- A. Introduction
- A.01. Course Overview
- Last pdf update 2021-01-03 13:56:44 UTZ

- B. Market Assumptions
- B.01. Market Assumptions
- Last pdf update 2021-01-19 15:27:21 UTZ

- C. Historical US Property-Casualty Profitability and Volatility (2020 Update)
- C.01. Premium to GDP Ratio, 1923-2020
- C.02. Surplus to GDP Ratio, 1931-2020
- C.03. Industry Volatility and Profitability Metrics, 1985-2020
- C.04. Direct and Net Volatility and Profitability by Major Line, 1992-2020
- C.05. Direct Premium Growth by Major Line, 1992-2020
- C.06. Implications
- Last pdf update 2021-11-15 16:30:43.766628 EST

- D. Model Specification and Properties
- D.01. Modeling Assumptions
- D.02. Model Portfolio
- D.03. Equal Priority
- D.04. ASTIN/CAS Slides
- D.05. Effective Diversification
- D.06. Measuring the Effects of Pooling
- Last pdf update 2021-01-19 08:51:26 UTZ

- E. Distortions: Definition, Examples, and Properties
- E.01. Distortions and Distortion Pricing Operators
- Last pdf update 2021-01-19 08:55:13 UTZ

- F. Cat Bonds, Their Pricing, and Its Implications for Pricing Non-Cat Lines
- F.01. Catastrophe Bonds and Their Pricing
- F.02. Creating a Distortion From Cat Bond Prices in Theory
- F.03. Creating a Distortion From Cat Bond Prices in Practice
- Last pdf update 2021-01-19 09:15:09 UTZ

- G. Comparative Pricing Across Different Methods and Lines
- G.01. Stand-Alone by Line and Portfolio Pricing
- G.02. Gross and Net Line-Level and Portfolio Pricing
- G.03. Line and Portfolio Multiline Pricing Across Multiple Methods
- G.04. Conclusions and Answers
- Last pdf update 2021-01-19 09:25:53 UTZ

- H. Convex Envelopes (coming soon)
- I. Theory in Practice and the Cost of Capital for Insurance Risk
- I.01. Introduction and Purpose
- I.02. Notional Portfolios
- I.03. Insurance Pricing and Insurer Capital Structure
- I.04. Comparative Pricing: Traditional, Stand-Alone
- I.05. Comparative Pricing: Distortion, Stand-Alone
- I.06. Comparative Pricing: Distortion, Multiline With Allocation
- I.07. Comparative Pricing: Distortion, Multiline With Allocation With Stricter Capital Standard
- I.08. Conclusions and Next Steps
- Last pdf update 2021-01-23 16:33:39 UTZ

- K. Gradients: Ibrgimov, Jaffee and Walden vs. Aumann-Shapley (coming soon)
- L. Simple Nine Scenario Example
- Last pdf update 2021-01-21 16:46:03 UTZ

- M. Severe Convective Storm and Hurricane Model Example (coming soon)
- N. More complex exercise proposed for the book (coming soon)

Lettered headings are links to the PDF file for each module. Bold bullets are sections. Numbered bullets correspond to individual page(s) in each presentation. Sub-bullets highlight content on each slide.

**Table of Contents**- Module A Contents

**A.01. Course Overview**- Objective
- Understand different approaches to pricing risk

- Methodology
- Questions
- Pricing and Return Related
- Capital Structure and Reinsurance Related

- Findings
- Pricing
- Pooling and reinsurance

- Applications
- Methodology has many applications

- Objective
**Appendix A.I. About the Author**

**Table of Contents**- Module B Contents

**B.01. Market Assumptions**- All Models Are Wrong—Some Are Useful
- Objective: build a useful simple model

- Simple Market Model: Initial and Final Transactions in a One-Period Model
- Simple Market Model: Initial and Final Transactions With an Insolvent Outcome
- Simple Market Model
- Three obvious questions

- Accounting Definitions
- Many Types of Risk Capital
- On- and off-balance sheet capital

- Why Equity is Special
- Non-equity capital has a pre-negotiated cost
- Non-equity cost characteristics

- Cost of Capital vs. Cost of Equity
- Weighted Average Cost of Capital (WACC)
- Target ROE

- What Is the Appropriate Level of Assets?
- Regulators or rating agencies determine or heavily influence asset levels

- Insurer Management: Conflicting Objectives
- Four insurance market constraints

- Two Paradigms of Insurance Pricing
- Financial and actuarial pricing

- Ingredients to Mix an Insurance Pricing Model
- Three ingredients specify an insurance pricing model
- Common variants

