The geometry of relative arbitrage
By Soumik Pal, Ting-Kam Leonard Wong. 2014
59 citations recorded by the source corpus.
Consider an equity market with n stocks. The vector of proportions of the total market capitalizations that belong to each stock is called the market weight. The market weight defines the market portfolio which is a buy-and-hold portfolio representing the performance of the entire stock market. Consider a function that assigns a portfolio vector to each possible value of the market weight, and we perform self-financing trading using this portfolio function. We study the problem of characterizing functions such that the resulting portfolio will outperform the market portfolio in the long run under the conditions of diversity and sufficient volatility. No other assumption on the future behavior of stock prices is made. We prove that the only solutions are functionally generated portfolios in the sense of Fernholz. A second characterization is given as the optimal maps of a remarkable optimal transport problem. Both characterizations follow from a novel property of portfolios called multiplicative cyclical monotonicity.
Subfields: Computational Theory and Mathematics, Economics and Econometrics, Finance
View Paper: https://www.semanticscholar.org/paper/83bed04bba9480fab7e37c019d2071cbf99d31c9
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Citations in the corpus
- On the difference between entropic cost and the optimal transport cost (2019, background): “Following our previous works [22, 23, 21] we call π the portfolio vector .”