Annals of Applied Statistics

Optimal asset allocation with multivariate Bayesian dynamic linear models

Jared D. Fisher, Davide Pettenuzzo, and Carlos M. Carvalho

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


We introduce a fast, closed-form, simulation-free method to model and forecast multiple asset returns and employ it to investigate the optimal ensemble of features to include when jointly predicting monthly stock and bond excess returns. Our approach builds on the Bayesian dynamic linear models of West and Harrison (Bayesian Forecasting and Dynamic Models (1997) Springer), and it can objectively determine, through a fully automated procedure, both the optimal set of regressors to include in the predictive system and the degree to which the model coefficients, volatilities and covariances should vary over time. When applied to a portfolio of five stock and bond returns, we find that our method leads to large forecast gains, both in statistical and economic terms. In particular, we find that relative to a standard no-predictability benchmark, the optimal combination of predictors, stochastic volatility and time-varying covariances increases the annualized certainty equivalent returns of a leverage-constrained power utility investor by more than 500 basis points.

Article information

Ann. Appl. Stat., Volume 14, Number 1 (2020), 299-338.

Received: January 2019
Revised: September 2019
First available in Project Euclid: 16 April 2020

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

62C10 62P20 91B28 91B84


Fisher, Jared D.; Pettenuzzo, Davide; Carvalho, Carlos M. Optimal asset allocation with multivariate Bayesian dynamic linear models. Ann. Appl. Stat. 14 (2020), no. 1, 299--338. doi:10.1214/19-AOAS1303.

