There is a perfect, safe haven for risk-averse investors i.e. the riskless asset. No one has any informational advantage in the CAPM world. Everyone has already generously shared all of their knowledge about the future risk and return of the securities, so no one disagrees about expected returns. There is no mystery about the shape of the future return distributions. Last but not least, decisions are not complicated by the ability to change your mind through time.
Terminal wealth is measured at that time.
The proof is actually an elegant equilibrium argument. The widths are proportional to the size of each company. Size in this case is determined by the number of shares times the price per share. From the two-fund separation picture above, we already know that all investors will hold the same portfolio of risky assets, i.e. that the weights for each risky asset j will be the same across all investor portfolios. As with companies, we vary the width of the slice according to the wealth of the individual.