9 8.5% 88.5% 3.8% 195,680K 18.5% 11.5%10 5.1% 84.6% 7.1% 202,541K 14.0% 15.4%
Average Growth Gain
Year 1-5 5.1% 2.0%Year 6-10 5.6% 6.8%Years 1-10 5.4% 4.9%
-15%
-10%
-5%
0%
5%
10%
15%
20%
25%
30%
35%
1 2 3 4 5 6 7 8 9 10
Year
0M
50M
100M
150M
200M
250M
Close Ratio1-PersistencyGainInforceGrowthInforce Premium
September 22, 2004
Maine Event 2004
Scenario Outcomes
Inforce Premium
100M
120M
140M
160M
180M
200M
220M
240M
260M
280M
1 2 3 4 5 6 7 8 9 10
Year
Target Pricing
Modest Acquisition
Aggressive Acquisition
Light Acquisition
Underwriting Cycle
Annual Gain
-10%
-5%
0%
5%
10%
15%
20%
1 2 3 4 5 6 7 8 9 10
Year
Target Pricing
Modest Acquisition
Aggressive Acquisition
Light Acquisition
Underwriting Cycle
September 22, 2004
Maine Event 2004
Scenario Outcomes (Years 6-10)
1 Priced at Target: No increase on renewal 5 Underwriting Cycle2 Priced at break even: 10% increase on renewal 6 Increasing Rates3 Priced at a loss: 20% increase on renewal 7 Decreasing Rates4 Initially priced below target: 5% increase on renewal 8 Low rates
0%
2%
4%
6%
8%
10%
12%
70M 75M 80M 85M 90M 95M 100M 105M 110M 115M 120M
5Yr Premium
5 Y
r G
ain
4
6
3
2
5
17
8
September 22, 2004
Maine Event 2004
Other Approaches?
Can Game Theory Help??
The theory of games is a theory of decision making in complex situations… when the outcome is uncertain (chance) and there are competing goals (other players)
1944, John Von Neumann – “Theory of Games and Economic Behavior”
1948, John Nash – “Nash’s Equilibrium” – identifies existence of optimal Strategy
September 22, 2004
Maine Event 2004
Game TheoryPure Skill Pure Luck Luck and Skill
Chess War PokerGo Stock Market
Checkers LTD ??Tic-Tac-Toe
Chutes and Ladders
Trivial !
Categories
Zero-Sum versus Non Zero-Sum
2 Person versus Multi-person
Cooperative versus Non-Cooperative
September 22, 2004
Maine Event 2004
Optimal Strategies??
Equilibrium Strategy
Defined as a strategy in which you will have no regrets regardless of what the other
players do
Nash Equilibrium – 1948
An equilibrium strategy exists for all two-person games
zero-sum and non-zero sum
September 22, 2004
Maine Event 2004
Prisoner’s Dilemma
Question: What is the equilibrium strategy?
Option 1 Option 2
Option 1 2,2 0,3
Option 2 3,0 1,1
Pla
yer
1 Player 2
September 22, 2004
Maine Event 2004
Prisoner’s Dilemma
You and your partner are caught leaving the scene of a crime with no other evidence. You are placed in separate rooms and pressured to testify. What should you do?
Keep Silent Testify
Keep Silent Both go FreeYou go to jail, but your
partner goes free
Testify You go free, but your partner goes to jail
Both convicted of a lesser charge
Your Partner
You
September 22, 2004
Maine Event 2004
Prisoner’s Dilemma
Best Possible Payoff: Keep Silent
If you keep silent and your partner testifies, you will regret decision
If you testify:
Partner keeps silent: You go free (Good decision)
Partner Testifies: Lesser charge (Good decision)
Both Partners testify = Nash Equilibrium
September 22, 2004
Maine Event 2004
Prisoner’s Dilemma
Nash Equilibrium minimizes expected payout.
Is this really the optimal strategy?
What strategy would you use over multiple games?
Option 1 Option 2
Option 1 2,2 0,3
Option 2 3,0 1,1
Pla
yer
1 Player 2
September 22, 2004
Maine Event 2004
Multi-player Games Complicated by Possibility of Alliances
Start-up company offers the following bonuses
24K
Actuary Underwriter
20K 16K
Claims
27K if all three join
Who should join? How much should each get?
September 22, 2004
Maine Event 2004
Multi player Games
Option 1: All three join and get $9K each
Option 2: Actuary and Underwriter get $12K each
… but wait,
Claims person offers the underwriter $13 (keeping $3)
Actuary offers the claims person $4 (keep $16)
Underwriter offers the claims person $5 (keeping $11)
… where will the negotiation end up?
September 22, 2004
Maine Event 2004
Multi-player Games
Any solution is unstable. There can always be an alliance with another player that works better for one member of the alliance.
No Optimal Solution: Too often all parties end up with nothing
September 22, 2004
Maine Event 2004
Game Theory
Interesting, but…
N-player, non-zero sum, cooperative games are poorly understood.
Game Theory can characterize optimal solutions, but does not do well at identifying actual solutions
Defining player utility in real life is difficult
Games are more fun to play than they are to study…