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# Class Note for EMSE 269 with Professor Dorp at GW (3)

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This 29 page Class Notes was uploaded by an elite notetaker on Saturday February 7, 2015. The Class Notes belongs to a course at George Washington University taught by a professor in Fall. Since its upload, it has received 18 views.

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Date Created: 02/07/15

Chapter 12 Value of Information Decisions R T Clemen T Reilly Draft Version 1 E Making Hard Decisions Chapter 12 Value of Information Slide 1 of 29 R y mm mm Le meNmesbv m vanDamandYA Mazzucm copvmwmuus mPlwwseasngedudamiv bvevvu Introduction Often you pay for information you are asking for Investment Advice Management Consultants Market Investigation Palm Reading You need this information to make a decision in the future To invest in a particular stock or not To restructure the organization of your company or not To introduce a product or not Should I marry this person or not Draft Version 1 Making Hard Decisions Chapter 12 Value of Information Slide 2 of 29 R r clemen r Reilly Le meNmesbv m vanDamandYA Mazzuchl copvmwezuus mPlwwseasngeduldavplvl bvcvvu Introduction Problem at hand Given your decision problem how much should you be willing to pay for this information To answer this questions you have to determine the value in dollars of information We will first discuss a method for determining the value of perfect information and next for imperfect information Draft Version 1 WHICH ONE DO YOU VALUE MORE 3 Making Hard Decisions Chapter 12 Value of Information Slide 3 of 29 a r cienem Reilly Le uveNmesbv J in am Mazzuchi conRicHiezuus mp waNv auwavpivi by cvvu Probability and Perfect Information Definition Clairvoyant Expert on event A If event A is about to occur the expert says it will If event A is not to occur the expert says it will not The expert is NEVER wrong His information is PERFECT A Dow Jones index goes up quotAquot Expert Says Dow Jones index goes up You are considering investing in a company but before you do you want to make sure that the Dow Jones index will go up as this increases your chances of making a good investment Therefore you decide to consult a clairvoyant expert on the event A Draft Version 1 3 Making Hard Decisions Chapter 12 Value of Information Slide 4 of 29 a r cienen r Remy Le uveNmesbv J in am Mazzuchi conRicHiezuus mp waNv auwavpivi by cvvu Probability and Perfect Information What does it mean to be clairvoyant in probabilistic terms Pr Expert Says Dow Jones T Dow Jones T Pr quotAquot IA 1 Similarly PrquotAquotA 1lt1 PrWA 1ltgtPIWA 0 PrquotAquotZ 0 ltgt1 PIWZ 0 ltgtPrWZ 1 Perhaps more importantly what about Draft Version 1 Pr Dow Jones T Expert Says Dow Jones T Pr quotAquot I A Making Hard Decisions Chapter 12 Value of Information Slide 5 of 29 r Ciemen l Remy Le meNmesbv m van dlA Mamcm copvmewezuus MPIvwwvseasg u m y bvevvu Probability and Perfect Information Prquot Aquot APrA PrH A H Prquot A quot APrA Prquot A quot APrA Prquot A quot APrA PrAIHAH 1 PrA 1 1PrA 0 PrA Conclusion Draft Versmn 1 PrAquotAquot equals 1 no matter what the value of PrA is Making Hard Decisions Chapter 12 Value of Information Slide 6 of 29 r C emen Remy Le uveNmeshv m YpandYA Mazzucm copvmwmuus humWm sawdamn bvevvu Probability and Perfect Information What about the probability Pr Expert Says Dow Jones T PrquotAquot Pr Expert Says Dow Jones T Prquot Aquot APrA Pr quot Aquot ZPrZ 1PrA 0 PrZ PrA PrDow Jones T This is true in general if we consult a clairvoyant expert about an event a with possible outcomes A1 An then Prquot Ai quot PrAi for all i 1n After consulting the clairvoyant expert about event a