Additivity of risk in portfolios
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A collection of gambles constituting a portfolio may itself be represented as a single gamble played once. A portfolio may be constructed by requiring each component gamble to be played once, and there is a theory of additive risk which requires that the perceived risk of the portfolio be an additive function of the perceived riskiness of the component gambles. Alternatively, a portfolio may be constructed as a probability mixture of the component gambles, and there is a theory of expected risk which requires that the perceived risk of the portfolio be the average of the riskiness of the component gambles. Existing evidence suggests that both of these theories cannot be true. A test of additivity of portfolios under both kinds of composition functions was made under two forms of display, the components displayed separately and fused as a single gamble. This experiment supports expected risk and rejects additive risk, especially under fused display.