Stochastic portfolio theory / E. Robert Fernholz.

Includes bibliographical references (p. [169]-174) and index.

Machine generated contents note: 1 Stochastic Portfolio Theory 1 -- 1.1 Stocks and Portfolios2 -- 1.2 Relative Return and the Market Portfolio13 -- 1.3 Portfolio Behavior and Optimization16 -- 1.4 Notes and Summary22 -- 2 Stock Market Behavior and Diversity 25 -- 2.1 The Long-Term Behavior of the Market26 -- 2.2 Stock Market Diversity31 -- 2.3 Entropy as a Measure of Market Diversity36 -- 2.4 Notes and Summary41 -- 3 Functionally Generated Portfolios 43 -- 3.1 Portfolio Generating Functions43 -- 3.2 Time-Dependent Generating Functions55 -- 3.3 The No-Arbitrage Hypothesis57 -- 3.4 Measures of Diversity62 -- 3.5 Notes and Summary65 -- 4 Portfolios of Stocks Selected by Rank 69 -- 4.1 Rank Processes and Local Times71 -- 4.2 Portfolios Generated by Functions of Ranked -- Market Weights79 -- 4.3 Examples of Rank-Dependent Portfolios85 -- 4.4 Notes and Summary90 -- 5 Stable Models for the Distribution of Capital 93 -- 5.1 The Capital Distribution Curve93 -- 5.2 dX(t) = -asgn(X(t))dt +dW(t)96 -- 5.3 The Structure of Stable Capital Distributions98 -- 5.4 Application to the U.S. Equity Market106 -- 5.5 A "First-Order" Market Model110 -- 5.6 Notes and Summary115 -- 6 Performance of Functionally Generated Portfolios 119 -- 6.1 Market Entropy120 -- 6.2 A Diversity-Weighted Portfolio125 -- 6.3 Turnover in a Diversity-Weighted Portfolio129 -- 6.4 The Size Effect133 -- 6.5 The Biggest Stock136 -- 6.6 Notes and Summary140 -- 7 Applications of Stochastic Portfolio Theory 143 -- 7.1 Optimization and the First-Order Model143 -- 7.2 Diversity-Weighted Indexing146 -- 7.3 Manager Performance and Change in Diversity151 -- 7.4 The Distributional Component of Equity Return153 -- 7.5 Measurement of the Distributional Component155 -- 7.6 An Analysis of Value Stocks160 -- 7.7 Notes and Summary162.