Skip to main content
SpringerLink
Log in

Asset Returns Under Model Uncertainty: Evidence from the Euro Area, the US and the UK

  • Published:
Computational Economics Aims and scope Submit manuscript

Abstract

We analyze predictability of risk premium in the context of model uncertainty. Using data for the euro area, the US and the UK, we show that there is a large amount of model uncertainty and one can improve the forecasts of stock returns with a Bayesian Model Averaging (BMA) approach. The empirical evidence for the euro area suggests that several macroeconomic, financial and macro-financial variables are consistently among the most prominent determinants of risk premium. As for the US, only a few number of predictors play an important role. In the case of the UK, future stock returns are better forecasted by financial variables. These results are corroborated for both the M-open and the M-closed perspectives, different model priors and in the context of “in-sample” and “out-of-sample” forecasting. Finally, we highlight that the predictive ability of the BMA framework is stronger at longer periods, and clearly outperforms the constant expected returns and the autoregressive benchmark models.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Notes

  1. Sousa (2015a) argues that housing can be used as a hedge against unfavourable wealth shocks.

  2. A recent work by Rubio et al. (2017) estimates efficiency scores based on a data envelopment approach. The authors show such rankings: (i) forecast stock returns; and (ii) help reducing asset mispricing errors.

  3. For an interesting application of BMA to the analysis of the determinants of horizontal spillovers from FDI, see Havránek and Irsová (2011).

  4. In this context, it should be noted that we rely on the BMA analysis as a way of improving the predictability of average stock returns. While this framework is particularly well suited to tackle the importance of model uncertainty, other methodologies may be more appropriate at capturing changes in the distribution of stock returns. For instance, quantile regressions can help to investigate the tent to which certain variables detect periods of “extreme” or “abnormal” returns, such as financial crashes or stock market booms. Sousa and Sousa (2007) use such framework and find that the lower quantiles of the distribution of asset returns are significantly less stable than the upper quantiles.

  5. As is well-known, real stock returns and excess stock returns display very similar statistical properties and exhibit strong correlation. The reason is that the inflation rate—which enters the computation of real stock returns—approximates well the short-term (risk-free) interest rate—which is used in the computation of excess stock returns. As a result, in the empirical finance literature, both variables are also widely used as proxies for risk premium. Therefore and without lack of generalisation, we focus our attention on real stock returns.

  6. In what follows, changes in a specific variable refer to absolute variations, while growth rates denote changes in relative terms. Unless stated otherwise, growth rates are computed at constant prices.

  7. Bonfim (2009) shows that periods of economic growth that are accompanied by strong credit growth typically lead to an excessive risk-taking behaviour.

  8. Sousa (2010b) highlights the importance of wealth at providing both utility and collateral services. The auhor shows that the ratio of collateralizable wealth to labour income strongly predicts equity and government bond risk premium.

  9. The weights are calculated using GDP at irrevocable fixed exchange rates. The use of long time-series of euro area aggregates has the drawbacks that (i) the historical data is originated from the time prior to EMU, and (ii) aggregation bias might be important. However, the main advantage is that the monetary policy framework is also set in terms of aggregates for the euro area (Beyer et al. 2001).

  10. For a recent investigation of stock return predictability in European countries in the presence of non-normality and time-varying volatility, see Kiani (2016).

  11. For an interesting analysis of the determinants of government bond spreads and measure bond and loan market integration, see Ebner (2009).

  12. Blenman (2004) argues that contagion between financial markets during periods of financial crises is typically large. In addition, Abreu et al. (2011) point that the correlation between stock returns across countries and the benefit from international diversification is generally low. This can be explained by the costs of acquiring experience in the domestic market before entering the foreign markets, which, in turn, leads investors to overweight domestic equities and underweight international equities. Ferreira et al. (2012) use mutual fund data to show that investors in industrialised countries have lower participation costs and are more sophisticated. The asymmetric response to good and bad news, the existence of bands for price movements, the interaction between noise and arbitrage traders and the presence of market friction and transaction costs are also pointed by Jawadi (2009) as causing a nonlinear behaviour of stock markets.

  13. In another robustness check, we have also considered a wide range of hyperparameters on the Zellner’s g-prior for the regression coefficients. The empirical evidence confirms that, for the euro area, some macroeconomic variables (such as the growth rate of the commodity price index, the inflation rate and the change in the inflation rate), financial indicators (such as the lagged stock returns and the dividend yield ratio) and macro-financial proxies (such as the stock price index scaled by the real GDP, the labour income-to-consumption ratio and the wealth composition risk) are more likely to capture the variation in future stock returns. In the case of the US, the largest probability inclution probabilities (PIPs) are associated with the consumption–(dis)aggregate wealth ratio, the change in the real government bond yield, the change in the inflation rate, the labour income-to-consumption ratio, the dividend yield, the stock price index scaled by GDP and the wealth-to-income ratio. Finally, for the UK, the PIPs of the dividend yield, the change in the real government bond yield and the real government bond yield rank among the largest ones. A number of macro-financial variables, such as the housing wealth-to-income ratio, the wealth-to-income ratio and the consumption–(dis)aggregate wealth ratio are also likely to capture the time-varying pattern of real stock returns. For brevity, these results are not reported in the paper, but they are available from the authors upon request.

