How Efficient Use of Information Changes Portfolio Allocations

Unknown model parameters, like expected returns, cannot be accurately estimated from short samples. Respective estimation error most likely leads to the portfolio, inconsistent with its target risk/return profile. We investigate the ways of reducing the impact of estimation error on portfolio selection in a particular mean-variance setting. We consider the cross-section of asset returns where assets possess predictability but up to an unknown scale function. Assuming stability in the return generating process, how best we use historical data to infer the optimal scaling of our expected return forecasts? In a Bayesian implementation we make inferences about unknown parameters using information on results of unrelated experiments coupled with the sample data. We express the optimal amount of money put at risk as a complicated function of a prior on manager's forecasting skills and observed returns. We find that, to fully exploit available information, an investor needs only first two moments of the posterior distribution of his forecasting skills. Portfolio holdings, derived under efficient use of information, strikingly differ from the holdings derived from the sample information only (i.e. using classical maximum likelihood estimation MLE). Optimization in the efficient way with prior favors concentrated portfolio holdings. Since concentrated holdings drive portfolio risk, fund managers should treat larger holdings with caution while they can afford not to be conservative on small holdings. Ignoring the prior and optimizing on observed returns only result in massively inflated allocations and leveraged portfolio, or no investments at all besides cash. Portfolio selection with prior that uses naive mode-estimates of the posterior instead of mean-estimates leads to as inconsistent portfolio, similar to the portfolio selection led by MLE-based estimates. The impact of efficient use of information on portfolio selection is generalized to the case of non-homogeneously predictable classes of assets, where each class has its own degree of predictability