Retention: A New Focus Lee Bowron CAS Ratemaking Seminar March 7 – 8, 2002 Tampa, FL.

Retention: A New Focus

Lee Bowron

CAS Ratemaking Seminar

March 7 – 8, 2002

Tampa, FL

Retention: Defining the Problem Retention Data is Not Publicly Available Retention is Not Always a Rating Variable Several Definitions of Retention, including:

– Ratio Method (Percent of Policies-in-Force / Original Policies-in-Force)

– Expected Policy Life

Retention: A Simple Example

Acme Auto Insurance Company writes 2,000 New Business and 8,000 Renewal Polices a Year

Currently, Acme renews 80% of their policies and policies-in-force are steady

Management wants to increase PIF to 10,500 this year

This will require a 25% increase in new business (2,500) or a 6.25% increase in renewals (8,500)

Impact of Retention on Calendar Year Results

Total New Bus RenewalsPolicies 1,000 200 800

Average Premium 500 500 500

Written Premium 500,000 100,000 400,000

Loss Ratio 72.0% 80.0% 70.0%

Expense Ratio 26.0% 30.0% 25.0%

COR 98.0% 110.0% 95.0%

Underwriting Profit 10,000 (10,000) 20,000

Same Example but 50 additional Renewals



Written Premium 525,000 100,000 425,000

Loss Ratio 71.9% 80.0% 70.0%

Expense Ratio 26.0% 30.0% 25.0%

COR 97.9% 110.0% 95.0%


Same Example but 50 additional New Business



Written Premium 525,000 125,000 400,000

Loss Ratio 72.4% 80.0% 70.0%

Expense Ratio 26.2% 30.0% 25.0%

COR 98.6% 110.0% 95.0%


Factors Impacting Retention

Retention can differ based on many factors, including:– Product Type– Rating Variable– Customer Demographics– Competitive Considerations– Softness of Market

The Real World: Policyholder Personalities Auto Insurance is sold to a wide demographic

market Short-term defectors

– Buy to renew a tag– Low priority of continuous insurance– High propensity to price insurance– Have more violations or accidents, which causes

large price swings– They are transient

The Real World: Policyholder Personalities Loyal Policyholders:

– Personal relationship with agent– Not likely to shop due to price increase– Low cost of auto insurance in relation to budget– Multiple products with the same company or

agency– Long-term residents of community

The Real World: Policyholder Personalities In-Betweeners:

– In the middle ground between the categories above

Each category requires it’s own retention strategy, both operational and pricing.

Operational Strategies to Improve Retention Retention issues may be better addressed

through operational changes than pricing strategies. Such strategies include:– Improved Service– Clearer Correspondence– Payment Options

Pricing Strategies - Renewal Discounts Most companies do not give the full

“indicated” discount– If companies gave the indicated discount, there

would be no difference in loss ratios between new and renewal business

In order to maximize profitability, any discount should “pay for itself” to be justified.

Renewal Discount Strategies

Strategy 1 Strategy 2 Strategy 3Renewal Discount 0% 3% 6%

Policies 800 1000 1150


Written Premium 400,000 485,000 540,500

Loss Ratio 70.0% 72.2% 74.5%

Expense Ratio 25.0% 23.0% 22.0%

COR 95.0% 95.2% 96.4%

Underwriting Profit 20,000 23,450 19,325

A New Product

It is very important that you know the retention characteristics of a new product that you introduce.

Retention characteristics will impact calendar year results until the product “matures.”

Preferred Auto Product – Loss Ratios by Number of Renewals

Percent LossYear of Business Ratio0 20.0% 85.0%1 14.0% 80.0%2 10.0% 75.0%3 7.5% 70.0%4 or more 48.5% 65.0%

72.5%

Accident Year Results for New Preferred Auto Product

LossYear Ratio1 85.0%2 82.9%3 81.1%4 79.5%

Retention is Important!

Retention issues are important in operational and pricing decisions.

Successful firms make retention considerations a part of both existing and new market strategies.

