CHAPTER 5 - UNCERTAINTY AND CONSUMER BEHAVIOR Key ...
CHAPTER 5 - UNCERTAINTY AND CONSUMER BEHAVIOR Key Concepts and Topics • • • • • •
Describing Risk Preferences Toward Risk Reducing Risk The Demand for Risky Assets Bubbles Behavioral Economics
Describing Risk • To measure risk we must know: 1. All of the possible outcomes 2. The probability or likelihood that a given outcome will occur • Interpreting Probability – Objective probability ♦ Observed frequency of past events – Subjective probability ♦ Perception that an outcome will occur ♦ Influenced by different information or different abilities to process the same information – based on judgment or experience • 2 measures to help describe and compare risky choices 1. Expected value 2. Variability • Expected Value – Probability-weighted average of the payoffs or values associated with all possible outcomes ♦ measures the central tendency; the payoff or value expected on average – Example: Investment in offshore drilling exploration: 2 possible outcomes ♦ ♦ ♦
Success – the stock price increases from $30 to $40/share Failure – the stock price falls from $30 to $20/share Objective Probability – 100 explorations: 25 successes and 75 failures – Probability of success = 0.25 and probability of failure = 0.75 – EV = Pr(success)(value of success) + Pr(failure)(value of failure)
Source: Pindyck and Rubinfeld (2013), Microeconomics, 8th Ed., Pearson Prentice Hall, Chapter 5.
1
= 0.25($40/share) + 0.75($20/share) = $25/share – In general, for n possible outcomes:
E(X) = Pr1X1 + Pr2X2 + … + PrnXn where X1, X2, … Xn = payoffs of possible outcomes Pr1, Pr2, … Prn = probabilities of each outcome • Variability – Extent to which possible outcomes of an uncertain event differ – How much variation exists in the possible choices – Example: Suppose you are choosing between two part-time sales jobs that
have the same expected income ($1,500) Outcome 1 Job 1: Commission
Outcome 2
Pr
Income
Pr
Income
0.5
$2,000
0.5
$1,000
Job 2: Fixed salary 0.99 $1,510 0.01 E(X1) = 0.5($2,000) + 0.5($1,000) = $1,500 E(X2) = 0.99($1,510) + 0.01($510) = $1,500 ♦ ♦ ♦
$510
Same expected values, but different variability Greater variability from expected values signals greater risk Variability comes from deviations in payoffs – Difference between expected payoff and actual payoff Deviations from Expected Income ($)
♦
♦
Outcome 1
Deviation
Outcome 2
Deviation
Job 1
$2,000
$500
$1,000
–$500
Job 2
$1,510
$10
$510
–$990
Average deviations are always zero so we must adjust for negative numbers by taking the squares of the deviations Measure variability with standard deviation, σ – Square root of the weighted average of the squares of the deviations (variance, σ2) – Measures how variable your payoff will be – More variability means more risk
Source: Pindyck and Rubinfeld (2013), Microeconomics, 8th Ed., Pearson Prentice Hall, Chapter 5.
2
– Individuals generally prefer less variability – less risk – The standard deviation is written:
σ = Pr1 ( X 1 − E ( X )) 2 + Pr2 ( X 2 − E ( X )) 2 ♦
Standard deviations of the two jobs are: σ 1 = .5(250,000) + .5(250,000) = 250,000 = 500 σ 2 = .99(100) + .01(980,100) = 9,900 = 99.50
♦
σ1 > σ2, Job 1 is therefore the riskier alternative. Choose Job 2.
– Example modified: Suppose we add $100 to each payoff in Job 1 ♦ ♦
Job 1: expected income $1,600 and a standard deviation of $500 Job 2: expected income $1,500 and a standard deviation of $99.50 – Which job should be chosen? o Depends on the individual o Some may be willing to take risk with higher expected income o Some will prefer less risk even with lower expected income
Preferences Toward Risk • Evaluate risky alternatives by measuring payoff in terms of utility – A consumer gets utility from income – Example: ♦ A person is earning $15,000 and receiving 13.5 units of utility from the job ♦ She is considering a new, but risky job – 0.50 chance of $30,000 and 0.50 chance of $10,000 – Utility($30,000) = 18 and Utility($10,000) = 10 – To evaluate the new job, she must compare the expected utility from the risky job with current utility of 13.5 ♦ Expected utility of the risky option is the sum of the utilities associated with all her possible incomes weighted by the probability that each income will occur E(U) = (Pr. of Utility 1)*(Utility 1) + (Pr. of Utility 2)*(Utility 2) = 0.5*U($10,000) + 0.5*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 13.5
and therefore preferred Source: Pindyck and Rubinfeld (2013), Microeconomics, 8th Ed., Pearson Prentice Hall, Chapter 5.
3
• People differ in their preference toward risk – People can be risk averse, risk neutral, or risk loving • Risk Averse – A person who prefers a certain given income to a risky income with the same expected value – Diminishing marginal utility of income – Most common attitude towards risk ♦ Ex: Market for insurance – Example: ♦
♦
♦
♦
♦
♦
A person can have a $20,000 job with 100% probability and receive a utility level of 16 The person could have a job with a 0.5 chance of earning $30,000 and a 0.5 chance of earning $10,000 Expected Income of risky job E(I) = (0.5)($30,000) + (0.5)($10,000) = $20,000 Expected Utility of risky job E(U) = (0.5)(10) + (0.5)(18) = 14 Both jobs have the same expected income but different expected utilities – Risk averse individual would choose the certain job for its greater utility Risk averse person’s losses (decreased utility) are more important than risky gains
– Risk averse utility function E Utility
18
Level of utility increases as income increases – marginal utility is diminishing
D
16
C
F
14
A risk-averse person prefers a certain income of $20,000 to an uncertain expected income of $20,000
A 10
0
10
16
20
30
Income ($1,000)
• Risk Neutral – A person is indifferent between a certain income and an uncertain income with the same expected value – Constant marginal utility of income Source: Pindyck and Rubinfeld (2013), Microeconomics, 8th Ed., Pearson Prentice Hall, Chapter 5.
