5. Uncertainty and Consumer Behavior

Transcription

1 5. Uncertainty and Consumer Behavior Literature: Pindyck und Rubinfeld, Chapter Prof. Dr. Kerstin Schneider Chair of Public Economics and Business Taxation Microeconomics Chapter 5 Slide 1

2 Chapter Outline Describing Risk Preferences Toward Risk Reducing Risk The Demand for Risky Assets Prof. Dr. Kerstin Schneider Chair of Public Economics and Business Taxation Microeconomics Chapter 5 Slide 2

3 Introduction To examine ways that people can compare and choose among risky alternatives, we take the following steps: 1. In order to compare the riskiness of alternative choices, we need to quantify risk. 2. We will examine people s preferences towards risk. 3. We will see how people can sometimes reduce or eliminate risk. 4. In some situations, people can choose the amount of risk they wish to bear. 5. Sometimes demand for a good is driven partly or entirely by speculation people buy the good because they think its price will increase Prof. Dr. Kerstin Schneider Chair of Public Economics and Business Taxation Microeconomics Chapter 5 Slide 3

4 Describing Risk Probability Likelihood that a given outcome will occur. Objective Interpretation Is based on the observed frequency of the occurrence of past events Prof. Dr. Kerstin Schneider Chair of Public Economics and Business Taxation Microeconomics Chapter 5 Slide 4

5 Describing Risk Interpretation of probability Subjective probability is the perception that an outcome will occur. Different information or different methods of processing the same information can influence the subjective probability Prof. Dr. Kerstin Schneider Chair of Public Economics and Business Taxation Microeconomics Chapter 5 Slide 5

6 Describing Risk Expected Value Probability-weighted average of the payoffs associated with all possible outcomes. The probability of the respective payoffs are used as weighted averages. The expected value measures the central tendency, i.e., the payoff or value that we would expect on average Prof. Dr. Kerstin Schneider Chair of Public Economics and Business Taxation Microeconomics Chapter 5 Slide 6

7 Describing Risk Example: Investment in an off-shore oil drilling project: Two results are possible: Success the stock price increases from 30 to 40/ share. Failure the stock price decreases from 30 to 20/ share. Objective probability Out of 100 drillings, 25 are successful and 75 fail. Probability of success (Pr) = 1/4 and probability of failure = ¾ Prof. Dr. Kerstin Schneider Chair of Public Economics and Business Taxation Microeconomics Chapter 5 Slide 7

8 Describing Risk Expected Value (EV) An example: EV Pr(success)( 40/share) Pr(failure)( 20/share) EV 1 4( 40/share) 3 4( 20/share) EV 25/share Prof. Dr. Kerstin Schneider Chair of Public Economics and Business Taxation Microeconomics Chapter 5 Slide 8

9 Describing Risk Generally, the expected value is written as follows: E(X) Pr X Pr X... Pr X n n Prof. Dr. Kerstin Schneider Chair of Public Economics and Business Taxation Microeconomics Chapter 5 Slide 9

10 Describing Risk Variability The Variability Extent to which possible outcomes of an uncertain event differ. Consider the following, henceforth called Scenario A: Let's say we choose between two part-time sales jobs with the same expected income ( 1,500). The first job is entirely based on commission payments. The second job is remunerated with a salary Prof. Dr. Kerstin Schneider Chair of Public Economics and Business Taxation Microeconomics Chapter 5 Slide 10

11 Describing Risk Variability Scenario A For the first job, there are two equally likely (commission based) results for one s efforts: 2,000 and 1,000. In the second job, the remuneration is usually 1,510 (0.99 probability), but you will only earn 510 if the company goes out of business (0.01 probability) Prof. Dr. Kerstin Schneider Chair of Public Economics and Business Taxation Microeconomics Chapter 5 Slide 11

12 Describing Risk Scenario A Income from sales jobs Outcome 1 Outcome 2 Probability Income ( ) Probability Income ( ) Expected Income ( ) Job 1: Commission Job 2: Fixed Salary 0.5 2, ,000 1, , , Prof. Dr. Kerstin Schneider Chair of Public Economics and Business Taxation Microeconomics Chapter 5 Slide 12

13 Scenario A Describing Risk Income from sales jobs: Job 1 expected income ) E(X 1 0.5( 2000) 0.5( 1000) 1500 Job 2 expected income E(X 2 ) 0.99( 1510) 0.1( 510) Prof. Dr. Kerstin Schneider Chair of Public Economics and Business Taxation Microeconomics Chapter 5 Slide 13

