Chapter Choice Under Uncertainty Topics to be Discussed  Describing Risk  Preferences Toward Risk  Reducing Risk  The Demand for Risky Assets Chapter Slide Introduction  Choice with certainty is reasonably straightforward.  How we choose when certain variables such as income and prices are uncertain (i.e. making choices with risk)? Chapter Slide Describing Risk  To measure risk we must know: 1) All of the possible outcomes. 2) The likelihood that each outcome will occur (its probability). Chapter Slide Describing Risk  Interpreting Probability  The likelihood that a given outcome will occur Chapter Slide Describing Risk  Interpreting Probability  Objective  Chapter Interpretation Based on the observed frequency of past events Slide Describing Risk  Interpreting Probability  Subjective  Based on perception or experience with or without an observed frequency  Chapter Different information or different abilities to process the same information can influence the subjective probability Slide Describing Risk  Expected Value  The weighted average of the payoffs or values resulting from all possible outcomes. Chapter  The probabilities of each outcome are used as weights  Expected value measures the central tendency; the payoff or value expected on average Slide Describing Risk  An Example  Investment  Two Chapter in offshore drilling exploration: outcomes are possible  Success -- the stock price increase from $30 to $40/share  Failure -- the stock price falls from $30 to $20/share Slide Describing Risk  An Example  Objective Chapter Probability  100 explorations, 25 successes and 75 failures  Probability (Pr) of success = 1/4 and the probability of failure = 3/4 Slide Reducing Risk  Three ways consumers attempt to reduce risk are: 1) Diversification 2) Insurance 3) Obtaining more information Chapter Slide The Demand for Risky Assets  Assets  Something that provides a flow of money or services to its owner.  The flow of money or services can be explicit (dividends) or implicit (capital gain). Chapter Slide The Demand for Risky Assets  Capital Gain  An increase in the value of an asset, while a decrease is a capital loss. Chapter Slide The Demand for Risky Assets Risky Risky & & Riskless Riskless Assets Assets  Risky Asset  Provides an uncertain flow of money or services to its owner.  Examples  Chapter apartment rent, capital gains, corporate bonds, stock prices Slide The Demand for Risky Assets Risky Risky & & Riskless Riskless Assets Assets  Riskless Asset  Provides a flow of money or services that is known with certainty.  Examples  Chapter short-term government bonds, shortterm certificates of deposit Slide The Demand for Risky Assets  Asset Returns  Return  The total monetary flow of an asset as a fraction of its price.  Real  Chapter on an Asset Return of an Asset The simple (or nominal) return less the rate of inflation. Slide The Demand for Risky Assets  Asset Returns Monetary Flow Asset Return = Purchase Price Flow $100/yr. Asset Return = = = 10% Bond Price $1,000 Chapter Slide The Demand for Risky Assets Expected Expected vs. vs. Actual Actual Returns Returns  Expected Return  Return that an asset should earn on average Chapter Slide The Demand for Risky Assets Expected Expected vs. vs. Actual Actual Returns Returns  Actual Return  Return Chapter that an asset earns Slide Investments--Risk and Return (1926-1999) Risk Real Rate of (standard Common stocksdeviation,%) (S&P 500) 20.2 Return (%) 9.5 Long-term corporate bonds 2.7 8.3 U.S. Treasury bills 0.6 3.2 Chapter Slide The Demand for Risky Assets Expected Expected vs. vs. Actual Actual Returns Returns  Higher returns are associated with greater risk.  The risk-averse investor must balance risk relative to return Chapter Slide Investing in the Stock Market  Observations  Percent of American families who had directly or indirectly invested in the stock market Chapter  1989 = 32%  1995 = 41% Slide Summary  Consumers and managers frequently make decisions in which there is uncertainty about the future.  Consumers and investors are concerned about the expected value and the variability of uncertain outcomes. Chapter Slide Summary  Facing uncertain choices, consumers maximize their expected utility, and average of the utility associated with each outcome, with the associated probabilities serving as weights.  A person may be risk averse, risk neutral or risk loving. Chapter Slide Summary  The maximum amount of money that a risk-averse person would pay to avoid risk is the risk premium.  Risk can be reduced by diversification, purchasing insurance, and obtaining additional information. Chapter Slide End of Chapter Choice Under Uncertainty [...]