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– Expected utility for risky option is the same as for certain outcome
E(I) = (0.5)($10,000) + (0.5)($30,000) = $20,000 E(U) = (0.5)(6) + (0.5)(18) = 12 – This is the same as the certain income of $20,000 with utility of 12 Utility 18
Level of utility increases as income increases – marginal utility is constant
12
A risk-neutral person is indifferent between certain events and uncertain events with the same expected income
6
0
10
20
30 Income ($1,000)
• Risk Loving – A person prefers an uncertain income to a certain income with the same expected value ♦ Examples: Gambling, some criminal activity – Increasing marginal utility of income – Expected value for risky option E(I) = (0.5)($10,000) + (0.5)($30,000) = $20,000 E(U) = (0.5)(3) + (0.5)(18) = 10.5 – Certain income is $20,000 with utility of 8 – Risky alternative is preferred Utility 18
Level of utility increases as income increases – marginal utility is increasing
10.5
A risk-loving person prefers uncertain events to certain events with the same expected income
8 3 0
10
20
30
Income ($1,000)
• Risk Premium – The maximum amount of money that a risk-averse person would pay to avoid taking a risk – Depends on the risky alternatives the person faces Source: Pindyck and Rubinfeld (2013), Microeconomics, 8th Ed., Pearson Prentice Hall, Chapter 5.
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– Example: ♦
♦
A person has a 0.5 probability of earning $30,000 and a 0.5 probability of earning $10,000 The expected income is $20,000 with expected utility of 14 Utility
G
20 18
C
The risk premium is $4,000 because a certain income of $16,000 gives the person the same expected utility as the uncertain income with expected value of $20,000
E
14
F
A 10
0 ♦
♦
10
16
20
30
40
Income ($1,000)
Point F shows the risky scenario – the utility of 14 can also be obtained with certain income of $16,000 This person would be willing to pay up to $4,000 (20 – 16) to avoid the risk of uncertain income – Can be shown graphically by drawing a straight line (CF) between the two points
• Risk Aversion and Income – Variability in potential payoffs increases the risk premium – Example: ♦ A job has a 0.5 probability of paying $40,000 (utility = 20) and a 0.5 probability of paying 0 (utility = 0) ♦ The expected income is still $20,000, but the expected utility falls to 10 E(U) = (0.5)U($0) + (0.5)U($40,000) = 0 + 0.5(20) = 10 ♦ The certain income of $20,000 has utility of 16 ♦ If a person must take new job, his utility will fall by 6 ♦ He can get 10 units of utility by taking a certain job paying $10,000 ♦ The risk premium, therefore, is $10,000 (i.e. he would be willing to give up $10,000 of the $20,000 and have the same E(U) as the risky job) – The greater the variability, the more the person would be willing to pay to
avoid the risk and the larger the risk premium
Source: Pindyck and Rubinfeld (2013), Microeconomics, 8th Ed., Pearson Prentice Hall, Chapter 5.
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• Risk Aversion & Indifference Curves – Indifference curves that relate expected income to variability of income (standard deviation) can be used to represent a person’s risk aversion (Risk/Return Tradeoffs) – Since risk is undesirable, greater risk requires greater expected income to make the person equally well off – Indifference curves are therefore upward sloping U3 Expected Income
U2 U1
Highly Risk Averse: An increase in standard deviation requires a large increase in income to maintain satisfaction
Standard Deviation of Income Expected Income U3 U2 U1
Slightly Risk Averse: A large increase in standard deviation requires only a small increase in income to maintain satisfaction
Standard Deviation of Income
• Risk Neutrality and Indifference Curves – A person who is risk neutral (only care about income; does not care about risk) will have horizontal indifference curves in the return–risk tradeoffs • Risk Loving and Indifference Curves – A person who is risk loving (derives greater utility as risk increases) will have downward sloping indifference curves in the return–risk tradeoffs
Source: Pindyck and Rubinfeld (2013), Microeconomics, 8th Ed., Pearson Prentice Hall, Chapter 5.
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Reducing Risk • 3 ways to reduce risks: diversification, insurance, and obtaining more information • Diversification – allocating resources to a variety of activities whose outcomes are not closely related (positively or negatively correlated) – Investing in a portfolio of 10 or 20 different stocks – Buying shares in mutual funds ♦ Organization that pools funds of individual investors to buy a large number of different stock or other financial assets • Insurance – paying a premium (= the expected loss from the risky situation) to avoid risk – A risk-averse individual counts losses (in terms of changes in utility) more than gains – The law of large numbers – although single events may be random and largely unpredictable, the average outcome of many similar events can be predicted – Actuarial fairness – the insurance premium is equal to the expected payout – Example: Burglary insurance: 100 people are similarly situated and face a 10-percent probability of a $10,000 loss ♦ Premium from the 100 individuals: $100,000 ♦ Expected payout to the 100 individuals as a whole: $100,000 • Obtaining more information – if more information were available, a person could make better predictions and reduce risk – 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 – Example: There is a 0.5 probability that 100 suits will be sold and a 0.5 probability that 50 suits will be sold. How many suits to order if each suit sells for $300 and any unsold suits can be returned for half of the price paid? Profits from sales of suits: Sales (unit of suits) Buy 50 @$200 100 @$180
50
100
$5,000 $1,500
$5,000 $12,000
Expected profit With With uncertainty complete information $5,000 $5,000 $6,750 $12,000
Source: Pindyck and Rubinfeld (2013), Microeconomics, 8th Ed., Pearson Prentice Hall, Chapter 5.
