CAPM in Real World: Risk-Friendly Investments

Abstract

The aim of this paper is to show how the existence of equilibrium in CAPM may be obtained when individuals/investors are risk friendly. This assumption is closer to the real world, since risk aversion is rare and the portfolios implying a greater payoff are the ones which increase the variance of the payoff itself. Specifically, we assume that the wage vectors of the individuals/investors do not lie in the market space, which is the usual assumption for CAPM, namely, the payoff of any portfolio is replicated by the wage of the individuals/investors. The interpretation of such an assumption is that the wealth of the individuals/investors may not invest in financial markets as a whole. The second main result is that the perception of risk by the objective probabilities for the states of the world does not affect the equilibrium existence. This is a consequence of the No-Arbitrage assumption. This condition may be stated in terms of the existence of the objective probabilities for the states of the world. Since CAPM is usually considered as a way to compare the return of the so-called “market portfolio” and the return of any other portfolio, in the final section of this paper, we do provide the regression form of this altered form of CAPM.