Risk free asset demand in the classic portfolio problem is shown to decrease with income if and only if the consumer's uncertainty preferences over assets satisfy the preference condition that the risk free asset is more readily substituted for the risky asset as the quantity of the latter increases. In this case, the risky asset is said to be "urgently needed" following the terminology of the classic certainty analysis of Johnson (1913). The urgently needed property tends to be more readily satisfied in uncertainty versus certainty settings. Asset pricing implications of this property are provided.
Kubler, Felix, Larry Selden, and Xiao Wei. "When Is a Risky Asset 'Urgently Needed'?" American Economic Journal: Microeconomics 6, no. 2 (2014): 131-162.
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