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This paper uses topological data analysis (TDA) tools and introduces a data-driven clustering-based stock selection strategy tailored for sparse portfolio construction. Our asset selection strategy exploits the topological features of stock…
In this article, the long-term behavior of the stock market index of the New York Stock Exchange is studied, for the period 1950 to 2013. Specifically, the CRSP Value-Weighted and CRSP Equal-Weighted index are analyzed in terms of market…
With the improvement of computer performance and the development of GPU-accelerated technology, trading with machine learning algorithms has attracted the attention of many researchers and practitioners. In this research, we propose a novel…
We study decades-long historic distributions of accumulated S\&P500 returns, from daily returns to those over several weeks. The time series of the returns emphasize major upheavals in the markets -- Black Monday, Tech Bubble, Financial…
We show that recent stock market fluctuations are characterized by the cumulative distributions whose tails on short, minute time scales exhibit power scaling with the scaling index alpha > 3 and this index tends to increase quickly with…
Portfolio management is an essential part of investment decision-making. However, traditional methods often fail to deliver reasonable performance. This problem stems from the inability of these methods to account for the unique…
We analyze annual revenues and earnings data for the 500 largest-revenue U.S. companies during the period 1954-2007. We find that mean year profits are proportional to mean year revenues, exception made for few anomalous years, from which…
In this paper we consider the problem of minimising drawdown in a portfolio of financial assets. Here drawdown represents the relative opportunity cost of the single best missed trading opportunity over a specified time period. We formulate…
We consider the following problem in stochastic portfolio theory. Are there portfolios that are relative arbitrages with respect to the market portfolio over very short periods of time under realistic assumptions? We answer a slightly…
We investigate how and when to diversify capital over assets, i.e., the portfolio selection problem, from a signal processing perspective. To this end, we first construct portfolios that achieve the optimal expected growth in i.i.d.…
In this paper, motivated by the celebrated work of Kelly, we consider the problem of portfolio weight selection to maximize expected logarithmic growth. Going beyond existing literature, our focal point here is the rebalancing frequency…
A geometric analysis of the time series of returns has been performed in the past and it implied that the most of the systematic information of the market is contained in a space of small dimension. Here we have explored subspaces of this…
Kelly's Criterion is well known among gamblers and investors as a method for maximizing the returns one would expect to observe over long periods of betting or investing. These ideas are conspicuously absent from portfolio optimization…
In this paper, we revisit the relationship between investors' utility functions and portfolio allocation rules. We derive portfolio allocation rules for asymmetric Laplace distributed $ALD(\mu,\sigma,\kappa)$ returns and compare them with…
In this paper we apply second-order stochastic dominance (SSD) to the problem of enhanced indexation with asset subset (sector) constraints. The problem we consider is how to construct a portfolio that is designed to outperform a given…
We analyse the effect of a proportional wealth tax on asset returns, portfolio choice, and asset pricing. The tax is levied annually on the market value of all holdings at a uniform rate. We show that such a tax is economically equivalent…
This paper aims to develop new mathematical and computational tools for modeling the distribution of portfolio returns across portfolios. We establish relevant mathematical formulas and propose efficient algorithms, drawing upon powerful…
We consider the problem of choosing a portfolio that maximizes the cumulative prospect theory (CPT) utility on an empirical distribution of asset returns. We show that while CPT utility is not a concave function of the portfolio weights, it…
This work proposes a unified framework for portfolio allocation, covering both asset selection and optimization, based on a multiple-hypothesis predict-then-optimize approach. The portfolio is modeled as a structured ensemble, where each…
Mean-reverting portfolios with volatility and sparsity constraints are of prime interest to practitioners in finance since they are both profitable and well-diversified, while also managing risk and minimizing transaction costs. Three main…