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Richard D. Phillips Bruce A. Palmer Professor of Risk Management and Insurance Georgia State University

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What Did We Learn? Conclusions from the Risk Premium ProjectPresentation made at the 2005 Casualty Actuarial Society’s Ratemaking SeminarMarch 2005New Orleans, LA

Richard D. Phillips

Bruce A. Palmer Professor of Risk Management and Insurance

Georgia State University

Risk Premium Project

- Overall Research Objective
- Identify appropriate risk adjustments for insurer liabilities to determine equilibrium prices for insurance
- Milestones
- Phase 1 – Literature Review
- Actuarial literature
- Finance literature
- Phase 2 – Analysis and Theoretical Conclusions
- Report CAS Forum Fall 2000
- Phase 3 – Empirical Research Complete
- Estimate equity cost of capital by-line of insurance
- Prices reflect allocations of capital

Theory Review: Prices in Perfect Capital Markets

- With perfect and complete markets assumption
- No need for capital (Modigliani-Miller)
- No default risk (perfect enforceability)
- Nothing to allocate
- Pricing done under the risk neutral probability measure

Theory Review: Prices in Perfect Capital Markets with Default Risk

- With insurer default still no need to allocate capital (surplus is a pooled asset)
- Allocate default costs ala
- Black and Cox (1976)
- Phillips, Cummins and Allen (1998)
- D = Equilibrium value of default option

Theory Review: Prices in Perfect Capital Markets with Default Risk and Capital Market Imperfections

- With market imperfections and default costs
- Allocate default cost by priority rule
- Allocate costs of capital to individual lines
- Frictional costs are related to capitalization, i.e., t = f(S)

Pricing Intermediated Risks: Summary

- With market imperfections, insurance prices should reflect

1. Expected cash flow with adjustments for systematic risk

2. Production costs (expenses)

3. Default risk

- Frictional capital costs

Project 1: Estimating Cost of Equity Capital for Property-Liability Insurers

Forthcoming in Journal of Risk and Insurance

- Primary research questions
- What is the cost of equity capital for P&L insurers using
- Capital Asset Pricing Model
- Multi-factor model proposed by Professors Fama and French
- Are there significant differences in the cost of equity capital across different lines of insurance?

Traditional Asset Pricing Model

- Dominant model has been Capital Asset Pricing Model
- CAPM cost of equity capital

E(ri)= rf + bi[E(rm) – rf]

- where

E(ri) = expected return for firm i

rf = risk-free rate of interest

E(rm) = expected return on market portfolio

Failure of the CAPM? What Failure?

Note: Average annual returns vs. beta for 10 size-sorted stock portfolios.

Sample period 1947-1996.

Source: Cochrane, John H., 1999, “New Facts in Finance,” Economic Perspectives 23(3): 36-58.

Fama-French Multifactor Asset Pricing Model

- Fama-French 3 Factor Model
- Multi-factor asset pricing model
- Cost of capital estimate is

E(ri)= rf + bi[E(rm) – rf] + bs,iE(ps) + bv,iE(pv)

- where

E(ri) = expected return for firm i

rf = risk-free rate of interest

E(rm) = expected return on market portfolio

E(ps) = expected market premium for firm size

E(pv) = expected market premium for financial distress

bi = market beta to adjust for systematic portfolio risk

bi = beta to adjust for systematic risk associated with firm size

bi = beta to adjust for systematic associated with financial distress

Cost of Equity Capital Estimates for Pure Play U.S. Property & Liability Insurers Using CAPM: 1997-2000

Table shows average CAPM beta for firms which self-identify as property-liability insurers by listing their overall NAICS code as 524126 or 52413.

Cost of Equity Capital Estimates for Pure Play U.S. Property & Liability Insurers Using Fama-French 3 Factor Model: 1997-2000

Table shows average Fama French beta coefficient estimates for firms which self-identify as property-liability insurers by listing their overall NAICS code as 524126 or 52413.

Recent Update: Results from 1999 - 2003

Results are derived using Full Information Industry Beta methodology (details available in

Kaplan and Petersen 1998 and Cummins and Phillips 2005)

Which Asset Pricing Model Better Reflects Historical Experience?

The P&L index is the cumulative return on the market capitalization weighted portfolio of all

NYSE, AMEX, and NASDAQ firms with SIC code 6331.

Which Asset Pricing Model Better Reflects Historical Experience?

The P&L index is the cumulative return on the market capitalization weighted portfolio of all

NYSE, AMEX, and NASDAQ firms with SIC code 6331.

