Equity Risk Premium: Equity Risk Premium: Expectations Great and Expectations Great and

SmallSmallRichard A. Derrig and Elisha D. OrrRichard A. Derrig and Elisha D. Orr

North American Actuarial JournalV8 N1 pp 45-69 2004

Equity Risk Premium (ERP)Equity Risk Premium (ERP)

Definition: Definition:

Difference between the market Difference between the market returnreturn

and a risk-free returnand a risk-free return

Why the ERP is Important Why the ERP is Important for Insurers ?for Insurers ?

Universally accepted benchmark Universally accepted benchmark for pricing riskfor pricing risk

Input into simple CAPM and Input into simple CAPM and Fama-French 3-factor modelFama-French 3-factor model

Affects other cost of capital Affects other cost of capital estimates and discount ratesestimates and discount rates

Market value of liabilities Market value of liabilities Insurers’ asset allocationsInsurers’ asset allocations

Objectives of PaperObjectives of Paper

Introduction to the ERP PuzzleIntroduction to the ERP Puzzle Types of ERP Types of ERP Time Series AnalysisTime Series Analysis Catalogue ERP Puzzle LiteratureCatalogue ERP Puzzle Literature Selection of an ERP (-0.9 to 9.0%)Selection of an ERP (-0.9 to 9.0%)

ERP PuzzleERP Puzzle

Mehra and Prescott (1985): Mehra and Prescott (1985): – Anomalous results when historical Anomalous results when historical

realized ERP compared to asset realized ERP compared to asset pricing theory valuespricing theory values

– Otherwise, must assume risk aversion Otherwise, must assume risk aversion level outside of “reasonable” rangelevel outside of “reasonable” range

– Either realized returns are biased Either realized returns are biased (high) or asset pricing models are (high) or asset pricing models are mispecified mispecified

Led to literature to solve the “ERP Led to literature to solve the “ERP puzzle”puzzle”

US Equity Risk Premia US Equity Risk Premia S&P 500 1926-2004S&P 500 1926-2004

HorizoHorizonn

Equity Equity ReturnReturn

ss

Risk-Risk-Free Free

ReturnReturn

ERPERP

ShortShort 12.39%12.39% 3.76%3.76% 8.63%8.63%InterInter 12.39%12.39% 4.76%4.76% 7.63%7.63%LongLong 12.39%12.39% 5.23%5.23% 7.17%7.17%

Source: Ibbotson Yearbook (2005)

ERP TypesERP Types

Geometric vs. arithmeticGeometric vs. arithmetic Short vs. long investment horizonShort vs. long investment horizon Short vs. long-run expectationShort vs. long-run expectation Unconditional vs. conditional Unconditional vs. conditional US vs. international market data US vs. international market data Data sources and periodsData sources and periods Real vs. nominal returnsReal vs. nominal returns

ERP using same historical ERP using same historical data (1926-2002)data (1926-2002)

Investment Investment HorizonHorizon

Type of Type of AverageAverage

ERP ERP Historical Historical

ReturnReturnShortShort ArithmeticArithmetic 8.4%8.4%ShortShort GeometricGeometric 6.4%6.4%InterInter ArithmeticArithmetic 7.4%7.4%InterInter GeometricGeometric 5.4%5.4%LongLong ArithmeticArithmetic 7.0%7.0%LongLong GeometricGeometric 5.0%5.0%Source: Ibbotson Yearbook (2003)

Converting from Geometric to Converting from Geometric to Arithmetic ReturnsArithmetic Returns