- All Models Are Wrong—Some Are Useful
**Appendix B.I. Accounting and Priority Details**- Technical Loss Ratios vs. Combined Ratios
- Accounting Definitions
- Premium as Capital
- Premium accounting

- Default Priorities by State
- Insurance Pricing: Three Degrees of Freedom

**Table of Contents**- Module C Contents

**C.01. Premium to GDP Ratio, 1923-2020e**- Premium to GDP Ratio
- Premium to GDP Ratio: Cyclical Growth Between 1947 and 1997
- Premium to GDP Ratio: 1968 Watershed
- Annual Change in Statutory Surplus, 1932 to 2020
- Annual Change in Statutory Surplus, 1932 to 2020 With 10- And 25-Year Rolling SD
- Multi-Year Change in Statutory Surplus, 1932 to 2020
- Premium to Surplus Ratio, 1932 to 2020
- Premium to GDP vs. Suprlus to GDP
- Three Phases of the Market 1931-2020
- Market Dynamics Since 1986 Explained by Prior Year Surplus Levels

**C.02. Surplus to GDP Ratio, 1931-2020e**- Surplus to GDP Ratio, 1931-2020e
- The Surplus to GDP Ratio Has Increased During the Modern Period, 1968-2020

**C.03. Industry Volatility and Profitability Metrics, 1985-2019**- Industry Net Volatility and Profitability Metrics, 1985-2019
- Insurance Volatility and Profitability Metrics: Underwriting and Operating
- Insurance Volatility and Profitability Metrics: Investments and Returns
- Insurance Volatility and Profitability Metrics
- Gloss for rows

- Time Series of Volatility and Profitability Metrics
- Time Series of Volatility and Profitability Metrics
- Title decoder:
`Net Earned Premium; SD=1.33e+11 linear fit, r2=0.967, rse0=2.46e+10`

- Line legend
- Interpretation

- Title decoder:

**C.04. Direct and Net Volatility and Profitability by Major Line, 1992-2019**- Direct and Net Calendar Year Loss Ratio Average, Standard Deviation, Coefficient of Variation, Skewness, and Kurtosis by Major Line
- Direct and Net Calendar Year Combined Ratio Average, Standard Deviation, and Coefficient of Variation by Major Line
- Direct and Net Average Loss Ratio and Combined Ratio by Line
- Direct and Net Average Combined Ratio vs. Standard Deviation Combined Ratio
- Mapping Statutory Lines to Major Lines
- US Statutory lines grouped as follows

- Loss Ratio Correlation by Major Line
- Loss Ratio, Premium Change, and Loss Change Correlation
- Correlation Between Annual Change in Losses, by Major Line
- Correlation Between Annual Change in Premium, by Major Line
- Direct Loss Ratio Statistics by Major Line of Business
- Net Loss Ratio Statistics by Major Line of Business
- Loss Ratio Statistics by Major Line of Business
- Key

- Direct Loss Ratio Time Series by Major Line
- Net Loss Ratio Time Series by Major Line
- Loss Ratio Time Series by Major Line
- Title decoder:
`CMP; SD=0.111 (0.0661), cor=0.915 ar fit, r2=0.268, rse0=0.089`

- Interpretation
- Line Legend

- Title decoder:
- Total Loss Ratio Time Series, Direct and Net
- Direct Loss Ratio Time Series by Major Line, Loss Ratio Scale 0 to 150 Percent
- Net Loss Ratio Time Series by Major Line, Loss Ratio Scale 0 to 150 Percent
- Some Lines Are More Volatile Than Others…
- Reinsurance More Effective for Some Lines Than Others…
- Direct Premium and Loss Dynamics
- Net Premium and Loss Dynamics
- Direct Premium and Loss Dynamics
- Net Direct Premium and Loss Dynamics
- Premium and Loss Dynamics
- Calm Surface Masks Inner Turmoil
- The Underwriting Cycle Is Driven by Commercial Lines
- Direct and Net Premium and Loss
- Direct and Net Combined Ratio and Loss Ratio by Line by Year
- Net Operating Results
- Average Margins, All Lines Combined
- Target average margins

**C.05. Direct Premium Growth by Major Line, 1992-2019**- Average Direct Premium Growth Rates by Line (Percent)
- Annual Change in Direct Premium by Line
- Annual Change in Direct Premium Detailed by Line
- Annual Change in Direct Premium by Line Common Scale
- Premium and GDP Growth Since 1992 (1992=1.0)

