1. Choices Involving Risk
chapter 11
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2. Learning Objectives Define and measure economic risk.
Illustrate an individual’s risk preferences graphically.
Explain why people purchase insurance policies.
Analyze why people take certain risks and avoid others.
Identify and explain several strategies for managing risk.
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3. Overview
Many decisions involve risk, and it will be useful to define it and measure it with some precision.
Consumers can have different preferences toward risk.
Insurance and other methods of managing risk can make some consumers better off.
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4. Possibilities
State of nature: one possible way in which events relevant to a risky decision can unfold
When analyzing a risky decision, economist begin by describing every possible state of nature.
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5. Probability
Probability: measure of the likelihood that a state of nature will occur
Objective probability: measure of the likelihood that a state of nature will occur based on the frequency with which it has occurred in the past under comparable conditions
Subjective probability: measure of the likelihood that an event will occur based on subjective judgment
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6. Uncertain Payoffs Payoffs are the financial consequences of choices
Probability distribution: the likelihood that each possible payoff will occur
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7. Uncertain Payoffs
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8. Expected Payoff and Variability
When evaluating a choice with risky financial prospects there are two questions:
What do we expect to gain or lose, on average? Expected payoff
Do we expect the actual gain or loss to be close to that average or far from it? Variability
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9. Expected Payoff
Expected payoff: weighted average of all the possible payoffs, using the probability of each payoff as its weight
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10. Variability Variability: an indication of risk
- Little variability: actual payoff is almost always close to the expected payoff
- Substantial variability: actual payoff and expected payoff differ significantly
Deviation: difference between the actual payoff and the expected payoff
Variance: expected value of a squared deviation
Standard deviation: square root of the variance
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11. Expected Payoffs and Deviations
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12. Variability
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13. Consumption Bundles
Guaranteed consumption line: shows the consumption bundles for which the level of consumption does not depend on the state of nature
For bundles that do not lie on the GCL, the payoff is uncertain
45o line
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14. Expected Consumption
Constant expected consumption line: shows all the risky consumption bundles with the same level of expected consumption
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15. Preferences for Risky Consumption Bundles
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16. Risk Aversion
When comparing a riskless bundle with the same level of expected consumption, a risk averse person prefers the riskless bundle (e.g. point A)
Even a risk averse person may allow for some risk (e.g. point A is preferred to B)
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17. Certainty Equivalent and the Risk Premium
Certainty equivalent: the amount of consumption that, if provided with certainty, would make the consumer equally well off
C is the certainty equivalent of the risky bundle B
The expected level of consumption is the same at A and B
Thus, the risk premium is the difference between A and C (expected consumption vs. certainty equivalent)
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18. Degrees of Risk Aversion
Maria and Arnold are are both risk averse
Maria would be willing to swap A for risky bundle D, but Arnold would not
Arnold is more risk averse than Maria
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19. Risk Loving Consumer
A person is risk loving if when comparing a riskless bundle to a risky bundle with the same level of expected consumption, one prefers the risky bundle (e.g. they prefer all points on this line to point A)
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20. Risk Neutral Consumer
Risk neutral: when one is indifferent between all bundles with the same level of expected consumption
The indifference curves of risk neutral consumers coincide with the constant expected consumption lines
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21. Expected Utility Functions
An expected utility function assigns a benefit level to each possible state of nature based only on what is consumed, and then takes the expected value of those benefits
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22. Expected Utility for a Risk-Averse Consumer
FH: food when hurricane
FS: food when sunny
C: risky bundle
E: certainty equivalent
D: riskless bundle with same expected consumption on C
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23. Expected Utility and the Degree of Risk Aversion
Arnold is more risk averse than Maria
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24. Nature of Insurance
Insurance policy: a contract that reduces the financial loss associated with some risky event
Insurance premium (M): amount of money the policyholder pays for the insurance policy
Insurance benefit (B): amount of money a policyholder receives if a specific loss occurs
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25. Demand for Fair Insurance
Fair insurance: when an insurance policy’s expected net payoff is zero
Requires:
π: probability of avoiding the loss
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26. Demand for Fair Insurance
Full insurance: the promised benefit equals the potential loss
Partial insurance: the promised benefit is less than the potential loss
Point B represents full insurance
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27. Demand for Unfair Insurance
Can reach any point on solid green line by purchasing unfair insurance
If Maria is risk averse, she’ll prefer point E
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28. Value of Insurance
Without insurance, G is the certainty equivalent of the risky bundle A
Maria obtains point B with fair insurance
With unfair insurance Maria obtains point E
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29. Other Methods of Managing Risk
Risk management: making risky activities more attractive by taking steps to moderate the potential losses while preserving much of the potential gains
Risk sharing
Hedging
Diversification
Information acquisition
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30. Risk Sharing
Risk sharing: dividing a risky prospect among several people
Maria can make an investment to swap A for risky bundle B, which provides higher expected consumption
However, Maria prefers A to B, given her risk aversion
If Maria finds partners to share the profits and the risk she can be anywhere on the green line in particular reaching D (preferred to A)
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31. Hedging
Hedging: the practice of taking on two risky activities with negatively correlated financial payoffs
B: risky venture in sunscreen business
E: risky business in emergency generators
A is preferred to B and E individually
However, if B and E are both undertaken, point F is the expected payoff, strictly preferred to A
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32. Diversification
Diversification: the practice of undertaking many risky activities, each on a small scale, rather than a few risky activities (or just one) on a large scale
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33. Information Acquisition
Individuals often try to reduce or eliminate risk by acquiring information
With perfect information about weather, Maria could reach point G
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34. Review
A risk averse consumer’s preferred point on any constant expected consumption line lies on the guaranteed consumption line.
If insurance is actuarially fair, a risk-averse consumer will always purchase full insurance.
The amount of less-than-actuarially-fair insurance purchased depends on the degree of risk aversion. Those that are not very risk averse will purchase no insurance.
Risk sharing, hedging, diversification, and information acquisition reduce risk.
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35. Looking Forward
Next we will switch gears, analyzing strategic decisions – situations where the effects of your actions depend on the actions and reactions of other people.
In particular, we will learn of a specific approach called game theory that is useful in many economic interactions.
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