Quản trị kinh doanh - Chapter 15: Risk and information

1Risk and InformationChapter 15Copyright (c)2014 John Wiley & Sons, Inc.2Chapter Fifteen OverviewIntroduction: Amazon.comDescribing Risky Outcome – Basic ToolsLotteries and ProbabilitiesExpected ValuesVarianceEvaluating Risky OutcomesRisk Preferences and the Utility FunctionAvoiding and Bearing RiskThe Demand for Insurance and the Risk PremiumAsymmetric Information and InsuranceThe Value of Information and Decision TreesChapter FifteenCopyright (c)2014 John Wiley & Sons, Inc.3Chapter FifteenTools for Describing Risky OutcomesDefinition: A lottery is any event with an uncertain outcome.Examples: Investment, Roulette, Football Game.Definition: A probability of an outcome (of a lottery) is the likelihood that this outcome occurs. Example: The probability often is estimated by the historical frequency of the outcome.Copyright (c)2014 John Wiley & Sons, Inc.4Chapter FifteenDefinition: The probability distribution of the lottery depicts all possible payoffs in the lottery and their associated probabilities.Property: The probability of any particular outcome is between 0 and 1 The sum of the probabilities of all possible outcomes equals 1.Definition: Probabilities that reflect subjective beliefs about risky events are called subjective probabilities.Probability DistributionCopyright (c)2014 John Wiley & Sons, Inc.5ProbabilityPayoff.80.70.60.50.40.30.20.100.901 $2567% chance of losingChapter FifteenProbability DistributionCopyright (c)2014 John Wiley & Sons, Inc.633% chance of winningChapter FifteenProbability DistributionProbabilityPayoff.80.70.60.50.40.30.20.100.901 $25 $10067% chance of losingCopyright (c)2014 John Wiley & Sons, Inc.7Chapter FifteenExpected ValueDefinition: The expected value of a lottery is a measure of the average payoff that the lottery will generate.EV = Pr(A)xA + Pr(B)xB + Pr(C)xCWhere: Pr(.) is the probability of (.) A,B, and C are the payoffs if outcome A, B or C occurs.Copyright (c)2014 John Wiley & Sons, Inc.8Chapter FifteenExpected ValueIn our example lottery, which pays $25 with probability .67 and $100 with probability 0.33, the expected value is:EV = .67 x $25 + .33 x 100 = $50. Notice that the expected value need not be one of the outcomes of the lottery.Copyright (c)2014 John Wiley & Sons, Inc.9Chapter FifteenDefinition: The variance of a lottery is the sum of the probability-weighted squared deviations between the possible outcomes of the lottery and the expected value of the lottery. It is a measure of the lottery's riskiness. Var = (A - EV)2(Pr(A)) + (B - EV)2(Pr(B)) + (C - EV)2(Pr(C))Definition: The standard deviation of a lottery is the square root of the variance. It is an alternative measure of riskVariance & Standard DeviationCopyright (c)2014 John Wiley & Sons, Inc.10Chapter FifteenVariance & Standard DeviationThe squared deviation of winning is: ($100 - $50)2 = 502 = 2500The squared deviation of losing is: ($25 - $50)2 = 252 = 625The variance is: (2500 x .33)+ (625 x .67) = 1250For the example lotteryCopyright (c)2014 John Wiley & Sons, Inc.11Chapter FifteenEvaluating Risky OutcomesExample: Work for IBM or Amazon.com?Suppose that individuals facing risky alternatives attempt to maximize expected utility, i.e., the probability-weighted average of the utility from each possible outcome they face.U(IBM) = U($54,000) = 230U(Amazon) = .5xU($4,000) + .5xU($104,000) = .5(60) + .5(320) = 190Note:EV(Amazon) = .5($4000)+.5($104,000) = $54,000Copyright (c)2014 John Wiley & Sons, Inc.12Income (000 $ per year)Utility4104Utility functionU(104) = 3200Chapter FifteenEvaluating Risky OutcomesCopyright (c)2014 John Wiley & Sons, Inc.13Income (000 $ per year)U(54) = 230U(4) = 60.5u(4) + .5U(104)= 190454104Utility functionU(104) = 3200Chapter FifteenUtilityEvaluating Risky OutcomesCopyright (c)2014 John Wiley & Sons, Inc.14Chapter FifteenDefinition: The risk preferences can be classified as follows:An individual who prefers a sure thing to a lottery with the same expected value is risk averseAn individual who is indifferent about a sure thing or a lottery with the same expected value is risk neutralAn individual who prefers a lottery to a sure thing that equals the expected value of the lottery is risk loving (or risk preferring)Risk PreferencesNotes: Utility as a function of yearly income only Diminishing marginal utility of incomeCopyright (c)2014 John Wiley & Sons, Inc.15Chapter FifteenSuppose that an individual must decide between buying one of two stocks: the stock of an Internet firm and the stock of a Public Utility. The values that the shares of the stock may take (and, hence, the income from the stock, I) and the associated probability of the stock taking each value are: Internet firm Public Utility I Probability I Probability $80 .3 $80 .1 $100 .4 $100 .8 $120 .3 $120 .1Risk PreferencesExamplesCopyright (c)2014 John Wiley & Sons, Inc.16Chapter FifteenWhich stock should the individual buy if she has utility function U = (100I)1/2? Which stock should she buy if she has utility function U = I?EU(Internet) = .3U(80) + .4U(100) + .3U(120) EU(P.U.) = .1U(80) + .8U(100) + .1U(120) a. U = (100I)1/2: U(80) = (8000)1/2 = 89.40 U(100) = (10000)1/2 = 100 U(120) = (12000)1/2 = 109.5Risk PreferencesExamplesCopyright (c)2014 John Wiley & Sons, Inc.17Chapter FifteenRisk Preferences EU(Internet) = .3(89.40)+.4(100)+.3(109.50) = 99.70 EU(P.U.) =.1(89.40) + .8(100) + .1(109.50) = 99.9 The individual should purchase the public utility stockExamplesCopyright (c)2014 John Wiley & Sons, Inc.18Chapter FifteenRisk PreferencesExamplesU = I: EU(Internet) = .3(80)+.4(100)+.3(120)=100 EU(P.U.).1(80) + .8(100) + .3(120) = 100This individual is indifferent between the two stocks.Copyright (c)2014 John Wiley & Sons, Inc.19UtilityIncomeUtility function0U(100) U(25)$25U(50)$50 $100Chapter FifteenUtility Function – Risk Averse Decision MakerCopyright (c)2014 John Wiley & Sons, Inc.20IncomeUtility function$100$25•A$50Chapter FifteenUtility Function – Risk Averse Decision MakerUtility0U(100) U(25)U(50)Copyright (c)2014 John Wiley & Sons, Inc.21IncomeUtility function0 U1IIChapter FifteenUtility Function – Risk Averse Decision MakerUtilityCopyright (c)2014 John Wiley & Sons, Inc.22IncomeUtility function0 U1IU2Chapter FifteenIUtility Function – Risk Averse Decision MakerUtilityCopyright (c)2014 John Wiley & Sons, Inc.23UtilityIncomeUtility Function0 UtilityIncomeUtility FunctionRisk Neutral Preferences Risk Loving PreferencesChapter FifteenUtility Function – Two Risk ApproachesCopyright (c)2014 John Wiley & Sons, Inc.24Income (000 $ per year)UtilityU(54) = 230U(4) = 60.5u(4) + .5U(104)= 190454104Utility functionU(104) = 32001700037Risk premium = horizontal distance $17000DE••Chapter FifteenAvoiding Risk - InsuranceCopyright (c)2014 John Wiley & Sons, Inc.25Chapter FifteenRisk PremiumDefinition: The risk premium of a lottery is the necessary difference between the expected value of a lottery and the sure thing so that the decision maker is indifferent between the lottery and the sure thing.pU(I1) + (1-p)U(I2) = U(pI1 + (1-p)I2 - RP)The larger the variance of the lottery, the larger the risk premiumCopyright (c)2014 John Wiley & Sons, Inc.26Chapter FifteenComputing Risk PremiumExample: Computing a Risk Premium U = I(1/2); p = .5 I1 = $104,000 I2 = $4,000Copyright (c)2014 John Wiley & Sons, Inc.27Chapter FifteenVerify that the risk premium for this lottery is approximately $17,000.5(104,000)1/2 + .5(4,000)1/2 = (.5(104,000) + .5(4,000) - RP)1/2$192.87 = ($54,000 - RP)1/2$37,198 = $54,000 - RPRP = $16,802Computing Risk PremiumCopyright (c)2014 John Wiley & Sons, Inc.28Chapter FifteenComputing Risk Premium Let I1 = $108,000 and I2 = $0. What is the risk premium now? .5(108,000)1/2 + 0 = (.5(108,000) + 0 - RP)1/2.5(108,000)1/2 = (54,000 - RP)1/2RP = $27,000(Risk premium rises when variance rises, EV the same)Copyright (c)2014 John Wiley & Sons, Inc.29Chapter FifteenThe Demand for Insurance Lottery:$50,000 if no accident (p = .95) $40,000 if accident (1-p = .05) (i.e. "Endowment" is that income in the good state is 50,000 and income in the bad state is 40,000)EV = .95($50000)+.05($40000) = $49,500Copyright (c)2014 John Wiley & Sons, Inc.30Chapter FifteenThe Demand for InsuranceInsurance: Coverage = $10,000Price = $500$49,500 sure thing. Why? In a good state, receive 50000-500 = 49500In a bad state, receive 40000+10000-500=49500Copyright (c)2014 John Wiley & Sons, Inc.31Chapter FifteenThe Demand for InsuranceIf you are risk averse, you prefer to insure this way over no insurance. Why?Full coverage ( no risk so prefer all else equal)Definition: A fairly priced insurance policy is one in which the insurance premium (price) equals the expected value of the promised payout. i.e.:500 = .05(10,000) + .95(0)Copyright (c)2014 John Wiley & Sons, Inc.32Chapter FifteenInsurance company expects to break even and assumes all risk – why would an insurance company ever offer this policy?The Supply of InsuranceDefinition: Asymmetric Information is a situation in which one party knows more about its own actions or characteristics than another party.Copyright (c)2014 John Wiley & Sons, Inc.33Chapter FifteenAdverse Selection & Moral HazardDefinition: Moral Hazard is opportunism characterized by an informed person's taking advantage of a less informed person through an unobserved action.Definition: Adverse Selection is opportunism characterized by an informed person's benefiting from trading or otherwise contracting with a less informed person who does not know about an unobserved characteristic of the informed person.Copyright (c)2014 John Wiley & Sons, Inc.34Chapter FifteenAdverse Selection & Market FailureLottery: $50,000 if no blindness (p = .95) $40,000 if blindness (1-p = .05) EV = $49,500 (fair) insurance: Coverage = $10,000 Price = $500 $500 = .05(10,000) + .95(0)Copyright (c)2014 John Wiley & Sons, Inc.35Chapter FifteenSuppose that each individual's probability of blindness differs  [0,1]. Who will buy this policy?Now, p' = .10 so that:EV of payout = .1(10,000) + .9(0) = $1000 while price of policy is only $500. The insurance company no longer breaks even.Adverse Selection & Market FailureCopyright (c)2014 John Wiley & Sons, Inc.36Chapter FifteenAdverse Selection & Market FailureSuppose we raise the price of policy to $1000.Now, p'' = .20 so that.EV of payout = .2(10,000) + .8(0) = $2000. So the insurance company still does not break even and thus the Market Fails.Copyright (c)2014 John Wiley & Sons, Inc.37Chapter FifteenDecision TreesDefinition: A decision tree is a diagram that describes the options available to a decision maker, as well as the risky events that can occur at each point in time.1. Decision Nodes 2. Chance Nodes3. Probabilities4. PayoffsKey ElementsWe analyze decision problems by working backward along the decision tree to decide what the optimal decision would Be.Copyright (c)2014 John Wiley & Sons, Inc.38Chapter FifteenDecision TreesCopyright (c)2014 John Wiley & Sons, Inc.39Chapter FifteenDecision TreesSteps in constructing and analyzing the tree:1. Map out the decision and event sequence2. Identify the alternatives available for each decision3. Identify the possible outcomes for each risky event4. Assign probabilities to the events5. Identify payoffs to all the decision/event combinations6. Find the optimal sequence of decisionsCopyright (c)2014 John Wiley & Sons, Inc.40Chapter FifteenPerfect InformationDefinition: The value of perfect information is the increase in the decision maker's expected payoff when the decision maker can -- at no cost -- obtain information that reveals the outcome of the risky event.Copyright (c)2014 John Wiley & Sons, Inc.41Chapter FifteenPerfect InformationExample: Expected payoff to conducting test: $35M Expected payoff to not conducting test: $30MThe value of information: $5MThe value of information reflects the value of being able to tailor your decisions to the conditions that will actually prevail in the future. It should represent the agent's willingness to pay for a "crystal ball".Copyright (c)2014 John Wiley & Sons, Inc.42Chapter FifteenAuctions - TypesEnglish Auction – An auction in which participants cry out their bids and each participant can increase his or her bid until the auction ends with the highest bidder winning the object being sold.First-Price Sealed-Bid Auction – An auction in which each bidder submits one bid, not knowing the other bids. The highest bidder wins the object and pays a price equal to his or her bid.Second-Price Sealed-Bid Auction – An auction in which each bidder submits one bid, not knowing the other bids. The highest bidder wins the object but pays a price equal to the second-highest bid.Dutch Descending Auction – An auction in which the seller of the object announces a price which is then lowered until a buyer announces a desire to buy the item at that price.Copyright (c)2014 John Wiley & Sons, Inc.43Chapter FifteenAuctionsPrivate Values – A situation in which each bidder in an auction has his or her own personalized valuation of the object.Revenue Equivalence Theorem – When participants in an auction have private values, any auction format will, on average, generate the same revenue for the seller.Common Values – A situation in which an item being sold in an auction has the same intrinsic value to all buyers, but no buyer knows exactly what that value is.Winner’s Curse – A phenomenon whereby the winning bidder in a common-values auction might bid an amount that exceeds the item’s intrinsic value.Copyright (c)2014 John Wiley & Sons, Inc.44Chapter FifteenSummary1. We can think of risky decisions as lotteries. 2. We can think of individuals maximizing expected utility when faced with risk.3. Individuals differ in their attitudes towards risk: those who prefer a sure thing are risk averse. Those who are indifferent about risk are risk neutral. Those who prefer risk are risk loving.4. Insurance can help to avoid risk. The optimal amount to insure depends on risk attitudes.Copyright (c)2014 John Wiley & Sons, Inc.45Chapter Fifteen5. The provision of insurance by individuals does not require risk lovers. 6. Adverse Selection and Moral Hazard can cause inefficiency in insurance markets.7. We can calculate the value of obtaining information in order to reduce risk by analyzing the expected payoff to eliminating risk from a decision tree and comparing this to the expected payoff of maintaining risk. 8. The main types of auctions are private values auctions and common values auctions.SummaryCopyright (c)2014 John Wiley & Sons, Inc.