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MPRA A Note on the Two-fund Separation Theorem∗ Jan Wenzelburger Center for Economic Research Keele University Keele, ST5 5BG, UK j.wenzelburger@econ.keele.ac.uk Keele Economic Research Paper No. 1 Abstract Keywords: Portfolio choice, CAPM, Risk aversion, Equilibrium, Market Par- ticipation JEL Classification: G10, C62 First version: Feb. 2008, this version: Sep. 2008. This note contains two remarks on the traditional capital asset pricing model (CAPM) with one risk-free asset. Firstly, an elementary proof of the two-fund separation theo- rem is provided showing that asset-demand may become undefined if the limiting slope of the investor’s indifference curves is finite. Secondly, it is shown that an additional limiting condition on the risk aversion is generally necessary to guarantee existence of an equilibrium in the CAPM with one risk-free asset. The role of these two limiting conditions seems to have been overlooked in the established literature. A generalized existence result is formulated which allows for the case in which in equilibrium not all investors participate in the market for risky assets. ∗Acknowledgment. I would like to thank Tim Worrall and Gauthier Lanot for stimulating discussions. 1 Introduction One the most central results of the capital asset pricing model (CAPM), developed by Sharpe (1964), Lintner (1965), and Mossin (1966), is the two-fund separation theorem. In an agent-based modelling framework, B¨ohm Chiarella