Equity Risk Premium: Expectations Great and Small

1. 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

2. Equity Risk Premium (ERP) • Definition: Difference between the market return and a risk-free return

3. US Equity Risk Premia S&P 500 1926-2002 Source: Ibbotson Yearbook (2003)

4. 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 • Insurers’ asset allocations

5. 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”

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

7. 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

8. ERP using same historical data (1926-2002) Source: Ibbotson Yearbook (2003)

9. Converting from Geometric to Arithmetic Returns • Formula: AR = GR + var/2, var, variance of the return process

10. Short-Horizon ERP

11. ANOVA Regressions ERP on Time

12. T-Test Under the Null Hypothesis:ERP (1960-2002)=ERP (1926-2002)=8.17%

13. 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

14. 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

15. Short-Horizon ERP bySub-periods Source: Siegel (2002)

16. 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

17. 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)

18. 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

19. Behavioral Finance • Benartzi and Thaler (1995) • Start with prospect theory • Asymmetric Loss Aversion • Add “mental accounting” • Myopic Loss Aversion

20. Classification of ERP TypesAppendix B Sample:

21. Adjusting ERP Estimates • 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

22. Adjusting ERP Estimates:Short-Horizon Arithmetic Unconditional ERP Estimate

23. 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

24. 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

25. TIPSInflation-Indexed Treasury Securities Source: WSJ

26. Selecting an ERP • Rely on past data to forecast the future OR • Analyze the past and apply informed judgment as to future differences

27. Wilson & Jones Data1871-2002 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

28. Wilson & Jones Data1871-1912 vs. 1926-2002

29. What You Need To Know About ERP Estimates • 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

30. 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.

31. 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.”