14 Describing Risk Scenario A While the expected values are the same, this does not apply to the variability. Higher variability in the expected value indicates higher risk. Deviation Extent to which possible outcomes of an uncertain event differ. Outcome 1 Deviation Outcome 2 Deviation Job 1 2, , Job 2 1, Prof. Dr. Kerstin Schneider Chair of Public Economics and Business Taxation Microeconomics Chapter 5 Slide 14

15 Describing Risk Variability Standard deviation: Square root of the weighted average of the squared deviations of payoffs associated with each outcome. 2 2 ( X E( X )) Pr ( X E( X Pr1 )) Prof. Dr. Kerstin Schneider Chair of Public Economics and Business Taxation Microeconomics Chapter 5 Slide 15

16 Describing Risk Scenario A Computing the variance ( ) Outcome 1 Deviation Squared Outcome 2 Deviation Squared Weighted Average Deviation Squared Standard Deviation Job 1 2, ,000 1, , , Job 2 1, ,100 9, Prof. Dr. Kerstin Schneider Chair of Public Economics and Business Taxation Microeconomics Chapter 5 Slide 16

17 Describing Risk Scenario A The standard deviations of job 1 and job 2 are not the same: ( 250,000) 0.99( 100) 9, , higher risk 0.5( 250,000) 0.01( 980,100) Prof. Dr. Kerstin Schneider Chair of Public Economics and Business Taxation Microeconomics Chapter 5 Slide 17

18 Describing Risk Example Scenario B Job 1 is a workplace where income is between 1,000 and 2,000, with increments of 100 each having equal probability of being achieved. Job 2 is a workplace where income is between 1,300 and 1,700, with increments of 100 each having equal probability of being achieved Prof. Dr. Kerstin Schneider Chair of Public Economics and Business Taxation Microeconomics Chapter 5 Slide 18

19 Scenario B Outcome Probabilities for Two Jobs Probability The distribution of payoffs associated with Job 1 have a greater variance, a greater standard deviation, and a greater overall risk than the distribution of payoffs associated with Job Job Job Income Prof. Dr. Kerstin Schneider Chair of Public Economics and Business Taxation Microeconomics Chapter 5 Slide 19

20 Describing Risk Scenario B Decision making A person that does not like to take risks would choose Job 2, which has the same expected income as Job 1 but with lower risk Prof. Dr. Kerstin Schneider Chair of Public Economics and Business Taxation Microeconomics Chapter 5 Slide 20

21 Income from Sales Job modified ( ) Scenario A: revisited Suppose we add 100 to each of the payoffs from job 1, so that the expected payoff increases from 1500 to Outcome 1 Deviation Squared Outcome 2 Deviation Squared Expected Income Job 1 2, ,000 1, ,000 1, Standard Deviation Job 2 1, , Prof. Dr. Kerstin Schneider Chair of Public Economics and Business Taxation Microeconomics Chapter 5 Slide 22

22 Decision Making Decision Making Job 1: Expected income of 1,600 and a standard deviation of 500. Job 2: Expected income of 1,500 standard deviation of Which job to choose? Higher income or lower risk? Prof. Dr. Kerstin Schneider Chair of Public Economics and Business Taxation Microeconomics Chapter 5 Slide 23

23 Describing Risk Example A state wants to prevent double parking. What are possible solutions? Assumptions: 1. The individual saves 5 (in terms of value of time), if he double parks instead taking the time to park properly. 2. The driver is risk neutral. 3. The costs of catching a double-parker are zero Prof. Dr. Kerstin Schneider Chair of Public Economics and Business Taxation Microeconomics Chapter 5 Slide 24

24 Describing Risk Example Paying a fine of 5.01 would prevent the driver from parking in second the row. The benefit from parking in the second row is ( 5), which is lower than the cost of ( 5.01); this corresponds to a net benefit (of -0.01) that is less than Prof. Dr. Kerstin Schneider Chair of Public Economics and Business Taxation Microeconomics Chapter 5 Slide 25

