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

SmallSmall

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

Bowles SymposiumBowles Symposium

April 2003April 2003

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

US Equity Risk Premia US Equity Risk Premia S&P 500 1926-2002S&P 500 1926-2002

HorizoHorizonn

Equity Equity ReturnReturn

ss

Risk-Risk-Free Free

ReturnReturn

ERPERP

ShortShort 12.20%12.20% 3.83%3.83% 8.37%8.37%

InterInter 12.20%12.20% 4.81%4.81% 7.40%7.40%

LongLong 12.20%12.20% 5.23%5.23% 6.97%6.97%

Source: Ibbotson Yearbook (2002) and December 2002 Market Report

Why the ERP is Important Why the ERP is Important for Actuaries ?for Actuaries ?

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

Paper ObjectivesPaper Objectives

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 ERPSelection of an ERP SummarySummary

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” range level outside of “reasonable” range

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

Literature to Solve the Literature to Solve the PuzzlePuzzle

11stst thread (Behavioral Finance) thread (Behavioral Finance)– New models and assumptions to New models and assumptions to

explain historical dataexplain historical data

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

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

2002)2002)Investment Investment

HorizonHorizonType of Type of AverageAverage

ERP ERP Historical Historical

ReturnReturn

ShortShort 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 (2002) and December 2002 Market

Report

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

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 IIIIII

1802-1802-18701870

1871-1871-19251925

1926-1926-19921992

Stock Stock ReturnsReturns

7.0%7.0% 6.6%6.6% 6.6%6.6%

Short-Short-term term Gov’tsGov’ts

5.1%5.1% 3.2%3.2% 0.5%0.5%

ERPERP 1.9%1.9% 2.8%2.8% 6.1%6.1%Source: Siegel (1994)

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)

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

The Next 10 YearsThe Next 10 Years

Social SecuritySocial Security– Lower return over next 10 yearsLower return over next 10 years– Remainder of 75 years likely to be similar Remainder of 75 years likely to be similar

to historical returnsto historical returns Campbell and ShillerCampbell and Shiller

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

forecast for next ten yearsforecast for next ten years Market decrease since 1999 is -37.6% Market decrease since 1999 is -37.6%

or or -14.6% annual-14.6% annual

TIPSTIPSInflation-Indexed Treasury Inflation-Indexed Treasury

SecuritiesSecurities

MaturitMaturityy

Coupon Issue Coupon Issue RateRate

Yield to Yield to MaturityMaturity

1/111/11 3.5003.500 1.7631.763

1/121/12 3.3753.375 1.8311.831

7/127/12 3.0003.000 1.8781.878

4/284/28 3.6253.625 2.4982.498

4/294/29 3.8753.875 2.4902.490

4/324/32 3.3753.375 2.4082.408

Source: WSJ 2/24/2003

Behavioral FinanceBehavioral Finance

Benartzi and Thaler (1995)Benartzi and Thaler (1995) Start with prospect theoryStart with prospect theory

– Loss AversionLoss Aversion Add “mental accounting”Add “mental accounting”

– Myopic Loss AversionMyopic Loss Aversion

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

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

Range of estimates Range of estimates – Appendix BAppendix B

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

Where to Go From HereWhere to Go From Here

Ibbotson and Chen (2003)Ibbotson and Chen (2003)– Appendix CAppendix C– 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…The puzzle is not yet solved…