Portfolio theory has traditionally started from the assumption that a portfolio can be separated into risk-free and risky assets. Jarrow (1988) proposes an alternative to the Capital Asset Pricing Model (CAPM) and the Security Market Line (SML) based on the definition given by Harry Markowitz for the mean-variance efficient frontier, and then uses the same mean-variance methodology to elaborate a test to measure the efficient frontier without the existence of risk-free assets. In a recent study, Parada (2008) develops some propositions for building a portfolio made up of risky assets to substitute a risk-free asset, further determining the proportions that should be invested to generate this portfolio and analyzing the construction of a portfolio to substitute the market portfolio. The present article builds on this earlier work to develop the implications of forming risk-free portfolios made up solely of risky assets. © EuroJournals Publishing, Inc. 2009.