Gain-Loss Portfolio Theory

Abstract

We show the existence of a viable gain-loss portfolio theory, relevant for investors seeking high expected gain compared to expected loss. Diversification, in gain-loss theory, raises a portfolio's gain-loss ratio even when all component assets have identical gain-loss ratios, as long as some of the assets' gains occur when other assets lose, i.e., as long as there are unmatched gains and losses. We derive a gain-loss asset pricing model which implies that the market portfolio possesses the highest gain-loss ratio of all assets and which yields each asset's reward measure (co-gain) as proportional to its risk measure (co-loss). We show that the market equilibrium and/or the absence of arbitrage profits imply equality of prices of gain and loss of individual assets, portfolios, and assets in portfolios. Further analysis of gain and loss includes applications to leverage, net present value, and the decomposition of variance.

JEL Classification: G12