Equity Risk Premium:
Expectations Great and Small
Richard A. Derrig and Elisha D. Orr
Bowles Symposium
April 2003
Equity Risk Premium (ERP)

Definition:
Difference between the market return
and a risk-free return
US Equity Risk Premia
S&P 500 1926-2002
Horizon
Equity Risk-Free
Returns
Return
ERP
Short
12.20%
3.83%
8.37%
Inter
12.20%
4.81%
7.40%
Long
12.20%
5.23%
6.97%
Source: Ibbotson Yearbook (2002) and December 2002 Market Report
Why the ERP is Important
for Actuaries ?
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Universally accepted benchmark for
pricing risk
Input into simple CAPM and FamaFrench 3-factor model
Affects other cost of capital estimates
and discount rates
Market value of liabilities
Paper Objectives

Introduction to the ERP Puzzle
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Types of ERP
Time Series Analysis
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Catalogue ERP Puzzle Literature
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Selection of an ERP
Summary
ERP Puzzle
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Mehra and Prescott (1985):
– Anomalous results when historical
realized ERP compared to asset pricing
theory values
– Otherwise, must assume risk aversion
level outside of “reasonable” range

Led to literature to solve the “ERP
puzzle”
Literature to Solve the Puzzle

1st thread (Behavioral Finance)
– New models and assumptions to explain
historical data

2nd thread
– Estimates of the ERP from standard
economic models
– Catalogue in Appendix B
ERP Types
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Geometric vs. arithmetic
Short vs. long investment horizon
Short vs. long run expectation
Unconditional vs. conditional
US vs. international market data
Data sources and periods
Real vs. nominal returns
ERP using same historical
data (1926-2002)
Investment
Horizon
Short
Short
Inter
Inter
Type of
Average
Arithmetic
Geometric
Arithmetic
Geometric
ERP Historical
Return
8.4%
6.4%
7.4%
5.4%
Long
Arithmetic
7.0%
Long
Geometric
5.0%
Source: Ibbotson Yearbook (2002) and December 2002 Market Report
Converting from Geometric to
Arithmetic Returns

Formula:
AR = GR + var/2,
var, variance of the return process
Time Series Analysis

Stationarity Assumption
– Supported by ANOVA regressions
– ARIMA model projects future years as
average of data
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No significant time trends
Mean of full Ibbotson series and
subset (1960+) not statistically
different
Why Different Estimates ?
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Historical
– 1926-2002
– 1802-2001 (Earlier period)
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Dividend Growth Model
– Next Ten Years + Remainder of 75 Years
– Historical ≠ Expected
– Conditional versus Unconditional
expectations
Short-Horizon ERP by
Sub-periods
Stock
Returns
Short-term
Gov’ts
ERP
I
18021870
7.0%
II
18711925
6.6%
III
19261992
6.6%
5.1%
3.2%
0.5%
1.9%
2.8%
6.1%
Source: Siegel (1994)
Catalogue of ERP Estimates
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Social Security (1999, 2001)
Puzzle Research
– Campbell and Shiller (2001)
– Arnott and Ryan (2001), Arnott and
Bernstein (2002)
– Fama and French (2002)
– Ibbotson and Chen (2003)
– Constantinides (2002)
Catalogue of ERP Estimates
(Cont.)
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Financial Analyst Estimates
– Claus and Thomas (2001)
– Harris and Marston (2001)
Surveys
– CFOs, Graham and Harvey (2002)
– Financial economists, Welch (2000 &
2001)
Behavioral Approach
The Next 10 Years

Social Security
– Lower return over next 10 years
– Remainder of 75 years likely to be similar to
historical returns

Campbell and Shiller
– Current P/E and Div/P ratios far from mean
– With mean reversion assumption, dismal
forecast for next ten years
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Market decrease since 1999 is -37.6% or
-14.6% annual
TIPS
Inflation-Indexed Treasury
Securities
Maturity
Coupon Issue
Rate
Yield to Maturity
1/11
1/12
7/12
4/28
4/29
4/32
3.500
3.375
3.000
3.625
3.875
3.375
1.763
1.831
1.878
2.498
2.490
2.408
Source: WSJ 2/24/2003
Behavioral Finance
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Benartzi and Thaler (1995)
Start with prospect theory
– Loss Aversion
Add “mental accounting”
– Myopic Loss Aversion
Selecting an ERP
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Rely on past data to forecast the
future
OR
Analyze the past and apply informed
judgment as to future differences
What You Need To Know About
ERP Estimates
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Range of estimates
– Appendix B
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Data and terminology
Underlying assumptions
Your independent analysis is required
if estimate differs from historical
average
Where to Go From Here

Ibbotson and Chen (2003)
– Appendix C
– Fundamental components of the historical
ERP
– Change estimates based upon good
judgment
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The puzzle is not yet solved…