Abstract
The effects of multivariate risk are examined in a model of portfolio choice. The conditions under which portfolio choices are separable from consumption decisions are derived. Unless the appropriate restrictions hold on investors' preferences or on the probability distribution of risks, the optimal portfolio is affected by other risks. This requires generalizing the usual measures of risk aversion. With one risky asset, matrix measures of risk aversion are used to generalize the results of Arrow (1965) and Pratt (1964) concerning the effects of risk aversion and wealth on the optimal portfolio. With two risky assets, the choices made by two investors coincide if and only if their generalized risk-aversion measures are identical. Ross's notion of stronger risk aversion is then used to characterize the effect of risk aversion on the level of investment in the riskier asset.
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