On the Long-Run Volatility of Stocks

Carlos M. Carvalho, Hedibert F. Lopes, Robert McCulloch

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


In this article, we investigate whether or not the volatility per period of stocks is lower over longer horizons. Taking the perspective of an investor, we evaluate the predictive variance of k-period returns under different model and prior specifications. We adopt the state-space framework of Pástor and Stambaugh to model the dynamics of expected returns and evaluate the effects of prior elicitation in the resulting volatility estimates. Part of the developments includes an extension that incorporates time-varying volatilities and covariances in a constrained prior information set-up. Our conclusion for the U.S. market, under plausible prior specifications, is that stocks are less volatile in the long run. Model assessment exercises demonstrate the models and priors supporting our main conclusions are in accordance with the data. To assess the generality of the results, we extend our analysis to a number of international equity indices. Supplementary materials for this article are available online.

Original languageEnglish (US)
Pages (from-to)1050-1069
Number of pages20
JournalJournal of the American Statistical Association
Issue number523
StatePublished - Jul 3 2018


  • Covariance matrix
  • Dynamic models
  • Long-run investing
  • Volatility

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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