References

  • Abreu, M., Mendes, V., & Santos, J. A. C. (2011). Home country bias: Does domestic experience help investors enter foreign markets? Journal of Banking and Finance, 35(9), 2330–2340.

    Article  Google Scholar 

  • Adrian, T., Moench, E., & Shin, H. S. (2010). Financial intermediation, asset prices, and macroeconomic dynamics. Staff Report No: Federal Reserve Bank of New York. 422.

    Book  Google Scholar 

  • Ang, A., & Bekaert, G. (2007). Stock return predictability: Is it there? Review of Financial Studies, 20(3), 651–707.

    Article  Google Scholar 

  • Armada, M. J. R., Sousa, R. M., & Wohar, M. E. (2015). Consumption growth, preference for smoothing, changes in expectations and risk premium. Quarterly Review of Economics and Finance, 56, 80–97.

    Article  Google Scholar 

  • Avramov, D. (2002). Stock return predictability and model uncertainty. Journal of Financial Economics, 64, 423–458.

    Article  Google Scholar 

  • Bansal, R., & Yaron, A. (2004). Risks for the long run: A potential resolution of asset pricing puzzles. Journal of Finance, 59(4), 1481–1509.

    Article  Google Scholar 

  • Barberis, N. (2000). Investing for the long run when returns are predictable. Journal of Finance, 55, 225–264.

    Article  Google Scholar 

  • Beyer, A., Doornik, J., & Hendry, D. (2001). Constructing historical euro-zone data. Economic Journal, 111, 102–121.

    Article  Google Scholar 

  • Blenman, L. P. (1991). A model of covered interest arbitrage under market segmentation. Journal of Money, Credit and Banking, 23(4), 706–717.

    Article  Google Scholar 

  • Blenman, L. P. (2004). Financial crisis: Contagion effects, risk premiums and returns in equity and currency markets. International Review of Financial Analysis, 13, 367–380.

    Article  Google Scholar 

  • Bonfim, D. (2009). Credit risk drivers: Evaluating the contribution of firm level information and of macroeconomic dynamics. Journal of Banking and Finance, 33(2), 281–299.

    Article  Google Scholar 

  • Bossaerts, P., & Hillion, P. (1999). Implementing statistical criteria to select return forecasting models: What do we learn? Review of Financial Studies, 12(2), 405–428.

    Article  Google Scholar 

  • Breeden, D. T. (1979). An intertemporal asset pricing model with stochastic consumption and investment opportunities. Journal of Financial Economics, 7, 265–296.

    Article  Google Scholar 

  • Campbell, J. Y. (1987). Stock returns and the term structure. Journal of Financial Economics, 18(2), 373–399.

    Article  Google Scholar 

  • Campbell, J. Y., & Shiller, R. (1988). The dividend-price ratio, expectations of future dividends and discount factors. Review of Financial Studies, 1, 195–227.

    Article  Google Scholar 

  • Chen, N., Roll, R., & Ross, S. (1986). Economic forces and the stock market. Journal of Business, 59, 383–403.

    Article  Google Scholar 

  • Cooper, I., & Priestley, R. (2009). Time-varying risk premiums and the output gap. Review of Financial Studies, 22(7), 2801–2833.

    Article  Google Scholar 

  • Cremers, K. J. M. (2002). Stock return predictability: A Bayesian model selection perspective. Review of Financial Studies, 15(4), 1223–1249.

    Article  Google Scholar 

  • Ebner, A. (2009). An empirical analysis on the determinants of CEE government bond spreads. Emerging Markets Review, 10(2), 97–121.

    Article  Google Scholar 

  • Fama, E., & French, K. (1989). Business conditions and expected returns on stocks and bonds. Journal of Financial Economics, 25(1), 23–49.

    Article  Google Scholar 

  • Fama, E., & Schwert, G. W. (1977). Asset returns and inflation. Journal of Financial Economics, 5, 115–146.

    Article  Google Scholar 

  • Fernandez-Corugedo, E., Price, S., & Blake, A. (2007). The dynamics of consumers’ expenditure: The UK consumption ECM redux. Economic Modelling, 24, 453–469.

    Article  Google Scholar 

  • Ferreira, M. A., Keswani, A., Miguel, A. F., & Ramos, S. (2012). The flow-performance relationship around the world. Journal of Banking & Finance, 36(6), 1759–1780.

