Decision Making

Question 1

why is including peoples preferences of risk important?

Answer 1

• if you had 0 risk - you would invest in asset with highest average return
• if you are risk averse - will you prefer a high risk asset with high returns over a low risk asset with low returns?
• risk aversion = tendency of people to prefer outcomes with low uncertainty to those outcomes with high uncertainty

Question 2

what is the difference between risk and uncertainty

Answer 2

unknown events - which we know the objective probabilities to all the possibilities

unknown events - which the probabilities cant be assigned

Question 3

what are the 3 models that are used to incorporate risk?

Answer 3

1. state preference model
2. expected utility hypothesis
3. mean variance model

Question 4

what is the state preference model?

Answer 4

describes preferences over future possibilities
- many states of the world (mutually exclusive)
- each state = description of an event
- only one state occurs
- actions you can take
- there is a consequence depending on the state and action = function
- payoff to a unit of asset j if the state k occurs
- utility depends on consequences (final utility)

Question 5

describe what happends in a 2 state period

Answer 5

• the more information you get each period, the more knowledge you know - your information set gets smaller (choosing from smaller options)

Question 6

what is application 1 from state preference model?

Answer 6

• maximise utility by choosing a portfolio that satisfies wealth constraint
• W = terminal wealth in different states
• utility = depends on all the possibilities tomorrow and assets you choose
• A = initial wealth
• wealth constraint –> p1x1+p2x2=A –>
  Wk = uk1x1+uk2x2

Question 7

what is application 2 from state preference model?
- when is there a complete market?

Answer 7

• complete market = when there is a AD security for each state of the world
• there are k states
• there are k assets with linear independent returns
• there is complete insurance against risk - you know you will get 1 unit in every state of the world

Question 8

what is an arrow debreu security?

Answer 8

a security that has a payoff of 1 unit in a particular state and 0 in every other state

Question 9

how do you calculate if it is possible to have complete markets with AD security

Answer 9

• if you have enough assets whose returns are linearly independent
• can simultaneously solve - what quantities of shares are needed to achieve a payoff of 1 unit in each state

Question 10

what is the expected utility hypothesis?

Answer 10

• assigns probabilities and allows the derivation of expectations
• probabilities of each state
• probabilities used as weights to calculate expected utility

Question 11

what do the derivatives of utility suggest

Answer 11

• FOD = utility is increasing in wealth
• SOD < 0 = utility increasing at a decreasing rate = risk averse
• risk averse = expected value > expected utility (straight line) - would rather take the certain money over the lottery
• SOD > 0 = concave = risk seeking
• risk seeking = expected value < expected utility

Question 12

what is the index of absolute risk aversion?
what is the index of relative risk aversion?

Answer 12

-SOD/FOD
- so the bigger the SOD - the more risk averse the person is

• WSOD/FOD

Question 13

what is the mean variance model?

Answer 13

• quadratic form for the utility function
• the only thing investors care about is expected return on the asset (mean) and the risk (variance)
• expected utility is a function of the expected value of wealth (mean) and the expected variance of wealth (risk)
• can express in terms of rate of return