Risk Premium Project Phase III: Final Report

Academic Investigators Industry Investigators

J. David Cummins

University of Pennsylvania

Richard A. Derrig

Automobile Insurers Bureau

Richard D. Phillips

Georgia State University

Robert P. Butsic

Fireman’s Fund

Casualty Actuarial Society Meeting

Colorado Springs, CO, May 17, 2004

Copyright 2004, J. David Cummins and Richard D. Phillips, all rights reserved. Not to be reproduced without permission.

Plan of Presentation

Introduction and Summary: Risk-Premium Project Richard A. Derrig

Cost of Capital Estimation J. David Cummins

Capital Allocation Richard D. Phillips

Discussion

Risk Premium Project Overview

Overall Research Objective Identify appropriate risk adjustments for insurer liabilities to determine

equilibrium prices for insurance and fair valuation of reserves Milestones

Phase 1 – Literature Review Actuarial literature Finance literature

Phase 2 – Analysis and Theoretical Conclusions Report CAS Forum Fall 2000

Phase 3 – Empirical Research By-line costs of capital estimates Report CAS Forum Winter 2003 Parameterization of recent capital allocation models

Primary Theoretical Conclusions

Conclusion I

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

Conclusion II

A linkage exists between systematic risk and duration

Conclusion III

Multifactor asset pricing models are superior to the CAPM

Conclusion IV

Theoretically appealing surplus allocation model now exists, and Insurer default should be recognized in pricing risk transfer

Estimating the Cost of Equity CapitalFor Property-Liability Insurers

Objective of Study

Estimate overall costs of capital for P-L insurers Capital asset pricing model (CAPM) Fama-French three factor method (FF3F)

Estimate costs of capital by line of insurance Full information beta (FIB) approach

Cost of Capital: Defined

The cost of capital is the rate of return a firm must earn on projects to avoid destroying firm value Cost of equity capital Cost of debt capital Overall cost of capital

Consequences of erroneous cost of capital estimates Underpricing – lose money on policies underwritten Overpricing – lose business to competitors

Uses of the Cost of Capital

Project decision making – accept or reject projects Product pricing Entry or exit lines of business or geographical

markets Mergers and acquisitions

Estimating Cost of Capital By Line

Cost of capital is known to vary By industry By firm within an industry By line of business within a firm

Little or no prior research on cost of capital by line for insurance

Estimating the Divisional Cost of Capital

Divisional cost of capital or project cost of capital is the required rate of return on project that will not destroy firm value Adjusted present value method – each cash flow has its

own cost of capital Financial pricing models utilize cost of capital for

individual lines of business

Cost of capital for diversified (conglomerate) firms Overall cost of capital can be estimated using market data However, the overall cost of capital may over or under-

estimate the cost of capital for lines of business (divisions)

Estimating Divisional Cost of Capital: Traditional Methodology

Pure play approach: Identify publicly traded firms that specialize in the

same product as the division (i.e., that have a “pure play” in that product)

Approximate the divisional cost of capital as the average cost of capital for the pure play firms.

Pure Play Approach: Limitations

Few specialist firms may be available Most P-L insurance written by multiple line firms Specialized subs of conglomerates are not publicly

traded

Specialist firms in many industries may not be representative of divisions of conglomerate firms (e.g., may be smaller) Because the cost of capital is higher for small firms,

using pure play estimates of the cost of capital for the divisions of a conglomerate may yield biased results

The Full-Information Industry Beta Method

The full-information industry beta (FIB) method provides a promising alternative to the pure play approach (Kaplan and Peterson 1998).

The FIB approach Uses a sample of conglomerate and specialist firms to

estimate cost of capital by line (division) Fundamental insight: the observable beta for the

conglomerate is a weighted average of the unobservable betas of the underlying lines of business

The Full Information Industry Beta Method II

Regress the firm’s observable cost of capital parameters on variables measuring the firm’s participation in various industries and business lines

Coefficients of the line of business participation variables are then interpreted as the full-information beta coefficients for the business lines

Firms outside of the estimation sample (e.g., mutuals or non-traded stock firms) can estimate the cost of capital for their own line of business compositions

FIB Estimation Outline

Estimate the FIB costs of capital using all firms in the Compustat data base for the period 1997-2000

Regression analyses All insurance and non-insurance firms based on 2-digit

industry categories from the North American Industry Classification System (NAICS)

All insurance and non-insurance firms with P-L insurance lines subdivided based on National Association of Insurance Commissioners database