25 Describing Risk Example A policy that combines a high fine with a low probability of apprehension is likely to reduce enforcement costs. A fine of 50 with a probability of being caught of 0.1 will result in an expected penalty of 5. A fine of 500 with a probability of being caught of 0.01 will result in an expected penalty of 5. To have an effective fine, the more risk-loving the population of drivers are, the higher the fine must be Prof. Dr. Kerstin Schneider Chair of Public Economics and Business Taxation Microeconomics Chapter 5 Slide 26

26 Preferences Toward Risk Choosing between risky alternatives Assumptions Consumption of a single product. The consumer knows all outcomes and their associated probabilities. Payoffs are measured in terms of utility. Utility function is given Prof. Dr. Kerstin Schneider Chair of Public Economics and Business Taxation Microeconomics Chapter 5 Slide 27

27 Preferences Toward Risk Example A woman has an income of 15,000 and a utility of 13 units. She is considering a new but risky sales job. Her income will either double to 30,000 or will fall to 10,000. Each possibility has a probability of 50%. To evaluate the new job, she can calculate the expected value of the resulting income. Because we are measuring value in terms of her utility, we must calculate the expected utility, E(u), that she can obtain Prof. Dr. Kerstin Schneider Chair of Public Economics and Business Taxation Microeconomics Chapter 5 Slide 28

28 Preferences Toward Risk Utility C D E 13 B 10 A Income ( thousands) Prof. Dr. Kerstin Schneider Chair of Public Economics and Business Taxation Microeconomics Chapter 5 Slide 29

29 Preferences Toward Risk Example Expected utility: Sum of the utilities associated with all possible outcomes, weighted by the probability of each outcome occurring Prof. Dr. Kerstin Schneider Chair of Public Economics and Business Taxation Microeconomics Chapter 5 Slide 30

30 Preferences Toward Risk Example The expected utility can be written as follows: E(u) = (1/2)u( 10,000) + (1/2)u( 30,000) = 0.5(10) + 0.5(18) = 14 The risky new job is thus preferred to the original job, because the expected utility of 14 is greater than the original utility of Prof. Dr. Kerstin Schneider Chair of Public Economics and Business Taxation Microeconomics Chapter 5 Slide 31

31 Preferences Toward Risk Individuals differ in their preferences toward risk. People can be risk averse, risk loving, or risk neutral. risk averse: The condition of preferring a certain income to an income subject to risk, with both having the same expected value. A consumer is risk averse when, his marginal utility diminishes as income increases. The use of insurance illustrates the risk averse behavior of individuals Prof. Dr. Kerstin Schneider Chair of Public Economics and Business Taxation Microeconomics Chapter 5 Slide 32

32 Preferences Toward Risk Risk averse Consider the following scenario: An individual can have a job earning 20,000 with 100% probability and an expected utility of 16. An Individual can have a job with 0.5 probability of earning 30,000 and 0.5 probability of earning 10,000. Expected income = (0.5)( 30,000) + (0.5)( 10,000) = 20, Prof. Dr. Kerstin Schneider Chair of Public Economics and Business Taxation Microeconomics Chapter 5 Slide 33

33 Preferences Toward Risk Risk averse The expected income from both jobs is the same. Thus, the risk averse person will choose the (certain) income. The expected utility from the uncertain income: E(u) = (1/2)u( 10,000) + (1/2)u( 30,000) E(u) = (0.5)(10) + (0.5)(18) = 14 E(u) from job 1 is 16, which is greater than E(u) from job 2 which is Prof. Dr. Kerstin Schneider Chair of Public Economics and Business Taxation Microeconomics Chapter 5 Slide 34

34 Preferences Toward Risk Utility Risk averse D C B A E The consumer is risk averse, because she would prefer an income of 20,000 with certainty instead of gambling with a 0.5 probability of earning 10,000 and a 0.5 probability of earning 30, Income ( thousands) Prof. Dr. Kerstin Schneider Chair of Public Economics and Business Taxation Microeconomics Chapter 5 Slide 35

35 Preferences Toward Risk Risk neutral Risk neutral: is a condition of being indifferent between a risky income and a certain income with the same expected value Prof. Dr. Kerstin Schneider Chair of Public Economics and Business Taxation Microeconomics Chapter 5 Slide 36

36 Preferences Toward Risk Risk neutral 18 Utility 12 C E The consumer is risk neutral and indifferent between certain and uncertain events with the same expected income. 6 A Income ( thousands) Prof. Dr. Kerstin Schneider Chair of Public Economics and Business Taxation Microeconomics Chapter 5 Slide 37

