Decision Under Uncertainty & Information Economics

Transcription

1 Decision Under Uncertainty & Information Economics Kaipichit Ruengsrichaiya (ไกรพ ช ต เร องศร ไชยะ) 1

2 Topics I. Decision Under Uncertainty & Expected Utility II. Risk Sharing : Securities & Insurance Market III. Asymmetric Information (Hidden Information) : Signaling & Screening 2

3 I. Decision under Uncertainty Ques%ons What is uncertainty? How can we model uncertainty and analyze it? If uncertain situafon changes, how can we explain it in a systemafc way? How should we make a decision under uncertainty? How can we analyze our decisions under uncertainty? 3

4 I. Decision under Uncertainty If we know well about how to model uncertainty & risky situafons How to make good decisions under uncertainty Behavior & preference toward risk We can understand / analyze / improve Risky situafons to gain benefits & avoid losses Strategic decisions when informafon is unequal Strategic decisions to mofvate our agent 4

5 I. Decision under Uncertainty Modeling Uncertainty Let s consider the following picture chance node 5

6 I. Decision under Uncertainty At chance node, you face 4 possible (future) outcomes : {100, 50, 0, - 200} 4 chances (probabilifes) corresponding to each possible future outcome : {0.3, 0.2, 0.4, 0.1} No%ce : The 4 chances/ probabilifes sum up to 1.0 6

7 I. Decision under Uncertainty From informafon about 1. possible outcomes together with 2. corresponding probabili8es We call this lo$ery (to reflect the future uncertainty and the possibilifes of each outcome) 7

8 I. Decision under Uncertainty Modeling General Lo8ery a Loaery (N possible outcomes) composes of (i) QuanFFes of possible outcomes, denoted by ( x1, x2,.., x N ) (ii) ProbabiliFes corresponding to each outcome, denoted N by ( p, p,.., p ) where p = p( x) and p = N i i i= 1 i So a lo9ery can be denoted by ( x, x,.., x ; p, p,.., p ) 1 2 N 1 2 N 8

9 I. Decision under Uncertainty We can calculate the expected monetary value (EMV) or mean of a loaery by mulfplying each possible outcome by its corresponding probability and adding ($100) (0.3) + ($50) (0.2) + ($0) (0.4) + ($- 200) (0.1) = $20 9

10 I. Decision under Uncertainty Suppose we offer two choices to you between (i) (ii) The loaery, you sfll face uncertainty / risk Its Expected Monetary Value (EMV, or mean ) for sure If you choose EMV (not choose loaery) => Risk Averse Loaery (not choose EMV) => Risk Seeking Being indifferent b/w both choices => Risk Neutral 10

11 I. Decision under Uncertainty FACT : Most people is risk- averse, but has different degree of risk aversion (In plain words : people are afraid of risk & uncertainty, but they are different in how much they are afraid of it) Suppose, you have a loaery with EMV Y. Then, if you are offered money X for sure What will you choose between Loaery (uncertainty) with EMV Y or Sure money X? 11

12 I. Decision under Uncertainty Your answer will depend on how much X!! IF X is set to make you indifferent between a loaery (with EMV Y ) and sure money X, THEN we say that X is your CERTAINTY EQUIVALENCE (CE) to the loaery 12

13 I. Decision under Uncertainty If loaery has EMV Y = 20. If you choose CE < EMV => RISK AVERSE If you choose CE = EMV => RISK NEUTRAL If you choose CE > EMV => RISK SEEKING 13

14 I. Decision under Uncertainty For Risk Averse person, CE < EMV, the difference (EMV CE) is called RISK PREMIUM (RP) for the loaery. The larger the risk premium is, the more risk averse he will be Ex. For a loaery with EMV = 20, John has CE = 15, RP = 5 Jack has CE = 12, RP = 8 => Jack is more risk averse than John and he is willing to pay Higher Risk Premium to avoid the risk of the loaery!! 14

15 The Expected UFlity Model is a framework to help use analyze decision under uncertain situafons (captured by loaeries) Help us to make the best decision under uncertainfes Basic idea is similar to the calculafon of EMV More general to capture the human feeling about uncertainfes and risk preferences (risk averse / neutral / seeking behavior) 15

16 In EMV, we DIRECTLY calculate the monetary value of the loaery / gamble. In Expected UFlity Model, we calculate PREFERENCE / UTILITY of each possible outcomes and calculate the expected uflity from the loaery / gamble by using probabilifes of each possible outcome 16

17 CalculaFon of Expected Monetary Value (EMV) or mean of a loaery by mulfplying each possible outcome by its corresponding probability and adding ($100) (0.3) + ($50) (0.2) + ($0) (0.4) + ($- 200) (0.1) = $20 17

18 CalculaFon of Expected U%lity of a loaery by mulfplying each possible u%lity of each outcome by its corresponding probability and adding each u%lity up Let uflity funcfon be u() u($100) (0.3) + u($50) (0.2) + u($0) (0.4) + u($- 200) (0.1) = E[ u(lo8ery) ] 18