no uncertainty remains about event a Draft Version 1 Making Hard Decisions Chapter 12 Value of Information Slide 7 of 29 r Clemen l my Le uveNmesbv m Mazzucm conRicHrezuus Nipivwwvse bvcvvu Expected Value of Perfect Information STOCK MARKET EXAMPLE MAX PROFIT EMV 580 1500 Hi h Risk 9 100 1000 EMV 580 1000 200 100 S 39 A t avmgs ccoun 500 Draft Versmn 1 Making Hard Decisions Chapter 12 Value of Information Slide 8 of 29 r Ciemen i Remy Le meNmesbv m vanDamandYA Mazzucm copvmwmuus mpvwwvseasngeduldamyv bvevvu Draft Version 1 Expected Value of Perfect Information Consider first talking to a clairvoyant expert and then making the investment decision MAX PROFIT EMV High Risk Stock 1500 1500 Up 05 1 Low Risk Stock 1000 I Savings Account 500 EMV 1000 EMV High Risk Stock 500 100 Flat 03 Low Risk Stock 200 Savings Account 500 EMV High Risk Stock to 0 2 500 h 1 000 quot 39 Low Risk Stock 100 Savings Account 500 Making Hard Decisions Chapter 12 Value of Information i Clemen l My Le uveNmesbv m vanDaYPandiA Mazzuchi Niplvwwvseasngeduldavpiv Slide 9 of 29 COPVRlGHY o zuus hvGWU Expected Value of Perfect Information Draft Version 1 Of course the clairvoyant expert will charge a fee and you would like to know how much you would be willing to pay before using his services MAX PROFIT Do not Consult Clairvoyant EMV 580 Consult Clairvoyant EMV 1000 X X Consulting Fee Conclusion You would be willing to consult the clairvoyant expert if 1000 X 2 580 ltgt X S1000 580 420 EVPI 39 Making Hard Decisions Chapter 12 Va Lena by J R Slide 10 of 29 copvmew o zuus hvGWU of Information R r Clem r Remy r Expected Value of Perfect Information EVPI Expected Value of Perfect Information Interpretation EVPI is the maximum amount of money you would be willing to pay for the services of the clairvoyant expert If he charges more than 420 you would not consult the expert A Dow Jones index goes up quotAquot Expert Says Dow Jones index goes up Consider an Expert about event A who is not clairvoyant but is considered to be an expert What does it mean in for an expert not to be perfect in his assessment about event A Draft Version 1 3 Making Hard Decisions Chapter 12 Value of Information Slide 11 of 29 a r Clemenil Reilly Le uveNmesbv J in am Mazzuchi conRicHrezuus Mullvwwv dul39vdamn bv cvvu Expected Value of Imperfect Information Pr Expert Says Dow Jones T Dow Jones T PrquotAquot A lt1 Hopefully the probability above is close to 1 otherwise why consider himher and Expert Pr Expert Says Dow Jones T Dow Jones J PrquotAquot Z gt 0 Hopefully the probability above is close to 0 otherwise why consider himher and Expert When an expert about an event is not clairvoyant you need to express your trust in his assessment by for example checking his past performances and inter viewing references Draft Version 1 Making Hard Decisions Chapter 12 Value of Information Slide 12 of 29 r Clemen l my rammest m Mazzuchr conRchrezuus Niplvwwvse bvcvvu Draft Version 1 Expected Value of Imperfect Information Based on your backgroundcheck of the expert you assess your trust in terms of subjective probabilities True Market State Expert UP FLAT DOWN Prediction quotUPquot PrquotUPquotUP PrquotUPquotFLAT PrquotUPquotDOWN quotFLATquot PrquotFLATquotUP PrquotFLATquot FLAT PrquotFLATquotquotDOWN quotDOWNquot PrquotDOWNquotUP PrquotDOWNquot PrquotDOWNquotquotDOWN FLAT Total 1 1 1 Making Hard Decisions Chapter 12 Value of Information Slide 13 of 29 R r Clemen i RellW Le meNmesbv m vanDamandYA Mazzucm mp wwwseas ng eduldam1U copvmew zuus vaWU Draft Versmn 1 Expected Value of Imperfect Information Actual Assessment of the Expert True Market State Expert UP FLAT DOWN Prediction quotUPquot 80 15 20 quotFLATquot 10 70 20 quotDOWNquot 10 15 60 Total 1 1 1 