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Modeling risk attitudes

Modeling risk attitudes. Objective: Develop tools to compare alternative courses of action with uncertain outcomes (lotteries or deals). (0.5). $30. A. (0.5). -$15. (0.5). $100. B. (0.5). -$40. Expected monetary value (EMV) is not a good measure of the value of a deal.

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Modeling risk attitudes

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  1. Modeling risk attitudes • Objective: Develop tools to compare alternative courses of action with uncertain outcomes (lotteries or deals) (0.5) $30 A (0.5) -$15 (0.5) $100 B (0.5) -$40

  2. Expected monetary value (EMV) is not a good measure of the value of a deal • Play same lottery many times, EMV is a good measure of value of a lottery. • Play a lottery once, EMV is not a good measure (0.5) $30 EMV(B)>EMV(A), most people prefer A A (0.5) -$1 (0.5) $2,000 B (0.5) -$1,900

  3. Utility function: risk averse decision-maker (0.5) xmin Lottery A (0.5) xmax Utility of EMV of lottery A Expected utility of lottery A Certain equivalent (CE) xmin xmax EMV(A) Risk aversion: Expected utility of lottery is less than the utility of sure amount equal to expected monetary value

  4. How to specify utility function • Graph • Mathematical function • Look-up table

  5. Attitudes toward risk Risk seeking Risk neutral Risk averse xmin Lottery A xmax Risk premium CE CE Risk averse: CE<EMV(A) Risk neutral: CE=EMV(A) Risk seeking: CE>EMV(A) EMV(A)

  6. Risk premium of a lottery • How much we must pay decision-maker to take lottery A instead of sure amount equal to the expected mean value of the lottery. • Risk premium=EMV(A)-CE • Risk averse decision-maker: Risk premium>0 • Risk neutral decision-maker: Risk premium=0 • Risk seeking decision-maker: Risk premium<0

  7. Properties of utility function • U(X+Y) not equal to U(X)+U(Y) • Can scale utility by a constant and/or add to it another constant without changing the rank order of the alternative courses of action. • Can scale utility function in any way you want. Usually, U(best consequence)=1, U(worst consequence)=0 • To make a decision, need only part of utility function for region from minimum and maximum amounts • Cannot compare utility functions of different decision-makers.

  8. Assessment of utility function • Assess a decision-maker’s utility by observing what gambles he/she is willing to take • Assessment using certainty equivalents • Assessment using probabilities

  9. Assessment using certainty equivalents (0.5) xmax A (0.5) xmin B CE Find CE so that decision-maker is indifferent between deals A and B U(CE)=0.5U(xmax)+0.5U(xmin)

  10. Assessment using probabilities (p) xmax A (1-p) xmin B x Find probability p so that decision-maker is indifferent between deals A and B U(x)=pU(xmax)+(1-p)U(xmin) If U(xmax)=1 and U(xmin)=0, then U(x)=p

  11. Standard types of utility function • Exponential -I • Logarithmic • Square root of x • Exponential -II

  12. Decreasing risk aversion • When we increase payoffs of a deal by the same amount, decision-maker becomes less risk averse (0.5) (0.5) $150 $50 B A (0.5) (0.5) $75 -$25 Risk premium of lottery A greater than that of B

  13. Decreasing risk aversion Although risk aversion occurs in real life it is not always important to account for it. Only need approximation of utility function to select best alternative

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