Formula:Formula:AR = GR + var/2,AR = GR + var/2,

var, variance of the return processvar, variance of the return process

Short-Horizon ERPShort-Horizon ERP

Short-Horizon Equity Risk Premium

-60%-40%-20%

0%20%40%60%

1920 1930 1940 1950 1960 1970 1980 1990 2000 2010Year

Actual ERP Long-term Mean Mean pre-1960 Mean 1960+

Long-term Mean =8.17%

Mean 1926 to 1959 = 11.82% Mean 1960 to 2002 = 5.27%

Source: Ibbotson Yearbook (2003), Geometric DifferencesFigure 1

ANOVA Regressions ANOVA Regressions ERP on TimeERP on Time

PeriodPeriod Time Time CoefficienCoefficien

tt

P-ValueP-Value

1926-19591926-1959 0.0040.004 0.3550.355

1960-20021960-2002 0.0010.001 0.7490.749

1926-20021926-2002 0.0010.001 0.4430.443

Time Series AnalysisTime Series Analysis

Stationarity AssumptionStationarity Assumption– Supported by ANOVA regressionsSupported by ANOVA regressions– ARIMA model projects future years ARIMA model projects future years

as average of dataas average of data No significant time trendsNo significant time trends Mean of full Ibbotson series and Mean of full Ibbotson series and

subset (1960+) not statistically subset (1960+) not statistically differentdifferent

Why Different Why Different Estimates ?Estimates ? HistoricalHistorical

– 1926-20021926-2002– 1802-2001 (Earlier period)1802-2001 (Earlier period)

Dividend Growth ModelDividend Growth Model– Next Ten Years + Remainder of 75 Next Ten Years + Remainder of 75

YearsYears– Historical ≠ ExpectedHistorical ≠ Expected– Conditional versus Unconditional Conditional versus Unconditional

expectationsexpectations

Short-Horizon ERP byShort-Horizon ERP bySub-periodsSub-periods

II IIII IIIIII1802-1802-18701870

1871-1871-19251925

1926-1926-20012001

Real Geom Real Geom Stock Stock Returns Returns

7.0%7.0% 6.6%6.6% 6.9%6.9%

Real Long-Real Long-term term Gov’ts Gov’ts

4.8%4.8% 3.7%3.7% 2.2%2.2%

ERPERP 2.2%2.2% 2.9%2.9% 4.7%4.7%Source: Siegel (2002)

Literature to Solve the Literature to Solve the PuzzlePuzzle

11stst thread thread – New models and assumptions to explain New models and assumptions to explain

historical datahistorical data– Includes Behavioral FinanceIncludes Behavioral Finance

22ndnd thread thread– Estimates of the ERP from standard Estimates of the ERP from standard

economic modelseconomic models– Catalogue in Appendix BCatalogue in Appendix B

Areas of ERP Research

Social Security

Puzzle Research

Financial Analysts Estimates

Behavioral Approach

Surveys

Areas of ERP Research

Social Security

Puzzle Research

Financial Analysts Estimates

Behavioral Approach

Surveys

Campbell & Shiller Arnott & RyanArnott & Bernstein Fama & French Ibbotson & Chen Constantinides Mehra

OCACT 3 Experts

Catalogue of ERP EstimatesCatalogue of ERP Estimates

Social Security Social Security (1999, 2001)(1999, 2001) Puzzle ResearchPuzzle Research

– Campbell and Shiller (2001)Campbell and Shiller (2001)– Arnott and Ryan (2001), Arnott and Arnott and Ryan (2001), Arnott and

Bernstein (2002)Bernstein (2002)– Fama and French (2002)Fama and French (2002)– Ibbotson and Chen (2003)Ibbotson and Chen (2003)– Constantinides (2002)Constantinides (2002)– Mehra (2002)Mehra (2002)

Areas of ERP Research

Social Security

Puzzle Research

Financial Analysts Estimates

Behavioral Approach

Surveys

Claus & Thomas Harris & Marston

Graham & Harvey Welch

Benartzi & Thaler

Catalogue of ERP Estimates Catalogue of ERP Estimates (Cont.)(Cont.)