**C.06. Implications**- Implications
- Loss ratio and margin expectations
- Margin expectations

- Implications

**Table of Contents**- Module D Contents

**D.01. Modeling Assumptions**- Modeling Assumptions
- Standard simplifying assumptions

- Modeling Output
- Ratios
- Gross margin vs. net margin

- Modeling Assumptions
**D.02. Model Portfolio**- Model Portfolio
- Summary

`Aggregate`

Program: Gross`Aggregate`

Program: Net- Density and Log-Density by Line
- Properties of Model Portfolio Loss Distributions
- VaR, TVaR, EPD, and CV by Line
- Detailed Gross Portfolio Statistics
- Detailed Net Portfolio Statistics

- Model Portfolio
**D.03. Equal Priority**- Description of Equal Priority

**D.04. ASTIN/CAS Slides**- Alpha and Kappa Description

**D.05. Effective Diversification**- Effective Diversification
- Characteristics of effective diversification
- Determining if diversification is effective
- Application to capital structure

- Testing Effective Diversification in a Portfolio
- Three equivalent views
- Examples

- Effective Diversification: Quantile View
- Effective Diversification: Expected Loss View
- Effective Diversification: Alpha View

- Effective Diversification
**D.06. Measuring the Effects of Pooling**- Measuring the Effects of Pooling
- Which lines benefit from pooling?

- Conditional Layer Effectiveness
- Stand-alone basis
- By line on pooled basis

- Gross Loss CLE
- Gross Loss CLE on Return Period Scale
- Net Loss CLE
- Net Loss CLE on Return Period Scale

- Measuring the Effects of Pooling

**Table of Contents**- Module E Contents
- Summary

**E.01. Distortions and Distortion Pricing Operators**- Distortions
- Distortion functions
- Universal properties

- Distortion Pricing Operator
- Simulation Interpretation of Distortions
- Astin / Cas

- Distortions

**Table of Contents**- Module F Contents

**F.01. Catastrophe Bonds and Their Pricing**- Catastrophe Bonds
- Coverage, perils, geography, and triggers

- Catastophe Bonds
- Pricing statistics
- Factors that influence pricing

- Historical US Wind Cat Bond Pricing
- Historical US Wind Cat Bond Pricing (2009-2020)
- Cat Bond Statistics, All Years
- Cat Bond Statistics, 2009-2020

- Catastrophe Bonds
**F.02. Creating a Distortion From Cat Bond Prices in Theory**- Creating a Distortion From Cat Bond Prices
- Objective: use cat bond prices to calibrate a distortion that gives reasonable prices for all lines
- Philosophies of modeling

- Creating a Distortion From Cat Bond Prices: Difficulties
- Data limitations
- Equity returns

- Creating a Distortion From Cat Bond Prices
- Families of distortions
- Explore four approaches, all using PLDs

- Piecewise Linear Distortions (PLD)
- A PLD is a weighted average of TVaRs at different probability levels
- Advantages of PLDs
- Gotcha

- Point Distortions
- A point distortion (PD) is a PLD defined by a single price point

- Average of Points Distortions
- Average individual prices

- Average individual prices
- Convex Envelope Distortion
- Convex envelope: join extreme points

- Bagged Convex Envelope Distortion
- Bootstrap Aggregation (bagging)

- Regression Fits
- One TVaR; Two TVaRs plus mean
- Three TVaRs plus mean; bagged convex

- Creating a Distortion From Cat Bond Prices
**F.03. Creating a Distortion From Cat Bond Prices in Practice**- How Should General Insurance Market Prices Relate to Cat Bond Market Prices?
- Cat bond market prices
- General insurance market prices

- Base Distortion
- Base distortion: bagged convex envelope

`Base`

Bagged Convex Envelope Distortion- Distortions Calibrated to Cat Bond Pricing
- Distortions Calibrated to Cat Bond Pricing, Log Scale
- Gross Portfolio Statistics by Cat Bond Distortion, 2009 to 2020
- Net Portfolio Statistics by Cat Bond Distortion, 2009 to 2020
- Gross and Net Loss Ratio by Cat Bond Distortion
- Gross and Net Loss Ratio and Roe by Cat Bond Distortion
- Pricing Non-Cat Business Using Cat Bond Data
- Gross and Net Loss Ratio by Line and Distortion on Stand-Alone Basis
- Gross and Net ROE by Line and Distortion on Stand-Alone Basis
- Return Discount vs Exceeding Probability for Cat Bond Distortions

- How Should General Insurance Market Prices Relate to Cat Bond Market Prices?

