Equity Risk Premium: Expectations Great and Small

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Equity Risk Premium Expectations Great and Small

• Richard A. Derrig and Elisha D. Orr
• Bowles Symposium
• April 2003

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Equity Risk Premium (ERP)

• Definition
• Difference between the market return
• and a risk-free return

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US Equity Risk Premia SP 500 1926-2002
Horizon Equity Returns Risk-Free 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
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Why the ERP is Important for Actuaries ?

• Universally accepted benchmark for pricing risk
• Input into simple CAPM and Fama-French 3-factor
  model
• Affects other cost of capital estimates and
  discount rates
• Market value of liabilities

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Paper Objectives

• Introduction to the ERP Puzzle
• Types of ERP
• Time Series Analysis
• Catalogue ERP Puzzle Literature
• Selection of an ERP
• Summary

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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
• Led to literature to solve the ERP puzzle

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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

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ERP Types

• 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

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ERP using same historical data (1926-2002)
Investment Horizon Type of Average ERP Historical Return
Short Arithmetic 8.4
Short Geometric 6.4
Inter Arithmetic 7.4
Inter Geometric 5.4
Long Arithmetic 7.0
Long Geometric 5.0
Source Ibbotson Yearbook (2002) and December
2002 Market Report
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Converting from Geometric to Arithmetic Returns

• Formula
• AR GR var/2,
• var, variance of the return process

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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

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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

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Short-Horizon ERP bySub-periods
I II III
1802-1870 1871-1925 1926-1992
Stock Returns 7.0 6.6 6.6
Short-term Govts 5.1 3.2 0.5
ERP 1.9 2.8 6.1
Source Siegel (1994)
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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)

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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

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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
• Market decrease since 1999 is -37.6 or
• -14.6 annual

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TIPSInflation-Indexed Treasury Securities
Maturity Coupon Issue Rate Yield to Maturity
1/11 3.500 1.763
1/12 3.375 1.831
7/12 3.000 1.878
4/28 3.625 2.498
4/29 3.875 2.490
4/32 3.375 2.408
Source WSJ 2/24/2003
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Behavioral Finance

• Benartzi and Thaler (1995)
• Start with prospect theory
• Loss Aversion
• Add mental accounting
• Myopic Loss Aversion

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Selecting an ERP

• Rely on past data to forecast the future
• OR
• Analyze the past and apply informed judgment as
  to future differences

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What You Need To Know About ERP Estimates

• Range of estimates
• Appendix B
• Data and terminology
• Underlying assumptions
• Your independent analysis is required if estimate
  differs from historical average

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Where to Go From Here

• Ibbotson and Chen (2003)
• Appendix C
• Fundamental components of the historical ERP
• Change estimates based upon good judgment
• The puzzle is not yet solved