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Value of complete information: Expected value with complete information Less: Expected value with uncertainty (buy 100 suits) Value of complete information
$8,500 6,750 $1,750
The Demand for Risky Assets • Even though most people are risk averse, they still invest all or part of their savings in stocks, bonds, and other assets that carry some risk – An asset – something that provides a flow of money or services to its owner, e.g., an apartment building, a savings account, or shares of a company ♦ Capital gain (loss) – increase (decrease) in value of an asset – Risky asset – asset that provides an uncertain flow of money or services to its owner (e.g., stocks) – Riskless (risk-free) asset – asset that provides a flow of money or services that is known with certainty (e.g., Treasury bills) – Nominal return – total money flow of an asset as a fraction of its price – Real return – nominal return less the rate of inflation – Expected return – return that an asset should earn on average – Actual return – return that an asset earns • The trade-off between risk and return – The higher the expected return, the higher the risk ♦ Expected return from investing in the stock market, Rm > expected return from investing in Treasury bills, Rf – The investment portfolio ♦
♦
Expected return on a 2-asset portfolio, Rp, with b (% of the portfolio) invested in the stock market and (1 – b) invested in T-bills: Rp = bRm + (1 – b)Rf Rp = Rf + b(Rm – Rf ) Standard deviation of the portfolio, σp, is the % of the portfolio invested in the stock market times the standard deviation of the stock market: σp = bσm
• The investor’s choice problem: – Risk and the budget line – describes the trade-off between risk (σp) and expected return (Rp) (R − R f ) Rp = R f + m σp σm Source: Pindyck and Rubinfeld (2013), Microeconomics, 8th Ed., Pearson Prentice Hall, Chapter 5.
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♦
♦
Expected return on the portfolio, Rp, increases as the standard deviation of that return σp increases (Rm – Rf ) /σm is the price of risk – extra risk that an investor must incur to enjoy a higher expected return – No risk – invest all the funds in T-bills (b = 0) and earn an expected return Rf – Incur a risk level of σm – invest all the funds in stocks (b = 1) and earn an expected return Rm – Incur a risk level between 0 and σm – invest some funds in each type of asset and earn an expected return somewhere between Rf and Rm Expected return, Rp
U3 U2 U1
Rm Budget line R*
Rf 0
σ*
σm
Standard deviation of return, σp
– Risk and indifference curves – describes combinations of risk and return that
leave the investor equally satisfied ♦ Upward-sloping because risk is undesirable ♦ With a greater amount or risk, it takes a greater expected return to make the investor equally well-off – The choices of different investors ♦ ♦ ♦
Investor A is highly risk averse – he invests mostly in risk-free asset Investor B is less risk averse – he invests mostly in stocks Investor C has very low degree of risk aversion – he invests more than 100% of his wealth in stocks (buy stocks on margin)
Source: Pindyck and Rubinfeld (2013), Microeconomics, 8th Ed., Pearson Prentice Hall, Chapter 5.
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Expected return, Rp
UA
UB
UC
Budget line
RC Rm RB
RA Rf 0
σA
σB
σm
σC
Standard deviation of return, σp
Bubbles • An increase in the price of a good based not on the fundamentals of demand or value, but instead on a belief that the price will keep going up – The result of irrational behavior – People stop thinking straight • Examples: the Internet bubble, the housing price bubble • Informational cascades – an assessment (e.g., of an investment opportunity) based in part on the actions of others, which in turn were based on the actions of others – The bubble can in fact be rational in the sense that there is a basis for believing that investing in the bubble will yield a positive return – The expected gain to an investor down the chain will be positive if investors early in the chain indeed obtained positive information and based their decisions on that information – However, the risk involved will be considerable, and it is likely that at least some investors will underestimate that risk
Behavioral Economics • Individual behavior sometimes seems unpredictable, even irrational, and contrary to the basic utility-maximizing assumptions: Source: Pindyck and Rubinfeld (2013), Microeconomics, 8th Ed., Pearson Prentice Hall, Chapter 5.
