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CML and Market Portfolio

Is the market portfolio the tangency portfolio? If the answer is yes, why would the market portfolio have the largest sharpe ratio? Is it mathematically proved or just an assumption?It looks to me that the sharpe ratio of the market portfolio should be average since the market includes all securities -- undervalued, fair-valued and overvalued.

What makes things complicated is that this market portfolio is a moving target -- the weight of each asset could change over time.

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