**Table of Contents**- Module G Contents

**G.01. Stand-Alone by Line and Portfolio Pricing**- Stand-Alone by Line and Portfolio Pricing
- Stand-Alone By Line Pricing
- Amount of Capital
- No Allocation

- Stand-Alone by Line and Portfolio Pricing for Constant ROE, Bagged Bond Base Distortion, and Traditional Methods
- Cost of Capital
- Distortions

- Gross Stand-Alone Traditional and Distortion
- Data elements
- Loss Ratio and ROE by line using stand-alone distortion pricing

- Net Traditional and Distortion Stand-Alone
- Net Traditional and Distortion Stand Alone
- Gross Minus Net Statistics
- Concluding Comments
- Gross minus net does not equal ceded
- Market premiums support optimal capital structure

- Stand-Alone by Line and Portfolio Pricing
**G.02. Gross and Net Line-Level and Portfolio Pricing**- Roadmap: Multiline Pricing
- Analysis proceeds in three steps

- Multiline Pricing
- Allocation
- Losses
- Distortion methods

- The Natural Allocation
- The
**natural allocation**is a conditional measure approach to premium allocation that applies to distortion methods

- The
- Gross Traditional Stand-Alone vs Natural Allocation Margin by Line
- Net Traditional Stand-Alone vs Natural Allocation Margin by Line
- Summary of Gross and Net Margin and Assets: Natural Allocation, Base
- Summary of Gross and Net Margin and Assets: Natural Allocation, Constant Roe
- Gross and Net Margin and Assets: Natural Allocation
- Offsetting Dynamics

- Gross and Net Loss Ratios by Method by Line
- Gross to Net Transition: Summary
- In total, gross to net shows…
- By line, gross to net shows…

- Gross Loss Ratio by Cat Bond Distortion
- Net Loss Ratio by Cat Bond Distortion

- Roadmap: Multiline Pricing
**G.03. Line and Portfolio Multiline Pricing Across Multiple Methods**- Road Map: Multiline Pricing
- Analysis proceeds in three steps

- Overview
- Recall objective: understand different approaches to pricing risk
- Common calibration

- Pricing Methods
- Distortion methods
- What are traditional methods?
- Traditional methods

- Calibrated Standard Distortions
- Calibrated Standard Distortions, Log Scale
- Roe vs Exceeding Probability for Standard Distortions
- ROE vs. Exceeding Probability
- Distinguishing distortion behavior

- Gross Loss Ratio, by Method by Line
- Net Loss Ratio, by Method by Line
- Gross Margin, by Method by Line
- Net Margin, by Method by Line
- Gross Allocated Capital, by Method by Line
- Net Allocated Capital, by Method by Line
- Gross Leverage, by Method by Line
- Net Leverage, by Method by Line
- Gross ROE, by Method by Line
- Net Roe, by Method by Line
- ROE by Method by Line
- Hard to interpret

- Gross and Net Pricing, by Method by Line
- Loss Ratio Ranges, by Method by Line

- Road Map: Multiline Pricing
**G.04. Conclusions and Answers**- Questions & Answers
- How does price vary with risk? With volatility vs. tail risk?

- Can reasonable risk loads for non-cat lines be estimated from cat bond price data?

- Are negative risk loads ever appropriate? Why? When?

- Should all lines target the same return on capital (ROE)?

- Should target ROE be calibrated to gross or net returns? Are the two the same?

- Can the same distortion be used to price gross and net? All lines?

- Is pricing in one line independent of reinsurance on other lines?

- Questions & Answers

**Table of Contents**- Module I Contents

**I.01. Introduction and Purpose**- What Is the Cost of Capital for Insurance Risk?
- Equity vs. Capital: Two Measures of Net Assets
- Capital
- Equity

- More Accounting Basics
- Accounting assets and liabilities
- Accounting conventions

- Fundamental Equation of Insurance Accounting
- Traditional Accounting Presentation Distinguishes Insurance From Reinsurance
- Example, assuming assets
*a* - Traditional reinsurance accounting
- Economic reinsurance accounting

- Example, assuming assets
- Traditional Reinsurance Accounting
- Assets
- Liabilities

- Unified Insurance and Reinsurance Accounting Presentation
- Insurance transaction
- Reinsurance transaction

