1. Equity Risk Premium: Expectations Great and Small Richard A. Derrig and Elisha D. Orr North American Actuarial Journal V8 N1 pp 45-69 2004

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

3. Why the ERP is Important for Insurers ? 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 Insurers’ asset allocations Insurers’ asset allocations

4. Objectives of Paper 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 (-0.9 to 9.0%) Selection of an ERP (-0.9 to 9.0%)

5. 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 –Either realized returns are biased (high) or asset pricing models are mispecified Led to literature to solve the “ERP puzzle” Led to literature to solve the “ERP puzzle”

6. US Equity Risk Premia S&P 500 1926-2004 Horizon Equity Returns Risk-Free Return ERP Short12.39%3.76%8.63% Inter12.39%4.76%7.63% Long12.39%5.23%7.17% Source: Ibbotson Yearbook (2005)

7. 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

8. 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 (2003)

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

10. Short-Horizon ERP

11. ANOVA Regressions ERP on Time Period Time Coefficient P-Value 1926-19590.0040.355 1960-20020.0010.749 1926-20020.0010.443

12. T-Test Under the Null Hypothesis: ERP (1960-2002)= ERP (1926-2002)=8.17% Sample mean 1960-2002 5.27% Sample s.d. 1960-2002 15.83% T value (DF=42) -1.20 PR > |T| 0.2376 Confidence interval 95% (0.0040, 0.1014) Confidence interval 90% (0.0121, 0.0933)

13. 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

14. 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

15. Short-Horizon ERP by Sub-periods IIIIII 1802- 1870 1871- 1925 1926- 2001 Real Geom Stock Returns 7.0%6.6%6.9% Real Long- term Gov’ts 4.8%3.7%2.2% ERP2.2%2.9%4.7% Source: Siegel (2002)

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

17. Areas of ERP Research Social Security Puzzle Research Financial Analysts Estimates Surveys Behavioral Approach

18. Areas of ERP Research Social Security OCACT3 Experts Puzzle Research Campbell & Shiller Arnott & Ryan Arnott & Bernstein Fama & FrenchIbbotson & ChenConstantinidesMehra Financial Analysts Estimates Surveys Behavioral Approach

19. 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) –Mehra (2002)

20. Areas of ERP Research Social Security Puzzle Research Financial Analysts Estimates Claus & ThomasHarris & Marston Surveys Graham & Harvey Welch Behavioral Approach Benartzi & Thaler

21. 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

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

23. Classification of ERP Types Appendix B RNGALHSHSELECU Ibbotson (Hist) XXXXX DiamondXXXXX Arnott & Ryan XXXXX Fama & French XXXXX Ivo Welch XXXXX Sample:

24. Adjusting ERP Estimates Approximations shown in Appendix C Approximations shown in Appendix C Add RFR & ERP provided by source (stock return estimate) Add RFR & ERP provided by source (stock return estimate) Convert from geom to arith (hist diff) Convert from geom to arith (hist diff) Convert from real to nominal (hist diff) Convert from real to nominal (hist diff) Conditional to unconditional (est from FF) Conditional to unconditional (est from FF) Remove historical short-horizon RFR Remove historical short-horizon RFR Short-horizon arithmetic unconditional ERP estimate for each source Short-horizon arithmetic unconditional ERP estimate for each source

25. Adjusting ERP Estimates: Short-Horizon Arithmetic Unconditional ERP Estimate RFRERP Stock Ret G to A R to N C to U Short -hor RFR Estimate Diamond3.0 3.0- 3.5 6.0- 6.5 2.03.10.463.8 7.8%- 8.3% Arnott & Ryan 4.1-0.93.22.03.10.463.85.0% Ibbotson & Chen 2.056.08.050.03.10.03.87.35%

26. Ibbotson & Chen (2003) Forecast Models Reconciliation of Earnings and Dividends 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

27. The Next 10 Years Social Security (1999, 2001) Social Security (1999, 2001) –Lower return over next 10 years –Remainder of 75 years likely to be similar to historical returns Campbell and Shiller (2001) Campbell and Shiller (2001) –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 Market decrease 1999-2002 is -37.6% or -14.4% annual; but increase 2003-2004 is + 42.7% or +19.5% annual +19.5% annual

28. Wilson & Jones Data 1871-2002

29. Similar Results as Ibbotson Series Neither 1871-1925 period nor 1926-2002 period’s ERP significantly different from ERP of 1871-2002 period Neither 1871-1925 period nor 1926-2002 period’s ERP significantly different from ERP of 1871-2002 period No trends over time No trends over time

30. Wilson & Jones Data 1871-1912 vs. 1926-2002

31. Goyal-Welch Study 2005 Empirical Prediction Performance * Data US market 1872-2003 * Data US market 1872-2003 * Tests out-of-sample prediction of ERP * Tests out-of-sample prediction of ERP * Tests next month, year, 5-years * Tests next month, year, 5-years * Tests predictors: D/P, DY, E/P, B/M, * Tests predictors: D/P, DY, E/P, B/M, interest rates, consumption variables interest rates, consumption variables * Finds no one (or all) predicts out-of-sample * Finds no one (or all) predicts out-of-sample better than historical realized mean better than historical realized mean

32. What You Need To Know About ERP Estimates Types of estimates – Appendix B Types of estimates – Appendix B Range of estimates – Appendix C Range of estimates – Appendix C 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

33. 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

34. Where to Go From Here Ibbotson and Chen (2003) 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. The puzzle is not yet solved, but better models seem to be needed.

35. 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.” “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.”