This appendix outlines the wild fixed-regressor bootstrap used to calculate the p-value for the Hansen (2005) studentized maximum statistic in our reality check. We first estimate the constant expected equity premium (random walk with drift) model, corresponding to the null of no pre-dictability: ¯r = ∑Tt=1rt. We next estimate an unrestricted model that includes all of the potential predictors as regressors using OLS; denote the OLS residuals from this model as { ˆut}Tt=1. We then generate a pseudo sample of equity premium observations under the null of no predictability as rt,b = ¯r + vt,buˆt for t = 1, . . . , T , where vt,b is a draw from an i.i.d. N(0, 1) process. Generating residual draws in this manner allows for conditional heteroskedasticity and makes this a “wild”
bootstrap. Denote the pseudo sample of equity premium observations as {rt,b}t=1T . We compute fundamental, technical, and pooled forecasts for the last q2 simulated equity premium observa-tions using {rtb}Tt=1 in conjunction with the economic fundamentals and technical trading signals from the original sample. Using fundamentals and signals from the original sample makes this a
“fixed-regressor” bootstrap. Based on {rt,b}Tt=q
1+1 and the simulated forecasts, we compute the studentized maximum statistic for the pseudo sample, τmax,b. Generating B = 1, 000 pseudo sam-ples in this manner yields an empirical distribution of studentized maximum statistics, {τmax,b}Bb=1. The boostrapped p-value is given by B−1∑Bb=1Ib, where Ib= 1 for τmax,b≥ τmaxand zero otherwise and τmax is the studentized maximum statistic from the original sample (see footnote 11).
References
Ang, Andrew, and Geert Bekaert, 2007, Return predictability: is it there? Review of Financial Studies20, 651–707.
Baker, Malcolm, and Jeffrey Wurgler, 2000, The equity share in new issues and aggregate stock returns, Journal of Finance 55, 2219–2257.
Bansal, Ravi, Dana Kiku, and Amir Yaron, 2009, An empirical evaluation of the long-run risk model for asset prices, manuscript, Duke University.
Bansal, Ravi, and Amir Yaron, 2004, Risks for the long run: A potential resolution of asset pricing puzzles, Journal of Finance 59, 1481–1590.
Bekaert, Geert, Eric Engstrom, and Yuhang Xing, 2009, Risk, uncertainty, and asset prices, Journal of Financial Economics91, 59–82.
Bollerslev, Tim, George Tauchen, and Hao Zhou, 2009, Expected stock returns and variance risk premia, Review of Financial Studies 22, 4463–4492.
Boudoukh, Jacob, Roni Michaely, Matthew P. Richardson, and Michael R. Roberts, 2007, On the importance of measuring payout yield: Implications for empirical asset pricing, Journal of Finance62, 877–915.
Breen, William, Lawrence R. Glosten, and Ravi Jagannathan, 1989, Economic significance of predictable variations in stock index returns, Journal of Finance 64, 1177–1189.
Bry, Gerhard, and Charlotte Boschan, 1971, Cyclical Analysis of Time Series: Selected Procedures and Computer Programs(NBER, New York).
Brock, William, Josef Lakonishok, and Blake LeBaron, 1992, Simple technical trading rules and the stochastic properties of stock returns, Journal of Finance 47, 1731–1764.
Campbell, John Y., 1987, Stock returns and the term structure, Journal of Financial Economics 18, 373–399.
Campbell, John Y., and John H. Cochrane, 1999, By force of habit: A consumption-based expla-nation of aggregate stock market behavior, Journal of Political Economy 107, 205–251.
Campbell, John Y., and Robert J. Shiller, 1988a, The dividend-price ratio and expectations of future dividends and discount factors, Review of Financial Studies 1, 195–228.
Campbell, John Y., and Robert J. Shiller, 1988b, Stock prices, earnings, and expected dividends, Journal of Finance43, 661–676.
Campbell, John Y., and Samuel B. Thompson, 2008, Predicting excess stock returns out of sample:
Can anything beat the historical average? Review of Financial Studies 21, 1509–1531.
Campbell, John Y., and Tuomo Vuolteenaho, 2004, Inflation illusion and stock prices, American Economic Review94, 19–23.
