Positively Weighted Portfolios on the Minimum-Variance Frontier
用对偶理论给出了最小方差前沿上所有资产权重为正的充要条件，并证明这些条件直观合理且不限于CAPM，但指出在资产数量大时权重符号对条件偏离很敏感。
Duality theory is employed to provide necessary and sufficient conditions for portfolios on the minimum-variance frontier to have positive investment proportions in all assets. These conditions involve the feasibility of portfolios that have non-negative correlation with all assets and positive correlation with at least one. Using these results, several “qualitative” results concerning the signs of investment proportions in efficient portfolios are proved. It is argued that the conditions that ensure all-positive weights in efficient portfolios are intuitively compelling and are not unique to the CAPM. With large numbers of assets, however, the signs of weights in minimum-variance portfolios can be very sensitive to slight departures from these conditions due to, for example, sampling error.