An Economic Index of Relative Riskiness
33 Pages Posted: 19 Jan 2012 Last revised: 31 Jan 2012
Date Written: January 19, 2012
In their seminal works, Arrow (1965) and Pratt (1964) defined two aspects of risk aversion: absolute risk aversion and relative risk aversion. Based on their definitions, we define two aspects of risk: absolute risk and relative risk. We consider situations in which, by making an investment, an agent exchanges a certain amount of wealth w by a random distributed level of wealth rw. In such situations, we define absolute risk as the riskiness of a gamble that is distributed as rw-w, and relative risk as the riskiness of a security that is distributed as rw/w. We measure absolute risk by the Aumann and Serrano (2008) index of riskiness and relative risk by an equivalent index that we develop in this paper. The two concepts of risk do not necessarily agree on which one of two investments is riskier, and hence they capture two different aspects of risk.
Keywords: riskiness, Absolute Risk Aversion, Relative Risk Aversion, gamble, security
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