Why Averaging Portfolio Weights Fails to Beat Input Shrinkage

A quantitative finance blog tested a simple idea: if you cannot decide which shrinkage method to use for mean-variance optimization, average the portfolio weights from different methods. The result was clear. It does not work as well as shrinking the inputs directly.

The post is the fifth in a series on portfolio optimization. Earlier tests found that the optimal shrinkage for Bayesian mean-variance optimization shifts with the size of the in-sample and out-of-sample periods. The surfaces are flat. T-statistics are insignificant. Random methods like Monte Carlo and bootstrapping perform worse than the best shrinkage methods. A shrinkage of 0.5 on Sharpe ratios and 0.75 on correlations seemed reasonable. The author stressed that the true optimum is uncertain.

The new idea came from Resolve Asset Management, which averages models when multiple approaches work equally well. The blog applied that logic to shrinkage: average the weights from naive mean variance (zero shrinkage) and equal weights (full shrinkage). That effectively shrinks the weights rather than the inputs.

The test results were unambiguous. The weight-averaging approach did not outperform the best input-shrinkage methods. In some cases it did worse. The author concluded that shrinking the inputs directly – the covariance matrix and expected returns – is more reliable than blending extreme weight vectors. Averaging weights adds another layer of noise without solving the underlying uncertainty.

For anyone running a stock market analysis portfolio, the practical takeaway is that the input stage matters more than the output stage. The uncertainty about the right shrinkage parameter is real. Trying to average your way out of it does not help. A fixed shrinkage of 0.5 on Sharpe ratios and 0.75 on correlations remains a reasonable default, even if it is not perfect. The search for a universal solution continues. This test suggests that weight averaging is not the answer.