37 Preferences Toward Risk Risk loving Risk loving: Condition of preferring a risky income to a certain income with the same expected value. E.g., Gambling, some criminal activities Prof. Dr. Kerstin Schneider Chair of Public Economics and Business Taxation Microeconomics Chapter 5 Slide 38

38 Preferences Toward Risk Utility Risk loving 18 8 C E The consumer is risk loving; she would prefer the uncertain income instead of the certain income when both have the same expected value. 3 0 A Income ( thousands) Prof. Dr. Kerstin Schneider Chair of Public Economics and Business Taxation Microeconomics Chapter 5 Slide 39

39 Preferences Toward Risk RISK PREMIUM Risk premium: Maximum amount of money that a risk-averse person will pay to avoid taking a risk. Consider the following scenario: With a probability of 0.5, the consumer could earn an income of 30,000, and with a 0.5 probability, she could earn an income of 10,000 (expected income = 20,000). The expected utility is then E(u) = 0.5(18) + 0.5(10) = Prof. Dr. Kerstin Schneider Chair of Public Economics and Business Taxation Microeconomics Chapter 5 Slide 40

40 How much would the consumer pay to avoid risk? RISK PREMIUM Utility A C RISK PREMIUM E F G Here the risk premium is 4,000, because a certain income of 16,000 gives her the same expected utility (14) as the uncertain income that has an expected value of 20, Income ( thousands) Prof. Dr. Kerstin Schneider Chair of Public Economics and Business Taxation Microeconomics Chapter 5 Slide 41

41 Preferences Toward Risk Indifference Curves Combinations of the expected value of income and its standard deviation with which the same expected utility can be achieved Prof. Dr. Kerstin Schneider Chair of Public Economics and Business Taxation Microeconomics Chapter 5 Slide 42

42 Risk Aversion and Indifference Curves Expected Income U 3 U 2 U 1 Highly risk averse: an increase in the standard deviation of this individual s income requires a large increase in expected income if he or she is to remain equally well off. Standard deviation of income Prof. Dr. Kerstin Schneider Chair of Public Economics and Business Taxation Microeconomics Chapter 5 Slide 43

43 Risik Aversion and Indifference Curves Expected Income Slightly risk averse: an increase in the standard deviation of income requires only a small increase in expected income if he or she is to remain equally well off. U 3 U 2 U 1 Standard deviation of income Prof. Dr. Kerstin Schneider Chair of Public Economics and Business Taxation Microeconomics Chapter 5 Slide 44

44 Example Business Executives and Risk Preferences In one study, 464 executives were asked questions describing their risk preferences. The results were as follows: 20% were risk neutral 40% were risk loving. 20% were risk averse. 20% did not answer the questionnaire Prof. Dr. Kerstin Schneider Chair of Public Economics and Business Taxation Microeconomics Chapter 5 Slide 45

45 Reducing Risk There are three methods which consumers use to try to avoid risk: 1) Diversification 2) Insurance 3) The value of complete information Prof. Dr. Kerstin Schneider Chair of Public Economics and Business Taxation Microeconomics Chapter 5 Slide 46

46 Reducing Risk Diversification Assume that a company can decide between selling air conditioners and heaters or both. The probability of hot or cold weather is 0.5. If the company diversifies, it is probably better off Prof. Dr. Kerstin Schneider Chair of Public Economics and Business Taxation Microeconomics Chapter 5 Slide 47

47 Income from sales of appliances Income from sales of appliances in s: Hot Weather Cold Weather Air Conditioner sales 30,000 12,000 Heater sales 12,000 30, Prof. Dr. Kerstin Schneider Chair of Public Economics and Business Taxation Microeconomics Chapter 5 Slide 48

48 Reducing Risk Diversification If the company sells only air conditioners or only heaters, the actual income will be either 12,000 or 30,000. Expected income will be 1/2( 12,000) + 1/2( 30,000) = 21,000 Diversification between the products will yield half of what would have been earned from only selling heaters plus half that which would have been earned from only selling air conditioners Prof. Dr. Kerstin Schneider Chair of Public Economics and Business Taxation Microeconomics Chapter 5 Slide 49

49 Reducing Risk Diversification If the weather is hot, the company will earn 15,000 from air conditioner sales and 6,000 from heater sales; thus earning a total of 21,000 in sales. If the weather is cold, the company will earn 6,000 from air conditioners and 15,000 from heaters earning a total income of 21, Prof. Dr. Kerstin Schneider Chair of Public Economics and Business Taxation Microeconomics Chapter 5 Slide 50

