Showing papers on "Efficient frontier published in 1967"
TL;DR: This paper suggests that portfolio selection problems be re-formulated as parametric linear-programming problems, utilizing a linear approximation to the true (quadratic) formula for a portfolio's risk.
Abstract: The portfolio selection problem faced by a mutual fund manager can be formulated following the Markowitz approach: find those portfolios that are efficient in terms of predicted expected return and standard deviation of return, subject to legal constraints in the form of upper bounds on the proportion of the fund invested in any single security. This paper suggests that such problems be re-formulated as parametric linear-programming problems, utilizing a linear approximation to the true (quadratic) formula for a portfolio's risk. Limited empirical evidence suggests that the approximation is acceptable. Moreover, it allows the use of an extremely simple and efficient special-purpose solution algorithm. With appropriate modifications, this algorithm may prove useful to the managers of mutual funds with a wide variety of objectives.
185 citations
TL;DR: In this paper, the shape of the efficient frontier of security portfolios and the determination of an optimal investment policy were discussed using a model similar to Sharpe's, and it was shown that in equilibrium, the expected returns and standard deviations of all efficient security portfolios lie along a straight line, but this conclusion depends on the assumptions that there exist both a risk-free asset and a single interest rate at which all investors can borrow or lend funds.
Abstract: Using a model similar to Sharpe's, the author discusses the shape of the efficient frontier of security portfolios and the determination of an optimal investment policy. Sharpe shows that in equilibrium, the expected returns and standard deviations of all efficient security portfolios lie along a straight line. In this article, the author demonstrates that this conclusion depends on the assumptions that there exist both a risk-free asset and a single interest rate at which all investors can borrow or lend funds. If either assumption is removed, the expected returns and standard deviations of efficient portfolios will not be linearly related. The author suggests that in equilibrium, the efficient frontier is not unique for all investors, but that the efficient frontier will be different for investors with different borrowing rates. Furthermore, if no risk-less asset exists, a portfolio may exist which has both higher expected real return and lower risk than does a default-free security.
6 citations