Western Finance Association Meetings Park City, Utah June 2002 Expectations of Equity Risk Premia, Volatility, and Asymmetry: From a Corporate Finance Perspective John R. Graham Duke University, Durham, NC USA http://www.duke.edu/~jgraham Campbell R. Harvey Duke University, Durham, NC USA National Bureau of Economic Research, Cambridge, MA USA http://www.duke.edu/~charvey 1 Graham/Harvey: Expectations of Risk Premia Measuring CFO Market Expectations • Survey CFOs every quarter • Q2 2000 through Q2 2002 (nine quarters) • ~200 responses per quarter (1,900+ total obs.) • Why CFOs? – We know they use CAPM from previous surveys – Hence, they have thought hard about risk premium – Should not be biased the way that analyst forecasts might be 2 Graham/Harvey: Expectations of Risk Premia Across Time and Different Horizons • Ten-year risk premium around 3.5% and stable whereas one-year risk premium quite variable 5 5 4 4 3 3 2 2 1 1 0 0 6-Jun-00 10-Sep-01 7-Sep-00 4-Dec-01 4-Dec-00 11-Mar-02 12-Mar-01 4-Jun-02 10-year premium 7-Jun-01 6-Jun-00 10-Sep-01 7-Sep-00 4-Dec-01 4-Dec-00 11-Mar-02 12-Mar-01 4-Jun-02 7-Jun-01 1-year premium 3 Graham/Harvey: Expectations of Risk Premia Across Respondents at a Point in Time Proportion 0.40 10-year premium September 10, 2001 0.35 0.30 0.25 0.20 0.15 0.10 0.05 20 18 16 14 12 10 8 6 4 2 0 -2 -4 -6 -8 -1 0 -1 2 -1 6 -1 4 -1 8 m or e < -2 0 0.00 4 Graham/Harvey: Expectations of Risk Premia Across Respondents at a Point in Time Proportion 0.40 1-year premium September 10, 2001 0.35 0.30 0.25 0.20 0.15 0.10 0.05 18 16 14 12 10 8 6 4 2 0 -2 -4 -6 -8 -1 0 -1 2 -1 6 -1 4 -1 8 20 m or e < -2 0 0.00 5 Graham/Harvey: Expectations of Risk Premia Past Returns and Expected Premia • One-year risk premium sensitive to past returns 5 One-year premium y = 0.1298x + 3.0165 R2 = 0.5377 4 3 2 1 0 -20 -15 -10 -5 0 5 10 15 Past quarters' return 6 Graham/Harvey: Expectations of Risk Premia Past Returns and Expected Premia • 10-year risk premium not sensitive Ten-year premium 5 4 3 2 y = -0.0008x + 3.9002 R2 = 0.0001 1 0 -20 -15 -10 -5 0 5 10 15 Past quarters' return 7 Graham/Harvey: Expectations of Risk Premia Measuring Volatility 8 Graham/Harvey: Expectations of Risk Premia Measuring Volatility • Able to deduce each respondent’s probability distribution • Market volatility is average of individual volatilities (average volatility) + dispersion of risk premium forecasts (disagreement) • We consider both components 9 Graham/Harvey: Expectations of Risk Premia Past Returns Impact Expected Volatility • Average one-year volatility not related to past quarter’s returns 8 Average volatility 7 6 5 y = 0.0214x + 6.5153 R2 = 0.0373 4 3 2 -20 -15 -10 -5 0 5 10 15 Past quarter's return 10 Graham/Harvey: Expectations of Risk Premia Past Returns Impact Expected Volatility • Average one-year volatility not related to past month’s returns 8 Average volatility 7 6 5 y = -0.0215x + 6.4125 R2 = 0.0158 4 3 2 -15 -10 -5 0 5 10 Past month's return 11 Graham/Harvey: Expectations of Risk Premia Past Returns Impact Expected Volatility Disagreement volatility • One-year disagreement volatility not linearly related to past quarter’s returns 8 y = -0.0342x + 3.9939 R2 = 0.0773 7 6 5 4 3 2 -20 -15 -10 -5 0 5 10 15 Past quarter's return 12 Graham/Harvey: Expectations of Risk Premia Past Returns Impact Expected Volatility • Maybe non-linear – but too little data Disagreement volatility 2 8 + 0.0727x + 3.2025 y = 0.015x 2 = 0.8158 R 7 6 5 4 3 2 -20 -15 -10 -5 0 5 10 15 Past quarter's return 13 Graham/Harvey: Expectations of Risk Premia Past Returns Impact Expected Volatility • One-year disagreement volatility negatively related to past month’s returns 8 Disagreement volatility y = -0.1105x + 3.9944 7 R2 = 0.3377 6 5 4 3 2 -15 -10 -5 0 5 10 Past month's return 14 Graham/Harvey: Expectations of Risk Premia Past Returns Impact Expected Volatility Disagreement volatility • Ten-year disagreement weakly negatively related to past returns 3 3 2 2 y = -0.013x + 2.2725 R2 = 0.1152 1 1 0 -20 -15 -10 -5 0 5 10 15 Past quarter's return 15 Graham/Harvey: Expectations of Risk Premia Past Returns Impact Expected Volatility Disagreement volatility • Ten-year disagreement