Clark, Todd E., and Michael W. McCracken, 2001, Tests of equal forecast accuracy and encom-passing for nested models, Journal of Econometrics 105, 85–110.
Clark, Todd E., and Michael W. McCracken, 2009, Improving forecast accuracy by combining recursive and rolling forecasts, International Economic Review 50, 363–395.
Clark, Todd E., and Michael W. McCracken, 2010, Reality checks and nested forecast model comparisons, manuscript, Federal Reserve Bank of Kansas City.
Clark, Todd E., and Kenneth D. West, 2007, Approximately normal tests for equal predictive accuracy in nested models, Journal of Econometrics 138, 291–311.
Cochrane, John H., 2008, The dog that did not bark: A defense of return predictability, Review of Financial Studies21, 1533–1575.
Covel, Michael W., 2005, Trend Following: How Great Traders Make Millions in Up or Down Markets(Prentice-Hall, New York).
Cowles, Alfred, 1933, Can stock market forecasters forecast? Econometrica 1, 309–324.
Diebold, Francis X., and Robert S. Mariano, 1995, Comparing predictive accuracy, Journal of Business and Economic Statistics13, 253–263.
Epstein, Lawrence, and Stanley Zin, 1989, Substitution, risk aversion and the temporal behavior of consumption and asset returns: A theoretical framework, Econometrica 57, 937–969.
Fama, Eugene F., 1991, Efficient capital markets: II, Journal of Finance 46, 1575–1617.
Fama, Eugeme F., and Marshall E. Blume. 1966. Filter rules and stock market trading, Journal of Business39, 226–41.
Fama, Eugene F., and Kenneth R. French, 1988, Dividend yields and expected stock returns, Jour-nal of Financial Economics22, 3–25.
Fama, Eugene F., and Kenneth R. French, 1989, Business conditions and expected returns on stocks and bonds, Journal of Financial Economics 25, 23–49.
Fama, Eugene F., and G. William Schwert, 1977, Asset returns and inflation, Journal of Financial Economics5, 115–146.
Ferson, Wayne E., and Campbell R. Harvey, 1991, The variation of equity risk premiums, Journal of Political Economy99, 385–415.
French, Kenneth R., G. William Schwert, and Robert F. Stambaugh, 1987, Expected stock returns and volatility, Journal of Financial Economics 19, 3–29.
Geweke, John, and Gianni Amisano, 2009, Optimal prediction pools, European Central Bank Working Paper No. 1017.
Goyal, Amit, and Ivo Welch, 2008, A comprehensive look at the empirical performance of equity premium prediction, Review of Financial Studies 21, 1455–1508.
Granville, Joseph, 1963, Granville’s New Key to Stock Market Profits (Prentice Hall, Englewood Cliffs, N.J.).
Guo, Hui, 2006, On the out-of-sample predictability of stock market returns, Journal of Business 79, 645–670.
Hansen, Peter R., 2005, A test for superior predictive ability, Journal of Business and Economic Statistics23, 365–380.
Harding, Don, and Adrian Pagan, 2002, Dissecting the cycle: A methodological investigation, Journal of Monetary Economics49, 365–381.
Harvey, Campbell R., 2001, The specification of conditional expectations, Journal of Empirical Finance8, 573–637.
Henkel, Sam James, J. Spencer Martin, and Frederico Nadari, 2009, Time-varying short-horizon predictability, Journal of Financial Economics, forthcoming.
Hong, Harrison, and Jeremy C. Stein, 1999, A unified theory of underreaction, momentum trading and overreaction in asset markets, Journal of Finance 54, 2143–2184.
Hong, Harrison, Terence Lim, and Jeremy C. Stein, 2000, Bad news travels slowly: Size, analyst coverage, and the profitability of momentum strategies, Journal of Finance 55, 265–295.
Jensen, Michel C., and George A. Benington, 1970, Random walks and technical theories: Some additional evidence, Journal of Finance 25, 469–482.
Kandel, Shmuel, and Robert F. Stambaugh, 1996, On the predictability of stock returns: An asset allocation perspective, Journal of Finance 51, 385–424.
Keim, Donald B., and Robert F. Stambaugh, 1986, Predicting returns in the stock and bond mar-kets, Journal of Financial Economics 17, 357–390.
