Kinh tế học - Chapter 15: Decisions under risk and uncertainty

Chapter 15Decisions Under Risk and UncertaintyRisk vs. UncertaintyRiskMust make a decision for which the outcome is not known with certaintyCan list all possible outcomes & assign probabilities to the outcomesUncertaintyCannot list all possible outcomesCannot assign probabilities to the outcomes2Measuring Risk with Probability DistributionsTable or graph showing all possible outcomes/payoffs for a decision & the probability each outcome will occurTo measure risk associated with a decisionExamine statistical characteristics of the probability distribution of outcomes for the decision3Probability Distribution for Sales (Figure 15.1)4Expected ValueExpected value (or mean) of a probability distribution is:Where Xi is the ith outcome of a decision,pi is the probability of the ith outcome, andn is the total number of possible outcomes5Expected ValueDoes not give actual value of the random outcomeIndicates “average” value of the outcomes if the risky decision were to be repeated a large number of times6VarianceVariance is a measure of absolute riskMeasures dispersion of the outcomes about the mean or expected outcomeThe higher the variance, the greater the risk associated with a probability distribution7Identical Means but Different Variances (Figure 15.2)8Standard DeviationStandard deviation is the square root of the varianceThe higher the standard deviation, the greater the risk9Probability Distributions with Different Variances (Figure 15.3)10Coefficient of VariationWhen expected values of outcomes differ substantially, managers should measure riskiness of a decision relative to its expected value using the coefficient of variationA measure of relative risk11Decisions Under RiskNo single decision rule guarantees profits will actually be maximizedDecision rules do not eliminate riskProvide a method to systematically include risk in the decision making process12Summary of Decision Rules Under Conditions of RiskExpected value ruleMean-variance rulesCoefficient of variation ruleChoose decision with highest expected valueGiven two risky decisions A & B:If A has higher expected outcome & lower variance than B, choose decision AIf A & B have identical variances (or standard deviations), choose decision with higher expected valueIf A & B have identical expected values, choose decision with lower variance (standard deviation)Choose decision with smallest coefficient of variation13Probability Distributions for Weekly Profit (Figure 15.4)E(X) = 3,500 A = 1,025  = 0.29E(X) = 3,750 B = 1,545  = 0.41E(X) = 3,500 C = 2,062  = 0.5914Which Rule is Best?For a repeated decision, with identical probabilities each timeExpected value rule is most reliable to maximizing (expected) profitAverage return of a given risky course of action repeated many times approaches the expected value of that action15Which Rule is Best?For a one-time decision under riskNo repetitions to “average out” a bad outcomeNo best rule to followRules should be used to help analyze & guide decision making processAs much art as science16Expected Utility TheoryActual decisions made depend on the willingness to accept riskExpected utility theory allows for different attitudes toward risk-taking in decision makingManagers are assumed to derive utility from earning profits17Expected Utility TheoryManagers make risky decisions in a way that maximizes expected utility of the profit outcomesUtility function measures utility associated with a particular level of profitIndex to measure level of utility received for a given amount of earned profit18Manager’s Attitude Toward RiskDetermined by manager’s marginal utility of profit:Marginal utility (slope of utility curve) determines attitude toward risk19Manager’s Attitude Toward RiskRisk averseIf faced with two risky decisions with equal expected profits, the less risky decision is chosenRisk lovingExpected profits are equal & the more risky decision is chosenRisk neutralIndifferent between risky decisions that have equal expected profit20Manager’s Attitude Toward RiskCan relate to marginal utility of profitDiminishing MUprofitRisk averseIncreasing MUprofitRisk lovingConstant MUprofitRisk neutral21Manager’s Attitude Toward Risk (Figure 15.5)22Manager’s Attitude Toward Risk (Figure 15.5)23Manager’s Attitude Toward Risk (Figure 15.5)24Finding a Certainty Equivalent for a Risky Decision (Figure 15.6)25Manager’s Utility Function for Profit (Figure 15.7)26Expected Utility of ProfitsAccording to expected utility theory, decisions are made to maximize manager’s expected utility of profitsSuch decisions reflect risk-taking attitudeGenerally differ from those reached by decision rules that do not consider riskFor a risk-neutral manager, decisions are identical under maximization of expected utility or maximization of expected profit27Decisions Under UncertaintyWith uncertainty, decision science provides little guidanceFour basic decision rules are provided to aid managers in analysis of uncertain situations28Summary of Decision Rules Under Conditions of UncertaintyMaximax ruleMaximin ruleMinimax regret ruleEqual probability ruleIdentify best outcome for each possible decision & choose decision with maximum payoff.Determine worst potential regret associated with each decision, where potential regret with any decision & state of nature is the improvement in payoff the manager could have received had the decision been the best one when the state of nature actually occurred. Manager chooses decision with minimum worst potential regret.Assume each state of nature is equally likely to occur & compute average payoff for each. Choose decision with highest average payoff.Identify worst outcome for each decision & choose decision with maximum worst payoff.29