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Why the Tangency Portfolio Equals the Market Portfolio in CAPM Equilibrium

Article Quant Q&A · Author: Dadoo
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Summary

This short explanation connects the tangency portfolio in mean–variance theory with the market portfolio. The tangency portfolio is the risky portfolio with the highest Sharpe ratio relative to the risk-free asset. Under the stated framework, investors are assumed to be rational and to choose that same optimal risky-asset mix.

If all investors hold the same risky portfolio in the same proportions, aggregating their holdings gives those proportions for the market’s risky assets. This is the intuition for identifying the tangency portfolio with the market portfolio in equilibrium. The explanation is brief and rests on strong assumptions: it does not derive the result formally, and it leaves out differences in beliefs, constraints, investment opportunities, and investor objectives that can prevent everyone from choosing the same portfolio.

Key ideas

  • The tangency portfolio maximizes the Sharpe ratio in the Markowitz framework.
  • The explanation assumes investors are rational and select the same optimal risky portfolio.
  • When all investors hold the same risky-asset weights, their aggregate holdings have those weights as well.
  • The identification depends on shared assumptions and is not established for markets with heterogeneous beliefs or constraints.

Tags

Portfolio constructionRisk managementStatistics
Full text
# Why is the tangency portfolio the market portfolio?


# Why is the tangency portfolio the market portfolio?












Except for the fact that in equilibrium demand must equal supply, I do not understand why, by chance, this tangency portfolio is the market portfolio. Do you have any idea?

## Answer by Julie Taylor (score 1)

https://quant.stackexchange.com/a/69744

The tangency portfolio is the portfolio which maximises the Sharpe ratio in the Markowitz setting. It is assumed that all participants in this setting are rational agents and maximizing the Sharpe ratio is a rational choice hence everyone would opt to choose this portfolio weighting. Since everyone (the whole market) has this portfolio weighting, we also call it the market portfolio.

HTH

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.