Negative Maximum Sharpe Ratios in Tangency Portfolios

Summary

The document poses a mean-variance portfolio question involving the market excess return and two long-short factor portfolios. Transaction costs have already been deducted from the factors, leaving their expected net returns negative. Under these assumptions, the calculated tangency portfolio has a negative maximum Sharpe ratio, prompting the author to ask why this can occur and why holding only the market excess return would not be mean-variance efficient.

No answer, derivation, data, or empirical evidence is included, so the document identifies a portfolio-theory issue rather than resolving it. It raises questions about optimization over risky assets when some expected returns are negative, but does not specify covariance estimates, constraints, or whether the risk-free asset is available for allocation. Those details are important for interpreting a tangency solution and comparing it with a market-only portfolio.

Key ideas

• The example combines market excess returns with two long-short factor portfolios.
• The factors have negative expected net returns after estimated transaction costs.
• The stated tangency portfolio has a negative maximum Sharpe ratio.
• The document asks why a market-only allocation is not efficient but provides no resolution.
• Covariances and portfolio constraints are unspecified and would affect the analysis.

Tags

# Tangency portfolio negative maximum Sharpe ratio


# Tangency portfolio negative maximum Sharpe ratio












Suppose I have three assets: the market, factor A and factor B. The market is in excess returns of the risk free rate. The other two factors are long-short portfolios. I have net returns for these factors, since I deduct estimated transaction costs. The expected net returns for these factors are negative

The mean variance tangency portfolio produces a negative maximum Sharpe ratio in this case. How and why is this possible? Why is it not mean variance efficient to just allocate 100% of the weight in the excess market return?

I am looking forward hearing your answers.

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