A Note on the Two-fund Separation Theorem

Wenzelburger, Jan (2008): A Note on the Two-fund Separation Theorem.

Abstract

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 theorem 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.

• Item Type: MPRA Paper
• Language: English
• Keywords: Portfolio choice, CAPM, risk aversion, equilibrium, market participation
• Subjects: G - Financial Economics > G1 - General Financial Markets > G11 - Portfolio Choice ; Investment Decisions; G - Financial Economics > G1 - General Financial Markets > G10 - General; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C62 - Existence and Stability Conditions of Equilibrium

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