lecture 2 - stochastic dominance

Question 1

what is stochastic dominance?

Answer 1

Stochastic dominance is a criterion for ranking assets without the need to compare expected utilities.

Question 2

what is first order stochastically dominance?

Answer 2

An asset or a portfolio defined with a cumulative
distribution function F is said to first-order
stochastically dominate another asset defined
with a cumulative distribution G if F(X) <= G(X) with the strict inequality applying for some X

Question 3

what is second order stochastic dominance?

Answer 3

Graphically second-order stochastic dominance
requires that the area under F is smaller than the
area under G for all x.

Question 4

if the distribution of returns offered by assets and portfolio is normal then how can investors maximise the expected utility?

Answer 4

it can maximise the distribution of returns offered by assets by selecting the best combinations of mean and variance according to their preferences

Question 5

what are the mean variance criteria for a risk averse investor?

Answer 5

1) smaller standard deviation given mean value
2) larger mean given standard deviation
3) or generally an asset that allows them to reach their highest possible indifference curve

Question 6

what is the mean variance paradox?

Answer 6

If the distribution of returns is not normal, then using the mean-variance criterion, we might obtain that asset A is preferable to asset B even if asset B first-order stochastically dominates asset A.