19 How to comparing many loaeries/gambles and choose the best loaery for an individual? 19

20 CalculaFng loaery / gamble X = ($750, $0 ; 0.7, 0.3) Two possible outcomes : $750 and $0 Corresponding probabilifes are 0.7 and 0.3 The uflity of $750 => u($750) = 2.0 The uflity of $0 => u($0) = 1.0 The expected uflity is E[u(X )] = p 1 u(x 1 ) + p 2 u(x 2 ) E[u(X)] = 2.0 (0.7) (0.3) =

21 Applying the same methods to loaeries / gambles Y and Z, we have uflity level in [. ] 21

22 We now know that the expected uflity of each loaery is following E[u(X)] = 1.7 [ EMV (X) = ] E[u(Y)] = [ EMV (Y) = ] E[u(Z)] = [ EMV (Z) = ] The best choice of this person (with uflity funcfon u(.) ) is the loaery / gamble that gives highest expected uflity. So X gives highest expected uflity than Y and Z. 22

23 ProperFes of uflity funcfon u(.) 1. Increasing funcfon : more money is beaer than less : u($50) > u($10) 2. Con%nuous funcfon : uflity level does not change much for a small change in outcome 3. Concave : uflity funcfon reflects risk averse behavior of a person : for a loaery k and EMV E[k], u( E[k] ) > E[ u(k) ] or u''(x) < 0 (see figure next page) 23

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25 Risk Preference and UFlity FuncFon Risk Averse => u(.) is CONCAVE funcfon E[u(k)] > u(e[k]) Risk Neutral => u(.) is LINEAR funcfon E[u(k)] = u(e[k]) Risk Seeking => u(.) is CONVEX funcfon E[u(k)] < u(e[k]) 25

26 DRAW UFlity FuncFon for Risk Averse preference (in class) [ Draw Your Graph Here ] 26

27 DRAW UFlity FuncFon for Risk Neutral preference (in class) [ Draw Your Graph Here ] 27

28 DRAW UFlity FuncFon for Risk Seeking preference (in class) [ Draw Your Graph Here ] 28

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31 From risk preference, consider the case of Risk AVERSION : for an uncertain situafon of WEALTH (W), with average value E[W ], people with concave uflity would prefer the the average value FOR SURE to the expected uflity E[u(W )] < u(e[w ]) for uncertain loaery (risky wealth), RISK PREMIUM is the amount of money that a consumer is willing to PAY to have the level of uflity for sure thing equal to the expected level of uncertain wealth 31

32 RISK PREMIUM : the definifon 32

33 RISK PREMIUM : properfes 33

34 RISK PREMIUM : properfes (confnued) 34

35 DRAW UFlity FuncFon for Risk Averse preference and RISK PREMIUM [ Draw Your Graph Here ] 35

36 Measure of Degree of Risk Aversion 36

37 Measure of Degree of Risk Aversion (confnued) 37

38 Measure of Degree of Risk Aversion (confnued) 38

39 Measure of Degree of Risk Aversion : Example 1 39

40 Measure of Degree of Risk Aversion : Example 2 40

41 Many Fmes, we face complex uncertain situa%ons, e.g. series/chain of uncertainfes We need to model it in order to analyze and make the best decision : How can we do it, based on our model of loaery/gamble? 41

42 Consider the following COMPOUND LOTTERY/GAMBLE (a series of uncertainfes /gambles) 42

43 We now have 3 steps of uncertainfes 1 st step has 5 possible outcomes 2 nd step (from 2 nd outcome of the 1 st step) has two possible outcomes 3nd step (from 2 nd outcome of the second step) has two possible outcome How can we analyze the compound uncertain8es and calculate the EMV or Expected U8lity? 43

44 We simplify it : Turning compound loaery (3- step uncertainty) into the simplified loaery (1- step uncertainty) and Applying the calculafon of EMV and Expected UFlity Look at the 2 nd outcome on the 1 st step of compound loaery => Simplify it into 1- step uncertainty with 3 outcomes : ($400, $500, $0) with associated probabilifes. 44

45 For outcome $400, it associated probability is (1/6) * (1/2) = (1/12) For outcome $500, its associated probability is (1/6) * (1/2) * (1/2) = (1/24) For outcome $0, its associated probability is (1/6) * (1/2) * (1/2) = (1/24) 45

46 No%ce : There is another possible outcome with $500 (the first possible outcome in 1 st step uncertainty) with associated probability (1/3) To simplify the compound loaery to the simple loaery, we have 1- step uncertainty with disfnct possible outcomes. => Since we have repeated outcome of $500, we combine the associated probability to make simple loaery/gamble The associated probability of $500 in simple loaery is (1/3) + (1/24) = (9/24) 46

47 A}er simplifying compound loaery, the equivalent simple lo$ery has 1- step uncertainty and becomes 47

48 I. Decision under Uncertainty We use the ideas Modeling uncertainty / risky situafon => it is represented by Lo8ery/Gamble CalculaFon of Expected Monetary Value (EMV), and Expected U%lity of the loaery/gamble Preferences toward risk and uncertainty (Risk Averse / Neutral / Seeking) and corresponding Certainty Equivalence (CV) To study many topics of informafon economics 48

