Behavioral eco-lect 4: Choice under risk and uncertainty part 1

3 puzzling phenomena

Equity premium puzzle: “stocks have outperformed bonds over the last century by a surprisingly large margin”

House money effect: a prior gain can increase the willingness to take risks

End-of-the-day-effect: in racetrack betting people are more willing to bet on longshots at the end than at the start of the betting day.

Risk and uncertainty

Uncertainty: probabilities are not known

Risk: probabilities are known

Acts and lotteries

Act: Specifies the outcome for each state of the world. A=(S1:C1,...,Sn:Cn) gives outcome Ci in state Si

Under risk, when probabilities are known we can also write the probabilities instead of the states of the world:
Lottery / prospect: specifies the outcome for each probability
L = (p1: C1, … , pn: Cn) gives outcome Ci with probability pi

Example: in the umbrella example you choose between two acts - taking or leaving the umbrella.

Choice under risk : expected utility

Structure

Choice under risk – violations of expected utility

Choice under uncertainty – a few simple models

Choice under risk – expected utility

Choice under uncertainty – violations of expected utility

Risk and uncertainty

Diminishing sensitivity and mental accounting

Consider lottery L = (p1: C1, … , pn: Cn)

Expected value: EV(L) = p1C1 + … + pnCn = ∑i=

example

Choice under risk : expected utility cont.

St Petersburg paradox

Consider game:fair coin tosses repeatedly until we obtain heads. If it takes n tosses yo earn $2

Question: How much are you willing to pay to play this game?

Question: What is the expected value of this game?

EV = ½ x 2 + ¼ x4 + …. = an infinite amount
→ An EV maximizer would be willing to pay a very large amount

Conclusion: most people are no EV maximizers.