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Ann Finance (2010) 6:221239
DOI 10.1007/s10436-009-0144-8
RESEARCH ARTICLE
Received: 27 April 2009 / Accepted: 1 December 2009 / Published online: 19 December 2009 Springer-Verlag 2009
Abstract This paper resolves two issues regarding the traditional capital asset pricing model with one risk-free asset which seem to have been overlooked in the literature. First, it provides an elementary and complete proof of the two-fund separation theorem which accounts for the fact that asset demand may become undened if the limiting slopes of the investors indifference curves are nite. Second, it shows that an additional limiting condition on investors risk aversions is generally necessary to guarantee existence of an equilibrium. Moreover, a generalized existence result is formulated which includes investors who in equilibrium may not invest in risky assets and a simple condition ensuring positive equilibrium asset prices is given.
Keywords Portfolio choice CAPM Risk aversion Equilibrium Market
participation
JEL Classication C62 D11 G11 G12
1 Introduction
In the vast amount of current research into the dynamics of nancial markets, asset demand functions play a central role in describing agents investment behavior, e.g., see the recent handbook in nance edited by Hens and Schenk-Hopp (2009). In a mean-variance framework such asset demand functions are characterized by the
This paper was previously entitled A note on the two-fund separation theorem.
J. Wenzelburger (B)
Centre for Economic Research, Keele University, Keele ST5 5BG, UK e-mail: [email protected]
The two-fund separation theorem revisited
Jan Wenzelburger
123
222 J. Wenzelburger
two-fund separation theorem which is one of the most central results of the capital asset pricing model (CAPM).
The equilibrium formulation of the CAPM dates back to Sharpe (1964), Lint-ner (1965), and Mossin (1966). Recently Bhm and Chiarella (2005) investigated a dynamic intertemporal extension of the CAPM which is founded on a modern formulation of the two-fund separation theorem (Lemma 2.3) and an existence result of intertemporal CAPM equilibria (Lemma 2.5) which is based on Dana (1999) and Hens et al. (2002). For the proofs of these two lemmas the reader is referred to Bhm (2002). Unfortunately, however, the proof of the separation theorem there is incomplete, leaving the existence result in suspension. There are two unresolved core issues. First, the asset demand function may become undened if the limiting slopes of...