Making Hard Decisions Chapter 12 Value of Information Slide 14 of 29 R r Clemen l Remy Le meNmesbv m vanDamandlA Mazzucm copvmew zuus mp lvwwvseas ng eduldam1U bv cvvu Expected Value of Imperfect Information STOCK MARKET EXAMPLE MAX PROFIT EMV 580 1500 Hi h Risk 9 100 1000 EMV 580 1000 200 100 S 39 A t avmgs ccoun 500 Draft Versmn 1 Making Hard Decisions Chapter 12 Value of Information Slide 15 of 29 r Ciemen i Remy Le meNmesbv m vanDamandYA Mazzucm copvmwmuus mpvwwvseasngeduldamyv bvevvu Draft Version 1 Expected Value of Imperfect Information Consider rst talking to an quotImperfect expert and then making the investment decision Up 0 Original Decision Problem Up F39a ltgt Original Decision Problem Flat Original Decision Problem Down 39 Making Hard Decisions Chapter 12 Value of Information Le ureNmesbv m vanDaipandiA Mazzuchi mPlwmwseasngeduldamiil Slide 16 of 29 conRicHr o zuus hvGWU R r Cieriieriii ReiiW Expected Value of Imperfect Information Suppose the Imperfect expert said Dow Jones will go U P 7 Up 39 1500 ngh Rlsk Flat a 100 1000 U up 7 p 1000 39 Low Rlsk Hat 2 St k 200 cc 7 Down 1 00 Savings Account 500 E E g a a 6 Making Hard Decisions Chapter 12 Value of Information Slide 17 of 29 R r Ciemen i Remy Le uveNmesbv m vanDavpandYA Mazzucm cowewmuua millvwwvseasngedul39vdamn bvcvvu Expected Value of Imperfect Information Draft Versmn 1 Suppose the Imperfect expert said Dow Jones will stay F LAT 7 Up 39 1500 ngh Rlsk Flat 0 100 1000 U H H p 1000 Flat 7 Low Risk Hat 7 St k 200 cc 7 Down 1 00 Savings Account 500 Making Hard Decisions Chapter 12 Value of Information Slide 18 of 29 R r Ciemen i Remy Le uveNmesbv m vanDamandYA Mazzucm mp lvwwvseas ng 200mm copvmew o 2005 hvGWU Expected Value of Imperfect Information Suppose the Imperfect expert said Dow Jones will go DOW N 7 Up 39 1500 ngh Rlsk Flat 0 100 1000 U p 1000 Low Risk Hat 7 s k 200 Down 0 00 V Down 1 00 Savings Account 500 a E g a a 6 Making Hard Decisions Chapter 12 Value of Information Slide 19 of 29 R r Ciemen i Remy Le uveNmesbv m vanDavpandYA Mazzucm cowewmuua millvwwvseasngedul39vdamn bvcvvu Expected Value of Imperfect Information Note That After consulting the expert the uncertainty remains After consulting an imperfect expert the original decision problem still remains The only difference is that probabilities of the original decision problem have changed to re ect the additional information ie the expert39s advise To calculate the EMV of the decision problem after consulting the imperfect expert we have to solve for the probabilities in the decision tree above Calculating these probabilities is equivalent with FLIPPING the order of the uncertainty nodes Draft Version 1 3 Making Hard Decisions Chapter 12 Value of Information Slide 20 of 29 a r cienenr Reilly Le uveNmesbv J in am Mazzuchi conRicHrozuus MPIvwwv dul39vdamlvl bv cvvu Draft Version 1 Expected Value of Imperfect Information Market Expenvs Expert s Market Behavior Forecast Forecast Behavior U pquot 080 Up Up 05 Flat 010 Dovm 010 Up 015 Flat 03 quotY Flat 070 Down 015 U pquot 020 Flat 020 Dovm 02 Dovm 060 Flat UP 7 Flat Y Flat Down UP Flat Dovm How can we solve for these probabilities Via Bayes theorem using a probability table Making Hard Decisions R r ClemenJ ReilW Chapter 12 Value of Information Le uveNmesbv m vanDamandlA Mazzucm mPiwwseasngeduidamlv hvGWU Slide 21 of 29 copvmew e 2005 Expected Value of Imperfect Information Draft Versmn 1 STEP 1 Construct a probability table PrUp PrFlat PrDown 0500 0300 0200 quotAquot PrquotAquotUp PrquotAquotFlat PrquotAquotDown quotUpquot 0800 0150 0200 quotFlatquot 0100 0700 0200 quotDownquot 0100 0150 0600 Check 1000 1000 1000 PrquotAquot n Up PrquotAquot n Flat PrquotAquot A Down PrquotAquot Pr UpquotAquot