Finalnub

"since this is true for all investors, portfolio M must be the market portfolio "

I agree with Bruin, but remember that this statement is a consequence of all those assumptions about investors in CAPM that you surely don't believe (because they aren't true) incl. all of them have the same quadratic loss utility function which they all use to maximize their individual utilities, they are all rational, they understand and can predict all the risks/returns for all possible securities, yada, yada...

If all these things are true, you invest your risky assets in the tangency portfolio because all other portfolios are inferior. If that's the one everyone invests in, by definition it's the market portfolio. It's not really the S&P 500; it's all the investable assets in the world.

Nobody really believes CAPM but that's why it's taught in an exam called "Level 1".