Financial Analyst EstimatesFinancial Analyst Estimates– Claus and Thomas (2001)Claus and Thomas (2001)– Harris and Marston (2001)Harris and Marston (2001)

SurveysSurveys– CFOs, Graham and Harvey (2002)CFOs, Graham and Harvey (2002)– Financial economists, Welch (2000 & Financial economists, Welch (2000 &

2001)2001) Behavioral ApproachBehavioral Approach

Behavioral FinanceBehavioral Finance Benartzi and Thaler (1995)Benartzi and Thaler (1995) Start with prospect theoryStart with prospect theory

– Asymmetric Loss AversionAsymmetric Loss Aversion Add “mental accounting”Add “mental accounting”

– Myopic Loss AversionMyopic Loss Aversion

Classification of ERP Classification of ERP TypesTypes

Appendix BAppendix B

RR NN GG AA LLHH

SHSH SSEE

LELE CC UU

Ibbotson Ibbotson (Hist)(Hist)

XX XX XX XX XX

DiamondDiamond XX XX XX XX XXArnott & Arnott & RyanRyan

XX XX XX XX XX

Fama & Fama & FrenchFrench

XX XX XX XX XX

Ivo WelchIvo Welch XX XX XX XX XX

Sample:

Adjusting ERP EstimatesAdjusting ERP Estimates

Approximations shown in Appendix CApproximations shown in Appendix C Add RFR & ERP provided by source (stock Add RFR & ERP provided by source (stock

return estimate)return estimate) Convert from geom to arith (hist diff)Convert from geom to arith (hist diff) Convert from real to nominal (hist diff)Convert from real to nominal (hist diff) Conditional to unconditional (est from FF)Conditional to unconditional (est from FF) Remove historical short-horizon RFRRemove historical short-horizon RFR Short-horizon arithmetic unconditional Short-horizon arithmetic unconditional

ERP estimate for each sourceERP estimate for each source

Adjusting ERP Estimates:Adjusting ERP Estimates:Short-Horizon Arithmetic Short-Horizon Arithmetic

Unconditional ERP EstimateUnconditional ERP EstimateRFRRFR ERPERP StocStoc

k k RetRet

G G to to AA

R R to to NN

C to C to UU

ShorShort-hor t-hor RFRRFR

EstimatEstimatee

DiamonDiamondd

3.03.0 3.03.0- -

3.53.5

6.0-6.0-6.56.5

2.2.00

3.13.1 0.40.466

3.83.8 7.8%-7.8%-8.3%8.3%

Arnott & Arnott & RyanRyan

4.14.1 --0.90.9

3.23.2 2.2.00

3.13.1 0.40.466

3.83.8 5.0%5.0%

Ibbotson Ibbotson & Chen& Chen

2.02.055

6.06.0 8.08.055

0.0.00

3.13.1 0.00.0 3.83.8 7.35%7.35%

Ibbotson & Chen Ibbotson & Chen (2003)(2003)

Forecast ModelsForecast Models Reconciliation of Earnings and Reconciliation of Earnings and

Dividends Forecast ModelsDividends Forecast Models– Current div yld lower than historical Current div yld lower than historical – Historical dividend growth lower Historical dividend growth lower

than historical earnings growththan historical earnings growth– Current high P/E: expectation of Current high P/E: expectation of

higher earnings growth in futurehigher earnings growth in future– Use Earnings Forecast and adjust Use Earnings Forecast and adjust

Dividends Forecast upwardsDividends Forecast upwards

The Next 10 YearsThe Next 10 Years Social Security (1999, 2001)Social Security (1999, 2001)

– Lower return over next 10 yearsLower return over next 10 years– Remainder of 75 years likely to be similar to historical Remainder of 75 years likely to be similar to historical

returnsreturns Campbell and Shiller (2001) Campbell and Shiller (2001)

– Current P/E and Div/P ratios far from meanCurrent P/E and Div/P ratios far from mean– With mean reversion assumption, pessimistic forecast for With mean reversion assumption, pessimistic forecast for

next ten yearsnext ten years Market decrease 1999-2002 is -37.6% or Market decrease 1999-2002 is -37.6% or

