Chapter 5 - Uncertainty and behavior Flashcards
Define objective vs subjective probability
Objective probability refers to relative frequency based on actual events.
Subjective is based on judgement. Not really a good way to do it.
What are the two important measures we use when calculating risk?
Expected value and variability
Define expected value
Weighted average of the outcomes. The probabilities are the weights, and the possible values are the “values”.
Define deviation
Deviation is the difference between expected payoff and actual pay off.
How do we calculate expected utility?
Expected utility is the same as expected value or expected payoff, the difference is we use utility instead of money or whatever. We still use probabilities/relative frequencies as the weights.
What are the 3 risk preferences?
Risk averse.
Risk neutral
Risk loving
Risk averse choose the steady option with limited risk.
risk neutral take the option that maximize utility or money or whatever.
Risk loving takes the option with the highest possible payoff/utility.
How do we find utility from a certain income?
We use some sort of utility function.
How do we calculate utility of an option when the possible income is either 10 000 USD or 30 000 USD and the probability is the same?
This depends on whether the consumer is risk averse, loving or neutral. If neutral, the utility will be equal to the utility of actually getting the expected value/income.
IF risk loving, the utility will be higher than the utility of actually getting the income of the expected value. Key here is that the expected utility is larger than the utility from expected value.
If risk averse, the expected utility from the steady income is greater than the utility from the expected potential income.
We first find the expected value of the income, which is 20 000.
Then we plot this number into the utility function, which gives some utility value.
What is risk premium?
Risk premium is the max amount of money that a risk averse person/consumer is willing to pay to reduce risk/avoid taking a risk.’
IMP: Elaborate on how we determine, given a utility(income) graph, whether the consumer is risk averse, neutral or seeking
Connect this to risk premium
To gain the basic understanding, we consider the following:
Say the consumer has utility of 16 for an income of 20. This income is certain. Say the consumer is given the opportunity to take a job that pays 30 with 50% probability or 10 with 50% probability. To consider this, we calculate expected utility. Therefore, we do EU = 0.5u(30) + 0.5u(10) = 0.518 + 0.510 = 14. The expected utility from the job that gives risky income is 14. Since the consumer already had 16 utiltiy with the same income (since expected income for new job was also 20), the consumer is risk averse.
if the consumer found expected utility to be higher from the new job than the current, he is risk loving.
If consumer expected utility is equal to current, he is risk neutral.
Risk premium is the difference between the point where expected utility intersects income from new job, and the point on the utility curve that corresponds to this level of utility. therefore, this essentially means that the consumer would be willing to pay the income difference between the two points in order to keep the safe income. Risk premium therefore represent the max amount the consumer is willing to “give up” by maintaining a riskfree income.
Define risk premium
When the risk premium is added to the level of income, the consumer is indifferent between choosing the risky option or the risk free option, because his expected utility is equal. This marks a point where, if given more income to make the risky choice, his expected utility would be larger for the risky case than the risk free case.
Thus, risk premium is defined as the required amount for a risk averse consumer to make the risky call.
What is the “law of large numbers”?
The law of large numbers says that, while it may be very difficult to predict individual outcomes, it can be fairly easy to predict aggregate behavior. This is basically the principle/law that insurance companies utilize.
Define risk premium graphically IMP
Risk premium is the difference between the expected income that gives expected utility equal to the utility we get by the risk free option, and the risk-free income.
So, we consider the point where we have some utility given by the utility function. this will relate a risk free income to a level of utility.
Then we consider what the expected income would have to be for us to achieve the same utility for both choices.
