Utility and Portfolio Choice

P kolm 12 exponential utility function 1 ux e x

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Unformatted text preview: b , 1 − bx b>0 rR (x ) = bx 1 − bx This utility function satisfies u ′ > 0 only when x < 1 / b , which implies that there are certain states where the investor would choose less wealth over more. This is a problem with the quadratic utility function RISK AND PORTFOLIO MANAGEMENT WITH ECONOMETRICS, VER. 10/23/2012. © P. KOLM. 12 • Exponential utility function 1 u(x ) = − e −λx , λ ≠ 0 λ rA (x ) = λ, rR (x ) = λx This utility function is referred to as constant absolute risk aversion (CARA) because the absolute risk aversion is constant • Power utility function u(x ) = x α , rA (x ) = 0 < α <1 1−α , x rR (x ) = 1 − α This utility function is referred to as constant relative risk aversion (CRRA) because the relative risk aversion is constant RISK AND PORTFOLIO MANAGEMENT WITH ECONOMETRICS, VER. 10/23/2012. © P. KOLM. 13 • Logarithmic utility function u(x ) = ln(x ) rA (x ) = 1 , x rR (x ) = 1 This utility function is part of the CRRA family. The logarithmic utility function is an extension of the power utility function for that case α = 0 by the nature of xα −1 lim = ln(x ) α→0 α RISK AND PORTFOLIO MANAGEMENT WITH ECONOMETRICS, VER. 10/23/2012...
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This document was uploaded on 02/17/2014 for the course COURANT G63.2751.0 at NYU.

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