Are Gain and Loss Respectable?
9 Pages Posted: 22 May 2006
This article presents a series of transparent arguments in favor of using gain and loss as return and risk concepts. Gain and loss are widely used in markets where returns are asymmetric, such as betting markets, bond markets, option markets, and insurance. When properly (and intuitively) defined with respect to risk-free rates, a number of remarkably simple and beautiful propositions follow: (1)The value of gain equals the value of loss. (2) An asset's risk premium equals its expected gain minus its expected loss. (3) An asset's beta coefficient equals its ratio of expected co-loss with the market to expected market loss, and also its expected co-gain with the market to expected market gain. (4) In CAPM, an asset's co-gain is directly proportional to its co-loss. Closed-form formulas show how a portfolio's gain-loss ratio rises with diversification. In this paper, the empirical benefits of diversification are demonstrated using stock return data.
Keywords: gain, loss, diversification, capm
JEL Classification: G11, G12
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