Stochastic Portfolio Theory (SPT), introduced by E. Robert Fernholz in 2002,74 is a mathematical framework for analyzing portfolio behavior and performance. Unlike MPT and PMPT, SPT does not rely on the assumption of market equilibrium or investor rationality. Instead, it focuses on the empirical behavior of asset prices and portfolios.
Two ideas carry the framework. Market diversity is the empirical fact that capital is never permanently concentrated in a handful of names: relative weights churn constantly, and that churn is itself a source of return. Relative arbitrage is the payoff — SPT proves that, under conditions that genuinely hold in real markets, a diversity-weighted portfolio (one weighting each name by its market capitalization raised to a power below one, deliberately tilting toward smaller companies) outperforms the capitalization-weighted index over a long enough horizon.74,75 This is a constructive mathematical result, not a hopeful one, and it is derived without any appeal to market equilibrium, rational investors, or normally distributed returns — the very assumptions on which MPT and the CAPM rest. It is the cleanest demonstration that the cap-weighted “market portfolio” those theories treat as optimal is in fact just a convention.
The practitioner’s takeaway is modest but real: a deliberate, rules-based tilt away from pure cap-weighting — toward equal weight, fundamental weight, or an explicit diversity weight — is theoretically defensible rather than a reckless bet against efficient markets. The small-cap and value premia are the same effect seen from a different angle. The full machinery is institutional; the lesson that cap-weighting is a habit, not a law, is not.