50 Reducing Risk Diversification In this instance, diversification eliminates all risk because the certain income from diversification is 21,000. Companies can reduce risk by dividing their business into a series of activities whose outcomes are not closely related Prof. Dr. Kerstin Schneider Chair of Public Economics and Business Taxation Microeconomics Chapter 5 Slide 51

51 Reducing Risk The Stock Market Questions to be discussed How can diversification reduce the risk of investment in the stock market? Can diversification eliminate the risk of investment in the stock market? Prof. Dr. Kerstin Schneider Chair of Public Economics and Business Taxation Microeconomics Chapter 5 Slide 52

52 Reducing Risk Insurance For a risk-averse individual, losses count more (in terms of changes in utility) than gains. A risk-averse homeowner, therefore, will enjoy higher utility by purchasing building insurance Prof. Dr. Kerstin Schneider Chair of Public Economics and Business Taxation Microeconomics Chapter 5 Slide 53

53 The Decision to Buy Insurance The decision to buy insurance ( ) with insurance costs of 1,000. Insurance Burglary (Probability 0.1) No Burglary (Probability 0.9) Expected Wealth Standard Deviation No 40,000 50,000 49,000 3,000 Yes 49,000 49,000 49, Prof. Dr. Kerstin Schneider Chair of Public Economics and Business Taxation Microeconomics Chapter 5 Slide 54

54 Reducing Risk Insurance While the expected payout is the same, the expected utility is greater when having insurance. Since, the marginal utility in the event of a loss is greater than when no loss occurs. When buying insurance, we can expect to have an insurance premium which is equal to the total expected payout (to all insurance customers). Thus, this increases our utility Prof. Dr. Kerstin Schneider Chair of Public Economics and Business Taxation Microeconomics Chapter 5 Slide 55

55 Reducing Risk The Law of Large Numbers Although single events may be random and largely unpredictable, the average outcome of many similar events can be predicted. Example A single toss of a coin and a large number of such coin tosses. The question of which driver suffers a total loss and the amount of total damage caused by a large group of drivers Prof. Dr. Kerstin Schneider Chair of Public Economics and Business Taxation Microeconomics Chapter 5 Slide 56

56 Reducing Risk Actuarial Fairness Assumption: The probability of a loss of 10,000 from home burglary is 10%. Expected loss = 0.10 x 10,000 = 1,000 at high risk (the probability of a loss of 10,000 amounts to 10%) 100 individuals will be confronted with the same risk Prof. Dr. Kerstin Schneider Chair of Public Economics and Business Taxation Microeconomics Chapter 5 Slide 57

57 Reducing Risk Actuarial Fairness Hence: With a premium of 1,000, a fund of 100,000 will be created from which the losses can be covered. Actuarial justice Applies when: Insurance premium = expected payout Prof. Dr. Kerstin Schneider Chair of Public Economics and Business Taxation Microeconomics Chapter 5 Slide 58

58 Reducing Risk The Value of Information Value of complete information Difference between the expected value of a choice when there is complete information and the expected value when information is incomplete. Suppose that the manager of a clothing business must decide how many suits he has to order for autumn: 100 suits cost 180/suit. 50 suits cost 200/suit. The price of the suits is Prof. Dr. Kerstin Schneider Chair of Public Economics and Business Taxation Microeconomics Chapter 5 Slide 59

59 Reducing Risk The Value of Information Suppose that the manager of a clothing business must decide how many suits he has to order for autumn: Unsold suits can be returned at half of the original cost. Without further information, the probability of selling 100 suits is equal to 50% and the probability of selling 50 suits is equal to 50% Prof. Dr. Kerstin Schneider Chair of Public Economics and Business Taxation Microeconomics Chapter 5 Slide 60

60 The Decision of sales of suits Profits from Sales of Suits ( ) Sales of 50 units Sales of 100 units Expected Profits Buy 50 units 5,000 5,000 5,000 Buy 100 units 1,500 12,000 6,750 With incomplete information: Risk neutral: Buy 100 suits Risk averse: Buy 50 suits Prof. Dr. Kerstin Schneider Chair of Public Economics and Business Taxation Microeconomics Chapter 5 Slide 61

