Valuation, Downside Risk Measures and Asymmetrical Information: A Portfolio Optimization Approach
28 Pages Posted: 16 Aug 2010 Last revised: 27 Sep 2010
Date Written: August 15, 2010
This paper presents an optimal portfolio algorithm under equilibrium conditions to evaluate future cash flows. The Algorithm employs expected return-risk approximation of utility function and bivariate distribution of cash flows of an investment and returns on market portfolios. The proposed procedure replaces the traditional discounting cash flow valuation approach that employs CAPM Risk Adjusted Cost of Capital (RACC). Only under symmetrical distribution assumption the proposed procedure and the conventional CAPM yields identical valuation. When downside risk measure is employed and asymmetrical distribution is assumed, then the proposed algorithm and the three moment extensions of CAPM may yield close but not necessarily identical valuation, while Estrada's downside risk extension of CAPM leads to erroneous valuation. The impact of skewness on valuation under symmetrical, as well as asymmetrical, information is examined in this paper by shifting a cash flow by "Mean Variance Preserving Shifts" (MVPS) that preserve both means and variance but generate skewer cash flow and Third-degree Stochastic Dominance (TSD). The proposed equilibrium valuation algorithm of this paper yields discount rates that consider downside risk measures as well as higher moments of the distribution.
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