Lettau, Martin, and Sydney C. Ludvigson, 2001, Consumption, aggregate wealth, and expected stock returns, Journal of Finance 56, 815–849.
Lettau, Martin, and Sydney C. Ludvigson, 2009, Measuring and modeling variation in the risk-return tradeoff, in Yacine A¨ıt-Sahal¨ıa and Lars P. Hansen, eds., Handbook of Financial Econo-metrics(Elsevier, Amsterdam).
Lo, Andrew W., Harry Mamaysky, and Jiang Wang, 2000, Foundations of technical analysis:
Com-putational algorithms, statistical inference, and empirical implementation, Journal of Finance 55, 1705–1065.
Ludvigson, Sydney C., and Serena Ng, 2007, The empirical risk-return relation: A factor analysis approach, Journal of Financial Economics 83, 171–222.
Lundblad, Christian, 2007, The risk return tradeoff in the long run: 1836–2003, Journal of Finan-cial Economics85, 123–150.
Mamaysky, Harry, Matthew Spiegel, and Hong Zhang, 2007, Improved forecasting of mutual fund alphas and betas, Review of Finance 11, 359–400.
Mamaysky, Harry , Matthew Spiegel, and Hong Zhang, 2008, Estimating the dynamics of mutual fund alphas and betas, Review of Financial Studies 21, 233–264.
Marquering, Wessel, and Marno Verbeek, 2004, The economic value of predicting stock index returns and volatility, Journal of Financial and Quantitative Analysis 39, 407–429.
McCracken, Michael W., 2007, Asymptotics for out of sample tests of Granger causality, Journal of Econometrics140, 719–752.
Nelson, Charles R., 1976, Inflation and the rates of return on common stock, Journal of Finance 31, 471–483.
Nison, Steve, 1991, Japanese Candlestick Charting Techniques: A Contemporary Guide to the Ancient Investment Techniques of the Far East(Simon & Schuster, New York).
Odean, Terrance, 1998, Are investors reluctant to realize their losses? Journal of Finance 53, 1775–1798.
Park, Cheol-Ho, and Scott H. Irwin, 2007, What do we know about the profitability of technical analysis? Journal of Economic Surveys 21, 786–826.
P´astor, ˘Lubo˘s, and Robert F. Stambaugh, 2009, Predictive systems: Living with imperfect predic-tors, Journal of Finance 64, 1583–1628.
Pesaran, M. Hashem, and Allan Timmermann, 2007, Selection of estimation window in the pres-ence of breaks, Journal of Econometrics 137, 134–161.
Rapach, David E., Jack K. Strauss, and Guofu Zhou, 2010, Out-of-sample equity premium pre-diction: Combination forecasts and links to the real economy, Review of Financial Studies 23, 821–862.
Rozeff, Michael S., 1984, Dividend yields are equity risk premiums, Journal of Portfolio Manage-ment11, 68–75.
Schwager, Jack D., 1993, Market Wizards: Interviews with Top Traders (Harper-Collins, New
York).
Schwager, Jack D., 1995, The New Market Wizards: Conversations with America’s Top Traders (Wiley, New York).
Schwert, G. William, 1989, Why does stock market volatility change over time? Journal of Fi-nance44, 1115–1153.
Schwert, G. William, 1990, Stock volatility and the crash of ’87, Review of Financial Studies 3, 77–102.
Sullivan, Ryan, Allan Timmermann, and Halbert White, 1999, Data-snooping, technical trading rule performance, and the bootstrap, Journal of Finance 54, 1647–1691.
Timmermann, Allan, 2006, Forecast combinations, in Graham Elliott, Clive W.J. Granger, and Allan Timmermann, eds., Handbook of Economic Forecasting (Elsevier, Amsterdam).
Timmermann, Allan, 2008, Elusive return predictability, International Journal of Forecasting 24, 1–18.
Wachter, Jessica A., 2005, Solving models with external habit, Finance Research Letters 2, 210–
226.
Wachter, Jessica A., 2006, A consumption-based model of the term structure of interest rates, Journal of Financial Economics79, 365–399.
Weil, Philippe, 1989, The equity premium puzzle and the risk-free rate puzzle, Journal of Monetary Economics24, 401–421.
