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TL;DR

A partial ordering on distributions. X first-order dominates Y if \( F_X(t) \leq F_Y(t) \) for all t (X is always at least as likely to exceed any threshold). Second-order dominance additionally accounts for risk aversion.

By Valenke Exam Prep Team·Last updated 2026-06-03

Stochastic Dominance

A partial ordering on distributions. X first-order dominates Y if \( F_X(t) \leq F_Y(t) \) for all t (X is always at least as likely to exceed any threshold). Second-order dominance additionally accounts for risk aversion.

Why it matters for interviews

Stochastic dominance provides model-free rankings of investments: if X dominates Y, all rational (or risk-averse) investors prefer X. It is a stronger statement than comparing means or Sharpe ratios.

Definition and Mathematical Foundation

A partial ordering on distributions. X first-order dominates Y if \( F_X(t) \leq F_Y(t) \) for all t (X is always at least as likely to exceed any threshold). Second-order dominance additionally accounts for risk aversion.

Application in Quantitative Finance

Stochastic dominance provides model-free rankings of investments: if X dominates Y, all rational (or risk-averse) investors prefer X. It is a stronger statement than comparing means or Sharpe ratios.

Related Terms

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Frequently Asked Questions

What is first-order stochastic dominance?▼
X FSD Y means \( P(X > t) \geq P(Y > t) \) for all t, with strict inequality somewhere. Equivalently, all investors who prefer more to less choose X. It implies \( E[u(X)] \geq E[u(Y)] \) for all increasing u.
What is second-order stochastic dominance?▼
X SSD Y means \( E[u(X)] \geq E[u(Y)] \) for all increasing concave u (all risk-averse investors prefer X). Equivalently, \( \int_{-\infty}^t F_X(s)ds \leq \int_{-\infty}^t F_Y(s)ds \) for all t.
How is stochastic dominance used in portfolio theory?▼
If portfolio A dominates portfolio B, B is inefficient -- no rational investor would hold it. This provides a model-free efficiency criterion that does not require specifying a utility function or assuming normality.