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1. Consumers have clear preferences for some goods over others 2. Consumers face budget constraints 3. Given their preferences, limited incomes, and the prices of different goods,
consumers choose to buy combinations of goods that maximize their utility – These assumptions are not always realistic • Examples: – There has just been a big snowstorm, so you stop at the hardware store to buy a snow shovel. You had expected to pay $20 for the shovel—the price that the store normally charges. However, you find that the store has suddenly raised the price to $40. Although you would expect a price increase because of the storm, you feel that a doubling of the price is unfair and that the store is trying to take advantage of you. Out of spite, you do not buy the shovel. – Tired of being snowed in at home you decide to take a vacation in the
country. On the way, you stop at a highway restaurant for lunch. Even though you are unlikely to return to that restaurant, you believe that it is fair and appropriate to leave a 15% tip in appreciation of the good service that you received. – You buy this textbook from an Internet bookseller because the price is lower than the price at your local bookstore. However, you ignore the shipping cost when comparing prices. • Reference Points and Consumer Preferences – Basic model: consumers place unique values on goods and services that they purchase – Psychologist: perceived value depends on the circumstances – The Reference Point ♦ ♦
♦
The point from which the individual makes a consumption decision Develop for many reasons: past consumption, experience in a market, expectations about how prices should behave, and even the context in which a good is consumed Affect the way people approach economic decisions
– The Endowment Effect ♦
♦
Tendency of individuals to value an item more when they own it than when they do not Consider the gap between the price that a person is willing to pay for a good and the price of which she is willing to sell the same good to someone else – Basic model says that this price should be the same
Source: Pindyck and Rubinfeld (2013), Microeconomics, 8th Ed., Pearson Prentice Hall, Chapter 5.
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– Many experiments suggest that is not what happens in practice – Loss Aversion ♦ ♦
♦
♦
Tendency for individuals to prefer avoiding losses over acquiring gains Giving up a good was perceived to be a greater “loss” to those who had one than the “gain” from obtaining a good for those without one Example: people are hesitant to sell stocks at a loss, even if they could invest the proceeds in other stocks that they think are better investments – The high original price paid for the stock acts as a reference point – People are averse to losses o A $1000 loss on an investment seems to hurt more than the perceived benefit from a $1000 gain Endowment effects tend to disappear as consumers gain relevant experience – Not expect to see stockbrokers or other investment professionals exhibit the loss aversion
– Framing ♦
♦
Tendency to rely on the context in which a choice is described when making a decision How choices are framed – the names they are given, the context in which they are described, and their appearance – can affect the choices that individuals make
• Fairness – People do things because they think it is appropriate or fair to do so, even though there is no financial or other material benefit (e.g., charitable giving, volunteering time, tipping in a restaurant) – People’s views about fairness affect their behavior ♦ Workers who do not get a wage that they feel is fair may not put much effort into their work ♦ Firms can more easily raise prices in response to higher costs than to increases in demand • Rules of Thumb and Biases in Decision Making – Depend on both the context in which the decisions are made and the information available – Anchoring ♦
Tendency to rely heavily on one or two pieces of information when making a decision
Source: Pindyck and Rubinfeld (2013), Microeconomics, 8th Ed., Pearson Prentice Hall, Chapter 5.
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♦
Example: many price tags end with the digits 95 or 99 because marketers understand consumers tend to overemphasize the first digit of prices $19.95 seems much cheaper than $20.01
– Rule of Thumb ♦
♦
A common way to economize on the effort involved in making decisions is to ignore seemingly unimportant pieces of information (e.g., shipping costs of goods purchased over the Internet) Helps to save time and effort and result in biases in decision making
– The Law of Small Numbers ♦
♦
Tendency to overstate the probability that a certain event will occur when faced with relatively little information – Research has shown that investors in the stock market are often subject to a small-numbers bias, believing that high returns over the past few years are likely to be followed by more high returns over the next few years – thereby contributing to the kind of “herd behavior” – When people assess the likelihood that housing prices will rise based on several years of data, the resulting misperceptions can result in housing price bubbles Forming subjective probabilities is not always an easy task and people are generally prone to several biases in the process – Overestimate the probability that a particular event will occur if such an event has occurred recently – Ignore the possibility in decision making when a probability for a particular event is very, very small
• Summing up – Basic theory helps us to understand and evaluate the characteristics of consumer demand and to predict the impact on demand of changes in prices or incomes – Behavioral economics tries to explain and to elaborate on those situations that are not well explained by the basic consumer model
Source: Pindyck and Rubinfeld (2013), Microeconomics, 8th Ed., Pearson Prentice Hall, Chapter 5.
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Quick Quiz 1. George has $5,000 to invest in a mutual fund. The expected return on mutual fund A is 15 percent and the expected return on mutual fund B is 10 percent. Should George pick mutual fund A or fund B? 2. Jennifer is shopping and sees an attractive shirt. However, the price of $50 is more than she is willing to pay. A few weeks later, she finds the same shirt on sale for $25 and buys it. When a friend offers her $50 for the shirt, she refuses to sell it. Explain Jennifer’s behavior. 3. Suppose that Natasha’s utility function is given by uI = √10I , where I represents annual income in thousands of dollars. a. Is Natasha risk loving, risk neutral, or risk averse? Explain. b. Suppose that Natasha is currently earning an income of $40,000 (I = 40) and can earn that income next year with certainty. She is offered a chance to take a new job that offers a 0.6 probability of earning $44,000 and a 0.4 probability of earning $33,000. Should she take the new job? c. In (b), would Natasha be willing to buy insurance to protect against the variable income associated with the new job? If so, how much would she be willing to pay for that insurance? 4. Suppose that two investments have the same three payoffs, but the probability associated with each payoff differs, as illustrated in the table below: Payoff
Probability (Investment A)
Probability (Investment B)
$300 $250
0.10 0.80
0.30 0.40
$200
0.10
0.30
a. Find the expected return and standard deviation of each investment. b. Jill has the utility function U = 5I, where I denotes the payoff. Which investment will she choose? c. Ken has the utility function U = 5√ . Which investment will he choose? d. Laura has the utility function U = 5I 2. Which investment will she choose?