PrtFlatquotAquot PrDownquotAquot Check 0400 0045 0040 0485 0825 0093 0082 1000 0050 0210 0040 0300 0167 0700 0133 1000 0050 0045 0120 0215 0233 0209 0558 1000 Check 0500 0300 0200 1000 Making Hard Decisions Chapter 12 Value of Information Slide 22 of 29 R r cwemem ReHW Le meNmesbv m vanDamandYA Mazzucm MPlvwwvseasngeduldavmv copvmew mus bv ewu Expected Value of Imperfect Information STEP 2 Insert the probabilities in the probability tree Market Ex en39s Expert s Market Behavior 39 Forecast Forecast Behavior U pquot 080 Up 0025 Up 05 Flat 010 U pquot 0485 Flat 0093 Down 010 Down 0082 Up 0167 Flat 0300f f Flat 0700 Down 0133 Up 015 Flat03 Y Flat 070 39 Down 015 F U pquot 020 Up 0233 g Fiat 020 Flat 0209 gt g Down 02 Dovm 060 Dowrf 0215 Down 0558 O 3 Making Hard Decisions Chapter 12 Value of Information Slide 23 of 29 a i am Rap WWWst m 0mm Mam conRieHrezuus mPlwwseasngedudamiv hvGWU Expected Value of Imperfect Information STEP 3 Calculate EMV after consulting the expert Up 0025 1500 High Ris 1164 Flat 0 093 39 100 Down 0082 1000 1164 U 0825 835 p 1000 UP 0485 Low Ri Flat 0093 St k 200 00 Down 0082 1 00 Savings Account 500 E E g a a 6 Making Hard Decisions Chapter 12 Value of Information Slide 24 of 29 v Ciemen Remy Le uveNmesbv m vanDavpandYA Mazzucm covvmewezuus millvwwvseasngedul39vdamn bvevvu Expected Value of Imperfect Information STEP 3B Calculate EMV after consulting the expert 187 Up 0167 1500 Flat 0700 100 Down 0133 1 000 500 293 Up 0167 1000 LOW Ri Flat 0700 St k 200 00 Down 0133 400 Savings Account 500 E E g a a 6 Making Hard Decisions Chapter 12 Value of Information Slide 25 of 29 v C emen Y Remy Le uveNmeshv m vanDavpandYA Mazzucm covvmewozuus mpuwwseasgvmuwuamw bvevvu Expected Value of Imperfect Information STEP 3C Calculate EMV after consulting the expert 488 Up 0233 1500 Flat 0209 100 Down 0558 1000 500 219 Up 0233 1000 Low Bifk Flat 0209 St I 200 Down 0215 Down 0550 1 00 Savings Accou nt 500 Draft Versmn 1 Making Hard Decisions Chapter 12 Value of Information Slide 26 of 29 R r Ciemen i Remy Le meNmesbv m vanDamandYA Mazzucm copvmewmuus millvwwvseasngedul39vdamn bvevvu Expected Value of Imperfect Information STEP 3D Calculate EMV after consulting the expert Up 0405 1164 Original Decision Problem Up 822 500 Flat 0300 Original Decision Problem Flat Original Decision Problem Down Dovm 0215 Draft Version 1 Making Hard Decisions Chapter 12 Value of Information Slide 27 of 29 R r Clemen l Reilly Le meNmesbv m vanDamandlA Mazzuchi conRicHrezuus Niplvwwvseasngeduldamlvl bvcvvu Draft Version 1 Expected Value of Imperfect Information STEP 4 Calculate EVII for consulting the expert MAX PROFIT Do not Consult Imperfect Expert EMV 580 Consult Imperfect Expert EMV 822 X X Consulting Fee Conclusion You would be willing to consult the clairvoyant expert if 822 X 2 580 ltgt X S 822 580 242 EVII EVII Expected Value of Imperfect Information 39 Making Hard Decisions Chapter 12 Va Lena W J R Slide 28 of 29 copvmew e zuus vaWU of Information R r Clem r Remy I Expected Value of Imperfect Information Interpretation EVII is the maximum amount of money you would be willing to pay for the services ofthe imperfect expert If he charges more than 242 you would not consult the expert Note EVPI 2 EVII Interpretation Perfect Information is always better than imperfect information When performing sensitivity analysis EVPI calculation of every uncertain event should be considered When EVPI is high for a particular uncertain event investment to reduce uncertainty may be warranted Draft Version 1 E Making Hard Decisions Chapter 12 Value of Information Slide 29 of 29 a r cienem Reilly Le uveNmesbv J in am Mazzuchi conRicHrezuus mp waNv auwavpivi by cvvu

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