negatively related to past month’s returns 3 3 2 2 y = -0.0244x + 2.2925 R2 = 0.1701 1 1 0 -15 -10 -5 0 5 10 Past month's return 16 Graham/Harvey: Expectations of Risk Premia Past Returns Impact Expected Skewness Average asymmetry • One-year average skewness weakly positively related to past quarter’s returns 3 y = 0.0395x - 2.0587 R2 = 0.0792 2 1 0 -20 -15 -10 -5 -1 0 5 10 15 -2 -3 -4 -5 Past quarter's return 17 Graham/Harvey: Expectations of Risk Premia Past Returns Impact Expected Skewness Average asymmetry • One-year average skewness weakly positively related to past month’s returns 3 y = 0.0782x - 2.1149 R2 = 0.1301 2 1 0 -15 -10 -5 -1 0 5 10 -2 -3 -4 -5 Past month's return 18 Graham/Harvey: Expectations of Risk Premia Past Returns Impact Expected Skewness Disagreement asymmetry • One-year disagreement skewness positively related to past quarter’s returns 3 2 1 0 -20 -15 -10 -5 -1 0 5 10 15 -2 y = 0.0389x + 0.1577 R2 = 0.3512 -3 -4 -5 Past quarter's return 19 Graham/Harvey: Expectations of Risk Premia Past Returns Impact Expected Skewness Disagreement asymmetry • One-year disagreement skewness positively related to past month’s returns 3 2 1 0 -15 -10 -5 -1 0 5 10 -2 y = 0.0618x + 0.0854 R2 = 0.3731 -3 -4 -5 Past month's return 20 Graham/Harvey: Expectations of Risk Premia Expected Reward and Risk • Literature split – Some find negative relation between risk and expected returns which is consistent with asset pricing models – Some find a positive relation 21 Graham/Harvey: Expectations of Risk Premia Expected Reward and Risk Expected premia • One-year average volatility weakly negatively related5 to expected returns 4 3 y = -0.6051x + 6.4669 R2 = 0.1321 2 1 0 1 2 3 4 5 6 7 8 Average volatility 22 Graham/Harvey: Expectations of Risk Premia Expected Reward and Risk • One-year disagreement volatility negatively related to expected returns Expected premia 5 y = -0.6927x + 5.4253 R2 = 0.213 4 3 2 1 0 1 2 3 4 5 6 7 8 Disagreement volatility 23 Graham/Harvey: Expectations of Risk Premia Expected Reward and Risk • One-year disagreement volatility negatively related to median expected returns Expected premia 5 4 y = -0.8196x + 5.5895 R2 = 0.4862 3 2 1 0 1 2 3 4 5 6 7 8 Disagreement volatility 24 Graham/Harvey: Expectations of Risk Premia Expected Reward and Risk • Ten-year disagreement volatility positively related to expected returns Expected premia 5 4 y = 0.8732x + 1.8371 R2 = 0.2271 3 2 1 0 1 2 3 4 5 6 7 8 Disagreement volatility 25 Graham/Harvey: Expectations of Risk Premia Impact of September 11, 2001 Pre-Sept. 11 Post-Sept. 11 1-year premium Mean premium Average volatility Disagreement volatility 0.05 6.79 6.61 -0.70 9.76 7.86 10-year premium Mean premium Disagreement volatility Observations 3.63 2.36 127 4.82 3.03 33 26 Graham/Harvey: Expectations of Risk Premia What have we learned? • Forecasts impacted by past returns (expectational momentum) • Some support for the leverage effect with new expectational data • Individual volatilities seem low • Positive relation between risk and expected return - only at longer horizons 27 Graham/Harvey: Expectations of Risk Premia Outstanding issues • One-year forecasts unlikely used as the “hurdle rate” for one-year project evaluation • Difference between what CFOs think will happen to the market and their internal hurdle rates 28 Graham/Harvey: Expectations of Risk Premia Interviews • Results of four randomly selected CFO interviews: – All used the CAPM for cost of capital – None viewed the one-year premium as the input in the cost of equity calculation – even if the project had a short life 29 Graham/Harvey: Expectations of Risk Premia Appendix • Market volatility Var[r]= E[Var(r|Z)] + Var(E[r|Z)] average vol. disagreement vol. • Individual volatilities (Davidson and Cooper) Variance = ([r(0.90) - r(0.10)]/2.65)2 30 Graham/Harvey: Expectations of Risk Premia Appendix Proportion 0.45 1-year individual volatilities September 10, 2001 0.40 0.35 0.30 0.25 0.20 0.15 0.10 0.05 0.00 <3 6 9 12 15 18 20 >20 31 Graham/Harvey: Expectations of Risk Premia Appendix Proportion 0.45 1-year individual skewness September 10, 2001 0.40 0.35 0.30 0.25 0.20 0.15 0.10 0.05 0.00 -20 -15 -10 -5 0 5 10 15 20 >20 32