Forecasting the Long-Term Equity Premium for Asset Allocation

Abstract

Long-term country equity premium forecasts based on a cross-sectional global factor model (CS-GFM), where factors represent compensation for risks proxied by valuation and financial variables are superior, statistically and economically, to forecasts based on time-series prediction models commonly used in academia and practice. CS-GFM equity premium forecasts produce significant utility gains compared to long-term asset allocation strategies based on eighteen commonly used prediction models, consistently across the US and eleven developed equity markets.

Keywords:

• asset allocation
• forecasting
• global factor model
• long-horizon predictability

PL Credits: 2.0:

Disclosure statement

No potential conflict of interest was reported by the author(s).

Acknowledgements

We are grateful to Nicole M. Boyson (co-editor) and two anonymous referees for their constructive comments. We thank Timotheos Angelidis, Abraham Lioui, and seminar participants at the ICMA Centre at Henley Business School, University of Reading, for helpful comments and suggestions.

Notes

1 An increasing number of investment houses publish annually long-term forecasts of asset returns to aid investors’ long-term investment decisions (https://www.savvyinvestor.net/blog/long-term-asset-return-forecasts).

2 Boudoukh, Richardson, and Whitelaw (2008) and Boudoukh, Israel, and Richardson (2019, 2021) question the statistical robustness of predictability, arguing that long-horizon return regressions effectively have small sample sizes. They argue that once appropriate methods are used to correct the bias due to overlapping errors, the evidence of predictability based on overlapping multiperiod returns is illusory.

3 When the cross-sectional model is estimated using market capitalization rather than equal weights, $r_{z,t:t+q-1}$ will be the return of the capitalization-weighted global equity portfolio.

4 The constant-mix strategy is different to the multi-period asset allocation strategy of Campbell and Viceira (1999), Brennan and Xia (2010), Campbell, Viceira, and White (2003) and Chacko and Viceira (2005), which takes into account the intertemporal hedging demands arising as a result of short-term return predictability. We ignore hedging demands consistent with the evidence presented in Brandt (1999), Ang and Bekaert (2002) and Diris, Palm, and Schotman (2015), which show that the economic value of intertemporal hedging demands in strategic (dynamic) asset allocation is insignificant in an out-of-sample setting.

5 We also calculate standard errors using (a) the standard lag truncation parameter of Newey and West (1987) and (b) setting the lag truncation parameter to q−1, where q denotes the investment horizon. Detailed results are available from the authors upon request. See also the discussion in the “Caveats” section.

6 We note that the intercepts in the models 1–7 of Table 1 are different because we do not necessarily have data for the same countries for each state variable.

7 We observe a negative $R_{\mathit{OOS}}^2,$ whilst the MSFE-adjusted t-statistic is significant at the 1% confidence level for the univariate and multivariate DY-based models for Australia. This evidence is plausible when comparing nested models. See the discussion in Clark and West (2007), McCracken (2007) and footnote 21 of Neely et al. (2014).

8 In Table A.2 of the online supplementary materials, we assess the predictive performance of every possible model comparison. The MSFE-adjusted Clark and West (2007) statistics suggest that the univariate DY and PE model forecasts have statistically significantly lower MSFE than the forecasts from all other factor models. Use of the more conservative Bonferroni adjustment to calculate standard errors confirms the superiority of the DY and PE model forecasts to all other univariate and multivariate factor models.

9 Rapach and Zhou (2020) provide a detailed discussion of machine learning techniques for forecasting cross-sectional equity returns in a time-series setting. Section B in the online supplementary materials describes in more detail the three machine learning models.

10 Pástor, Stambaugh, and Taylor (2017) show that, for one independent variable, the slope estimator using the Fama and MacBeth (1973) is the same to the estimator generated by a panel regression with time fixed effects if the panel is balanced and the variance of the independent variable is constant across all time-periods.

11 The main difference between the panel country fixed effects and the panel time fixed effects model or the CS-GFM is the assumption of a country specific component in country equity premiums. The worst forecasting performance of the country fixed effects model could be due to the estimation error in the estimation of country-specific intercepts. Hjalmarsson (2010) argue that even if the slopes or intercepts are not the same across countries, in a bias-variance trade-off restricted coefficients might still dominate country-specific slope and intercept estimates.

12 Rapach and Zhou (2013) provide a comprehensive survey of alternative equity premium prediction models. Dong et al. (2021) report strong statistical and economic evidence of US market return predictability using the information in 100 long-short anomaly portfolio returns and shrinkage techniques that guard against over-fitting.

13 We thank the referee for suggesting the “out-of-sample” evaluation of CS-GFM-based equity premium predictions using six countries not included in the estimation of the prediction model.

14 (Campbell and Vuolteenaho 2004 (PE, TS); Petkova 2006 (DY, TS, STIR, Default spread (DS)); Hahn and Lee 2006 (TS, DS); Barroso, Boons, and Karehnke 2021 (DY, TS, DS, PE); Maio and Santa-Clara 2012; Boons, 2016; Barbalau, Robotti, and Shanken 2019 (DY, TS, DF, STIR and PE); Campbell 1993, 1996; Bali and Engle 2010 (MVOL)). All variables exist at the country level except the default spread (DS).

Additional information

Notes on contributors

Athanasios Sakkas

Athanasios Sakkas is an assistant professor in the Department of Accounting and Finance, Athens University of Economics and Business, Athens, Greece.

Nikolaos Tessaromatis

Nikolaos Tessaromatis is a professor of finance at EDHEC Business School, Nice, France.