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Why Equal Weight Can Outperform an Ex Ante Tangency Portfolio

Article Quant Q&A · Author: Kostas
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Summary

The document explains how an equal-weight portfolio can end up with a higher Sharpe ratio than a portfolio selected to maximize Sharpe. The tangency portfolio is chosen using information available at the investment date, such as historical returns and covariances. Its optimality is conditional on those inputs and the assumptions of the estimation process.

The comparison occurs later, using realized outcomes. Future returns can differ from the historical data used to build the tangency portfolio, so an equal-weight portfolio may have a better realized Sharpe ratio over the evaluation period. This does not show that equal weighting was knowably superior in advance; it illustrates the distinction between ex ante optimization and ex post performance. The document offers a conceptual explanation rather than data, a formal comparison, or guidance on how to select a portfolio.

Key ideas

  • A tangency portfolio maximizes Sharpe based on estimates available when it is formed.
  • Its optimality is conditional on the input data and assumptions.
  • An equal-weight portfolio can have a higher Sharpe ratio in a later realized sample.
  • Ex post outperformance does not prove that equal weighting was optimal ex ante.

Tags

Portfolio constructionStatisticsBacktesting
Full text
# Equal Weight better sharpe than Tangency portfolio


# Equal Weight better sharpe than Tangency portfolio












Could you explain to me what it means to have better Sharpe Ratio in Equal Weight portfolio than tangency portfolio (max sharpe). Thank you.

## Answer by Alex C (score 2)

https://quant.stackexchange.com/a/43618

The Max Sharpe Ratio portfolio is determined ex-ante, using past data available at time t (say the previous 10 years returns and covariances). It is optimal given that data.

At time t two people invest: A invests in the Max Sharpe Ratio portfolio and B invests in the Equal Weighted Portfolio. At time $T > t$ we compare the results: it is possible that (ex-post) the Sharpe ratio of B turned out bigger than the Sharpe ratio of A.

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