Estimating Equity Cost of Capital by Line for CAPM

- Use Full-Information Industry Beta Methodology
- Kaplan and Peterson (1998)
- Firm specific betas are weighted average of betas from individual business units
- Two steps in estimation
- 1. Estimate firm specific equity betas - bi
- 2. Impute full – information industry betas. For CAPM

where wi,j = percent of firm i’s participation in line/industry j

bi = firm i’s overall CAPM beta

bfj = full information industry beta for line/industry j

- Extend Full-Information Industry Beta method for Fama/French model

Summary Estimated Costs of Equity Capital by Line of Business Pairs Dec. 2000: Panel Estimates from Market Value Weighted Regressions

***, **, * - statistically significant at the 1, 5, and 10 percent levels, respectively.

1 – H0: rAuto = rAll Others

Project 2: Allocating the Costs of Capital

“Pricing Financially Intermediated Risks with Costly External Finance: Evidence from the Insurance Industry”

by

J. David Cummins, Yijia Lin, and Richard D. Phillips

- Primary research questions
- Do insurer prices reflect capital allocation charges specific to the firm?
- Are the implied capital allocations at least correlated with the method proposed by Myers and Read?
- What is the implied per unit cost of allocated capital?

Myers and Read arrive at their suggested surplus allocation formula

They ask: “How does the firm default option change for a marginal increase in liability from line i?” I.e., what is

?

Myers and Read 2001Myers and Read (2001) Result

- where s = overall surplus-to-liability ratio of insurer
- si = surplus-to-liability ratio for line of business i
- s = overall volatility parameter of insurer
- d = insolvency put per dollar of liabilities
- di = default-to-liability ratio for line of business i
- siL = covariance between losses line i and overall loss portfolio
- sL2 = volatility parameter for total losses
- siV = covariance between losses for line i and firm assets
- sLV = covariance between assets and liabilities
- Using the equal priority rule, i.e., di = d, yields the surplus allocation formula

Primary Empirical Predictions

- Hypothesis 1
- Price differences between lines of insurance reflect market systematic risk differences
- Hypothesis 2
- Price for any line of business should be inversely related to firm default risk
- Hypothesis 3
- Price differences across insurers within a given line of insurance reflect firm specific capital allocation differences.
- Controlling for overall capital charges, lines requiring greater capital within the firm will require a higher returns
- Empirically test if is related to prices across insurers

Empirical Test: Dependent Variable

- Economic premium ratio
- NPWij = net premiums written line i insurer j
- DIVij = PH dividends paid line i insurer j
- UEXij = underwriting expenses paid line i insurer j
- NLIij = net losses incurred line i insurer j
- LAEij = net loss adjustment expenses incurred line i insurer j
- PVFi = discount factor for payout tail line i
- We consider two aggregated lines groupings
- Long-tail/Liability lines vs. Short-tail/Property lines

Economic Premium Ratio Histograms U.S. Property-Liability Insurers: 2000

Long-tail Lines

Short-tail Lines

Mean = 1.22

Median = 1.09

Std. Dev. = 0.59

Num Obs. = 1114

Mean = 1.09

Median = 1.04

Std. Dev. = 0.40

Num Obs. = 1331

Implementing Myers and Read Line Specific Surplus-to-Liability Ratio

- Volatilities and covariance parameters estimated from
- NAIC quarterly data 1991 – 2000
- Industry aggregate data
- Seasonally adjusted time series
- Discount losses incurred using risk-free term structure
- Asset return data for major asset classes
- Company specific values for
- Line of business liability weights
- Asset weights
- Capital ratios
- All adjusted to approximate market values

Summary Statistics: Overall and Line Specific Capitalization Ratios: Year = 2000

N=1114 for Property Lines

N=1331 for Liability Lines

Correlation Statistics: Year = 2000

N= 1040 observations

Univariate Test 1: Price Inversely Related to Default Risk

Chart shows average economic premium ratio by A.M. Best rating for all insurers 1997 – 2002.

Number of observations = 6681 for property and 8050 for liability.

Univariate Test 2: Price Positively Related to Insurer Overall Capitalization

Chart shows average economic premium ratio by overall capitalization deciles for all insurers

1997 – 2002. Number of observations = 6681 for property and 8050 for liability.

Univariate Test 3: Price Positively Related to Firm Specific Internal Capital Allocation

Chart shows average economic premium ratio by line specific surplus-to-liability ratio relative to the

overall surplus-to-liability ratio by deciles for all insurers 1997 – 2002.

Number of observations = 6681 for property and 8050 for liability.

