A natural approach to enhance portfolio diversification is to rely on factor-risk parity, which yields the portfolio whose risk is equally spread among a set of uncorrelated factors. The standard choice is to take the variance as risk measure, and the principal components (PCs) of asset returns as factors. Although PCs are unique and useful for dimension reduction, they are an arbitrary choice: any rotation of the PCs results in uncorrelated factors. This is problematic because we demonstrate that any portfolio is a factor-variance-parity portfolio for some rotation of the PCs. More importantly, choosing the PCs does not account for the higher moments of asset returns. To overcome these issues, we propose using the independent components (ICs) as factors, which are the rotation of the PCs that are maximally independent, and care about higher moments of asset returns. We demonstrate that using the IC-variance-parity portfolio helps to reduce the return kurtosis. We also show how to exploit the near independence of the ICs to parsimoniously estimate the factor-risk-parity portfolio based on value at risk. Finally, we empirically demonstrate that portfolios based on ICs outperform those based on PCs, and several state-of-the-art benchmarks.

We derive analytical expressions for the risk of an investor’s expected utility under parameter uncertainty. In particular, our analysis focuses on characterizing the out-of-sample utility variance of three portfolios: the classic mean-variance portfolio, the minimum-variance portfolio, and a shrinkage portfolio that combines both. We then use our analytical expressions to study a robustness measure that balances out-of-sample utility mean and volatility. We show that neither the sample mean-variance portfolio nor the sample minimum-variance portfolio exhibits maximal robustness individually, and one needs to combine both to optimize portfolio robustness. Accordingly, we introduce a robust shrinkage portfolio that delivers an optimal tradeoff between out-of-sample utility mean and volatility and is more resilient to estimation errors. Our results highlight the importance of considering out-of-sample performance risk in designing and evaluating investment strategies and stochastic discount factor models. This paper was accepted by Kay Giesecke, finance. Funding: N. Lassance gratefully acknowledges financial support by the Fonds de la Recherche Scientifique [Grant J.0115.22]. Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2023.00178 .

Existing portfolio combination rules that optimize the out-of-sample performance under parameter uncertainty assume multivariate normally distributed returns. However, we show that this assumption is not innocuous because fat tails in returns lead to poorer out-of-sample performance of the sample mean–variance and sample global minimum-variance (GMV) portfolios relative to normality. Consequently, when returns are fat-tailed, portfolio combination rules should allocate less to the sample mean–variance and sample GMV portfolios, and more to the risk-free asset, than the normality assumption prescribes. Empirical evidence shows that accounting for fat tails in the construction of optimal portfolio combination rules significantly improves their out-of-sample performance.