Decision-Making Under Uncertainty

Question 1

What is risk?

Answer 1

This is when the likelihood of each possible outcome is known or can be estimated, and no single possible outcome is certain to occur.

Estimates of how risky each outcome is allows us to estimate the most likely outcome.

Question 2

What is a probability?

Answer 2

This is a number between 0 and 1 that indicates the likelihood that a particular outcome will occur.

Question 3

What is the frequency?

Answer 3

This is the number of times that one particular outcome occurred (n) out of the total number of times an event occurred (N).
θ = n/N

Question 4

What is subjective probability?

Answer 4

This is our best estimate and is used when we don’t have a history of the event that allows us to calculate frequency.

Question 5

What is a probability distribution?

Answer 5

This relates the probability of occurrence to each possible outcome.

Question 6

What is the expected value?

Answer 6

This is the value of each possible outcome (Vi) times the probability of that outcome (θi), summed over all possible n outcomes:
n
EV = Σ θi Vi
i = 1

Question 7

What is variance?

Answer 7

This measures the spread of the probability distribution or how much variation there is between the actual value and the EV.
n
Variance = Σ θi (Vi – EV)⮝2
i = 1

Question 8

What is standard deviation?

Answer 8

σ is the square root of the variance and is a more commonly reported measure of risk.

Question 9

What is a fair bet?

Answer 9

This is a wager with an expected value of zero.

Example: you receive $1 if a flipped coin comes up heads and you pay $1 if a flipped coin comes up tails.

Question 10

What does it mean if someone is risk averse?

Answer 10

Someone who is unwilling to make a fair bet.

Question 11

What does it mean if someone is risk neutral?

Answer 11

Someone who is indifferent about a fair bet.

Question 12

What does it mean if someone is risk preferring?

Answer 12

Someone who is more willing/will make a fair bet.

Question 13

What is expected utility?

Answer 13

This is the probability-weighted average of the utility (U), from each possible outcome:
n
EU = Σ θi U(Vi)
i = 1

The weights are the probabilities that each state of nature will occur, just as in expected value.

Question 14

What is the relationship between utility functions and riskiness?

Answer 14

A person whose utility function is concave picks the less-risky choice if both choices have the same expected value.

Concave (curls towards horizontal axis) = risk averse
Convex (curls towards vertical axis) = risk preferring
Straight 45-degree line = risk neutral

Question 15

What is a risk premium?

Answer 15

This is the minimum amount of money by which the expected return on a risky asset must exceed the know return on a risk-free asset in order to induce an individual to hold the risky asset rather than the risk-free asset.

It is positive if the person is risk averse.

Question 16

How is the degree of risk aversion judged/determined?

Answer 16

It is judge by the shape of the utility function over wealth: U(W)

One common measure is the Arrow-Pratt measure of risk aversion.

Question 17

What is the Arrow-Pratt measure of risk aversion?

Answer 17

p(W) = (d⮝2U(W)/dW⮝2) / (dU(W)/dW

This measure is positive for risk-averse individuals, zero for risk neutral individuals and negative for those who prefer risk.

The larger the Arrow-Pratt measure, the more small gambles that an individual will take.

Question 18

What are ways to avoid risk?

Answer 18

1. Just say no
   o Abstaining from risky activities is the simplest way to avoid risk.
2. Obtain information
   o Armed with information, people avoid making a risky choice or take actions to reduce probability of a disaster.
3. Diversify
   o Don’t put all your eggs in one basket
4. Insurance
   o Insurance is like paying a risk premium to avoid risk

Question 19

Explain avoiding risk via diversification.

Answer 19

Diversification can eliminate risk if two events are perfectly negatively correlated.
- This means: if one event occurs, then the other wont occur.
Diversification does not reduce risk if two events are perfectly positively correlated
- This means: if one event occurs, then the other will occur too.

Example: investors reduce risk by buying share in a mutual fund, which is comprised of shares of many companies.

Question 20

Explain avoiding risk via insurance.

Answer 20

A risk-averse individual will full insure by buying enough insurance to illuminate risk if the insurance company offers a fair bet, or fair insurance.
- In this scenario, the EV of the insurance is zero; the policyholder’s EV with and without the insurance is the same.

Insurance companies never offer fair insurance, because they would not stay in business, so most people are not fully insured.

Question 21

How do you determine whether to buy or not buy insurance?

Answer 21

EXAMPLE
Without insurance:
Wa = m – L
Wna = m

With full insurance
Wa = m - x
Wna = m - x

Note:
W = wealth
L = accident expenses 
m = money
a = accident
na = no accident
x = insurance premium in x dollars

Question 22

What is behavioural economics?

Answer 22

The study of choices actually made by economic decision makers in an effort to access the strengths and weakness of the rational choice model that is the mainstay of modern economics.

Question 23

When is a decision maker’s choice rational?

Answer 23

If it is the most preferred choice from the choices that are available to the decision maker.

Question 24

What does the rational choice model predict?

Answer 24

It predicts that inferior choices will immediately be replaced.