West, Kenneth D., 1996, Asymptotic inference about predictive ability, Econometrica 64, 1067–
1084.
White, Halbert, 2000, A reality check for data snooping, Econometrica 68, 1097–1126.
Whitelaw, Robert F., 1994, Time variations and covariations in the expectation and volatility of stock market returns, Journal of Finance 49, 515–541.
Xu, Yexiao, 2004, Small levels of predictability and large economic gains, Journal of Empirical Finance11, 247–275.
Zhu, Yingzi, and Guofu Zhou, 2009, Technical analysis: An asset allocation perspective on the use of moving averages, Journal of Financial Economics 92, 519–544.
Table I
Out-of-sample equity premium forecasting results, 1960:01–2008:12
R2OSis the Campbell and Thompson (2008) out-of-sample R2statistic, which measures the percent re-duction in mean square prediction error (MSPE) for the forecast given in the first column relative to the historical average benchmark forecast. POOL-ECON (POOL-TECH) is a pooled forecast based on the individual fundamental (technical) forecasts in Panel A (Panel B); POOL-ALL is a pooled forecast based on the individual fundamental and technical forecasts. The R2OSstatistics and average forecasts are computed for the entire 1960:01–2008:12 forecast evaluation period (second and third columns) and separately for NBER-dated business-cycle expansions (fourth and fifth columns) and recessions (sixth and seventh columns). Average forecast is the average predicted equity premium during the indicated period. Statistical significance of R2OSis assessed with the Clark and West (2007) MSPE-adjusted statistic corresponding to the null hypothesis of equal MSPE against the alternative hypothesis that the forecast indicated in the first column has a lower MSPE than the historical average benchmark forecast;∗,∗∗, and
∗∗∗indicate significance at the 10%, 5%, and 1% levels, respectively.
Overall Expansion Recession
Average Average Average
Predictor R2OS(%) forecast (%) R2OS(%) forecast (%) R2OS(%) forecast (%) Panel A: Fundamental forecasts
DP 0.73∗∗∗ 0.25 0.15∗∗ 0.21 2.15∗∗ 0.52
DY 0.71∗∗∗ 0.22 −0.26 0.17 3.09∗∗ 0.48
EP −0.19 0.49 −0.15 0.44 −0.28 0.78
DE −0.76 0.79 −0.80 0.80 −0.65 0.75
SVAR −0.56 0.67 −0.60 0.67 −0.48 0.68
BM −1.64 0.50 −1.57 0.41 −1.79 1.02
NTIS −1.75 0.98 −0.34 0.96 −5.20 1.11
TBL 0.31∗ 0.38 0.11∗ 0.40 0.80 0.28
LTY 0.42∗∗ 0.30 0.25∗∗ 0.32 0.85 0.21
LTR 0.33∗ 0.77 −0.88 0.76 3.30∗∗∗ 0.83
TMS 0.14 0.81 −0.62 0.84 2.00∗∗ 0.65
DFY 0.39∗ 0.64 0.33∗ 0.62 0.55 0.78
DFR 0.22 0.71 0.04 0.71 0.65 0.67
INFL 0.18 0.64 0.20 0.67 0.14 0.50
Panel B: Technical forecasts
MA(1,3) −0.58 0.69 −1.09 0.70 0.67 0.61
MA(1,6) −0.68 0.70 −2.16 0.76 2.94∗∗ 0.34
MA(1,9) 0.08 0.69 −0.98 0.74 2.68∗∗ 0.38
MA(1,12) 0.78∗∗ 0.71 0.04 0.78 2.59∗∗ 0.33
MOM(3) −0.12 0.69 −0.25 0.69 0.20 0.66
MOM(6) 0.18 0.69 −0.48 0.74 1.79∗∗ 0.43
MOM(9) 0.18∗ 0.73 −0.57 0.81 2.02∗ 0.23
MOM(12) 0.26 0.71 −0.26 0.77 1.53∗ 0.41
VOL(1,3) −0.38 0.66 −1.07 0.68 1.31∗ 0.57
VOL(1,6) −0.29 0.66 −1.02 0.68 1.50∗ 0.52
VOL(1,9) 0.14 0.67 −0.78 0.71 2.40∗∗ 0.42
VOL(1,12) 0.42 0.65 −0.55 0.71 2.82∗∗ 0.32
Panel C: Pooled forecasts
POOL-ECON 0.80∗∗∗ 0.58 0.72∗∗ 0.57 1.01∗∗ 0.66
POOL-TECH 0.22 0.69 −0.52 0.73 2.02∗∗ 0.44
POOL-ALL 0.89∗∗∗ 0.63 0.27 0.63 2.40∗∗∗ 0.59
Table II
Asset-allocation results, 1960:01–2008:12
Average utility gain (∆) is the portfolio management fee (in annualized percent return) that an investor with mean-variance preferences and risk aversion coefficient of five would be willing to pay to have access to the forecast given in the first column relative to the historical average benchmark forecast. POOL-ECON (POOL-TECH) is a pooled forecast based on the individual fundamental (technical) forecasts in Panel A (Panel B); POOL-ALL is a pooled forecast based on the individual fundamental and technical forecasts.