Modeling Retention & Effective Rate Impact

Rob Walling

CAS Ratemaking Seminar

March 8 –9, 2002

Tampa, FL

Objectives

Characteristics of Retention Approach to Modeling Retention Effective Rate Impact (ERI) A Stochastic Approach to ERI Extensions and Considerations

What Characteristics Should a Retention Model Have? Has Flexible Shape Simplified Parameterization Creates Actuarially Intuitive Scenarios

– Decreasing Incremental Changes for larger rate actions

– Asymptotic Behaviors at Extremes Allows Different Retention Behavior for

Different Rating Characteristics

Renewal Rate (R)

Price (P)

100%

0%

Demand Curve

1P

1RR = f(P)

The Flexible Shape of the Retention Demand Curve

Retention Behavior Depends on Characteristics Like … Change in Pricing on Renewal Competitive Positioning Market Conditions (Inflation, U/W Cycle, etc.) Customer Rating Characteristics

– Age– Territory– Policy Size– Years on Risk

Premium Retention can be modeled as:

where: P1 = Proposed Rate Level P0 = Current Rate Level PM = Market Level

ii

m1

01

i

i

PP

PP1

1r

Modeling Retention

Premium Retention using:

where: P1 = 110 = .3 P0 = 100 = 2 r = 69.5% PM = 100 = 2

Modeling Retention - Example

ii

m1

01

i

i

PP

PP1

1r

Modeling Retention - Graphically

0.00

0.20

0.40

0.60

0.80

1.00

1.20

% Rate Change

Rete

nti

on

Retention Factors 1 Retention Factors 2

a1 0.4 0.3p0 100 100pm 100 100b1 1 4g1 1 4

Retention Analysis Goal

Based on the characteristics of a particular current policyholder, how likely is it that the policyholder will renew with me?

Factors to Consider in a Retention Analysis

Change Over Last Year’s Premium Market Competitiveness Traditional Rating Factors Age of Youngest Additional Driver Satisfaction with Agent/Service Number of Years Insured Etc.

Retention Modeling Database

Risk# Age Sex MS Terr Limit Ren? Comp Score

1 25 M S 1 2 Y 3 500

2 64 F S 1 6 Y 2 500

3 17 M S 2 1 Y 2 525

4 36 F S 2 4 Y 1 500

5 44 M S 1 4 N 5 500

6 21 F M 1 2 N 2 600

7 55 M M 2 5 N 2 625

8 70 F M 2 6 Y 3 500

9 29 M M 1 3 Y 1 500

10 40 F M 2 4 Y 4 656

Multivariate Analysis Determines Renewal Probability

Risk# Age Sex MS Terr Limit Comp Score P(Ren)

1 25 M S 1 2 3 500 .85

2 64 F S 1 6 2 500 .86

3 17 M S 2 1 2 525 .87

4 36 F S 2 4 1 500 .80

5 44 M S 1 4 5 500 .70

6 21 F M 1 2 2 600 .92

7 55 M M 2 5 2 625 .94

8 70 F M 2 6 3 500 .80

9 29 M M 1 3 1 500 .85

10 40 F M 2 4 4 656 .91

Modeling Rate Competitiveness

Competitive Analysis Tools– Average Income Analysis to Market Company(ies)– Competitive Analysis Batch Rater

Comparison to Benchmark Rates/Loss Costs Historical Variances off of Benchmarks Empirical Data from Quotes Qualitative Information from Marketing/Agents

Rate Impacts: The Current Problem

What’s the impact on loss ratio of a 25% rate increase?

Ignoring inflation momentarily.If Current Loss Ratio = Loss/PremiumProposed Loss Ratio = Loss/(Premium*1.25) = Loss/Premium*(1/1.25) = Loss/Premium*80% = 80% of Current Loss Ratio

The only answer is a 20% reduction in the Loss Ratio!

Editorial Comment

The Absurdity (If a little is good…)

What’s the impact on loss ratio of a 200% rate increase?

Ignoring inflation momentarily.If Current Loss Ratio = Loss/PremiumProposed Loss Ratio = Loss/(Premium*3) = Loss/Premium*(1/3) = Loss/Premium*33.3% = 33% of Current Loss Ratio

Problems with the Current Pricing World Current actuarial assumptions presuppose a static

book of business. This assumption does not respond to the impact of

shifts in mix of business – Maturity/Seasoning (New Business Penalty)– Class– Territory

Caused by:– Retention/Conversion Differences

• Policyholder Response Differences• Agent Satisfaction

– Changes in Growth Strategies – Competition

Effective Rate Impact

For actuarial purposes, the effective rate impact is:the inverse of the percent change in expected loss

ratios created by the proposed rate change.

