When Heuristic Portfolios Are Efficient

Summary

The document asks whether portfolios built from simple rules should be called efficient. In Markowitz portfolio theory, efficiency has a specific meaning: for a given expected return, a portfolio has the lowest possible risk, placing it on the efficient frontier. The question contrasts this definition with heuristic constructions such as equal weighting and inverse-volatility weighting, and notes the claim that equal weighting can outperform frontier portfolios out of sample.

It also asks whether hierarchical risk parity, maximum diversification, and maximum decorrelation portfolios qualify as efficient. No answers, derivations, or empirical results are included, so the document does not resolve those classifications. Its useful distinction is between formal mean-variance efficiency and broader practical performance: doing well out of sample does not, by itself, establish that a portfolio lies on the theoretical frontier. Assessing any candidate requires specifying its objective, assumptions, estimates, and comparison set.

Key ideas

• Markowitz efficiency means minimizing risk for a specified expected return.
• A portfolio is formally efficient when it lies on the efficient frontier under the chosen model.
• Out-of-sample performance and frontier efficiency are different criteria.
• Equal-weight and inverse-volatility portfolios are presented as heuristic allocation rules.
• The document raises, but does not answer, the efficiency status of HRP and diversification-based portfolios.

Tags

# Are heuristic portfolios efficient portfolios?


# Are heuristic portfolios efficient portfolios?












Markowitz's definition of an efficient portfolio is one that minimizes portfolio risk for a given level of expected return. He therefore calls portfolios along the efficient frontier "frontier portfolios" as well as "efficient portfolios".

There also exist well-performing strategies called heuristic portfolios including the equally-weighted (1/N) portfolio, and inverse-volatility portfolio (IVP). I know the 1/N portfolio doesn't lie on the efficient frontier, but is known to often outperform all frontier (efficient) portfolios out-of-sample. There's also no comment about the IVP being efficient. Can we call these two heuristic portfolios efficient portfolios?

optional question: Are the following strategies also efficient portfolios or no?

- hierarchical risk parity portfolio (HRP)

- maximum diversification portfolio (MDP)

- maximum decorrelation portfolio

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