We study the effect of parameter uncertainty on the long-run risk for three asset classes: stocks, bills and bonds. Using a Bayesian vector autoregression with an uninformative prior we find that parameter uncertainty raises the annualized long-run volatilities of all three asset classes proportionally with the same factor relative to volatilities that are conditional on maximum likelihood parameter estimates. As a result, the horizon effect in optimal asset allocations is much weaker compared to models in which only equity returns are subject to parameter uncertainty. Results are sensitive to alternative informative priors, but generally the term structure of risk for stocks and bonds is relatively flat for investment horizons up to 15 years.
Hoevenaars, R. P. P. M., Molenaar, R. D. J., Schotman, P. C., & Steenkamp, T. B. M. (2014). Strategic asset allocation for long-term investors: Parameter uncertainty and prior information. Journal of Applied Econometrics, 29(3), 353-376. https://doi.org/10.1002/jae.2331