1. Chapter 7 Appendix Stochastic Dominance

2. What can be added to the happiness of a man who is in health, out of debt, and has a clear conscience?
- Mark Twain

3. Outline Introduction Efficiency revisited
First-degree stochastic dominance
Second-degree stochastic dominance
Stochastic dominance and utility

4. Introduction
Stochastic dominance is an alternative technique employed in the portfolio construction process
Stochastic “denotes the process of selecting from among a group of theoretically possible alternatives those elements or factors whose combination will most closely approximate a desired result”
Stochastic models are not always exact
Stochastic models are useful shorthand representations of complicated processes

5. Efficiency Revisited
Portfolios are efficient is they are not dominated by other portfolios
Portfolios are inefficient if at least one other portfolio dominates them
Rational investors prefer efficient investments

6. First-Degree Stochastic Dominance
Cumulative distribution A will be preferred over cumulative distribution B if every value of distribution A lies below or on distribution B, provided the distributions are not identical
The distribution lines do not cross

7. Second-Degree Stochastic Dominance
Alternative A is preferred to Alternative B if the cumulative probability of B minus the cumulative probability of A is always non-negative
SSD can be a significant aid in reducing the security universe to a workable number of efficient alternatives

8. Stochastic Dominance and Utility
Introduction
Stochastic dominance and mean return
Higher orders of stochastic dominance
Practical problems with stochastic dominance

9. Introduction
Regardless of how much risk a person can tolerate, the FSD criterion is appropriate
Both the conservative investor and the gambler will prefer a first-degree stochastic dominant investment over an FSD inefficient alternative
Investors who are risk averse can use SSD to weed out inefficient alternatives

10. Stochastic Dominance and Mean Return
Alternative A is FSD efficient over Alternative B if the expected return of A is no less than the expected return of B
If alternatives are ranked by both geometric mean and level of stochastic dominance, no FSD-efficient portfolio can have a higher geometric mean return than an SSD-efficient portfolio

11. Higher Orders of Stochastic Dominance
For third-degree stochastic dominance:
The investor is risk averse
The investor’s degree of risk aversion declines as wealth increases

12. Practical Problems With Stochastic Dominance
FSD frequently fails to reduce the security universe very much
SSD is a much more powerful screening tool than FSD
It is difficult to calculate higher than third-degree stochastic dominance