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.

Yes it is a tangency portfolio. It is mathematically proven to have the highest sharpe ratio for THAT particular risk. However your saying that some securities are over or under valued is not correct. There is an assumption that all the securities are fairly valued as all investors have the same expectations regarding risk and return factors. The market portfolio will be a moving target but the tangent line will also change accordingly. For that PARTICULAR RISK, it will be have the highest sharpe ratio.

I think “Market Portfolio” when talking about portfolio theory is the optimal portfolio. Given completely efficient markets etc (in equilibrium…), the weights of the market portfolio should equal the optimal portfolio. i.e. all investors should want to hold the optimal portfolio (buying and selling until they get there) which means that it is now the market portfolio. I just dont think of the “market portfolio” when talking about the CML as the true market portfolio at any specific point in time. More of a theoretical portfolio. With that said, if we were given the weights etc of a portfolio on the test that was said to be the “market portfolio”, I would assume that the theory holds and that it was the optimal portfolio. Just a guess. Sort of confused myself at the end there.

think you have an element of security market line vs capital market line in there as well (the other poster touched on that)