-14.4% annual; but increase 2003-2004 is + 42.7% or -14.4% annual; but increase 2003-2004 is + 42.7% or +19.5% annual+19.5% annual

Wilson & Jones DataWilson & Jones Data1871-20021871-2002

Cumulative ERP over 30 Year Periods

0.00%

2.00%

4.00%

6.00%

8.00%

10.00%

12.00%

14.00%

16.00%

30 Year Time Periods

Arith

met

ic E

RP

Pre-Income Tax

3.89% Average

Post- Income Tax

7.36% Average

Transition Moving Averages

5.30% Average

Wilson & Jones DataWilson & Jones Data1871-20021871-2002

Similar Results as Ibbotson Similar Results as Ibbotson SeriesSeries

Neither 1871-1925 period nor Neither 1871-1925 period nor 1926-2002 period’s ERP 1926-2002 period’s ERP significantly different from significantly different from ERP of 1871-2002 periodERP of 1871-2002 period

No trends over timeNo trends over time

Wilson & Jones DataWilson & Jones Data1871-1912 vs. 1926-20021871-1912 vs. 1926-2002

Comparison of Short ERPs

0.00%

1.00%

2.00%

3.00%

4.00%

5.00%

6.00%

7.00%

8.00%

1871-1912 1926-2002

Time Period

Perc

ent

3.9%

7.5%

Income Tax LoadingMarginal

Rate 31% ?

Goyal-Welch Study 2005Goyal-Welch Study 2005 Empirical Prediction Empirical Prediction Performance Performance * Data US market 1872-2003* Data US market 1872-2003 * Tests out-of-sample prediction of ERP* Tests out-of-sample prediction of ERP * Tests next month, year, 5-years* Tests next month, year, 5-years * Tests predictors: D/P, DY, E/P, B/M,* Tests predictors: D/P, DY, E/P, B/M, interest rates, consumption variablesinterest rates, consumption variables * Finds no one (or all) predicts out-of-* Finds no one (or all) predicts out-of-

samplesample better than historical realized meanbetter than historical realized mean

What You Need To Know What You Need To Know About ERP EstimatesAbout ERP Estimates

Types of estimates – Appendix BTypes of estimates – Appendix B Range of estimates – Appendix CRange of estimates – Appendix C Data and terminologyData and terminology Underlying assumptions Underlying assumptions Your independent analysis is Your independent analysis is

required if estimate differs from required if estimate differs from historical averagehistorical average

Selecting an ERPSelecting an ERP

Rely on past data to forecast the Rely on past data to forecast the futurefuture

OROR Analyze the past and apply Analyze the past and apply

informed judgment as to future informed judgment as to future differencesdifferences

Where to Go From HereWhere to Go From Here

Ibbotson and Chen (2003)Ibbotson and Chen (2003)– Appendix DAppendix D– Fundamental components of the Fundamental components of the

historical ERPhistorical ERP– Change estimates based upon good Change estimates based upon good

judgmentjudgment The puzzle is not yet solved, but The puzzle is not yet solved, but

better models seem to be needed.better models seem to be needed.

Mehra (2002)Mehra (2002) ““Before we dismiss the premium, we not Before we dismiss the premium, we not

only need to have an understanding of only need to have an understanding of the observed phenomena but also why the observed phenomena but also why the future is likely to be different. In the the future is likely to be different. In the absence of this, we can make the absence of this, we can make the following claim based on what we know. following claim based on what we know. Over the long horizon the equity Over the long horizon the equity premium is likely to be similar to what it premium is likely to be similar to what it has been in the past and the returns to has been in the past and the returns to investment in equity will continue to investment in equity will continue to substantially dominate those in bonds substantially dominate those in bonds for investors with a long planning for investors with a long planning horizon.”horizon.”