- Economic Reinsurance Accounting
- Assets
- Liabilities

- Capital Structure
- Simple capital (liability) structure
- Illustrative capital structure
- Equity is unique: it is the only residual value
- Non-equity capital has an explicit cost
- Non-equity cost characteristics
- Dollar cost of capital vs. unit cost
- Impact of pooling on cost of capital

- Cost of Capital
- Why the complicated capital structure?
- Weighted Average Cost of Capital (WACC)

- Plan From Hereon

**I.02. Notional Portfolios**- Notional Portfolios
- Apply theory to four notional portfolios
- Portfolio characteristics

- Four Notional Portfolios, 1 and 2
`discrete`

`balanced`

- Four Notional Portfolios, 3 and 4
`mixed`

`cat`

- Notional Portfolio Statistics
- Notional Portfolio Densities, Log Densities, and Survival Functions

- Notional Portfolios
**I.03. Insurance Pricing and Insurer Capital Structure**- Pricing Statistics for Each Notional Portfolio
- All-Equity Capital (Liability) Structures
`discrete`

`balanced`

- All-Equity Capital Structures
`mixed`

`cat`

(different height scale)

**I.04. Comparative Pricing: Traditional, Stand-Alone**- Traditional Pricing
- Stand-alone traditional pricing
- All-or-nothing layer pricing
- Limited Liability
- Premium under limited liability

- Traditional Pricing Comparative Analysis Across Portfolios

- Traditional Pricing
**I.05. Comparative Pricing: Distortion, Stand-Alone**- Distortion Functions: Rate on Line vs. Expected Loss for an All-Or-Nothing Layer
- More General Distortion Functions
- Proportional Hazard Distortions Reproducing Total Pricing for Each Portfolios
- Pricing With General Distortion Functions
- Distortion Pricing Operator
- What distortion should we use?

- Cat Bond Price + POYA ROE Calibrated Distortion
- Constant ROE
- Fit to cat bond prices
- Cat with POYA ROE factor

- Tail Behavior and Return on Capital by Distortion
- Why Should Insurance Equity Returns Be Higher Than Cat Bond Returns?
- Cat Bonds Returns
- Insurance Equity Returns

- Stand-Alone Pricing Comparison: Stunner—Returns Vary by Line!

**I.06. Comparative Pricing: Distortion, Multiline With Allocation**- The Natural Allocation
- Detailed Pricing Statistics for
- Detailed Pricing Statistics for
- Detailed Pricing Statistics for
- Detailed Pricing Statistics for
- Efficient Capital Structure
- Integrating alternative capital
- Comparing three pricing distortions

- Blended Distortion
- Structure Diagram Key
- Left:
**Assets** - Middle: Details by Line
- Right:
**Liabitites**

- Left:
- Capital Structure for With All Equity Financing
- Capital structure and tranche returns for
`roe`

distortion

- Capital structure and tranche returns for
- Capital Structure for With Blended Equity and Alternative Capital Financing
- Capital structure and tranche returns for
`blended`

distortion

- Capital structure and tranche returns for
- Capital Structure for With All Equity Financing
- Capital structure and tranche returns for
`roe`

distortion

- Capital structure and tranche returns for
- Capital Structure for With Blended Equity and Alternative Capital Financing
- Capital structure and tranche returns for
`blended`

distortion

- Capital structure and tranche returns for
- Capital Structure for With All Equity Financing
- Capital structure and tranche returns for
`roe`

distortion

- Capital structure and tranche returns for
- Capital Structure for With Blended Equity and Alternative Capital Financing
- Capital structure and tranche returns for
`blended`

distortion

- Capital structure and tranche returns for
- Capital Structure for With All Equity Financing
- Capital structure and tranche returns for
`roe`

distortion

- Capital structure and tranche returns for
- Capital Structure for With Blended Equity and Alternative Capital Financing
- Capital structure and tranche returns for
`blended`

distortion

- Capital structure and tranche returns for
- Capital Structure: AAA Capital Standard, All Equity Capital
- Structure diagram

- Capital Structure: AAA Capital Standard, All Equity
- Capital Structure: AAA Capital Standard, All Equity Capital
- Structure diagram

- Capital Structure: AAA Capital Standard, All Equity, Blended Distortion
- Standard and Poor’s Default Probabilties by Bond Rating

**I.07. Comparative Pricing: Distortion, Multiline With Allocation With Stricter Capital Standard**- Distortion and Traditional Pricing: Details With Sticter Capital Standard

**I.08. Conclusions and Next Steps**- Conclusions and Next Steps
- Conclusions
- Next Steps

- Conclusions and Next Steps
**Appendix I.I. About**

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