61 Reducing Risk The Value of Information The expected profit with complete information is 8,500. 8,500 = 0.5(5,000) + 0.5(12,000) The expected profit with uncertainty (buy 100 suits) is 6,750. The value of complete information is equal to 1,750 (that is, the expected value with complete information minus the expected value with uncertainty (buy 100 suits)) Prof. Dr. Kerstin Schneider Chair of Public Economics and Business Taxation Microeconomics Chapter 5 Slide 62

62 The Demand for Risky Assets Assets Something that provides a flow of money or service to its owner. Capital gain The flow of money or money itself can be explicit (dividends) or implicit (capital gain). An increase in the value of an asset is a capital gain; a decrease is a capital loss Prof. Dr. Kerstin Schneider Chair of Public Economics and Business Taxation Microeconomics Chapter 5 Slide 63

63 The Demand for Risky Assets Risky & Riskless Assets Risky Assets: Asset that provides an uncertain flow of money or services to its owner. Examples Housing, capital gains, industrial bonds, investment prices Riskless (or risk-free) Assets Assets that provide a flow of money or services that is known with certainty. Examples Short term government bonds, short term money market papers Prof. Dr. Kerstin Schneider Chair of Public Economics and Business Taxation Microeconomics Chapter 5 Slide 64

64 The Demand for Risky Assets Asset returns Return Total monetary flow of an asset as a fraction of its price. Real return Simple (or nominal) return on an asset, less the rate of inflation Prof. Dr. Kerstin Schneider Chair of Public Economics and Business Taxation Microeconomics Chapter 5 Slide 65

65 The Demand for Risky Assets Returns on Assets Asset returns = money flow price payment 100/Y Asset returns 10% selling price 1, Prof. Dr. Kerstin Schneider Chair of Public Economics and Business Taxation Microeconomics Chapter 5 Slide 66

66 The Demand for Risky Assets Expected versus actual returns Expected return: Return that an asset should earn on average. Actual return: Return that an asset earns Prof. Dr. Kerstin Schneider Chair of Public Economics and Business Taxation Microeconomics Chapter 5 Slide 67

67 Investments Risk and Return ( ) Investments Risk and Return ( ) Average Real Rate of Return (%) Risk (Standard Deviation, %) Common stocks (S&P 500) Long-term corporate bonds U.S. Treasury bills Source: Stocks, Bands, Bills, and Inflation: 2007 Year book, Morningstar, Inc Prof. Dr. Kerstin Schneider Chair of Public Economics and Business Taxation Microeconomics Chapter 5 Slide 68

68 The Demand for Risky Assets Expected and Actual Return Higher returns are associated with higher risks. The risk-averse investor must adjust his risk in terms of his earnings Prof. Dr. Kerstin Schneider Chair of Public Economics and Business Taxation Microeconomics Chapter 5 Slide 69

69 The Demand for Risky Assets The Trade-off between Risk and Return The investor chooses between investing in treasury bills and stocks. Treasury bills (risk-free) and stocks (risky) R f = risk-free return on the Treasury bill Because the return is risk free, the expected and actual returns are the same R m = expected return from investing in the stock market r m = the actual return Prof. Dr. Kerstin Schneider Chair of Public Economics and Business Taxation Microeconomics Chapter 5 Slide 70

70 The Demand for Risky Assets The Trade-off Between Risk and Return At the time of making the decision on whether or not to invest, we know the set of possible results and the probability of each result occurring; however, we do not know what specific result we will end up with. The risky investment has a higher expected return than the risk-free investment (R m > R f ). If this was not the case, risk averse investors would only invest in treasury bills Prof. Dr. Kerstin Schneider Chair of Public Economics and Business Taxation Microeconomics Chapter 5 Slide 71

71 The Demand for Risky Assets The Investment Portfolio Distribution of savings b = the fraction of savings placed in the stock market 1 - b = fraction used to purchase Treasury bills Expected return on a portfolio of assets (total assets): R p : is a weighted average of the expected return from the two assets. R p = br m + (1-b)R f Prof. Dr. Kerstin Schneider Chair of Public Economics and Business Taxation Microeconomics Chapter 5 Slide 72

72 The Demand for Risky Assets The Investment Portfolio Expected Return: Question When R m = 12%, R f = 4%, and b = 1/2, R p = 1/2(0.12) + 1/2(0.04) = 8% How should the investor should choose the fraction b? Prof. Dr. Kerstin Schneider Chair of Public Economics and Business Taxation Microeconomics Chapter 5 Slide 73

