efficient portfolios:   1. Any portfolio constructed by combining efficient portfolios is itself on the efficient frontier. 2. Every portfolio on the efficient frontier has a "companion" portfolio on the bottom half (the inefficient part) of the minimum-variance frontier with which it is uncorrelated. Because the portfolios are uncorrelated, the companion portfolio is referred to as the zero-beta portfolio of the efficient portfolio. The expected return of an efficient portfolios zero-beta companion portfolio can be derived by the following graphical procedure. From any efficient portfolio such as P in Figure 9.7 on page 278 draw a tangency line to the vertical axis. The intercept will be the expected return on portfolio Ps zero-beta companion portfolio, denoted Z(P). The horizontal line from the intercept to the minimum-variance frontier     12 Fischer Black, "Capital Market Equilibrium with Restricted Borrowing," Journal of Business, July 1972. III. Equilibrium In Capital Markets 9. The Capital Asset Pricing Model The McGraw−Hill Companies, 2001           TALES FROM THE FAR SIDE       Financial markets evaluation of risk determines the way firms invest. What if the markets are wrong? Investors are rarely praised for their good sense. But for the past two decades a growing number of firms have based their decisions on a model which assumes that people are perfectly rational. If they are irrational, are businesses making the wrong choices? The model, known at the "capital-asset pricing model," or CAPM, has come to dominate modern finance. Almost any manager who wants to defend a project-be it a brand, a factory or a corporate merger-must justify his decision partly based on the CAPM. The reason is that the model tells a firm how to calculate the return that its investors demand. If shareholders are to benefit, the re- turns from any project must clear this "hurdle rate." Although the CAPM is complicated, it can be reduced to five simple ideas:   Investors can eliminate some risks-such as the risk that workers will strike, or that a firms boss will quit-by diversifying across many regions and sectors. Some risks, such as that of a global recession,