Equity Risk Premium:
Expectations Great and Small
Richard A. Derrig and Elisha D. Orr
CAS Seminar on Ratemaking
March 11-12, 2004
http://www.casact.org/pubs/forum/04wforum/04wf001.pdf
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
Short
12.20%
3.83%
8.37%
Inter
12.20%
4.81%
7.40%
Long
12.20%
5.23%
6.97%
Source: Ibbotson Yearbook (2003)
ERP
Why the ERP is Important
for Actuaries ?





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
Insurers’ asset allocations
ERP Puzzle

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
– Either realized returns are biased (high)
or asset pricing models are mispecified

Led to literature to solve the “ERP
puzzle”
Objectives of Paper

Introduction to the ERP Puzzle

Types of ERP
Time Series Analysis

Catalogue ERP Puzzle Literature



Selection of an ERP
Summary
ERP Types



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
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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 (2003)
Converting from Geometric to
Arithmetic Returns

Formula:
AR = GR + var/2,
var, variance of the return process
Short-Horizon ERP
Short-Horizon Equity Risk Premium
60%
Long-term Mean =8.17%
40%
20%
0%
-20%
-40%
Mean 1926 to 1959 = 11.82%
Mean 1960 to 2002 = 5.27%
-60%
1920
1930
1940
1950
1960
1970
1980
1990
2000
2010
Year
Actual ERP
Long-term Mean
Mean pre-1960
Source: Ibbotson Yearbook (2003), Geometric Differences
Figure 1
Mean 1960+
ANOVA Regressions
ERP on Time
Period
P-Value
1926-1959
Time
Coefficient
0.004
1960-2002
0.001
0.749
1926-2002
0.001
0.443
0.355
T-Test Under the Null Hypothesis:
ERP (1960-2002)=
ERP (1926-2002)=8.17%
Sample mean 1960-2002
Sample s.d. 1960-2002
T value (DF=42)
PR > |T|
5.27%
15.83%
-1.20
0.2376
Confidence interval 95%
(0.0040, 0.1014)
Confidence interval 90%
(0.0121, 0.0933)
Time Series Analysis

Stationarity Assumption
– Supported by ANOVA regressions
– ARIMA model projects future years as
average of data


No significant time trends
Mean of full Ibbotson series and
subset (1960+) not statistically
different
Why Different Estimates ?

Historical
– 1926-2002
– 1802-2001 (Earlier period)

Dividend Growth Model
– Next Ten Years + Remainder of 75 Years
– Historical ≠ Expected
– Conditional versus Unconditional
expectations
Short-Horizon ERP by
Sub-periods
Real Geom
Stock
Returns
Real Longterm Gov’ts
ERP
I
II
III
18021870
18711925
19262001
7.0%
6.6%
6.9%
4.8%
3.7%
2.2%
2.2%
2.9%
4.7%
Source: Siegel (2002)
Literature to Solve the Puzzle

1st thread
– New models and assumptions to explain
historical data
– Includes Behavioral Finance

2nd thread
– Estimates of the ERP from standard economic
models
– Catalogue in Appendix B
Catalogue of ERP Estimates


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)
– Mehra (2002)
Catalogue of ERP Estimates
(Cont.)



Financial Analyst Estimates
– Claus and Thomas (2001)
– Harris and Marston (2001)
Surveys
– CFOs, Graham and Harvey (2002)
– Financial economists, Welch (2000 &
2001)
Behavioral Approach
Behavioral Finance



Benartzi and Thaler (1995)
Start with prospect theory
– Asymmetric Loss Aversion
Add “mental accounting”
– Myopic Loss Aversion
Classification of ERP Types
Appendix B
Sample:
R N G A LH SH SE LE C U
Ibbotson (Hist)
X
X
X
X
Diamond
X
X
X
X X
Arnott & Ryan
X
X
X
X X
Fama & French X
Ivo Welch
X
X
X
X
X
X
X X
X
X
Adjusting ERP Estimates



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Approximations shown in Appendix C
Add RFR & ERP provided by source (stock
return estimate)
Convert from geom to arith (hist diff)
Convert from real to nominal (hist diff)
Conditional to unconditional (est from FF)
Remove historical short-horizon RFR
Short-horizon arithmetic unconditional ERP
estimate for each source
Adjusting ERP Estimates:
Short-Horizon Arithmetic
Unconditional ERP Estimate
RFR
ERP Stock G
Ret to
A
R to C to Short Estimate
N
U
-hor
RFR
Diamond
3.0 3.0- 6.0- 2.0 3.1 0.46 3.8
3.5 6.5
7.8%8.3%
Arnott &
Ryan
4.1 -0.9 3.2 2.0 3.1 0.46 3.8
5.0%
2.05 6.0 8.05 0.0 3.1 0.0
7.35%
Ibbotson
& Chen
3.8
Ibbotson & Chen (2003)
Forecast Models

Reconciliation of Earnings and
Dividends Forecast Models
– Current div yld lower than historical
– Historical dividend growth lower than
historical earnings growth
– Current high P/E: expectation of higher
earnings growth in future
– Use Earnings Forecast and adjust
Dividends Forecast upwards
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, pessimistic
forecast for next ten years

Market decrease 1999-2002 is -37.6% or
-14.6% annual
TIPS
Inflation-Indexed Treasury
Securities
Maturity
1/11
1/12
7/12
4/28
4/29
4/32
Coupon
Issue Rate
Yield to Maturity
2/24/2003
11/3/2003
3.500
3.375
3.000
3.625
3.875
3.375
1.763
1.831
1.878
2.498
2.490
2.408
1.734
1.847
1.889
2.482
2.480
2.381
Source: WSJ
Selecting an ERP


Rely on past data to forecast the
future
OR
Analyze the past and apply informed
judgment as to future differences
Wilson & Jones Data
1871-2002
Similar Results as Ibbotson Series
Neither 1871-1925 period nor
1926-2002 period’s ERP
significantly different from ERP of
1871-2002 period
 No trends over time

Wilson & Jones Data
1871-1912 vs. 1926-2002
Comparison of Short ERPs
8.00%
7.5%
7.00%
Income Tax
Loading
Marginal
Rate 31% ?
6.00%
Percent
5.00%
4.00%
3.9%
3.00%
2.00%
1.00%
0.00%
1871-1912
1926-2002
Time Period
What You Need To Know About
ERP Estimates
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Types of estimates – Appendix B
Range of estimates – Appendix C
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 D
– Fundamental components of the historical
ERP
– Change estimates based upon good
judgment

The puzzle is not yet solved, but
better models seem to be needed.
Mehra (2002)

“Before we dismiss the premium, we not
only need to have an understanding of the
observed phenomena but also why the
future is likely to be different. In the
absence of this, we can make the following
claim based on what we know. Over the
long horizon the equity premium is likely to
be similar to what it has been in the past
and the returns to investment in equity will
continue to substantially dominate those in
bonds for investors with a long planning
horizon.”