9 The Capital Asset Pricing Model 275     9.3 EXTENSIONS OF THE CAPM   The assumptions that allowed Sharpe to derive the simple version of the CAPM are admit- tedly unrealistic. Financial economists have been at work ever since the CAPM was de- vised to extend the model to more realistic scenarios. There are two classes of extensions to the simple version of the CAPM. The first at- tempts to relax the assumptions that we outlined at the outset of the chapter. The second ac- knowledges the fact that investors worry about sources of risk other than the uncertain value of their securities, such as unexpected changes in relative prices of consumer goods. This idea involves the introduction of additional risk factors besides security returns, and we discuss it further in Chapter 11.     The CAPM with Restricted Borrowing: The Zero-Beta Model   The CAPM is predicated on the assumption that all investors share an identical input list that they feed into the Markowitz algorithm. Thus all investors agree on the location of the efficient (minimum-variance) frontier, where each portfolio has the lowest variance among all feasible portfolios at a target expected rate of return. When all investors can borrow and lend at the safe rate, rf, all agree on the optimal tangency portfolio and choose to hold a share of the market portfolio. However, when borrowing is restricted, as it is for many financial institutions, or when the borrowing rate is higher than the lending rate because borrowers pay a default pre- mium, the market portfolio is no longer the common optimal portfolio for all investors. When investors no longer can borrow at a common risk-free rate, they may choose risky portfolios from the entire set of efficient frontier portfolios according to how much risk they choose to bear. The market is no longer the common optimal portfolio. In fact, with investors choosing different portfolios, it is no longer obvious whether the market portfo- lio, which is the aggregate of all investors portfolios, will even be on the efficient frontier. If the market portfolio is no longer mean-variance efficient, then the expected return-beta relationship of the CAPM will no longer characterize market equilibrium. An equilibrium expected return-beta relationship in the case of restrictions on risk-free investments has been developed by Fischer Black.12 Blacks model is fairly difficult and re- quires a good deal of facility with mathematics. Therefore, we will satisfy ourselves with a sketch of Blacks argument and spend more time