Source: Pindyck and Rubinfeld (2013), Microeconomics, 8th Ed., Pearson Prentice Hall, Chapter 5.
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Describing Risk Preferences Toward Risk Reducing Risk The Demand for Risky Assets Bubbles Behavioral Economics
Describing Risk • To measure risk we must know: 1. All of the possible outcomes 2. The probability or likelihood that a given outcome will occur • Interpreting Probability – Objective probability ♦ Observed frequency of past events – Subjective probability ♦ Perception that an outcome will occur ♦ Influenced by different information or different abilities to process the same information – based on judgment or experience • 2 measures to help describe and compare risky choices 1. Expected value 2. Variability • Expected Value – Probability-weighted average of the payoffs or values associated with all possible outcomes ♦ measures the central tendency; the payoff or value expected on average – Example: Investment in offshore drilling exploration: 2 possible outcomes ♦ ♦ ♦
Success – the stock price increases from $30 to $40/share Failure – the stock price falls from $30 to $20/share Objective Probability – 100 explorations: 25 successes and 75 failures – Probability of success = 0.25 and probability of failure = 0.75 – EV = Pr(success)(value of success) + Pr(failure)(value of failure)
Source: Pindyck and Rubinfeld (2013), Microeconomics, 8th Ed., Pearson Prentice Hall, Chapter 5.
1
= 0.25($40/share) + 0.75($20/share) = $25/share – In general, for n possible outcomes:
E(X) = Pr1X1 + Pr2X2 + … + PrnXn where X1, X2, … Xn = payoffs of possible outcomes Pr1, Pr2, … Prn = probabilities of each outcome • Variability – Extent to which possible outcomes of an uncertain event differ – How much variation exists in the possible choices – Example: Suppose you are choosing between two part-time sales jobs that
have the same expected income ($1,500) Outcome 1 Job 1: Commission
Outcome 2
Pr
Income
Pr
Income
0.5
$2,000
0.5
$1,000
Job 2: Fixed salary 0.99 $1,510 0.01 E(X1) = 0.5($2,000) + 0.5($1,000) = $1,500 E(X2) = 0.99($1,510) + 0.01($510) = $1,500 ♦ ♦ ♦
$510
Same expected values, but different variability Greater variability from expected values signals greater risk Variability comes from deviations in payoffs – Difference between expected payoff and actual payoff Deviations from Expected Income ($)
♦
♦
Outcome 1
Deviation
Outcome 2
Deviation
Job 1
$2,000
$500
$1,000
–$500
Job 2
$1,510
$10
$510
–$990
Average deviations are always zero so we must adjust for negative numbers by taking the squares of the deviations Measure variability with standard deviation, σ – Square root of the weighted average of the squares of the deviations (variance, σ2) – Measures how variable your payoff will be – More variability means more risk
Source: Pindyck and Rubinfeld (2013), Microeconomics, 8th Ed., Pearson Prentice Hall, Chapter 5.
2
– Individuals generally prefer less variability – less risk – The standard deviation is written:
σ = Pr1 ( X 1 − E ( X )) 2 + Pr2 ( X 2 − E ( X )) 2 ♦
Standard deviations of the two jobs are: σ 1 = .5(250,000) + .5(250,000) = 250,000 = 500 σ 2 = .99(100) + .01(980,100) = 9,900 = 99.50
♦
σ1 > σ2, Job 1 is therefore the riskier alternative. Choose Job 2.
– Example modified: Suppose we add $100 to each payoff in Job 1 ♦ ♦
Job 1: expected income $1,600 and a standard deviation of $500 Job 2: expected income $1,500 and a standard deviation of $99.50 – Which job should be chosen? o Depends on the individual o Some may be willing to take risk with higher expected income o Some will prefer less risk even with lower expected income
Preferences Toward Risk • Evaluate risky alternatives by measuring payoff in terms of utility – A consumer gets utility from income – Example: ♦ A person is earning $15,000 and receiving 13.5 units of utility from the job ♦ She is considering a new, but risky job – 0.50 chance of $30,000 and 0.50 chance of $10,000 – Utility($30,000) = 18 and Utility($10,000) = 10 – To evaluate the new job, she must compare the expected utility from the risky job with current utility of 13.5 ♦ Expected utility of the risky option is the sum of the utilities associated with all her possible incomes weighted by the probability that each income will occur E(U) = (Pr. of Utility 1)*(Utility 1) + (Pr. of Utility 2)*(Utility 2) = 0.5*U($10,000) + 0.5*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 13.5
and therefore preferred Source: Pindyck and Rubinfeld (2013), Microeconomics, 8th Ed., Pearson Prentice Hall, Chapter 5.
3
• People differ in their preference toward risk – People can be risk averse, risk neutral, or risk loving • Risk Averse – A person who prefers a certain given income to a risky income with the same expected value – Diminishing marginal utility of income – Most common attitude towards risk ♦ Ex: Market for insurance – Example: ♦
♦
♦
♦
♦
♦
A person can have a $20,000 job with 100% probability and receive a utility level of 16 The person could have a job with a 0.5 chance of earning $30,000 and a 0.5 chance of earning $10,000 Expected Income of risky job E(I) = (0.5)($30,000) + (0.5)($10,000) = $20,000 Expected Utility of risky job E(U) = (0.5)(10) + (0.5)(18) = 14 Both jobs have the same expected income but different expected utilities – Risk averse individual would choose the certain job for its greater utility Risk averse person’s losses (decreased utility) are more important than risky gains
– Risk averse utility function E Utility
18
Level of utility increases as income increases – marginal utility is diminishing
D
16
C
F
14
A risk-averse person prefers a certain income of $20,000 to an uncertain expected income of $20,000
A 10
0
10
16
20
30
Income ($1,000)
• Risk Neutral – A person is indifferent between a certain income and an uncertain income with the same expected value – Constant marginal utility of income Source: Pindyck and Rubinfeld (2013), Microeconomics, 8th Ed., Pearson Prentice Hall, Chapter 5.
