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Chapter 7 Appendix Stochastic Dominance

Chapter 7 Appendix Stochastic Dominance. What can be added to the happiness of a man who is in health, out of debt, and has a clear conscience? - Mark Twain. Outline. Introduction Efficiency revisited First-degree stochastic dominance Second-degree stochastic dominance

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Chapter 7 Appendix Stochastic Dominance

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  1. Chapter 7 AppendixStochastic 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

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