Export citation


  • Ang, A. and Bekaert, G. (2007). Stock return predictability: Is it there? Rev. Financ. Stud. 20 651–707.
  • Barnard, J., McCulloch, R. and Meng, X.-L. (2000). Modeling covariance matrices in terms of standard deviations and correlations, with application to shrinkage. Statist. Sinica 10 1281–1311.
  • Billio, M., Casarin, R., Ravazzolo, F. and van Dijk, H. K. (2013). Time-varying combinations of predictive densities using nonlinear filtering. J. Econometrics 177 213–232.
  • Bossaerts, P. and Hillion, P. (1999). Implementing statistical criteria to select return forecasting models: What do we learn? Rev. Financ. Stud. 12 405–428.
  • Brennan, M. J., Schwartz, E. S. and Lagnado, R. (1997). Strategic asset allocation. J. Econom. Dynam. Control 21 1377–1403.
  • Campbell, J. Y., Chan, Y. L. and Viceira, L. M. (2003). A multivariate model of strategic asset allocation. J. Financ. Econ. 67 41–80.
  • Campbell, J. Y. and Shiller, R. J. (1988). The dividend-price ratio and expectations of future dividends and discount factors. Rev. Financ. Stud. 1 195–228.
  • Carriero, A., Clark, T. E. and Marcellino, M. (2019). Large Bayesian vector autoregressions with stochastic volatility and non-conjugate priors. J. Econometrics 212 137–154.
  • Christoffersen, P. F. and Diebold, F. X. (1998). Cointegration and long-horizon forecasting. J. Bus. Econom. Statist. 16 450–458.
  • Cochrane, J. H. and Piazzesi, M. (2005). Bond risk premia. Am. Econ. Rev. 95 138–160.
  • Dangl, T. and Halling, M. (2012). Predictive regressions with time-varying coefficients. J. Financ. Econ. 106 157–181.
  • Dawid, A. P. (1981). Some matrix-variate distribution theory: Notational considerations and a Bayesian application. Biometrika 68 265–274.
  • Engle, R. (2002). Dynamic conditional correlation: A simple class of multivariate generalized autoregressive conditional heteroskedasticity models. J. Bus. Econom. Statist. 20 339–350.
  • Fama, E. F. and Bliss, R. R. (1987). The information in long-maturity forward rates. Am. Econ. Rev. 77 680–692.
  • Fama, E. F. and Schwert, G. W. (1977). Asset returns and inflation. J. Financ. Econ. 5 115–146.
  • Fan, J., Furger, A. and Xiu, D. (2016). Incorporating global industrial classification standard into portfolio allocation: A simple factor-based large covariance matrix estimator with high-frequency data. J. Bus. Econom. Statist. 34 489–503.
  • Gao, X. and Nardari, F. (2018). Do commodities add economic value in asset allocation? New evidence from time-varying moments. J. Financ. Quant. Anal. 53.
  • Gargano, A., Pettenuzzo, D. and Timmermann, A. G. (2019). Bond return predictability: Economic value and links to the macroeconomy. Manage. Sci. 65 508–540.
  • Gelman, A. and Hill, J. (2006). Data Analysis Using Regression and Multilevel/Hierarchical Models. Analytical Methods for Social Research. Cambridge Univ. Press, Cambridge.
  • Geweke, J. and Amisano, G. (2011). Optimal prediction pools. J. Econometrics 164 130–141.
  • Gruber, L. and West, M. (2016). GPU-accelerated Bayesian learning and forecasting in simultaneous graphical dynamic linear models. Bayesian Anal. 11 125–149.
  • Gurkaynak, R. S., Sack, B. and Wright, J. H. (2007). The U.S. Treasury yield curve: 1961 to the present. J. Monet. Econ. 54 2291–2304.
  • Johannes, M., Korteweg, A. and Polson, N. (2014). Sequential learning, predictability, and optimal portfolio returns. J. Finance 69 611–644.
  • Kim, C.-J., Morley, J. C. and Nelson, C. R. (2005). The structural break in the equity premium. J. Bus. Econom. Statist. 23 181–191.
  • Koop, G., Korobilis, D. and Pettenuzzo, D. (2019). Bayesian compressed vector autoregressions. J. Econometrics 210 135–154.
  • Lettau, M. and Ludvigson, S. (2001). Consumption, aggregate wealth, and expected stock returns. J. Finance 56 815–849.
  • Lettau, M. and Van Nieuwerburgh, S. (2008). Reconciling the return predictability evidence. Rev. Financ. Stud. 21 1607–1652.
  • Lewellen, J. (2004). Predicting returns with financial ratios. J. Financ. Econ. 74 209–235.
  • Ludvigson, S. C. and Ng, S. (2009). Macro factors in bond risk premia. Rev. Financ. Stud. 22 5027–5067.
  • Pastor, L. and Stambaugh, R. F. (2001). The equity premium and structural breaks. J. Finance 56 1207–1239.
  • Paye, B. S. and Timmermann, A. (2006). Instability of return prediction models. J. Empir. Finance 13 274–315.
  • Pettenuzzo, D. and Ravazzolo, F. (2016). Optimal portfolio choice under decision-based model combinations. J. Appl. Econometrics 31 1312–1332.
  • Pettenuzzo, D. and Timmermann, A. (2011). Predictability of stock returns and asset allocation under structural breaks. J. Econometrics 164 60–78.
  • Pettenuzzo, D., Timmermann, A. and Valkanov, R. (2014). Forecasting stock returns under economic constraints. J. Financ. Econ. 114 517–553.
  • Primiceri, G. E. (2005). Time varying structural vector autoregressions and monetary policy. Rev. Econ. Stud. 72 821–852.
  • Rapach, D. E., Strauss, J. K. and Zhou, G. (2010). Out-of-sample equity premium prediction: Combination forecasts and links to the real economy. Rev. Financ. Stud. 23 821–862.
  • Thornton, D. L. and Valente, G. (2012). Out-of-sample predictions of bond excess returns and forward rates: An asset allocation perspective. Rev. Financ. Stud. 25 3141–3168.
  • Viceira, L. (1997). Testing for structural change in the predictability of asset returns. Unpublished manuscript.
  • Wachter, J. A. and Warusawitharana, M. (2009). Predictable returns and asset allocation: Should a skeptical investor time the market? J. Econometrics 148 162–178.
  • Welch, I. and Goyal, A. (2008). A comprehensive look at the empirical performance of equity premium prediction. Rev. Financ. Stud. 21 1455–1508.
  • West, M. and Harrison, J. (1997). Bayesian Forecasting and Dynamic Models, 2nd ed. Springer Series in Statistics. Springer, New York.
  • Zhao, Z. Y., Xie, M. and West, M. (2016). Dynamic dependence networks: Financial time series forecasting and portfolio decisions. Appl. Stoch. Models Bus. Ind. 32 311–332.