The utility gains and average equity weights are computed for the entire 1960:01–2008:12 forecast evalu-ation period (second and third columns) and separately for NBER-dated business-cycle expansions (fourth and fifth columns) and recessions (sixth and seventh columns). Average equity weight is the average value during the indicated period.
Overall Expansion Recession
∆ Average ∆ Average ∆ Average
Predictor (ann. %) equity weight (ann. %) equity weight (ann. %) equity weight Panel A: Fundamental forecasts
DP 1.44 0.28 0.12 0.22 8.76 0.62
DY 1.82 0.22 −0.17 0.17 13.02 0.55
EP 1.23 0.53 0.76 0.48 3.71 0.81
DE −0.53 0.98 −0.27 0.98 −1.98 0.96
SVAR −0.31 0.88 −0.25 0.88 −0.66 0.88
BM −0.40 0.48 −0.94 0.41 2.37 0.87
NTIS −0.49 1.06 0.47 1.05 −5.97 1.12
TBL 1.65 0.53 0.71 0.55 6.92 0.40
LTY 1.63 0.42 0.82 0.44 6.22 0.30
LTR 0.68 0.94 −0.56 0.94 7.50 0.95
TMS 1.21 0.97 0.12 1.00 7.27 0.79
DFY 0.43 0.82 0.20 0.80 1.61 0.96
DFR 0.92 0.91 0.09 0.92 5.60 0.85
INFL 0.68 0.85 0.22 0.87 3.33 0.68
Panel B: Technical forecasts
MA(1,3) 0.19 0.86 −0.34 0.88 3.18 0.78
MA(1,6) 1.68 0.80 −0.48 0.87 13.90 0.43
MA(1,9) 2.06 0.84 0.05 0.90 13.39 0.48
MA(1,12) 3.07 0.86 0.97 0.94 14.97 0.40
MOM(3) −0.07 0.89 −0.22 0.89 0.81 0.86
MOM(6) 1.73 0.87 0.27 0.92 10.05 0.56
MOM(9) 3.01 0.84 1.00 0.94 14.47 0.27
MOM(12) 1.93 0.88 0.48 0.95 10.23 0.53
VOL(1,3) 0.62 0.86 −0.31 0.88 5.81 0.75
VOL(1,6) 0.78 0.85 −0.34 0.88 7.11 0.69
VOL(1,9) 1.66 0.85 −0.37 0.90 13.17 0.55
VOL(1,12) 2.50 0.84 −0.07 0.91 17.10 0.44
Panel C: Pooled forecasts
POOL-ECON 1.08 0.76 0.97 0.74 1.66 0.85
POOL-TECH 1.61 0.87 0.12 0.92 10.06 0.58
POOL-ALL 1.97 0.81 0.63 0.83 9.50 0.75
Table III
Empirical p-values (in percent) based on simulated data from habit-formation and long-run risks models
The table reports empirical p-values computed from 1,000 pseudo samples generated using either the Campbell and Cochrane (1999) habit-formation or Bansal and Yaron (2004) long-run risks model. The empirical p-values are the percent of simulated R2OS statistics and average utility gains greater than the corresponding values from Tables I and II.
