The Determination of Optimal Investment Policy

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.