    Article  Google Scholar 

  • Ferson, W. (1990). Are the latent variables in time-varying expected returns compensation for consumption risk? Journal of Finance, 45, 397–429.

    Article  Google Scholar 

  • Ferson, W., & Harvey, C. (1991). The variation of economic risk premiums. Journal of Political Economy, 99, 385–415.

    Article  Google Scholar 

  • Ferson, W., & Harvey, C. (1993). The risk and predictability of international equity returns. Review of Financial Studies, 6, 527–566.

    Article  Google Scholar 

  • Ferson, W., & Harvey, C. (1999). Conditioning variables and the cross-section of stock returns. Journal of Finance, 54, 1325–1360.

    Article  Google Scholar 

  • Harvey, C. R. (1989). Time-varying conditional covariances in tests of asset pricing models. Journal of Financial Economics, 24, 289–317.

    Article  Google Scholar 

  • Havránek, T., & Irsová, Z. (2011). Determinants of horizontal spillovers from FDI: Evidence from a large meta-analysis. Czech National Bank, CNB Working Paper No. 7.

  • Hiemstra, Y. (1996). Linear regression versus back propagation networks to predict quarterly stock market excess returns. Computational Economics, 9(1), 67–76.

    Article  Google Scholar 

  • Hodrick, R. (1992). Dividend yields and expected stock returns: Alternative procedures for inference and measurement. Review of Financial Studies, 3, 357–386.

    Article  Google Scholar 

  • Jawadi, F. (2009). Essay in dividend modelling and forecasting: Does nonlinearity help? Applied Financial Economics, 19(16), 1329–1343.

    Article  Google Scholar 

  • Julliard, C. (2004). Labor income risk and asset returns. Princeton University, Working Paper.

  • Julliard, C., & Sousa, R. M. (2007). Risks for the long-run and the cross-section of asset returns. London School of Economics and Political Science, Working Paper.

  • Kandel, S., & Stambaugh, R. (1996). On the predictability of stock returns: An asset allocation perspective. Journal of Finance, 51, 385–424.

    Article  Google Scholar 

  • Kass, R. E., & Wasserman, L. (1995). A reference Bayesian test for nested hypotheses and its relationship to the Schwarz criterion. Journal of the American Statistical Association, 90, 928–934.

    Article  Google Scholar 

  • Kiani, K. M. (2016). On modelling and forecasting predictable components in European stock markets. Computational Economics, 48(3), 487–502.

    Article  Google Scholar 

  • Koop, G. (2003). Bayesian econometrics. Chichester: Wiley.

    Google Scholar 

  • Lettau, M., & Ludvigson, S. (2001). Consumption, aggregate wealth, and expected stock returns. Journal of Finance, 56, 815–849.

    Article  Google Scholar 

  • Lintner, J. (1965). The valuation of risky assets and the selection of risky investments in stock portfolios and capital budgets. Review of Economics and Statistics, 47, 13–37.

    Article  Google Scholar 

  • Lucas, R. E. (1978). Asset prices in an exchange economy. Econometrica, 46, 1429–1445.

    Article  Google Scholar 

  • Lustig, H., & van Nieuwerburgh, S. (2005). Housing collateral, consumption insurance, and risk premia: An empirical perspective. Journal of Finance, 60(3), 1167–1219.

    Article  Google Scholar 

  • Madigan, D., & Raftery, A. E. (1994). Model selection and accounting for model uncertainty in graphical models using Occam’s window. Journal of the American Statistical Association, 89, 1535–1546.

    Article  Google Scholar 

  • Parker, J. A., & Julliard, C. (2005). Consumption risk and the cross section of expected returns. Journal of Political Economy, 113(1), 185–222.

    Article  Google Scholar 

  • Pastor, L., & Stambaugh, R. F. (2000). Comparing asset pricing models: An investment perspective. Journal of Financial Economics, 56, 335–381.

    Article  Google Scholar 

  • Pesaran, M. H., & Timmermann, A. (1995). Predictability of stock returns: Robustness and economic significance. Journal of Finance, 50, 1201–1228.

    Article  Google Scholar 

  • Piazzesi, M., Schneider, M., & Tuzel, S. (2007). Housing, consumption and asset pricing. Journal of Financial Economics, 83, 531–569.

    Article  Google Scholar 

  • Pontiff, J., & Schall, L. D. (1998). Book-to-market ratios as predictors of market returns. Journal of Financial Economics, 49, 141–160.

    Article  Google Scholar 

  • Raftery, A. E. (1995). Bayesian model selection in social research. Sociological Methodology, 25, 111–196.

    Article  Google Scholar 

  • Raftery, A. E., Madigan, D., & Hoeting, J. A. (1997). Bayesian model averaging for linear regression models. Journal of the American Statistical Association, 92, 179–191.

