The Theory and Practice of Investment Management: Asset Allocation, Valuation, Portfolio Construction, and Strategies, Second Edition

ROY CAPM

A second CAPM, which appeared shortly after that of the writings of Sharpe and Lintner, differs from the SL-CAPM only in its assumption concerning the investment constraint imposed by investors. More specifically, it assumes that each investor (I) can choose any portfolio that satisfies

(4.6)

without regard to the sign of the variables. Positive is interpreted as a long position in a security while a negative is interpreted as a short position in a security.

However, a negative is far from a realistic model of real-world constraints on shorting. For example, equation (4.6) would consider feasible a portfolio with

since the above sums to one. This would correspond to an investor depositing $1,000 with a broker; shorting $1,000,000 of stock 1; then using the proceeds of the sale, plus the $1,000 deposited with the broker to buy $1,001,000 worth of stock 2. In fact, in this example, Treasury Regulation T (Reg T) would require that the sum of long positions, plus the value ...