The habit-formation model uses the following parameter values: δ = 0.891/12, γ = 2, φ = 0.861/12, g = 0.0189/12, σv= 0.0150/√
12. The long-run risks model uses the following parameter values: δ = 0.9989, γ = 10, ψ = 1.5, µc= 0.0015, ρ = 0.975, ϕe= 0.038, ¯σ = 0.0072, ν = 0.999, σw= 0.0000028, µd = 0.0015, φ = 2.5, ϕd = 5.96, π = 2.6. ALL, EXP, and REC refer to R2OS statistics and average utility gains computing for the full sample, expansions, and recessions, respectively.
R2OS Average utility gain
Habit-formation model Long-run risks model Habit-formation model Long-run risks model
Predictor ALL EXP REC ALL EXP REC ALL EXP REC ALL EXP REC
Panel A: Economic forecasts
DP 52.20 92.00 19.20 2.60 34.90 1.60 4.50 62.00 13.40 0.00 24.90 0.00
DY 50.60 93.10 18.80 3.00 50.30 6.90 1.40 64.30 8.70 0.00 33.30 0.10
Panel B: Technical forecasts
MA(1,3) 94.20 97.60 19.20 94.10 97.50 7.00 13.20 72.10 9.00 10.40 72.70 0.60
MA(1,6) 95.70 99.90 1.30 95.70 99.80 0.20 0.40 84.70 0.00 0.00 83.80 0.00
MA(1,9) 10.70 97.50 2.80 12.90 97.60 0.10 0.00 18.50 0.00 0.00 20.60 0.00
MA(1,12) 0.30 17.80 3.20 0.20 20.80 0.20 0.00 0.60 0.20 0.00 0.90 0.00
MOM(3) 36.20 61.30 37.30 39.60 66.10 22.60 38.20 58.70 35.80 31.30 57.70 11.40
MOM(6) 7.80 86.50 5.50 8.20 87.70 0.90 0.10 6.30 0.50 0.00 8.30 0.00
MOM(9) 6.80 90.30 6.00 8.30 91.70 1.30 0.00 0.40 0.20 0.00 1.30 0.00
MOM(12) 3.70 57.70 10.90 4.00 65.40 2.40 0.10 2.40 0.60 0.00 3.10 0.10
1965 1975 1985 1995 2005
1965 1975 1985 1995 2005 0
1965 1975 1985 1995 2005 0
1965 1975 1985 1995 2005 0
1965 1975 1985 1995 2005 0
1965 1975 1985 1995 2005 0
1965 1975 1985 1995 2005 0
1965 1975 1985 1995 2005 0
1965 1975 1985 1995 2005 0
1965 1975 1985 1995 2005 0
1965 1975 1985 1995 2005 0
1965 1975 1985 1995 2005 0
1965 1975 1985 1995 2005 0
1965 1975 1985 1995 2005 0
1965 1975 1985 1995 2005 0
Figure 1. Out-of-sample equity premium forecasts based on economic fundamentals, 1960:01–2008:12. Black and gray lines delineate equity premium forecasts (in percent) based on the economic fundamental given in the panel heading and the historical average, respectively. POOL-ECON is a pooled forecast based on the individual fundamental forecasts. Vertical bars depict NBER-dated business-cycle recessions.
1965 1975 1985 1995 2005
1965 1975 1985 1995 2005
−0.03
1965 1975 1985 1995 2005
−0.03
1965 1975 1985 1995 2005
−0.03
1965 1975 1985 1995 2005
−0.03
1965 1975 1985 1995 2005
−0.03
1965 1975 1985 1995 2005
−0.03
1965 1975 1985 1995 2005
−0.03
1965 1975 1985 1995 2005
−0.03
1965 1975 1985 1995 2005
−0.03
1965 1975 1985 1995 2005
−0.03
1965 1975 1985 1995 2005
−0.03
1965 1975 1985 1995 2005
−0.03
1965 1975 1985 1995 2005
−0.03
1965 1975 1985 1995 2005
−0.03
Figure 2. Cumulative square prediction error differences, out-of-sample equity premium forecasts based on the historical average and economic fun-damentals, 1960:01–2008:12. The figure depicts cumulative differences between the mean square prediction errors for the historical average equity premium forecast and the equity premium forecast based on the economic fundamental indicated in the panel heading. POOL-ECON is a pooled forecast based on the individual fundamental forecasts. Vertical bars depict NBER-dated business-cycle recessions.