    Article  Google Scholar 

  • Rangvid, J. (2006). Output and expected returns. Journal of Financial Economics, 81, 595–624.

    Article  Google Scholar 

  • Reboredo, J. C., Matías, J. M., & Garcia-Rubio, R. (2012). Nonlinearity in forecasting of high-frequency stock returns. Computational Economics, 40(3), 245–264.

    Article  Google Scholar 

  • Rubinstein, M. (1976). The valuation of uncertain income streams and the pricing of options. Bell Journal of Economics, 7(2), 407–425.

    Article  Google Scholar 

  • Rubio, J. F., Maroney, N., & Hassan, M. K. (2017). Can efficiency of returns be considered as a pricing factor? Computational Economics,. doi:10.1007/s10614-017-9647-y.

    Article  Google Scholar 

  • Santos, T., & Veronesi, P. (2006). Labor income and predictable stock returns. Review of Financial Studies, 19, 1–44.

    Article  Google Scholar 

  • Schwarz, T. J. (1978). Estimating the dimension of a model. Annals of Statistics, 6, 416–464.

    Article  Google Scholar 

  • Sharpe, W. (1964). Capital asset prices: A theory of market equilibrium under conditions of risk. Journal of Finance, 19, 425–442.

    Google Scholar 

  • Sousa, R. M. (2010a). Consumption, (dis)aggregate wealth, and asset returns. Journal of Empirical Finance, 17(4), 606–622.

    Article  Google Scholar 

  • Sousa, R. M. (2010b). Collateralizable wealth, asset returns and systemic risk: International evidence. In W. A. Barnett & F. Jawadi (Eds.), Nonlinear modeling of economic and financial time-series. International symposia in economic theory and econometrics (Vol. 20). London: Emerald Group Publishing.

  • Sousa, R. M. (2010c). Housing wealth, financial wealth, money demand and policy rule: Evidence from the euro area. North American Journal of Economics and Finance, 21(1), 88–105.

    Article  Google Scholar 

  • Sousa, R. M. (2015a). What is the impact of wealth shocks on asset allocation? Quantitative Finance, 15(3), 493–508.

    Article  Google Scholar 

  • Sousa, R. M. (2015b). Linking wealth and labour income with stock returns and government bond yields. European Journal of Finance, 21(10–11), 806–825.

    Article  Google Scholar 

  • Sousa, R. M., & Sousa, J. (2007). Predicting risk premium under changes in the conditional distribution of stock returns. London School of Economics and Political Science, mimeo.

  • Wei, M. (2005). Human capital, business cycles and asset pricing. Board of Governors of the Federal Reserve—Division of Monetary Affairs, Working Paper.

  • Whelan, K. (2008). Consumption and expected asset returns without assumptions about unobservables. Journal of Monetary Economics, 55(7), 1209–1221.

    Article  Google Scholar 

  • Whitelaw, R. (1994). Time variations and covariations in the expectation and volatility of stock market returns. Journal of Finance, 49, 515–541.

    Article  Google Scholar 

  • Xia, Y. (2001). Learning about predictability: The effects of parameter uncertainty on dynamic asset allocation. Journal of Finance, 56, 205–246.

    Article  Google Scholar 

  • Yogo, M. (2006). A consumption-based explanation of expected stock returns. Journal of Finance, 61(2), 539–580.

    Article  Google Scholar 

  • Zellner, A. (1986). On assessing prior distributions and Bayesian regression analysis with g-prior distributions. In P. K. Goel & A. Zellner (Eds.), Bayesian inference and decision techniques: Essays in honour of Bruno de Finetti (pp. 233–243). Amsterdam: North-Holland.

    Google Scholar 

Download references

Acknowledgements

Sousa acknowledges that this work has been financed by Operational Programme for Competitiveness Factors—COMPETE and by National Funds through the FCT—Portuguese Foundation for Science and Technology within the remit of the project “FCOMP-01-0124-FEDER-037268 (PEst-C/EGE/UI3182/2013)”.

Author information

Authors and Affiliations

  1. European Central Bank, Sonnemannstrasse 22, 60314, Frankfurt am Main, Germany

    João M. Sousa

  2. Department of Economics and Economic Policies Research Unit (NIPE), University of Minho, Campus of Gualtar, 4710-057, Braga, Portugal

    Ricardo M. Sousa

  3. LSE Alumni Association, London School of Economics and Political Science, Houghton Street, London, WC2 2AE, UK

    Ricardo M. Sousa

Authors
  1. João M. Sousa
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ricardo M. Sousa
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ricardo M. Sousa.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sousa, J.M., Sousa, R.M. Asset Returns Under Model Uncertainty: Evidence from the Euro Area, the US and the UK. Comput Econ 54, 139–176 (2019). https://doi.org/10.1007/s10614-017-9696-2

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10614-017-9696-2

Keywords

JEL Classification

Search

Navigation