WEEK 6 - Uncertainty Flashcards
Why do we incorporate risk and uncertainty in models of choice?
can cause consumers and
firms to modify decisions about consumption and
investment choices
What is risk?
When the likelihood of each possible outcome is known or can be estimated and no single outcome is certain to occur
Estimates of how risky each outcome allows us to
estimate the most likely outcome.
How do you figure out what consumer’s would maximise given their choice?
The expected or mean value of the game
Same thing
How do we calculate the mean value of the game?
Use the Probability Concept
SEE EXAMPLE OF CALCULATING IN NOTES
What is Probability
A number between 0 and 1 that indicates the likelihood that a particular outcome will occur
How do we estimate probability?
With the frequency, the number of times that one particular outcome occurred (n) out of the
total number of times an event occurred (N).
θ = n/N
If we don’t have a history of the event how do we best calculate the probability/
Use our best estimate or Subjective Probability
What is a Probability Distribution?
Relates the probability of occurrence to each possible outcome
How do you calculate the expected value (EV)?
Value of each possible outcome (Vi) times the probability of that outcome (θi) summed over all n possible outcomes
SEE EXAMPLE IN NOTES
How do we use expected value to measure risk?
Use it in calculations for:
- Variance
- Standard Deviation
What is Variance?
Measure how much variation there is between the actual value and the expected value
(SEE FORMULA IN NOTES)
What is Standard Deviation?
The square root of the variance and is a more commonly reported measure of risk
EXAMPLE OF ASSESSING RISK
SEE IN NOTES
How do you analyse the expected utility?
Comparing the utility a person gets from all options
SEE IN NOTES FOR EXAMPLE
When does a person prefer a sure thing to a gamble even if the gamble has a higher EV?
When their utility function is concave, which means:
U’ > 0 and U’’ < 0
What is the intution behind being risk averse (using the pauper example)
Additional utility from the sure thing compared to 0 is huge (I.e getting 475,000 compared to 0)
- Additional utility from the risky reward relative to sure thing is much smaller
- So additional utility from winning the lottery (winning the risky reward) relatively small and not worth the additional risk
What is the diminishing marginal utility of wealth?
The utility from an additional dollar is lower
when you are rich than when you are poor
Same as saying the utility function is concave
How can people’s attitude toward risk be classified?
Via an example of a fair bet
Receive £1 if you win, lose £1 if you lose
What are Risk Avere, Risk Neutral and Risk Preferring people’s response to a fair game
Someone who is unwilling to make a fair bet is risk
averse.
• Someone who is indifferent about a fair bet is risk neutral.
• Someone who is risk preferring will make a fair bet
How do we calculate expected utility?
Sum of θi U (Vi)
Where:
θi is Probability of that outcome
Vi is value of each possible outcome
EXAMPLE OF CALCULATING UTILITY AND ATTITUDES TOWARD RISK
SEE NOTES FOR EXAMPLE
TRUST ME IS GUD SHIZ
What do the utility functions for Risk-neutral and Risk-preferring people look like?
Risk-neutral utility function - Straight line
Risk-preferring utility function - Convex
SEE GRAPH IN NOTES
What is a risk premium?
Amount a risk averse person would pay to avoid taking a risk
How do you measure the degree of Risk Aversion?
Using the Arrow-Pratt measure of risk aversion
p(W) = - d2U(W)/dW2 / dU(W)/dW
Where:
W is wealth
U(W) is the utility function over wealth
Measure is:
Positive for risk averse
Negative for risk preferring (the larger it is, the more they like to take risks)
SEE THE CALCULATION IN NOTES
What are the 4 ways for an individual to reduce risk?
- Say no
- Obtain Info
- Diversify
- Insure
How would you avoid risk via insurance?
Risk averse person fully insure to eliminate risk (Under the assumption that company offers fair bet)
- In real world, no such thing so people never fully insure
What are the responses from a risk-averse and a risk-neutral individual from investing under uncertainty?
- Risk Neutral:
Owner invests if and only if the expected value of the investment is
greater than the expected value of not investing. - Risk-averse
Owner invests if and only if the expected utility of the investment
exceeds the expected utility of not investing