ERI = E[Loss Ratio without rate change] - 1.00 E[Loss Ratio reflecting rate change]

Effective Rate Impact - Example

Suppose current trended expected loss ratio is 60% and a proposed class plan is expected to result in a loss ratio of 54%

ERI = 0.60 - 1.00 = +10% 0.54


1) Assume:a. Expected Number of Quotesb. Expected Loss Ratio prior to change

- Use rate level indications- Use assumptions underlying loss model- Simulate using same assumptions

2) Model Current Conversion/Retention Parameters3) Model Current Loss Parameters

a. Frequency & Severity or Loss Ratiob. New vs. Renewalc. Some Class Plan Detail is Preferable


4) Model/Select Proposed Rating Plan Factors a. May come from Loss Modelb. May be state mandated approach (CA Sequential)c. May be rate bureau or competitive benchmarks

5) Simulate Number of Policies Retained/Converted6) Calculate Premiums (Policies x Rate Levels)7) Simulate Losses8) Calculate Modeled Loss Ratio9) Calculate ERI

Note: This approach can be stochastic or deterministic.

Effective Rate Impact - Example

Current Expected Loss Ratio 75.0%Current Average Rate 635

New/ Quotes/ Average Conversion/ Policies Expected LossSegment Renewal Curr. PIF Rate Retention Written Premium Losses Ratio ERIClass 1 New 400 495 20% 80 39,600 31,680 80.0%

Renewal 1000 550 80% 800 440,000 286,000 65.0%Class 2 New 250 900 23% 58 51,750 38,813 75.0%

Renewal 500 1050 70% 350 367,500 257,250 70.0%

Total 698 1,288 898,850 613,743 68.3% 10%10%

New/ Quotes/ Average Conversion/ Policies Expected LossSegment Renewal Curr. PIF Rate Retention Written Premium Losses Ratio ERIClass 1 New 400 405 26% 104 42,120 41,184 97.8%

Renewal 1000 450 88% 880 396,000 314,600 79.4%Class 2 New 250 1065 18% 45 47,925 30,375 63.4%

Renewal 500 1250 64% 320 400,000 235,200 58.8%

Total 705 1,349 886,045 621,359 70.1% 7%11%

Strategy 1

Strategy 2

Why Hasn’t Retention Modeling Been Used for Ratemaking?

Established ratemaking techniques are path of least resistance

Parameterization issues Macro view of pricing

– Micro considerations (class plan, territory, etc.) are typically very simplified

Sensitive to many factors “Black Box” mentality

Why Hasn’t Retention Modeling Been Used for Ratemaking?

New business penalty impact poorly understood

Different Growth Strategies indicate different “indicated” rate changes to achieve the same efffective rate change

“Point Estimate” mentality Have you ever tried convincing 50+ different

regulators about a selection within a range of reasonable estimates?!

Another Way of Looking at Things

Have you ever tried to sell your underwriters, marketing reps and agents on a huge increase that makes no competitive sense?

or dreaded a big decrease presented as capable of doubling retention or hit ratios?

LCV - Definitions

Pr = Profit P = Premium L = Losses E = Expenses I = Investment Income t = time P(Ren) = probability of renewal thru time t P(Con) = probability of conversion thru time t d = discount rate E(Prt) = Pt + It – E(Lt) - Et

LCV – Renewal Component

Lifetime Customer Value (t): Expected profit at time t+1, t+2, etc. times the probability of realizing that profit in year t+1, t+2, etc. (retention ratio) adjusted for the time value of money

E(Prt) E(Prt+1) x P(Rent+1) E(Prt+2) x P(Rent+2) ------- + ----------------------- + ----------------------- + …..(1+d) (1+d)2 (1+d)3

LCV – New Business Component

Lifetime Customer Value (t): Expected profit at time t+1, t+2, etc. times the probability of realizing that profit in year t+1, t+2, etc. (renewal ratio) adjusted for the time value of money adjusted for the probability of writing the risk (conversion ratio)

)( x P(Cont)E(Prt) E(Prt+1) x P(Rent+1) E(Prt+2) x P(Rent+2) ------- + ----------------------- + ---------------------- +…(1+d) (1+d)2 (1+d)3

Retention: A New Focus Lee Bowron CAS Ratemaking Seminar March 7 – 8, 2002 Tampa, FL.

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Transcript of Retention: A New Focus Lee Bowron CAS Ratemaking Seminar March 7 – 8, 2002 Tampa, FL.