lecture 1 - utility theory and risk aversion

Question 1

what is utility?

Answer 1

it is a measureable and comparable proxy for happiness, must properly reflect how happiness changes with respect to inputs

Question 2

what is the law of diminishing marginal returns?

Answer 2

the change in utility gets smaller as input is increased

Question 3

what is utility maximisation?

Answer 3

an individual will always attempt to maximise utility by choosing an optimal input levle

Question 4

what is certainty?

Answer 4

“Certainty” refers to the situation where there is
only one possible outcome to a decision, and this
outcome is known precisely.

Question 5

what is risk?

Answer 5

“risk or uncertainty” refers to a situation where
there is more than one possible outcome to a
decision and the probability for each specific
outcome is known or can be estimated.
In the recent, behavioral finance literature
“uncertainty” has referred to a situation where
there is more than one possible outcome to a
decision, but the probabilities with which the
outcomes occur are unknown.

Question 6

what is the definition of risk aversion?

Answer 6

A decision maker is risk averse, if his or her utility
of expected wealth from a gamble is greater than
the expected utility of that gamble

Question 7

what is the definition of risk neutral?

Answer 7

a decision maker is risk neutral if the utility of expected wealth of a gamble is equal to the expected utility of that gamble?

Question 8

what is the defintion of risk loving

Answer 8

a decision maker is risk loving if the utility of expected wealth of a gamble is less than the expected utility of that gamble?

Question 9

what is the shape of a risk averse decision makers utility function?

Answer 9

the utility fucntion is concave so the marginal utility of wealth is decreasing?

Question 10

what is the shape of a risk neutrals decision makers utility function?

Answer 10

the utility function is a straight line as the marginal utility of wealth is constant

Question 11

what is the shape of a risk lovings decision makers utility function?

Answer 11

the utility function is a convex curve as the marginal utility of wealth is increasing

Question 12

what is the certainty equivalent wealth?

Answer 12

The certainty equivalent wealth (CE) of a lottery is the monetary amount received with certainty that generates the same utility as the expected utility of the lottery. E(U(X)) = U(CE)

Question 13

what is the risk premium for a risk averse individual?

Answer 13

Risk averse individuals have a positive risk premium. That is, they are willing to pay in order to eliminate the risk associated with the lottery.

Question 13

what is the markowitz risk premium?

Answer 13

The Markowitz risk premium of a lottery is the difference between the expected value of the lottery 𝐸(X) and the certainty equivalent wealth (CE)
𝜋(X) =E(X) -CE

Question 14

what is the arrow pratt measure of risk aversion?

Answer 14

The Arrow-Pratt measures of risk aversion show
the relationship between risk aversion and wealth

Question 15

what is the measure of absolute risk aversion formula?

Answer 15

ARA = - U”(W)/U’(W)

Question 16

what is the measure of relative risk aversion formula?

Answer 16

RRA = - W * U”(W)/U’(W)

Question 17

as wealth increases how does absolute risk aversion impact how much wealth in risky assets?

Answer 17

for increasing absolute risk aversion, As wealth increases, hold fewer pounds in risky assets
for constant absolute risk aversion, as wealth increases, hold the same amount in risky assets
for decreasing absolute risk aversion, as wealth increases hold more pounds in risky assets

Question 18

how does relative risk aversion impact percetnage of wealth held in risky assets?

Answer 18

increasing relative risk averse, as wealth increases hold a smaller percentage of wealth in risky assets
constant relative risk averse, as wealth increases hold the same percentage in risky assets
for decreasing relative risk aversion, as wealth increase, hold a larger percentage of wealth in risky assets

Question 19

how can the risk premium of a gamble be approximated and when is it most suitable ?

Answer 19

it can be approximated by the product of variance of the gamble and the arrow pratt measure of absolute risk aversion
it is most suitable for small symmetric actuarially neutral gambles