4
– Expected utility for risky option is the same as for certain outcome
E(I) = (0.5)($10,000) + (0.5)($30,000) = $20,000 E(U) = (0.5)(6) + (0.5)(18) = 12 – This is the same as the certain income of $20,000 with utility of 12 Utility 18
Level of utility increases as income increases – marginal utility is constant
12
A risk-neutral person is indifferent between certain events and uncertain events with the same expected income
6
0
10
20
30 Income ($1,000)
• Risk Loving – A person prefers an uncertain income to a certain income with the same expected value ♦ Examples: Gambling, some criminal activity – Increasing marginal utility of income – Expected value for risky option E(I) = (0.5)($10,000) + (0.5)($30,000) = $20,000 E(U) = (0.5)(3) + (0.5)(18) = 10.5 – Certain income is $20,000 with utility of 8 – Risky alternative is preferred Utility 18
Level of utility increases as income increases – marginal utility is increasing
10.5
A risk-loving person prefers uncertain events to certain events with the same expected income
8 3 0
10
20
30
Income ($1,000)
• Risk Premium – The maximum amount of money that a risk-averse person would pay to avoid taking a risk – Depends on the risky alternatives the person faces Source: Pindyck and Rubinfeld (2013), Microeconomics, 8th Ed., Pearson Prentice Hall, Chapter 5.
5
– Example: ♦
♦
A person has a 0.5 probability of earning $30,000 and a 0.5 probability of earning $10,000 The expected income is $20,000 with expected utility of 14 Utility
G
20 18
C
The risk premium is $4,000 because a certain income of $16,000 gives the person the same expected utility as the uncertain income with expected value of $20,000
E
14
F
A 10
0 ♦
♦
10
16
20
30
40
Income ($1,000)
Point F shows the risky scenario – the utility of 14 can also be obtained with certain income of $16,000 This person would be willing to pay up to $4,000 (20 – 16) to avoid the risk of uncertain income – Can be shown graphically by drawing a straight line (CF) between the two points
• Risk Aversion and Income – Variability in potential payoffs increases the risk premium – Example: ♦ A job has a 0.5 probability of paying $40,000 (utility = 20) and a 0.5 probability of paying 0 (utility = 0) ♦ The expected income is still $20,000, but the expected utility falls to 10 E(U) = (0.5)U($0) + (0.5)U($40,000) = 0 + 0.5(20) = 10 ♦ The certain income of $20,000 has utility of 16 ♦ If a person must take new job, his utility will fall by 6 ♦ He can get 10 units of utility by taking a certain job paying $10,000 ♦ The risk premium, therefore, is $10,000 (i.e. he would be willing to give up $10,000 of the $20,000 and have the same E(U) as the risky job) – The greater the variability, the more the person would be willing to pay to
avoid the risk and the larger the risk premium
Source: Pindyck and Rubinfeld (2013), Microeconomics, 8th Ed., Pearson Prentice Hall, Chapter 5.
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• Risk Aversion & Indifference Curves – Indifference curves that relate expected income to variability of income (standard deviation) can be used to represent a person’s risk aversion (Risk/Return Tradeoffs) – Since risk is undesirable, greater risk requires greater expected income to make the person equally well off – Indifference curves are therefore upward sloping U3 Expected Income
U2 U1
Highly Risk Averse: An increase in standard deviation requires a large increase in income to maintain satisfaction
Standard Deviation of Income Expected Income U3 U2 U1
Slightly Risk Averse: A large increase in standard deviation requires only a small increase in income to maintain satisfaction
Standard Deviation of Income
• Risk Neutrality and Indifference Curves – A person who is risk neutral (only care about income; does not care about risk) will have horizontal indifference curves in the return–risk tradeoffs • Risk Loving and Indifference Curves – A person who is risk loving (derives greater utility as risk increases) will have downward sloping indifference curves in the return–risk tradeoffs
Source: Pindyck and Rubinfeld (2013), Microeconomics, 8th Ed., Pearson Prentice Hall, Chapter 5.
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Reducing Risk • 3 ways to reduce risks: diversification, insurance, and obtaining more information • Diversification – allocating resources to a variety of activities whose outcomes are not closely related (positively or negatively correlated) – Investing in a portfolio of 10 or 20 different stocks – Buying shares in mutual funds ♦ Organization that pools funds of individual investors to buy a large number of different stock or other financial assets • Insurance – paying a premium (= the expected loss from the risky situation) to avoid risk – A risk-averse individual counts losses (in terms of changes in utility) more than gains – The law of large numbers – although single events may be random and largely unpredictable, the average outcome of many similar events can be predicted – Actuarial fairness – the insurance premium is equal to the expected payout – Example: Burglary insurance: 100 people are similarly situated and face a 10-percent probability of a $10,000 loss ♦ Premium from the 100 individuals: $100,000 ♦ Expected payout to the 100 individuals as a whole: $100,000 • Obtaining more information – if more information were available, a person could make better predictions and reduce risk – 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 – Example: There is a 0.5 probability that 100 suits will be sold and a 0.5 probability that 50 suits will be sold. How many suits to order if each suit sells for $300 and any unsold suits can be returned for half of the price paid? Profits from sales of suits: Sales (unit of suits) Buy 50 @$200 100 @$180
50
100
$5,000 $1,500
$5,000 $12,000
Expected profit With With uncertainty complete information $5,000 $5,000 $6,750 $12,000
Source: Pindyck and Rubinfeld (2013), Microeconomics, 8th Ed., Pearson Prentice Hall, Chapter 5.