Industry participation based on revenue measures

Betas Used As Dependent Variables

Capital asset pricing model (CAPM) betas Fama-French 3-factor betas

Responds to the criticism that the CAPM gives inaccurate estimates of the cost of capital because it omits important financial risk-factors

Fama-French risk factors CAPM systematic market risk factor Firm size (total market capitalization) Financial distress (book value (BV) of equity/market value (MV)

of equity

Capital Asset Pricing Model (CAPM)

( ) [ ( ) ]i f mi m fE r r E r r

Capital asset pricing model (CAPM) cost of capital:

Where

E(ri) = cost of capital for firm I

rf = the risk-free rate of interest

rm = the return on the “market” portfolio

βmi = Cov(rm,rf)/Var(rm) = beta for systematic market risk of firm I

Fama-French 3-Factor (FF3F) Model

FF3F cost of capital:

E(ri) = cost of capital for firm i

βmi = beta for systematic market risk of firm i

βsi = size beta for firm i

βvi = financial distress beta for firm i

πs = the expected market risk premium for firm size

πh = the expected market risk premium for financial distress risk

( ) [ ( ) ]i f mi m f si s vi hE r r E r r

Why the Fama-French 3 Factor Model?

Extensive research shows CAPM fails to capture accurately the cross-sectional differences in expected stock returns

Various multi-factor models have been proposed Arbitrage pricing theory Wei model FF3F model

FF3F has been extensively tested and has become the dominant multi-factor model in practical finance applications.

FF3F Model: What Do the Factors Represent?

Market risk factor, E(rm) – rf

Market systematic risk – same rationale as CAPM

Market risk premium for firm size, πs

“Small stock premium” – small stocks tend to have higher expected returns than large stocks

Market risk premium for financial distress, πh

Firms in financial distress (low growth prospects) have higher expected returns than healthier firms

Measured by the ratio of book to market equity, BE/ME Shown by FF to do better than the P/E ratio

Estimating Cost of Capital: Implementation

Implementing the cost of capital methodologies Estimate betas for each firm by regressing stock

returns on risk factor variable(s) Estimate expected market risk premia Plug beta coefficients and expected market risk premia

into cost of capital equations to estimate cost of capital

Implementation: The CAPM

First stage regression

60 monthly observations are used on the return of firm i, the risk free rate, and return on the market The market return is represented by a broad market index A U.S. government bill or bond rate is used to represent rf, with

the choice of rate depending upon the time horizon of the firm or project being evaluated

( )it ft i mi mt ft itr r r r

Implementation: The Sum Beta Approach

Using the time series regression to estimate beta may produce biased estimates for stocks that trade infrequently

To control for this problem, the sum beta method is used:

The beta coefficient for firm i is then given by

0 1 , 1 , 1( ) ( )it ft i mi mt ft mi m t f t itr r r r r r

0 1ˆ ˆ ˆ

mi mi mi

Implementation: The FF3F Method

The FF3F method uses the following regression:

A sum-beta regression also can be used:

( )it ft i mi mt ft si st vi vt itr r r r

0 1 , 1 , 1

1 0 , 1 1 1 0 , 1

( ) ( )it ft i mi mt ft mi m t f t

si st si s t vi v t vi v t it

r r r r r r

The FF3F Method: Estimating Size and BE/ME Factors

The firm size and financial distress (BE/ME) factors are estimated using procedures developed and extensively tested by Fama-French and other researchers

Generally, involves the formation of portfolios of stocks graded by market capitalization (size) and BE/ME ratios and computing returns for the portfolios

See cited literature and Ken French’s web site (url given in our paper) for details

Estimating Expected Risk Premia

CAPM systematic market risk premium is the arithmetic average of the difference between the return on a market index and the return on a risk-free asset. The usual averaging period is 1926-present, and The broad market index used here is value-weighted return on all

NYSE, AMEX, and Nasdaq stocks rf is a US government bond or bill rate with the choice of rate

depending upon the time horizon of the project being evaluated

Long-term averages of πst and πvt are used to estimate πs and πv

Full-Information Industry Beta Model

FIB methodology views the firm as a portfolio of assets, where the assets could represent divisions, lines of business, or projects

The firm’s overall market beta coefficients are weighted averages of the beta coefficients of the separate divisions of lines of business

Weights for beta coefficients In theory, the weight equals the market value of the

division divided by the overall market value of the firm Because divisions are not traded, divisional sales data are

used as proxies for market value weights (as in Kaplan and Peterson 1998)

FIB Model: Further Discussion

Decompose the overall market beta coefficient (for the CAPM) or coefficients (for the FF3F model) into separate beta coefficients for each industry in which firms participate.

