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Using the Tangency Portfolio to Assess Sharpe Ratio Efficiency

Article Quant Q&A · Author: Unix
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Summary

The note explains how a risk-free asset changes the efficient frontier into the Capital Market Line (CML), which connects the risk-free return to the tangency portfolio. The Sharpe ratio measures the slope of this line: excess expected return over the risk-free rate divided by return volatility. On this basis, a portfolio with a lower Sharpe ratio than the tangency portfolio is below the best available risk-return tradeoff and is not mean-variance efficient when investors can combine the risk-free asset with the tangency portfolio.

The explanation is brief and conceptual. It gives the Sharpe ratio definition and the CML relationship, but no numerical example or empirical evidence. The conclusion depends on the stated framework: a risk-free asset is available, and efficiency is evaluated using the standard mean-variance setup. The note does not address estimation error, constraints, or settings where the assumed risk-free borrowing and lending is unavailable.

Key ideas

  • With a risk-free asset, the efficient frontier is represented by the Capital Market Line.
  • The tangency portfolio sets the slope of the Capital Market Line.
  • A lower Sharpe ratio indicates a less favorable excess-return-to-volatility tradeoff.
  • Under the stated assumptions, a portfolio below the tangency portfolio's Sharpe ratio is not mean-variance efficient.

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Portfolio constructionStatistics
Full text
# Can I deduce a portfolio is inefficient by compare is Sharpe ratio to the on the one the tangent portfolio?


# Can I deduce a portfolio is inefficient by compare is Sharpe ratio to the on the one the tangent portfolio?












If I have a portfolio with a Sharpe ratio lower than the Sharpe ratio of the tangent portfolio, can I conclude something about whether or not it is efficient?

If so, how/why?

## Answer by e.mal (score 1)

https://quant.stackexchange.com/a/26116

Sure you can. Sharpe Ratio is defined as: $$ SR=\frac{E(R)-R_f}{\sqrt{Var(R)}} $$ When you have a risk-free asset, the efficient frontier becomes linear (i.e. the line that passes from the $R_f$ and the tangent portfolio), named Capital Market Line (CML) and $SR$ denotes its slope. So lower $SR$ means that your portfolio does not lie on the efficient frontier and hence it is not efficient.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

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