Walter Nicholson Christopher Snyder Amherst College Christopher Snyder Dartmouth College PowerPoint Slide Presentation | Philip Heap, James Madison University ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

CHAPTER 4 Uncertainty ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Chapter Preview We now want to introduce uncertainty into economic choices. Three issues to address: How does uncertainty affect people’s decisions? Why do people generally dislike risk? What can people do to reduce or avoid risk? ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Probability and Expected Value The relative frequency with which an event occurs. What is the probability of flipping a heads; rolling a 5 on a die? Expected value the average outcome from an uncertain gamble. Fair gamble is a gamble with an expected value of zero. ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Probability and Expected Value Let P1 = ½ and P2 = ½ be the probability that event 1 and 2 occur. If event 1 occurs you win X1 = $10, and if event 2 occurs you lose X2 = -$1. What is the expected value of the gamble? Expected value = P1X1 + P2X2 ½ x $10 + ½ x -$1 = $4.50 How much would you be willing to pay for the right to play this gamble? ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Risk Aversion Would you take the previous gamble if you had to pay $4.50 to participate? Risk aversion is the tendency of people to refuse to accept fair gambles. Do you care about the gamble’s monetary payoff or the utility associated with the gamble’s prizes? People tend to be risk averse due to diminishing marginal utility of income. ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Diminishing Marginal Utility of Income What happens to utility as income increases? As income rises, utility rises but at a diminishing rate. Utility Income ($1,000’s) 20 35 50 ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Diminishing Marginal Utility of Income U3 is the utility from $35,000 Utility Would you take a fair gamble with a 50:50 chance of winning or losing $5,000? U3 U2 Don’t take gamble: can get a sure U3 or an expected U2 Income ($1,000’s) 20 30 35 40 50 ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Diminishing Marginal Utility of Income What about a fair gamble with a 50:50 chance of winning or losing $15,000 U3 Don’t take gamble: can get a sure U3 or an expected U1 U1 Income ($1,000’s) 20 30 35 40 50 ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Willingness to Pay to Avoid Risk Utility How much would you be willing to pay to avoid the first gamble? U3 U2 To get U2 you would need $33,000. So you would pay $2,000 to avoid the gamble. Income ($1,000’s) 20 30 33 35 40 50 ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Degrees of Risk Aversion What does the shape of the utility curve tell you about the degree of risk aversion? The steeper the curve, the more risk averse the individual. What if the utility curve is linear? The person is risk neutral. A risk neutral person would always be willing to accept a fair gamble. For small gambles a risk averse person may be “nearly” risk neutral. ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

How To Reduce Risk and Uncertainty Four methods: Insurance Diversification Flexibility Information ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Reducing Risk w/ Insurance Suppose you make $35,000 per year. There is a 50% chance you will incur medical bills of $15,000. Utility Without insurance your expected utility is U1 U1 Income ($1,000’s) 20 27.5 35 ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Reducing Risk w/ Insurance Fair insurance: insurance for which the premium is equal to the expected value of the loss. The premium would be $7,500 (35 – 27.5). Utility A policy that costs $7,500 would allow the person to obtain a certain utility of U2. U2 U1 But an insurance company would never offer fair insurance. Why? Income ($1,000’s) 20 27.5 35 ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Reducing Risk w/ Insurance How much would this person be willing to pay for insurance? With no insurance, they get an expected utility of U1. Utility They can get a certain utility, U1 with $24,000 income. U2 U1 Therefore, they would be willing to pay up to $11,000 to get insurance. Income ($1,000’s) 20 24 27.5 35 ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Reducing Risk w/ Insurance In general: Risk averse people will buy insurance against risky outcomes as long as the premiums do not exceed the expected value by too much. There are uninsurable risks. Some risks may be unique or difficult to evaluate Problem of adverse selection Problem of moral hazard ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Reducing Risk w/ Diversification What is diversification? How does it allow you to spread risk? Suppose You have $35,000 to invest $15,000 in Company A and/or B. One share in each company costs $1. At the end of the year there is a 50:50 chance that the share price will rise to $2 and a 50:50 chance it will fall to $0. What is the expected value of your income if you put all your money in one company? $35k since you have a 50:50 chance of winning/losing $15k ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Reducing Risk w/ Diversification Now suppose you put half of your money in each company. There is a 25% probability that each outcome occurs. Like before, your expected value is $35,000 What’s the difference? Final Income Company B Poor Good Company A $20,000 $35,000 $50,000 ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Reducing Risk w/ Diversification The difference is your expected utility Utility You get U1 if you invest in only one company. But you can get U2 if you invest in both companies. U2 U1 So by diversifying you can increase your utility. Income ($1,000’s) 20 35 50 ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Reducing Risk w/ Flexibility Diversification works if you are able to allocate small amounts of some large quantity among a number of different choices. What if decisions are “all-or-nothing”? Flexibility. Keeps the decision maker from being tied to one course of action. Provides different options depending on the circumstances. ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Reducing Risk w/ Flexibility Suppose you can buy one of three coats. At equal prices, the 2-in-1 coat is clearly better since it provides more options. COAT BITTER COLD MILD PARKA 100 50 WINDBREAKER 2-in-1 ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Reducing Risk w/ Flexibility Option contract – a financial contract offering the right, not the obligation, to buy or sell an asset over a specified period of time. Attributes of options Specification of underlying transaction Definition of period during which option may be exercised Price of option Value of an option is influenced by: The value of the underlying transaction. The duration of the option. ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Reducing Risk w/ Information Why is information valuable? What are the costs and benefits? 2-in-1 coat expensive. Parka and windbreaker sell for same price. If knew for certain that it will be bitter cold you buy a Parka and gain 25 utils. In more extreme case the gain would be 75 utils. COAT BITTER COLD MILD PARKA 100 (150) 50 (0) WINDBREAKER ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Reducing Risk w/ Information COAT BITTER COLD MILD PARKA 100 (150) 50 (0) WINDBREAKER Would a risk neutral person gain from additional information? Assume the payoffs in the table represent $ values rather than utils. The risk neutral person would gain either $25 or $75 from a perfect forecast. Need to compare the benefits and costs of the information. ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Reducing Risk w/ Information What determines the amount of information someone will acquire? Costs: partly determined by skills and or experiences. Preferences: do you care about getting a good deal; do you like to bargain. Since costs and preferences are likely to differ the level of information people acquire will differ. Is procrastination a virtue or a curse? ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Pricing of Risk in Financial Assets Investors care about expected return and risk when deciding what financial assets to buy. Holding expected return constant, assets with less risk are preferred to assets with more risk. Holding risk constant, assets with greater expected return are preferred to assets with lower expected return. Investors need to be compensated for taking on more risk by getting a greater expected return. ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Pricing of Risk in Financial Assets Return AC is the market line It shows different assets that can be created by mixing the risk-free asset A and different risky assets. B Note that any asset on AC provides the greatest expected return for a given amount of risk. Risky assets A Risk-free asset Risk ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Pricing of Risk in Financial Assets UH UM UL C Return How do different investors decide which asset on AC they buy? B Different investors will choose an asset on the market line depending on their risk tolerance. Note that the flatter the indifference curve the higher the degree of risk tolerance. A Risk-free asset Risk ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Two State Model Want to develop a model that will tie everything we’ve discussed together. Assume there are two possible outcomes or states of the world. In each state, the individual’s consumption is either C1 or C2. There are four possible choices (gambles): A, B, D and F. Want to see how an individual decides which gamble to choose. ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Two State Model Which gamble will the person choose? Certainty line: C1=C2 Which gamble will the person choose? The individual will choose gamble B since it lies on the highest expected utility curve. D B EU3 F CA2 A EU2 EU1 C1 CA1 ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Two State Model and Risk Aversion Risk aversion is captured by the convexity of the indifference curves C2 Faced with a choice between gambles A, B and D, an individual would prefer D B D provides a balance in consumption: “averages are preferred to extremes” D EU3 A EU2 EU1 C1 ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Two State Model and Risk Aversion What do these two indifference curves tell you? C2 EU1 is an indifference curve for a risk averse person. EU2 is an indifference curve for a risk neutral person. EU1 EU2 C1 ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Two State Model and Insurance Suppose an accident can occur in state 2 but not state 1 A is the situation with no insurance With fair insurance a person can move to point D: pay CA1 - CD1 to get CD2 – CA2 D CD2 EU3 EU2 CA2 A EU1 C1 CD1 CA1 ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Two State Model and Insurance Even if only partial insurance is available, the person is better off with insurance than without. C1=C2 The person can move from A to B. Like before the amount they pay in C1 < the amount the gain in C2. D CD2 EU3 B EU2 CA2 A EU1 C1 CD1 CA1 ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Two State Model and Diversification An investor can put all their money in asset A1 or all their money in asset A2 C2 If they are indifferent, A1 and A2 lie on the same EU curve. By investing in a mix of both assets the investor can attain any point on a line between A1 and A2 A2 B So by diversifying they can receive greater expected utility. EU2 EU1 A1 C1 ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Summary When individuals face uncertain situations they consider their expected utility. If individuals have diminishing marginal utility for income, they are risk averse and will refuse fair gambles. Insurance allows risk averse individuals to avoid participating in fair gambles. Risk may also be reduced with diversification, buying options, or acquiring better information. ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Summary Individuals will compare expected return and risk when deciding what financial assets to buy. ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.