1. Equity Risk Premium: Expectations Great and Small Richard A. Derrig and Elisha D. Orr Bowles Symposium April 2003

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

3. US Equity Risk Premia S&P 500 1926-2002 Horizon Equity Returns Risk-Free Return ERP Short12.20%3.83%8.37% Inter12.20%4.81%7.40% Long12.20%5.23%6.97% Source: Ibbotson Yearbook (2002) and December 2002 Market Report

4. Why the ERP is Important for Actuaries ? Universally accepted benchmark for pricing risk Universally accepted benchmark for pricing risk Input into simple CAPM and Fama- French 3-factor model Input into simple CAPM and Fama- French 3-factor model Affects other cost of capital estimates and discount rates Affects other cost of capital estimates and discount rates Market value of liabilities Market value of liabilities

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

6. ERP Puzzle Mehra and Prescott (1985): 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” Led to literature to solve the “ERP puzzle”

7. Literature to Solve the Puzzle 1 st thread (Behavioral Finance) 1 st thread (Behavioral Finance) –New models and assumptions to explain historical data 2 nd thread 2 nd thread –Estimates of the ERP from standard economic models –Catalogue in Appendix B

8. ERP Types Geometric vs. arithmetic Geometric vs. arithmetic Short vs. long investment horizon Short vs. long investment horizon Short vs. long run expectation Short vs. long run expectation Unconditional vs. conditional Unconditional vs. conditional US vs. international market data US vs. international market data Data sources and periods Data sources and periods Real vs. nominal returns Real vs. nominal returns

9. ERP using same historical data (1926-2002) Investment Horizon Type of Average ERP Historical Return ShortArithmetic8.4% ShortGeometric6.4% InterArithmetic7.4% InterGeometric5.4% LongArithmetic7.0% LongGeometric5.0% Source: Ibbotson Yearbook (2002) and December 2002 Market Report

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

11. Time Series Analysis Stationarity Assumption Stationarity Assumption –Supported by ANOVA regressions –ARIMA model projects future years as average of data No significant time trends No significant time trends Mean of full Ibbotson series and subset (1960+) not statistically different Mean of full Ibbotson series and subset (1960+) not statistically different

12. Why Different Estimates ? Historical Historical –1926-2002 –1802-2001 (Earlier period) Dividend Growth Model Dividend Growth Model –Next Ten Years + Remainder of 75 Years –Historical ≠ Expected –Conditional versus Unconditional expectations

13. Short-Horizon ERP by Sub-periods IIIIII 1802- 1870 1871- 1925 1926- 1992 Stock Returns 7.0%6.6%6.6% Short-term Gov’ts 5.1%3.2%0.5% ERP1.9%2.8%6.1% Source: Siegel (1994)

14. Catalogue of ERP Estimates Social Security (1999, 2001) Social Security (1999, 2001) Puzzle Research Puzzle Research –Campbell and Shiller (2001) –Arnott and Ryan (2001), Arnott and Bernstein (2002) –Fama and French (2002) –Ibbotson and Chen (2003) –Constantinides (2002)

15. Catalogue of ERP Estimates (Cont.) Financial Analyst Estimates Financial Analyst Estimates –Claus and Thomas (2001) –Harris and Marston (2001) Surveys Surveys –CFOs, Graham and Harvey (2002) –Financial economists, Welch (2000 & 2001) Behavioral Approach Behavioral Approach

16. The Next 10 Years Social Security Social Security –Lower return over next 10 years –Remainder of 75 years likely to be similar to historical returns Campbell and Shiller 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 Market decrease since 1999 is -37.6% or -14.6% annual

17. TIPS Inflation-Indexed Treasury Securities Maturity Coupon Issue Rate Yield to Maturity 1/113.5001.763 1/123.3751.831 7/123.0001.878 4/283.6252.498 4/293.8752.490 4/323.3752.408 Source: WSJ 2/24/2003

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

19. Selecting an ERP Rely on past data to forecast the future Rely on past data to forecast the futureOR Analyze the past and apply informed judgment as to future differences Analyze the past and apply informed judgment as to future differences

20. What You Need To Know About ERP Estimates Range of estimates Range of estimates –Appendix B Data and terminology Data and terminology Underlying assumptions Underlying assumptions Your independent analysis is required if estimate differs from historical average Your independent analysis is required if estimate differs from historical average

21. Where to Go From Here Ibbotson and Chen (2003) Ibbotson and Chen (2003) –Appendix C –Fundamental components of the historical ERP –Change estimates based upon good judgment The puzzle is not yet solved… The puzzle is not yet solved…