1965 1975 1985 1995 2005
1965 1975 1985 1995 2005 0
0.5 1 1.5
MA(1,6)
1965 1975 1985 1995 2005 0
0.5 1 1.5
MA(1,9)
1965 1975 1985 1995 2005 0
0.5 1 1.5
MA(1,12)
1965 1975 1985 1995 2005 0
0.5 1 1.5
MOM(3)
1965 1975 1985 1995 2005 0
0.5 1 1.5
MOM(6)
1965 1975 1985 1995 2005 0
0.5 1 1.5
MOM(9)
1965 1975 1985 1995 2005 0
0.5 1 1.5
MOM(12)
1965 1975 1985 1995 2005 0
0.5 1 1.5
VOL(1,3)
1965 1975 1985 1995 2005 0
0.5 1 1.5
VOL(1,6)
1965 1975 1985 1995 2005 0
0.5 1 1.5
VOL(1,9)
1965 1975 1985 1995 2005 0
0.5 1 1.5
VOL(1,12)
1965 1975 1985 1995 2005 0
0.5 1 1.5
POOL−TECH
1965 1975 1985 1995 2005 0
0.5 1 1.5
POOL−ALL
Figure 3. Out-of-sample equity premium forecasts based on technical rules, 1960:01–2008:12. Black and gray lines delineate equity premium forecasts (in percent) based on the technical rule given in the panel heading and the historical average, respectively. POOL-TECH is a pooled forecast based on the individual technical forecasts. POOL-ALL is a pooled forecast based on the individual fundamental and technical forecasts. Vertical bars depict NBER-dated business-cycle recessions.
1965 1975 1985 1995 2005
1965 1975 1985 1995 2005
−0.01
1965 1975 1985 1995 2005
−0.01
1965 1975 1985 1995 2005
−0.01
1965 1975 1985 1995 2005
−0.01
1965 1975 1985 1995 2005
−0.01
1965 1975 1985 1995 2005
−0.01
1965 1975 1985 1995 2005
−0.01
1965 1975 1985 1995 2005
−0.01
1965 1975 1985 1995 2005
−0.01
1965 1975 1985 1995 2005
−0.01
1965 1975 1985 1995 2005
−0.01
1965 1975 1985 1995 2005
−0.01
1965 1975 1985 1995 2005
−0.01
Figure 4. Cumulative square prediction error differences, out-of-sample equity premium forecasts based on the historical average and technical rules, 1960:01–2008:12. The figure depicts cumulative differences between the mean square prediction errors for the historical average equity premium forecast and the equity premium forecast based on the technical rule indicated in the panel heading. POOL-TECH is a pooled forecast based on the individual technical forecasts.
POOL-ALL is a pooled forecast based on the individual fundamental and technical forecasts. Vertical bars depict NBER-dated business-cycle recessions.
1965 1975 1985 1995 2005
1965 1975 1985 1995 2005 0
0.5 1 1.5
DY
1965 1975 1985 1995 2005 0
0.5 1 1.5
EP
1965 1975 1985 1995 2005 0
0.5 1 1.5
DE
1965 1975 1985 1995 2005 0
0.5 1 1.5
SVAR
1965 1975 1985 1995 2005 0
0.5 1 1.5
BM
1965 1975 1985 1995 2005 0
0.5 1 1.5
NTIS
1965 1975 1985 1995 2005 0
0.5 1 1.5
TBL
1965 1975 1985 1995 2005 0
0.5 1 1.5
LTY
1965 1975 1985 1995 2005 0
0.5 1 1.5
LTR
1965 1975 1985 1995 2005 0
0.5 1 1.5
TMS
1965 1975 1985 1995 2005 0
0.5 1 1.5
DFY
1965 1975 1985 1995 2005 0
0.5 1 1.5
DFR
1965 1975 1985 1995 2005 0
0.5 1 1.5
INFL
1965 1975 1985 1995 2005 0
0.5 1 1.5
POOL−ECON
Figure 5. Equity portfolio weights computed using equity premium forecasts based on economic fundamentals, 1960:01–2008:12. Black (gray) lines delineate equity portfolio weights for an investor with mean-variance preferences and risk aversion coefficient of five who uses an equity premium forecast based on the economic fundamental given in the panel heading (historical average forecast). POOL-ECON is a pooled forecast based on the individual fundamental forecasts. Vertical bars depict NBER-dated business-cycle recessions.