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Value of complete information: Expected value with complete information Less: Expected value with uncertainty (buy 100 suits) Value of complete information
$8,500 6,750 $1,750
The Demand for Risky Assets • Even though most people are risk averse, they still invest all or part of their savings in stocks, bonds, and other assets that carry some risk – An asset – something that provides a flow of money or services to its owner, e.g., an apartment building, a savings account, or shares of a company ♦ Capital gain (loss) – increase (decrease) in value of an asset – Risky asset – asset that provides an uncertain flow of money or services to its owner (e.g., stocks) – Riskless (risk-free) asset – asset that provides a flow of money or services that is known with certainty (e.g., Treasury bills) – Nominal return – total money flow of an asset as a fraction of its price – Real return – nominal return less the rate of inflation – Expected return – return that an asset should earn on average – Actual return – return that an asset earns • The trade-off between risk and return – The higher the expected return, the higher the risk ♦ Expected return from investing in the stock market, Rm > expected return from investing in Treasury bills, Rf – The investment portfolio ♦
♦
Expected return on a 2-asset portfolio, Rp, with b (% of the portfolio) invested in the stock market and (1 – b) invested in T-bills: Rp = bRm + (1 – b)Rf Rp = Rf + b(Rm – Rf ) Standard deviation of the portfolio, σp, is the % of the portfolio invested in the stock market times the standard deviation of the stock market: σp = bσm
• The investor’s choice problem: – Risk and the budget line – describes the trade-off between risk (σp) and expected return (Rp) (R − R f ) Rp = R f + m σp σm Source: Pindyck and Rubinfeld (2013), Microeconomics, 8th Ed., Pearson Prentice Hall, Chapter 5.
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♦
♦
Expected return on the portfolio, Rp, increases as the standard deviation of that return σp increases (Rm – Rf ) /σm is the price of risk – extra risk that an investor must incur to enjoy a higher expected return – No risk – invest all the funds in T-bills (b = 0) and earn an expected return Rf – Incur a risk level of σm – invest all the funds in stocks (b = 1) and earn an expected return Rm – Incur a risk level between 0 and σm – invest some funds in each type of asset and earn an expected return somewhere between Rf and Rm Expected return, Rp
U3 U2 U1
Rm Budget line R*
Rf 0
σ*
σm
Standard deviation of return, σp
– Risk and indifference curves – describes combinations of risk and return that
leave the investor equally satisfied ♦ Upward-sloping because risk is undesirable ♦ With a greater amount or risk, it takes a greater expected return to make the investor equally well-off – The choices of different investors ♦ ♦ ♦
Investor A is highly risk averse – he invests mostly in risk-free asset Investor B is less risk averse – he invests mostly in stocks Investor C has very low degree of risk aversion – he invests more than 100% of his wealth in stocks (buy stocks on margin)
Source: Pindyck and Rubinfeld (2013), Microeconomics, 8th Ed., Pearson Prentice Hall, Chapter 5.
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Expected return, Rp
UA
UB
UC
Budget line
RC Rm RB
RA Rf 0
σA
σB
σm
σC
Standard deviation of return, σp
Bubbles • An increase in the price of a good based not on the fundamentals of demand or value, but instead on a belief that the price will keep going up – The result of irrational behavior – People stop thinking straight • Examples: the Internet bubble, the housing price bubble • Informational cascades – an assessment (e.g., of an investment opportunity) based in part on the actions of others, which in turn were based on the actions of others – The bubble can in fact be rational in the sense that there is a basis for believing that investing in the bubble will yield a positive return – The expected gain to an investor down the chain will be positive if investors early in the chain indeed obtained positive information and based their decisions on that information – However, the risk involved will be considerable, and it is likely that at least some investors will underestimate that risk
Behavioral Economics • Individual behavior sometimes seems unpredictable, even irrational, and contrary to the basic utility-maximizing assumptions: Source: Pindyck and Rubinfeld (2013), Microeconomics, 8th Ed., Pearson Prentice Hall, Chapter 5.
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1. Consumers have clear preferences for some goods over others 2. Consumers face budget constraints 3. Given their preferences, limited incomes, and the prices of different goods,
consumers choose to buy combinations of goods that maximize their utility – These assumptions are not always realistic • Examples: – There has just been a big snowstorm, so you stop at the hardware store to buy a snow shovel. You had expected to pay $20 for the shovel—the price that the store normally charges. However, you find that the store has suddenly raised the price to $40. Although you would expect a price increase because of the storm, you feel that a doubling of the price is unfair and that the store is trying to take advantage of you. Out of spite, you do not buy the shovel. – Tired of being snowed in at home you decide to take a vacation in the
country. On the way, you stop at a highway restaurant for lunch. Even though you are unlikely to return to that restaurant, you believe that it is fair and appropriate to leave a 15% tip in appreciation of the good service that you received. – You buy this textbook from an Internet bookseller because the price is lower than the price at your local bookstore. However, you ignore the shipping cost when comparing prices. • Reference Points and Consumer Preferences – Basic model: consumers place unique values on goods and services that they purchase – Psychologist: perceived value depends on the circumstances – The Reference Point ♦ ♦
♦
The point from which the individual makes a consumption decision Develop for many reasons: past consumption, experience in a market, expectations about how prices should behave, and even the context in which a good is consumed Affect the way people approach economic decisions
– The Endowment Effect ♦
♦
Tendency of individuals to value an item more when they own it than when they do not Consider the gap between the price that a person is willing to pay for a good and the price of which she is willing to sell the same good to someone else – Basic model says that this price should be the same
Source: Pindyck and Rubinfeld (2013), Microeconomics, 8th Ed., Pearson Prentice Hall, Chapter 5.
