Unformatted text preview: aper on risk measurement.1 He argued that utility for the
typical investor equals the natural logarithm of wealth. With this utility function utility rises with wealth but at a diminishing rate RISK AND PORTFOLIO MANAGEMENT WITH ECONOMETRICS, VER. 10/23/2012. © P. KOLM. 3 Utility Functions
• The economic “theory of choice” uses the concept of a utility function to
describe the way entities make decisions when faced with a set of choices
• A (von NeumannMorgenstern) utility function assigns a real number to each element of the outcome space X, such that if x is preferred to y then
u(x ) ≥ u(y ) for all x , y ∈ X u : X → RISK AND PORTFOLIO MANAGEMENT WITH ECONOMETRICS, VER. 10/23/2012. © P. KOLM. 4 What Do We Mean by Risk Aversion?
• Risk aversion is the reluctance to accept a bargain with an uncertain payoff
rather than another bargain with more certain (but possibly lower) expected
payoff
• Formally, (for stateindependent utility of wealth) the utility function is riskaverse at W if u(W ) > Eu(W + ε) f...
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This document was uploaded on 02/17/2014 for the course COURANT G63.2751.0 at NYU.
 Fall '14

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