Stochastic Dominance

Question 1

Absolute Dominance

Answer 1

• Said to exist when one investment portfolio provides a higher return than another in all possible circumstances

Question 2

First-Order Stochastic Dominance

Answer 2

The first-order stochastic dominance theorem states that assuming an investor prefers more to less, A first-order stochastically dominates B if:
FA(x)<=FB(x) for all x, and
FA(x) higher mean first-order dominates

Question 3

Second-Order Stochastic Dominance

Answer 3

The second-order stochastic dominance theorem states that assuming an investor is risk-averse and prefers more to less, A second-order stochastically dominates B if:
int{a->inf}FA(y)dy <= int{a->inf}FB(y)dy for all x
with equality holding for some value of x

{interpretation}

Same mean, different variance ==> lower variance second-order stochastically dominates

Question 4

Info required for different types of dominance to identify by only identifying the option that maximises E(U)

VRA

Answer 4

Absolute ==> Non-satuated
FOSD ==> Non-satuated
SOSD ==> Risk-averse & Non-satuated
None ==> Full Utility Function