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– Many experiments suggest that is not what happens in practice – Loss Aversion ♦ ♦
♦
♦
Tendency for individuals to prefer avoiding losses over acquiring gains Giving up a good was perceived to be a greater “loss” to those who had one than the “gain” from obtaining a good for those without one Example: people are hesitant to sell stocks at a loss, even if they could invest the proceeds in other stocks that they think are better investments – The high original price paid for the stock acts as a reference point – People are averse to losses o A $1000 loss on an investment seems to hurt more than the perceived benefit from a $1000 gain Endowment effects tend to disappear as consumers gain relevant experience – Not expect to see stockbrokers or other investment professionals exhibit the loss aversion
– Framing ♦
♦
Tendency to rely on the context in which a choice is described when making a decision How choices are framed – the names they are given, the context in which they are described, and their appearance – can affect the choices that individuals make
• Fairness – People do things because they think it is appropriate or fair to do so, even though there is no financial or other material benefit (e.g., charitable giving, volunteering time, tipping in a restaurant) – People’s views about fairness affect their behavior ♦ Workers who do not get a wage that they feel is fair may not put much effort into their work ♦ Firms can more easily raise prices in response to higher costs than to increases in demand • Rules of Thumb and Biases in Decision Making – Depend on both the context in which the decisions are made and the information available – Anchoring ♦
Tendency to rely heavily on one or two pieces of information when making a decision
Source: Pindyck and Rubinfeld (2013), Microeconomics, 8th Ed., Pearson Prentice Hall, Chapter 5.
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♦
Example: many price tags end with the digits 95 or 99 because marketers understand consumers tend to overemphasize the first digit of prices $19.95 seems much cheaper than $20.01
– Rule of Thumb ♦
♦
A common way to economize on the effort involved in making decisions is to ignore seemingly unimportant pieces of information (e.g., shipping costs of goods purchased over the Internet) Helps to save time and effort and result in biases in decision making
– The Law of Small Numbers ♦
♦
Tendency to overstate the probability that a certain event will occur when faced with relatively little information – Research has shown that investors in the stock market are often subject to a small-numbers bias, believing that high returns over the past few years are likely to be followed by more high returns over the next few years – thereby contributing to the kind of “herd behavior” – When people assess the likelihood that housing prices will rise based on several years of data, the resulting misperceptions can result in housing price bubbles Forming subjective probabilities is not always an easy task and people are generally prone to several biases in the process – Overestimate the probability that a particular event will occur if such an event has occurred recently – Ignore the possibility in decision making when a probability for a particular event is very, very small
• Summing up – Basic theory helps us to understand and evaluate the characteristics of consumer demand and to predict the impact on demand of changes in prices or incomes – Behavioral economics tries to explain and to elaborate on those situations that are not well explained by the basic consumer model
Source: Pindyck and Rubinfeld (2013), Microeconomics, 8th Ed., Pearson Prentice Hall, Chapter 5.
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Quick Quiz 1. George has $5,000 to invest in a mutual fund. The expected return on mutual fund A is 15 percent and the expected return on mutual fund B is 10 percent. Should George pick mutual fund A or fund B? 2. Jennifer is shopping and sees an attractive shirt. However, the price of $50 is more than she is willing to pay. A few weeks later, she finds the same shirt on sale for $25 and buys it. When a friend offers her $50 for the shirt, she refuses to sell it. Explain Jennifer’s behavior. 3. Suppose that Natasha’s utility function is given by uI = √10I , where I represents annual income in thousands of dollars. a. Is Natasha risk loving, risk neutral, or risk averse? Explain. b. Suppose that Natasha is currently earning an income of $40,000 (I = 40) and can earn that income next year with certainty. She is offered a chance to take a new job that offers a 0.6 probability of earning $44,000 and a 0.4 probability of earning $33,000. Should she take the new job? c. In (b), would Natasha be willing to buy insurance to protect against the variable income associated with the new job? If so, how much would she be willing to pay for that insurance? 4. Suppose that two investments have the same three payoffs, but the probability associated with each payoff differs, as illustrated in the table below: Payoff
Probability (Investment A)
Probability (Investment B)
$300 $250
0.10 0.80
0.30 0.40
$200
0.10
0.30
a. Find the expected return and standard deviation of each investment. b. Jill has the utility function U = 5I, where I denotes the payoff. Which investment will she choose? c. Ken has the utility function U = 5√ . Which investment will he choose? d. Laura has the utility function U = 5I 2. Which investment will she choose?
Source: Pindyck and Rubinfeld (2013), Microeconomics, 8th Ed., Pearson Prentice Hall, Chapter 5.
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