Exponentially Weighted Covariance for Equal Risk Contribution Portfolios

Summary

The article explains equal risk contribution (ERC) portfolio construction, which chooses asset weights so each holding contributes equally to portfolio risk. Because ERC depends on estimated covariances rather than expected returns, the quality of the covariance estimate matters. The author tests whether exponentially weighted covariance estimates may help, comparing them with rolling-window estimates in a daily-updated portfolio of liquid ETFs. The workflow estimates pairwise covariances, assembles a covariance matrix, adjusts matrices that are not positive semidefinite, and calculates portfolio weights.

The document reports annualized return, volatility, and Sharpe ratio for the exponentially weighted approach, and describes comparing its performance with the rolling estimate. Returns are calculated without transaction costs, and the portfolio uses a limited ETF universe and a historical sample, so the reported figures do not establish live performance or broad generality. The proposed benefit of exponential weighting is framed as a hypothesis; covariance estimates remain noisy and sensitive to choices in estimation and implementation.

Key ideas

• ERC weights seek to equalize each asset’s contribution to overall portfolio risk.
• ERC uses covariance estimates and does not require expected return forecasts.
• Exponentially weighted covariance estimates give more recent observations greater influence than a fixed rolling window.
• The example applies estimated covariance matrices to a daily updated ETF portfolio and repairs matrices that are not positive semidefinite.
• The reported performance excludes transaction costs and comes from a limited historical example.

Tags

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.