... probability) Chapter 5 Slide Describing Risk Income from Sales Jobs Outcome 1 Outcome 2 Expected Probability Income ($) Probability Income ($) Income Job 1: Commission 150 0 5 2000 5 1000 Job 2: Fixed salary 150 0 99 151 0 01 51 0 Chapter 5 Slide Describing Risk Income from Sales Jobs  Job 1 Expected Income E(X1 ) = 5( $2000) + 5( $1000) = $ 150 0  Job 2 Expected Income E(X 2 ) = 99($ 151 0) + 01( $51 0) = $ 150 0 Chapter. .. expected value Chapter 5 Slide Describing Risk Variability Variability  The standard deviation is written: σ = Pr1[ X 1 − E ( X )] + Pr2 [ X 2 − E ( X )] 2 Chapter 5 Slide 2 Describing Risk Calculating Variance ($) Standard Deviation Job 1 $ 250 ,000 Job 2 Deviation Outcome 1 Squared $2,000 $50 0.00 $ 250 ,000 1 ,51 0 100 99 .50 Chapter 5 Deviation Outcome 2 Squared $1,000 51 0 Deviation Squared $ 250 ,000 980,100... = 5( $ 250 ,000) + 5( $ 250 ,000 σ 1 = $ 250 ,000 σ 1 = 50 0 *Greater Risk σ 2 = 99($100) + 01($980,100) σ 2 = $9,900 σ 2 = 99 .50 Chapter 5 Slide Describing Risk  The standard deviation can be used when there are many outcomes instead of only two Chapter 5 Slide Describing Risk Decision Making Decision Making  Job 1: expected income $1,600 and a standard deviation of $50 0  Job 2: expected income of $1 ,50 0... person could have a job with a 5 chance of earning $30,000 and a 5 chance of earning $10,000 Chapter 5 Slide Preferences Toward Risk Risk Averse Risk Averse  Expected Income = (0 .5) ($30,000) + (0 .5) ($10,000) = $20,000 Chapter 5 Slide Preferences Toward Risk Risk Averse Risk Averse  Expected income from both jobs is the same risk averse may choose current job Chapter 5 Slide ... Chapter 5 Slide Describing Risk  While the expected values are the same, the variability is not  Greater variability from expected values signals greater risk  Deviation  Difference between expected payoff and actual payoff Chapter 5 Slide Describing Risk Deviations from Expected Income ($) Outcome 1 Deviation Outcome 2 Deviation Job 1 $50 0 $2,000 $50 0 $1,000 - Job 2 1 ,51 0 10 51 0 -900 Chapter 5 Slide... $ 25/ share Chapter 5 Slide Describing Risk  Given: n possible outcomes having payoffs X1, X2,…, Xn  Probabilities of each outcome is given by Pr1, Pr2,…, Prn Chapter 5 Slide Describing Risk  Generally, expected value is written as: E(X) = Pr1X1 + Pr2 X 2 + + Prn X n Chapter 5 Slide Describing Risk  Variability  The extent to which possible outcomes of an uncertain event may differ Chapter 5 Slide... occur Chapter 5 Slide Preferences Toward Risk Example Example  The expected utility can be written:  E(u) = (1/2)u($10,000) + (1/2)u($30,000) = 0 .5( 10) + 0 .5( 18) = 14  E(u) of new job is 14 which is greater than the current utility of 13 and therefore preferred Chapter 5 Slide Preferences Toward Risk  Different Preferences Toward Risk  People can be risk averse, risk neutral, or risk loving Chapter. .. standard deviation of $99 .50  Which job?  Greater Chapter 5 value or less risk? Slide Preferences Toward Risk  Choosing Among Risky Alternatives  Assume   The consumer knows all probabilities  Payoffs measured in terms of utility  Chapter 5 Consumption of a single commodity Utility function given Slide Preferences Toward Risk Example Example  A person is earning $ 15, 000 and receiving 13 units... utility from the job  She is considering a new, but risky job Chapter 5 Slide Preferences Toward Risk Example Example  She has a 50 chance of increasing her income to $30,000 and a 50 chance of decreasing her income to $10,000  She will evaluate the position by calculating the expected value (utility) of the resulting income Chapter 5 Slide Preferences Toward Risk Example Example  The expected... expected income ($1 ,50 0)  The first job is based entirely on commission  The Chapter 5 second is a salaried position Slide Describing Risk Variability Variability  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 ,51 0 most of the time (.99 probability), but you will earn $51 0 if the company . Commission .5 2000 .5 1000 150 0 Job 2: Fixed salary .99 151 0 .01 51 0 150 0 Expected Probability Income ($) Probability Income ($) Income Outcome 1 Outcome 2 Describing Risk Chapter 5 Slide 18 150 0$ .5( $1000) .5( $2000))E(X 1 =+=  Job. Chapter 5 Choice Under Uncertainty Chapter 5 Slide 2 Topics to be Discussed  Describing Risk  Preferences Toward Risk  Reducing Risk  The Demand for Risky Assets Chapter 5 Slide. 18 150 0$ .5( $1000) .5( $2000))E(X 1 =+=  Job 1 Expected Income $ 150 0.01( $51 0).99($ 151 0) )E(X 2 =+=  Job 2 Expected Income Income from Sales Jobs Describing Risk Chapter 5 Slide 19  While the