Decomposition based on cross-sectional regression for a sample of firms Overall market beta(s) as the dependent variable Line of business participation weights as independent variables

FIB Model: CAPM Regression Model

The CAPM FIB regression is

where ωij = firm i’s sales in line j divided by firm i’s total sales

βi = firm i’s overall market beta

βfj = full information industry beta for industry j

The βfj (varying by industry but not by firm) measure the impact of each line of business on the overall riskiness and hence the beta coefficient of the firm

1

J

i fj ij ij

FIB Model: FF3F Regressions

For the FF3F method there are 3 regressions, one for each risk factor

1 21

ln( )J

si f sj ij f s i sij

ME

1

J

mi fmj ij mij

1 21

ln( / )J

hi f hj ij f h i i hij

BE ME

FIB Model: FF3F Regressions

In the size factor equation, the log of ME is included to account for known inverse relationship between the size beta and firm size

In the financial distress equation, the log (BE/ME) is included to account for the known positive relationship between the financial distress beta and BE/ME.

βki = overall beta estimate of type k for firm i, k = m (market), s (size), and v (BV/MV),

βfkj = full-information industry beta of type k, industry j,ωij = industry-participation weight for firm i in industry j,νjj = random error term for firm i, equation j.

Cost of Capital Illustration: Data and Sample

Stock return data are from the University of Chicago’s Center for Research on Securities Pricing (CRSP) and include returns on all NYSE, AMEX, and Nasdaq stocks The CRSP data for the period 1992-2000, to estimate

costs of capital for the period 1997-2000 Standard 60 month estimation period used in

estimating CAPM and FF3F betas Estimation conducted separately for each year of

the sample period

Insurers in Sample: Revenues By Industry

Description Other Insurer   P/L Insurer

P/L Insurance $71,639.26 30.2%

$134,218.70 75.6%

Health Insurance 4,050.54 1.7%

9,283.92 5.2%

Life Insurance 93,430.59 39.4%

16,664.25 9.4%

Finance Excl Ins 26,456.14 11.1%

5,518.24 3.1%

Non-Finance 41,846.76 17.6% 11.867.40 6.7%

Number of firms 102 146

CAPM Cost of Capital: PC Insurers

Market Cap Quartile

No. PC Insurers Average β

AverageSum β

Cost of Capital

Small 21 0.646 0.893 12.5%

2 21 0.861 1.144 14.6%

3 21 0.709 0.809 11.8%

Big 22 0.820 0.932 12.8%

Total 85 0.760 0.944 12.03%

Note: Estimates for 1997. Assumes risk free rate = 4.93% and market risk premium = 7.88%.

FF3F Costs of Capital: PC Insurers

Sum βmSum βs Sum βv

Cost of Capital

1.189 0.766 1.086 20.9%

1.205 0.785 0.834 20.1%

0.978 0.093 0.608 15.7%

1.080 -0.220 0.355 14.9%

1.112 0.349 0.716 17.9%

Note: Estimates for 1997. Assumes risk free rate = 4.93% and market risk premium = 7.88%.

FF3F cost of capital significantly higher than CAPM.

FF3F Costs of Capital: Discussion

Insurer response to market risk factors Insurer stocks about average in their sensitivity to market

systematic risk and firm size Insurer stocks much more sensitive than average to

financial distress factor (BE/ME) – a regulated industry where buyers care about financial stability

FF3F cost of capital significantly larger than CAPM Primarily attributable to financial distress factor Somewhat higher due to size and higher FF3F systematic

market risk betas

FF3F By Line: Personal vs. Commercial

 Annual

AveragePanel

Estimate

Personal Lines versus Commercial Lines

Cost of Equity Capital (Equally Weighted)

Personal Lines 21.7% 21.7%

Commercial Lines 18.1% 18.2%

Cost of Equity Capital (Market Value Weighted)

Personal Lines 18.8% 17.6%

Commercial Lines 21.0% 20.5%

Discussion: Personal vs. Commercial Lines

Cost of capital estimates Equally weighted: Personal > commercial Value weighted: Personal < commercial

Explanation: Value weighted results primarily reflect large insurers – commercial business of large insurers is likely to be higher risk than that written by smaller insurers

FF3F By Line: Auto vs. Workers’ Comp

 Annual

AveragePanel

Estimate

Automobile Insurance versue Workers Compensation

Cost of Equity Capital (Equally Weighted)

Automobile Insurance 20.4% 20.7%

Workers' Compensation 17.9% 18.0%

Cost of Equity Capital (Market Value Weighted)

