Consumer choice under uncertainty Week 1 Flashcards
Uncertainty and risk
- Uncertainty affects consumption decisions
- Consumers consider outcomes of their choices under a number of possible circumstances (states of nature) - rejection or acceptance
- Risk is sometimes used to quantify these uncertainties
- Consumers have some idea of which outcomes are more likely than others
- Consumers modify their decisions as the degree of risk varies
- Choose a riskier option if they receive a higher payout?
- Probabilities are used to quantify how risky outcomes are
What is meant by risk?
A hazard or the chance of loss
Assessing risk
Probability indicates how likely an event is to occur
- Ranges between 0 and 1
- Sum of the probabilities of all possible outcomes is equal to 1
We use the frequency with which an outcomes occurred to estimate probability
- For instance, if it rained 20 times on August bank holiday in the last 40 years, then the frequency that it rained (theta) is given by; theta = n/N = 20/40 = 0.5
Probability
- But often there is no history o repeated events - because they happen infrequently
- So we are unable to calculate frequencies
- Then we use subjective probability
Probability Distribution
Predictions may be easier to make when the probability is distributed over fewer days even though the means and variances can be the same in both cases
Expected Value
-This is the amount an individual expects to receive (payoff) for a transaction
-Assume that there are two outcomes, X and Y;
EV = Pr(X)V(X) + Pr(Y)V(Y)
- Where PR() is the probability and V() is the value of the outcome
Expected Value - Example
Gregg, a promoter, schedules an outdoor concert for tomorrow
- How much money he’ll make depends on the weather
- If it doesn’t rain, his profit or value from the concert is V = $15
- If it rains, he’ll have to cancel the concert and he’ll lose V = -5, which he must pay the band
-He knows that the weather department forecasts a 50% chance of rain
- EV =[Pr(no rain) x Value(no rain)] + [Pr(rain) x Value(rain)]
=[1/2 x $15] + [1/2 x (-5)] = $5
Variance and Standard Deviation
- EV tells us the likely payout - the expected value of the payout
- Gregg cannot tell the risk simply by using the EV
- How can we determine the risk? Variance (standard deviation) is used
-Shows spread of the probability distribution; how close together are the possible outcomes - Var = [Pr(X)(V(X) - EV)^2] + [Pr(Y)(V(Y)-EC)^2]
-Standard deviation is the square root of the variance - The greater the SD relative to the EV, the greater the risk
Variance and Standard Deviation example
Example: Probability of rain = 0.5;
value of outcome if no rain = 15; value of outcome if rain = -5 Therefore EV = 5
Variance = [Pr(no rain) x (Value(no rain) - EV)^2] + [Pr(rain) - EV)^2]
= [1/2 X (15-5)^2] + [1/2 X (-5-5)^2]
=[1/2 X (10)^2] + [1/2 X (-10)^2] = 100
Standard deviation is the square root of the variance - Hence standard deviation = 10
Attitudes towards risk
- If individuals do not care about risks, they would choose the option with the highest expected value
- But most people are risk averse - and so are willing to pay a premium to avoid risk, especially if an option is particularly risky
- How can you determine if the EV of a riskier option is sufficiently higher to justify the greater risk?
- Extension of model of utility maximisation
Expected utility (risk)
Risk averters - prefer a choice with a more certain outcome to one with a less certain outcome (utility function has diminishing marginal utility)
Risk lovers - prefer a gamble with a less certain outcome to one with a more certain outcome (because they are willing to give up some expected return to take on more risk. Utility function has increasing marginal utility).
Risk neutral - they maximise expected wealth, regardless of risk (will choose whichever option has the higher rate of return because they do not care about risk. Utility function is linear and marginal utility is constant
Risk premium
Risk premium - the amount that a risk-averse person would pay to avoid taking a risk
E.g., the difference between the initial wealth (expected value) of the uncertain prospect and the certainty equivalent
Risk avoidance through risk sharing and spreading
Insurance: a way of removing risks for the risk averse
Insurers make profits by spreading or sharing their risks
- The law of large numbers - risk pooling - profits on average - as long as premium are high enough
- Problems - risks - for insurers - adverse selection & moral hazard
Diversification can also reduce risk - portfolio based investment
- Breaking risk into pieces (as longas gambles are not correlated) = securitisation
- Entrepreneurs share risks with venture capitalists
- Future markets share risks over time (insuring against price changes)
Different types of risk
Diversifiable risk, unsystematic risk, idiosyncratic risk or specific risk, is risk which is associated with a particular source or investment such a company’s stock
- This type of risk can be mitigated thorugh diversification, hence it is diversifiable
- Once diversified, economic agents are still subject to market-wide systematic, non-diversifiable risk i.e. the risk common to the entire class of assets or liabilites
Diversifiable risk definition
Diversifiable risk = risk that can be eliminated through diversification because it is specific to a single entity or situation, not the overall system
Example: A company’s stock drops because their CEO resigns. If you own other stocks in different industries, this loss is offset by the performance of your diversified portfolio
