Portfolio Theory

A mathematical study of the excess growth rate ArXiv ID: 2510.25740 “View on arXiv” Authors: Steven Campbell, Ting-Kam Leonard Wong Abstract We study the excess growth rate – a fundamental logarithmic functional arising in portfolio theory – from the perspective of information theory. We show that the excess growth rate can be connected to the Rényi and cross entropies, the Helmholtz free energy, L. Campbell’s measure of average code length and large deviations. Our main results consist of three axiomatic characterization theorems of the excess growth rate, in terms of (i) the relative entropy, (ii) the gap in Jensen’s inequality, and (iii) the logarithmic divergence that generalizes the Bregman divergence. Furthermore, we study maximization of the excess growth rate and compare it with the growth optimal portfolio. Our results not only provide theoretical justifications of the significance of the excess growth rate, but also establish new connections between information theory and quantitative finance. ...

Optimising cryptocurrency portfolios through stable clustering of price correlation networks ArXiv ID: 2505.24831 “View on arXiv” Authors: Ruixue Jing, Ryota Kobayashi, Luis Enrique Correa Rocha Abstract The emerging cryptocurrency market presents unique challenges for investment due to its unregulated nature and inherent volatility. However, collective price movements can be explored to maximise profits with minimal risk using investment portfolios. In this paper, we develop a technical framework that utilises historical data on daily closing prices and integrates network analysis, price forecasting, and portfolio theory to identify cryptocurrencies for building profitable portfolios under uncertainty. Our method utilises the Louvain network community algorithm and consensus clustering to detect robust and temporally stable clusters of highly correlated cryptocurrencies, from which the chosen cryptocurrencies are selected. A price prediction step using the ARIMA model guarantees that the portfolio performs well for up to 14 days in the investment horizon. Empirical analysis over a 5-year period shows that despite the high volatility in the crypto market, hidden price patterns can be effectively utilised to generate consistently profitable, time-agnostic cryptocurrency portfolios. ...

Indices of quadratic programs over reproducing kernel Hilbert spaces for fun and profit ArXiv ID: 2412.18201 “View on arXiv” Authors: Unknown Abstract We give an abstract perspective on quadratic programming with an eye toward long portfolio theory geared toward explaining sparsity via maximum principles. Specifically, in optimal allocation problems, we see that support of an optimal distribution lies in a variety intersect a kind of distinguished boundary of a compact subspace to be allocated over. We demonstrate some of its intelligence by using it to solve mazes and interpret such behavior as the underlying space trying to understand some hypothetical platonic index for which the capital asset pricing model holds. ...

An Analytic Solution for Asset Allocation with a Multivariate Laplace Distribution ArXiv ID: 2411.08967 “View on arXiv” Authors: Unknown Abstract In this short note the theory for multivariate asset allocation with elliptically symmetric distributions of returns, as developed in the author’s prior work, is specialized to the case of returns drawn from a multivariate Laplace distribution. This analysis delivers a result closely, but not perfectly, consistent with the conjecture presented in the author’s article Thinking Differently About Asset Allocation. The principal differences are due to the introduction of a term in the dimensionality of the problem, which was omitted from the conjectured solution, and a rescaling of the variance due to varying parameterizations of the univariate Laplace distribution. ...

The Theory of CorporateFinance: A Historical Overview ArXiv ID: ssrn-244161 “View on arXiv” Authors: Unknown Abstract Our purpose is to provide a review of the development of the modern theory of corporate finance. Through the early 1950s the finance literature consisted in lar Keywords: Modern Corporate Finance, Capital Budgeting, Portfolio Theory, Financial Management, Academic Review, Corporate Finance Complexity vs Empirical Score Math Complexity: 2.0/10 Empirical Rigor: 1.0/10 Quadrant: Philosophers Why: This is a historical review paper discussing the conceptual evolution of corporate finance theory, lacking advanced mathematical derivations or backtest-ready empirical implementation. flowchart TD A["Research Goal: Review Modern Corporate Finance Theory"] --> B["Methodology: Historical Literature Review"] B --> C["Data/Inputs: Early 1950s Finance Literature & Academic Texts"] C --> D["Computational Process: Thematic Analysis & Evolution Mapping"] D --> E["Key Finding 1: Emergence of Capital Budgeting"] D --> F["Key Finding 2: Integration of Portfolio Theory"] D --> G["Key Finding 3: Formalization of Financial Management"]