49 II. Risk Sharing & Securities Market Thinking about : a big company that wants to do IPO (inifal public offering) and sell its shares (ownership) to the general people who are risk averse. The company will have more money to invest in big project(s) to gain profit. However, the investment project(s) will also have uncertainfes and make loss!! The general public will get small frac8on of the profit AND also small part of loss when the project(s) fail. 49

50 II. Risk Sharing & Securities Market Ques%ons (1) Why does a company sell its stocks to general public? (if only to raise fund for investment, can it go to bank?) (2) Why do people buy the stocks? Conceptual Ques%ons : Any economic reasons of these decisions on both sides of transacfon? What is the value to each side? If so, is there any limitafon of creafng this economic value? 50

51 II. Risk Sharing & Securities Market Example : An investment project will give return If success : $50,000 with probability (1/2) If fail : (- $25,000) with probability (1/2) What is it EMV? => $12,500 If a company want to sell stocks 1,000 units to general public, who is risk averse, what should be the price of the stock? And why? Discussion (please write down your answers / reasons) 51

52 II. Risk Sharing & Securities Market General Principle : No matter how risk averse a person is, there is a small share/fraction in a lottery/gamble such that if we offer him a small enough share/fraction ( a ), he would be willing to pay for that share/fraction a because it is approximately equal to EMV of the lottery/gamble => The cost of risk premium for small share/fraction of lottery/gamble will become very small to him. 52

53 II. Risk Sharing & Securities Market General Principle (short version) If you spread risk thinly, you defeat risk aversion and winning risk aversion creates value (of risk sharing) [Ques%on : Can you apply the picture of concave uflity to this principle?] Financial market is one of many methods to do it => to spread & to trade uncertainfes of future outcome (loaery / gamble). 53

54 II. Risk Sharing & Securities Market Important conclusions & implica%ons (1) Risk should be spread out unfl no risk- averse individual holds substanfal fracfon of risk => b/c if a person holds big share of risk, he will value this risk less than the EMV. So spreading out this risk and he can have the full EMV which is greater. (2) Thus the value of any loaery/gamble to its inifal holder will be equal to EMV, since this is it value in the market once it has been securifzed and shared out to other people. 54

55 II. Risk Sharing & Securities Market However, the conclusions & implicafons could fail for many reasons On (1), risk might not be shared / spread out thinly because Withhold informafon about project (and its profit) to avoid compeffon on the investment Private benefit of control of large shareholder (conflicts of interest) 55

56 II. Risk Sharing & Securities Market Adverse SelecFon (hidden informafon) b/w company and investor Moral Hazard (hidden acfon) b/w company and investor On (2), the price of the share is not equal to its EMV It adds more risk into exisfng porolio that people already have This is about the volaflity and correlafons of assets of investor => porolio diversificafon (The content is beyond this course) 56

57 III. Asymmetric Information Defini%on : In many transacfon, one party has informafon that the counter party lacks and this is relevant to the counter party s evaluafon of the transacfon Examples : - - Used car market (who is seller & buyer? who has more info?) - - Insurance market (who is seller & buyer? Who has more info?) 57

58 III. Asymmetric Information Examples : - - Used car market - - Insurance market - - AucFon market Who is the seller(s)? Who is the buyer(s)? Market breakdown? How to solve problem? 58

59 III. Asymmetric Information The problem is about unequal informafon, an important mechanism is to force the party with more informafon to give informafon to his counter party (who has lesser informafon) by Freely available info (public info) Legally Mandated Info [e.g. insurance company, good- faith disclosure for real property] InformaFon requirement by independent authority [e.g. Disclosure on accounfng informafon before register to public exchange / stock market, cerfficafon mechanism] 59

60 III. Asymmetric Information An interesfng mechanism is Voluntarily Provided Informa8on by the informed party [e.g. Example : Job Market Signaling employer wants good quality worker but not known for sure by interview / appearance employee (more info about his quality) 60

61 III. Asymmetric Information Example : Job Market Signaling (confnued) Ques%on : If employee wants to convince the employer, how does he do it? How does employer know the quality (hidden info) for sure? Why? 61

62 III. Asymmetric Information Answer Signal (indirect info) must be able to refer or relevant to the hidden / unobservable info that is desirable quality to the employer (less informed) Signal must be costly (hard to do) for employee, so it is hard to copy Idea to Signal : Good- quality employee must send signal at cheaper cost than the Bad- quality employee => There is a level of signal (high enough) that can separate the good from the bad and employer can know it and separate them apart!! Examples : educafon, reputafon 62

63 III. Asymmetric Information If those condifons are not met, it is possible that the employer cannot separate the good from the bad => Both types of employee are in the same pool market could be break down Use other mechanisms to sustain market (previously menfoned) 63

64 III. Asymmetric Information What about Screening? The idea is similar to the signaling (in which the informed party provides signal to the uninformed party) In Screening Mechanism, the uninformed party ini8ates the menu of transacfons / contracts to the informed party. The informed party will choose the transacfon/contract that is best for him => Self- selec8on Mechanism The menu will screen the good from the bad Example : insurance menu (different claim with different price) 64