1965 1975 1985 1995 2005
1965 1975 1985 1995 2005 0
0.5 1 1.5
MA(1,6)
1965 1975 1985 1995 2005 0
0.5 1 1.5
MA(1,9)
1965 1975 1985 1995 2005 0
0.5 1 1.5
MA(1,12)
1965 1975 1985 1995 2005 0
0.5 1 1.5
MOM(3)
1965 1975 1985 1995 2005 0
0.5 1 1.5
MOM(6)
1965 1975 1985 1995 2005 0
0.5 1 1.5
MOM(9)
1965 1975 1985 1995 2005 0
0.5 1 1.5
MOM(12)
1965 1975 1985 1995 2005 0
0.5 1 1.5
VOL(1,3)
1965 1975 1985 1995 2005 0
0.5 1 1.5
VOL(1,6)
1965 1975 1985 1995 2005 0
0.5 1 1.5
VOL(1,9)
1965 1975 1985 1995 2005 0
0.5 1 1.5
VOL(1,12)
1965 1975 1985 1995 2005 0
0.5 1 1.5
POOL−TECH
1965 1975 1985 1995 2005 0
0.5 1 1.5
POOL−ALL
Figure 6. Equity portfolio weights computed using equity premium forecasts based on technical rules, 1960:01–2008:12. Black (gray) lines delineate equity portfolio weights for an investor with mean-variance preferences and risk aversion coefficient of five who uses an equity premium forecast based on the technical rule given in the panel heading (historical average forecast). POOL-TECH is a pooled forecast based on the individual technical forecasts. POOL-ALL is a pooled forecast based on the individual fundamental and technical forecasts. Vertical bars depict NBER-dated business-cycle recessions.
−2 −1 0 1 2 3 4
Figure 7. Actual equity premium and equity premium forecasts based on economic fundamentals near a U.S. business-cycle peak. The panels show the incremental change in the average difference between the actual equity premium or equity premium forecast based on the economic fundamental given in the panel heading and the historical average equity premium forecast two months before through four months after a business-cycle peak. POOL-ECON is a pooled forecast based on the individual fundamental forecasts. All forecasts are measured in percent. Circles indicate point estimates and shaded areas depict 90%
confidence bands.
−2 −1 0 1 2 3 4
Figure 8. Actual equity premium and equity premium forecasts based on technical rules near a U.S. business-cycle peak. The panels show the incre-mental change in the average difference between the actual equity premium or equity premium forecast based on the technical rule given in the panel heading and the historical average equity premium forecast two months before through four months after a business-cycle peak. POOL-TECH is a pooled forecast based on the individual technical forecasts. POOL-ALL is a pooled forecast based on the individual fundamental and technical forecasts. All forecasts are measured in percent.
Circles indicate point estimates and shaded areas depict 90% confidence bands.
−4 −3 −2 −1 0 1 2
Figure 9. Actual equity premium and equity premium forecasts based on economic fundamentals near a U.S. business-cycle trough. The panels show the incremental change in the average difference between the actual equity premium or equity premium forecast based on the economic fundamental given in the panel heading and the historical average equity premium forecast four months before through two months after a business-cycle trough. POOL-ECON is a pooled forecast based on the individual fundamental forecasts. All forecasts are measured in percent. Circles indicate point estimates and shaded areas depict 90%
confidence bands.
−4 −3 −2 −1 0 1 2
Figure 10. Actual equity premium and equity premium forecasts based on technical rules near a U.S. business-cycle trough. The panels show the in-cremental change in the average difference between the actual equity premium or equity premium forecast based on the technical rule given in the panel heading and the historical average equity premium forecast four months before through two months after a business-cycle trough. POOL-TECH is a pooled forecast based on the individual technical forecasts. POOL-ALL is a pooled forecast based on the individual fundamental and technical forecasts. All forecasts are measured in percent. Circles indicate point estimates and shaded areas depict 90% confidence bands.