1. EVPI and Utility Lecture 20 November 7, 2005 12-706 / 19-702 / 73-359

2. Admin Issues zHW 4 Solutions re-posted zHW 5 Due Wednesday zNormal Office Hours this week. zPreparing for Case Studies - Second Try

3. Agenda zValue of Information - Final Thoughts ySample EVPI additivity problem zRisk and Utility (Chapter 13)

4. Willingness to Pay = EVPI zWe’re interested in knowing our WTP for (perfect) information about our decision. zThe book shows this as Bayesian probabilities, but think of it this way.. yWe consider the advice of “an expert who is always right”. yIf they say it will happen, it will. yIf they say it will not happen, it will not. yThey are never wrong. zBottom line - receiving their advice means we have eliminated the uncertainty about the event.

5. Notes on EVPI zAs we discussed last time, key is understanding what the relevant information is, and how it affects the tree. zSee quotes on pp. 501, 509 of Clemen y“Redraw the tree so that the uncertainty nodes for which perfect information is (now) available come before the decision node(s).” y(When multiple uncertain nodes exist..) “Move those chance nodes for which information is to be obtained so that they (all) precede the decision node.”

6. Is EVPI Additive? zLet’s look at handout for simple “2 parts uncertainty problem” considering the choice of where to go for a date, and the utility associated with whether it is fun or not, and whether weather is good or not. zWhat is Expected value in this case? zWhat is EVPI for “date?”; EVPI for “weather?” yWhat do the revised decision trees look like? zWhat is EVPI for “date and Weather?” zIs EVPI date + EVPI weather = EVPI date+weather ?

7. Additivity, cont. zNow look at p,q labels on handout for the decision problem (top values in tree) zIs it additive if instead p=0.3, q = 0.8? zWhat if p=0.2 and q=0.2?

8. EVPI - Why Care? zJust like doing Tornado diagrams showed us which were the most sensitive variables zEVPI analysis shows us which of our uncertainties is the most important, and thus which to focus further effort on yIf we can spend some time/money to further understand or reduce the uncertainty, it is worth it when EVPI is relatively high.

9. Risk Attitudes (Clemen 13) zOur discussions and exercises have focused on EMV (and assume expected-value maximizing decision makers) yNot always the case. ySome people love the thrill of making tough decisions regardless of the outcome (not me) zA major problem with Expected Value analysis is that it assumes long-term frequency (recall lecture on subjective probability).

10. Example from Book Exp. value (playing many times) says we would expect to win $50 by playing game 2 many times. What’s chance to lose $1900 in Game 2?

11. Utility Functions zWe might care about utility function for wealth (earning money). Are typically: yUpward sloping - want more. yConcave (opens downward) - preferences for wealth are limited by your concern for risk. yNot constant across all decisions! zRisk-neutral (what is relation to EMV?) zRisk-averse zRisk-seeking

12. Individuals zMay be risk-neutral across a (limited) range of monetary values yBut risk-seeking/averse more broadly zMay be generally risk averse, but risk- seeking to play the lottery yCost $1, expected value much less than $1 zDecision makers might be risk averse at home but risk-seeking in Las Vegas xSuch people are dangerous and should be treated with extreme caution. If you see them, notify the authorities.

14. (Discrete) Utility Function Dollar ValueUtility Value 15001.00 10000.86 5000.65 2000.52 1000.46 -1000.33 -10000.00

15. Certainty Equivalent (CE) zAmount of money you would trade equally in exchange for an uncertain lottery zWhat can we infer in terms of CE about our stock investor? yEU(low-risk) - his most preferred option maps to what on his utility function? Thus his CE must be what? yEU(high-risk) -> what is his CE? yWe could use CE to rank his decision orders and get the exact same results.

16. Risk Premium zIs difference between EMV and CE. yThe risk premium is the amount you are willing to pay to avoid the risk (like an opportunity cost). yRisk averse: Risk Premium >0 yRisk-seeking: Premium <0 (would have to pay them to give it up!) yRisk-neutral: = 0.

17. Utility Function Assessment zBasically, requires comparison of lotteries with risk-less payoffs zDifferent people -> different risk attitudes -> willing to accept different level of risk. zIs a matter of subjective judgment, just like assessing subjective probability.

18. Utility Function Assessment zTwo utility-Assessment approaches: yAssessment using Certainty Equivalents xRequires the decision maker to assess several certainty equivalents yAssessment using Probabilities xThis approach use the probability-equivalent (PE) for assessment technique zExponential Utility Function: yU(x) = 1-e -x/R yR is called risk tolerance