73 The Demand for Risky Assets The Investment Portfolio The standard deviation of the risky stock market investment is equal to the proportion of the portfolio invested in risky investments times the standard deviation of this portfolio: b needs to be chosen p b m Prof. Dr. Kerstin Schneider Chair of Public Economics and Business Taxation Microeconomics Chapter 5 Slide 74

74 The Demand for Risky Assets The decision making problem of the investor choosing b: R br ( 1 b) R p m f R p R f b ( Rm R f ) Prof. Dr. Kerstin Schneider Chair of Public Economics and Business Taxation Microeconomics Chapter 5 Slide 75

75 The Demand for Risky Assets The decision making problem of the investor b Choosing : b We have / p m p b m, then: R p R f ( R m m R f ) p Prof. Dr. Kerstin Schneider Chair of Public Economics and Business Taxation Microeconomics Chapter 5 Slide 76

76 The Demand for Risky Assets The Risk and the Budget line Note that, this last equation R p R f (R R σ m m f ) σ p is a budget line describing the trade-off between risk and expected return ). (R p ( ) p Prof. Dr. Kerstin Schneider Chair of Public Economics and Business Taxation Microeconomics Chapter 5 Slide 77

77 The Demand for Risky Assets The Risk and the Budget line Note that a) the expected return on the portfolio, R p, increases as the standard deviation of that return, σ p, increases. b) the slope is equal to the price of the risk or the tradeoff between risk and return Prof. Dr. Kerstin Schneider Chair of Public Economics and Business Taxation Microeconomics Chapter 5 Slide 78

78 Choosing between Risk and Return Expected Return R p U 3 The utility-maximizing investment portfolio is at the point where the indifference curve U 2 is tangent to the budget line, because this point yields the highest expected feasible return for a given level of risk. U 2 U1 Budget line R m R * R f m Standard deviation 0 of return p Prof. Dr. Kerstin Schneider Chair of Public Economics and Business Taxation Microeconomics Chapter 5 Slide 79

79 The Choices of two different Investors Expected return R p U B R m R B R A R f U A Budget line Using the same budget line, investor A chooses the combination with lower return and lower risk, while investor B chooses the combination with higher return and higher risk. 0 A B m of return p Standard deviation Prof. Dr. Kerstin Schneider Chair of Public Economics and Business Taxation Microeconomics Chapter 5 Slide 80

80 Investing in the Stock Market Notice The percentage of American families that invested directly or indirectly in the stock market: 1989 = 32% 1995 = 41% Their share of total assets invested in the stock market: 1989 = 26% 1995 = 40% Prof. Dr. Kerstin Schneider Chair of Public Economics and Business Taxation Microeconomics Chapter 5 Slide 81

81 Investing in the Stock Market Note that: Participation in the stock market according to age Younger than 35 years 1989 = 23% 1995 = 29% Older than 35 year Slight increase Prof. Dr. Kerstin Schneider Chair of Public Economics and Business Taxation Microeconomics Chapter 5 Slide 82

82 Dividend Yield and P/E Ratio for S&P Prof. Dr. Kerstin Schneider Chair of Public Economics and Business Taxation Microeconomics Chapter 5 Slide 83

83 Concluding Remarks Consumers and managers often make decisions when there is uncertainty about the future. Consumers and investors are concerned about the expected value and the variability of uncertain results. In a case of uncertainty, consumers maximize their expected utility by using the respective weighted probabilities of the different outcomes. A person may be risk averse, risk neutral, or risk loving Prof. Dr. Kerstin Schneider Chair of Public Economics and Business Taxation Microeconomics Chapter 5 Slide 84

84 Concluding Remarks The maximum sum of money that a risk-averse person would pay to avoid a risk is called the risk premium. Risk can be reduced by diversification, the purchase of insurance, or the procurement of additional information Prof. Dr. Kerstin Schneider Chair of Public Economics and Business Taxation Microeconomics Chapter 5 Slide 85

85 Concluding Remarks The law of large numbers allows insurance companies to offer actuarially fair insurance in which the premium paid corresponds to the expected value of the insured loss. Consumption theory can be applied to decisions regarding investments in risky assets. Individual behavior is not always predictable Prof. Dr. Kerstin Schneider Chair of Public Economics and Business Taxation Microeconomics Chapter 5 Slide 86