,Chapter 5,Choice Under Uncertainty,1,Chapter 1,Topics to be Discussed,Describing Risk Preferences Toward Risk Reducing Risk The Demand for Risky Assets,2,Chapter 1,Introduction,Choice with certainty is reasonably straightforward. How do we choose when certain variables such as income and prices are uncertain (i.e. making choices with risk)?,3,Chapter 1,Describing Risk,To measure risk we must know: 1) All of the possible outcomes. 2) The likelihood that each outcome will occur (its probability).,4,Chapter 1,Describing Risk,Interpreting Probability The likelihood that a given outcome will occur,5,Chapter 1,Describing Risk,Interpreting Probability Objective Interpretation Based on the observed frequency of past events,6,Chapter 1,Describing Risk,Interpreting Probability Subjective Based on perception or experience with or without an observed frequency Different information or different abilities to process the same information can influence the subjective probability,7,Chapter 1,Describing Risk,Expected Value The weighted average of the payoffs or values resulting from all possible outcomes. The probabilities of each outcome are used as weights Expected value measures the central tendency; the payoff or value expected on average,8,Chapter 1,Describing Risk,An Example Investment in offshore drilling exploration: Two outcomes are possible Success - the stock price increase from $30 to $40/share Failure - the stock price falls from $30 to $20/share,9,Chapter 1,Describing Risk,An Example Objective Probability 100 explorations, 25 successes and 75 failures Probability (Pr) of success = 1/4 and the probability of failure = 3/4,10,Chapter 1,Describing Risk,An Example:,Expected Value (EV),11,Chapter 1,Describing Risk,Given: Two possible outcomes having payoffs X1 and X2 Probabilities of each outcome is given by Pr1 & Pr2,12,Chapter 1,Describing Risk,Generally, expected value is written as:,13,Chapter 1,Describing Risk,Variability The extent to which possible outcomes of an uncertain even may differ,14,Chapter 1,Describing Risk,A Scenario Suppose you are choosing between two part-time sales jobs that have the same expected income ($1,500) The first job is based entirely on commission. The second is a salaried position.,Variability,15,Chapter 1,Describing Risk,A Scenario There are two equally likely outcomes in the first job-$2,000 for a good sales job and $1,000 for a modestly successful one. The second pays $1,510 most of the time (.99 probability), but you will earn $510 if the company goes out of business (.01 probability).,Variability,16,Chapter 1,Income from Sales Jobs,Job 1: Commission.52000.510001500 Job 2: Fixed salary.991510.015101500,Expected ProbabilityIncome ($)ProbabilityIncome ($)Income,Outcome 1Outcome 2,Describing Risk,17,Chapter 1,Job 1 Expected Income,Job 2 Expected Income,Income from Sales Jobs,Describing Risk,18,Chapter 1,While the expected values are the same, the variability is not. Greater variability from expected values signals greater risk. Deviation Difference between expected payoff and actual payoff,Describing Risk,19,Chapter 1,Deviations from Expected Income ($),Job 1$2,000$500$1,000-$500 Job 21,51010510-900,Outcome 1 Deviation Outcome 2 Deviation,Describing Risk,20,Chapter 1,Adjusting for negative numbers The standard deviation measures the square root of the average of the squares of the deviations of the payoffs associated with each outcome from their expected value.,Variability,Describing Risk,21,Chapter 1,Describing Risk,The standard deviation is written:,Variability,22,Chapter 1,Calculating Variance ($),Job 1$2,000$250,000$1,000 $250,000 $250,000 $500.00 Job 21,510100510 980,100 9,900 99.50,DeviationDeviation Deviation Standard Outcome 1 SquaredOutcome 2 Squared Squared Deviation,Describing Risk,23,Chapter 1,Describing Risk,The standard deviations of the two jobs are:,*Greater Risk,24,Chapter 1,Describing Risk,The standard deviation can be used when there are many outcomes instead of only two.,25,Chapter 1,Describing Risk,Job 1 is a job in which the income ranges from $1000 to $2000 in increments of $100 that are all equally likely.,Example,26,Chapter 1,Describing Risk,Job 2 is a job in which the income ranges from $1300 to $1700 in increments of $100 that, also, are all equally likely.,Example,27,Chapter 1,Outcome Probabilities for Two Jobs,Income,0.1,$1000,$1500,$2000,0.2,Job 1,Probability,28,Chapter 1,Describing Risk,Outcome Probabilities of Two Jobs (unequal probability of outcomes) Job 1: greater spread & standard deviation Peaked distribution: extreme payoffs are less likely,29,Chapter 1,Describing Risk,Decision Making A risk avoider would choose Job 2: same expected income as Job 1 with less risk. Suppose we add $100 to each payoff in Job 1 which makes the expected payoff = $1600.,30,Chapter 1,Unequal Probability Outcomes,Job 1,Income,0.1,$1000,$1500,$2000,0.2,Probability,31,Chapter 1,