Optimal portfolio composition and the CAPM

It is commonly assumed that the CAPM implies that all investors hold a balanced portfolio, “the market portfolio,” and investors just determine the proportion of their wealth held in the market portfolio and the risk-free asset. That this is patently at odds with observed investor behavior is sometimes used to justify rejecting the CAPM. However, by assuming that substitute securities exist, in this paper we still obtain the CAPM, although investors neither hold all of the assets in the market nor a balanced shareholding in the assets they do hold.