Automobile Insurance 18.7% 17.5%

Workers' Compensation 15.0% 15.0%

Cost of Capital: Overall Conclusions

FF3F costs of capital are significantly higher than for CAPM – using the CAPM may lead to serious pricing errors

Cost of capital varies significantly by Firm size BE/ME ratio Line of business

Cost of Capital: Overall Conclusions II

Important to use the sum-beta adjustment to allow for infrequent trading

Value-weighted estimates differ signficantly from equally weighted estimates Therefore, using average cost of capital estimates in

rate regulation will result in significant pricing errors for most insurers

FF3F FII Betas: Auto and Workers’ Comp

    1997 1998 1999 2000 Avg Panel

Beta Auto 0.795 1.016 1.022 1.281 1.029 0.971

WC 0.905 0.927 0.807 0.542 0.795 0.864

Other 1.163 1.174 1.260 1.477 1.269 1.227

SMB Auto -0.470 -0.464 -0.261 -0.258 -0.363 -0.438

WC -0.606 0.561 0.471 0.496 0.231 0.071

Other -0.359 -0.168 0.050 -0.116 -0.148 -0.142

HML Auto 0.135 0.727 1.321 1.440 0.906 0.685

WC 0.148 0.761 0.124 -0.151 0.220 0.137

Other 0.276 0.674 0.891 1.010 0.713 0.708

Cost of Cap Auto 11.7% 16.2% 19.5% 22.1% 17.3% 15.7%

WC 12.3% 18.0% 13.9% 10.6% 13.7% 13.5%

  Other 15.5% 17.9% 20.1% 21.9% 18.8% 18.5%

The FF3F Method: Estimating Size and BV/MV Factors II

Stocks are divided into 6 portfolios by size and BVMV ratios (1) HMC and HBMV (2) HMC and MBMV (3) HMC and LBMV (4) LMC and HBMV (5) LMC and MBMV (6) LMC and LBMV

Market value-weighted average returns are obtained for each portfolio

The FF3F Method: Estimating Size and BV/MV Factors II

Size premium πs is obtained as the average return on the three “small” stock portfolios (portfolios (4), (5), and (6)) minus the average return on the three “large” stock portfolios ((1), (2), and (3))

The financial risk premium πv is obtained as the difference between the average return on the two “high” market-to-book portfolios ((1) and (4)) minus the average return on the two “low” market-to-book portfolios ((3) and (6)).

Estimation Methodology: FIIB Model

Estimating the FIIB equation using ordinary least squares yields equally-weighted average industry specific full-information betas.

However, industry participation weights should represent firm market value by industry, so we use an instrumental variables (IV) approach. The instrument for each firm is the ratio of its market

capitalization (Si) to the total market capitalization of the firms in the sample multiplied by its industry-participation weight, i.e.:

iij ij i ij N

ii=1

Sz =w p =w

S

Estimation Methodology: The Pure Play Approach

For comparison with the CAPM and FF3F cost of capital estimates, we also conduct a pure play analysis of property-liability (P/L) insurers

The pure play sample is a sub-sample from our overall sample of publicly traded insurers that consists of all firms that self-report their primary business as P/L insurance (primary NAICS codes of 524126 or 52413)

FF3F, FII Sum Betas: P/L Insurance

Factor 1997 1998 1999 2000 Avg Panel

Beta Factor 1.021 1.131 1.148 1.355 1.164 1.125

SMB Factor -0.387 -0.211 -0.015 -0.126 -0.185 -0.218

HML Factor 0.230 0.720 1.020 1.150 0.780 0.686

Cost of Capital 14.1% 17.6% 19.6% 21.6% 18.2% 17.4%

FIIB vs. Pure Play Costs of Capital

  1997 1998 1999 2000 Avg

Full Information Beta Methodology Estimates

CAPM Beta 13.3% 13.3% 12.0% 12.3% 12.7%

CAPM Sum Beta 12.6% 12.6% 11.9% 13.5% 12.6%

FF3F 17.1% 18.4% 19.7% 21.7% 19.2%

FF3F Sum Beta 14.1% 17.6% 19.6% 21.6% 18.2%

Pure Play Estimates

CAPM Beta 11.9% 11.6% 10.8% 10.5% 11.2%

CAPM Sum Beta 13.3% 13.1% 11.7% 11.6% 12.5%

FF3F 18.0% 18.3% 17.4% 19.7% 18.4%

FF3F Sum Beta 19.1% 13.1% 18.5% 21.2% 18.0%