Multivariate Empirical Test 1

- Panel data of all U.S. P&L Insurers
- Time period: 1997 – 2002
- Empirical test: Price differences across firms

where EPRijt = Economic premium ratio line i for company j in year t

A.M. Bestjt = Financial strength rating from A.M. Best company j year t

sijt = Line i surplus-to-liability ratio for company j in year t

sjt = Overall surplus-to-liability ratio for company j in year t

Xjt = Vector of other control variables for company j in year t

- Methodology: OLS and 2 way fixed effects

Regression Results: Price Differences Across Firms for Property Lines of Business: All Insurers 1997 - 2002

Note: 6681 Observations

***, **, * represents statistical significance at the 1, 5 and 10 percent level, respectively

Regression Results: Price Differences Across Firms for Liability Lines of Business: All Insurers 1997 - 2002

Note: 8050 Observations

***, **, * represents statistical significance at the 1, 5 and 10 percent level, respectively

Economic Significance – A First Look

- Coefficient estimates can be used to derive the insurer’s implied deadweight cost of allocated capital
- Discounted cash flow model of insurance premiums Cummins and Phillips (2000)

PV loss payments

at RADR at date 0

PV of future “taxes” on equity at date 0

Implied Equity Capital “Tax Rates”

- Methodology
- Estimate economic premium ratio using parameters for property of liability lines of insurance
- Assume we double the line-specific capitalization ratio
- Determine the capital “tax rate” that would imply an increase in the economic premium ratio equal to what was estimated from the reduced form price regressions
- Implied tax rates
- Property: 49%
- Liability: 43%
- Average simulated MTR of P&L insurers was 27% in 2000 (Graham)

Risk Premium Project Conclusions

- Primary theoretical predictions

Conclusion I

- Both systematic and non-systematic risk are relevant factors determining equilibrium prices for insurance

Conclusion II

- Multifactor asset pricing models empirically more successful than CAPM

Conclusion III

- Theoretically appealing surplus allocation models now exist

Risk Premium Project Conclusions

- Primary empirical results
- Cost of equity capital for insurers
- CAPM vs. Multi-factor models
- In general FF3F model produces higher estimated costs of equity capital vs. the CAPM
- Full information industry beta methodology
- In general cost of equity capital for property lines appears higher than liability lines
- Strong evidence prices vary across insurers as a function of
- Overall default risk
- Total capital charges
- Internal allocation of those capital charges
- Prices appear to be a function of a firm’s access to capital markets
- Limitations of competition and arbitrage
- Implementation issues

Suggested Reading

Butsic, Robert P, J. David Cummins, Richard A Derrig, and Richard D. Phillips, 2000, "The Risk Premium Project (RPP): Phase I and II Report," Casualty Actuarial Society Forum, Fall 2000: 165-230.

Cochrane, John H., 1999, “New Facts in Finance,” Economic Perspectives 23(3): 36-58.

Cummins, J. David and Richard D. Phillips, 2001, "Financial Pricing of Property-Liability Insurance," in Georges Dionne, ed., Handbook of Insurance (Boston, MA: Kluwer Academic Publishers)

Cummins, J. David and Richard D. Phillips, 2005, “Estimating the Cost of Equity Capital for Property & Liability Insurers,” forthcoming Journal of Risk and Insurance.

Cummins, J. David, Yijia Lin, and Richard D. Phillips, 2005, “Pricing Financially Intermediated Risks with Costly External Finance: Evidence from the Insurance Industry,” Working Paper Georgia State University, Atlanta, GA.

Derrig, Richard A.,and Elisha Orr, 2003, "Equity Risk Premium: Expectations Great and Small," presented at the 2003 Bowles Symposium, Georgia State University, Atlanta, GA.

Froot, Kenneth A., 2003, "Risk Management, Capital Budgeting and Capital Structure Policy for Insurers and Reinsurers," Harvard Working Paper, Boston MA.

Suggested Reading

Froot, Kenneth A. and Jeremy C. Stein, 1998, "Risk Management, Capital Budgeting, and Capital Structure Policy for Financial Institutions: An Integrated Approach," Journal of Financial Economics 47: 55-82.

Kaplan, Paul D. and James D. Peterson, 1998, "Full-Information Industry Betas," Financial Management 27: 85-93.

Merton, Robert C., and Andre F. Perold, 1993, “Theory of Risk Capital in Financial Firms,” Journal of Applied Corporate Finance 6:16-32.

Myers, Stewart C and James A. Read, Jr., 2001, "Capital Allocation for Insurance Companies," Journal of Risk & Insurance 68: 545-580.

Phillips, Richard D., J. David Cummins, and Franklin Allen, 1998, "Financial Pricing of Insurance in the Multiple Line Insurance Company," Journal of Risk and Insurance 65: 597-636.

Zanjani, George, 2002, “Pricing and Capital Allocation in Catastrophe Insurance,” Journal of Financial Economics 65: 283-305.

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