Polson and Tew present a technique for large-scale optimal portfolio selection that feeds a Bayesian predictive distribution of returns and predictive variance–covariance matrix — built from informative (hierarchical) priors — into the optimizer, rather than plug-in sample moments. Using high-frequency daily data with per-security holding limits and a dynamic re-estimate-and-rebalance scheme, the method is designed for problems where the number of candidate holdings is large relative to the estimation window. Applied to S&P 500 stocks over 1970–1996, the resulting portfolio outperforms the benchmark index.
"The key inputs to the optimization process are the predictive distributions of expected returns and the predictive variance–covariance matrix … In our application, we find that our optimal portfolio outperforms the underlying benchmark."
The constructive bookend to Britten-Jones's pessimism: if efficient weights are estimated too imprecisely to trust, the fix is to stop pretending the sample moments are the truth and optimize against the predictive distribution instead. The paper's value is in showing this works at realistic scale — hundreds of S&P names, daily data, holding constraints, and rolling rebalancing — and actually beats the index, which is a stronger claim than the usual in-sample or small-universe demonstrations. It is a natural companion on the estimation-risk page to the Barry (1974) predictive-distribution framing and the Black-Litterman shrinkage-toward-priors idea. The honest caveats are the usual ones for a single-market backtest — the informative priors and the constraints do real work, so results depend on both, and a 1970–1996 S&P study says little about tail regimes or transaction costs.