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Portfolio optimization has long been dominated by covariance-based strategies, such as the Markowitz Mean-Variance framework. However, these approaches often fail to ensure a balanced risk structure across assets, leading to concentration…
We construct a deep portfolio theory. By building on Markowitz's classic risk-return trade-off, we develop a self-contained four-step routine of encode, calibrate, validate and verify to formulate an automated and general portfolio…
A cryptocurrency is a digital asset maintained by a decentralised system using cryptography. Investors in this emerging digital market are exploring the profitability potential of portfolios in place of single coins. Portfolios are…
This paper introduces a software component created in Visual Basic for Applications (VBA) that can be applied for creating an optimal portfolio using two different methods. The first method is the seminal approach of Markowitz that is based…
The stock market offers a platform where people buy and sell shares of publicly listed companies. Generally, stock prices are quite volatile; hence predicting them is a daunting task. There is still much research going to develop more…
Portfolio theory is a very powerful tool in the modern investment theory. It is helpful in estimating risk of an investor's portfolio, which arises from our lack of information, uncertainty and incomplete knowledge of reality, which forbids…
Asset allocation is an investment strategy that aims to balance risk and reward by constantly redistributing the portfolio's assets according to certain goals, risk tolerance, and investment horizon. Unfortunately, there is no simple…
Since decades, the data science community tries to propose prediction models of financial time series. Yet, driven by the rapid development of information technology and machine intelligence, the velocity of today's information leads to…
Portfolio optimization methods have evolved significantly since Markowitz introduced the mean-variance framework in 1952. While the theoretical appeal of this approach is undeniable, its practical implementation poses important challenges,…
Markowitz's celebrated mean--variance portfolio optimization theory assumes that the means and covariances of the underlying asset returns are known. In practice, they are unknown and have to be estimated from historical data. Plugging the…
Individual investors are now massively using online brokers to trade stocks with convenient interfaces and low fees, albeit losing the advice and personalization traditionally provided by full-service brokers. We frame the problem faced by…
Given two random realized returns on an investment, which is to be preferred? This is a fundamental problem in finance that has no definitive solution except in the case one investment always returns more than the other. In 1952 Markowitz…
Motivated by recent advances in the spectral theory of auto-covariance matrices, we are led to revisit a reformulation of Markowitz' mean-variance portfolio optimization approach in the time domain. In its simplest incarnation it applies to…
The main purpose of this study is the determination of the optimal length of the historical data for the estimation of statistical parameters in Markowitz Portfolio Optimization. We present a trading simulation using Markowitz method, for a…
As the cornerstone of modern portfolio theory, Markowitz's mean-variance optimization is considered a major model adopted in portfolio management. However, due to the difficulty of estimating its parameters, it cannot be applied to all…
This survey article is dedicated to the life of the famous American economist H. Markowitz (1927--2023). We do revisit the main statements of the portfolio selection theory in terms of mathematical completeness including all the necessary…
In his famous paper, Markowitz (1952) derived the dependence of portfolio random returns on the random returns of its securities. This result allowed Markowitz to obtain his famous expression for portfolio variance. We show that Markowitz's…
In this paper we propose a novel application of Gaussian processes (GPs) to financial asset allocation. Our approach is deeply rooted in Stochastic Portfolio Theory (SPT), a stochastic analysis framework introduced by Robert Fernholz that…
An investment portfolio consists of $n$ algorithmic trading strategies, which generate vectors of positions in trading assets. Sign opposite trades (buy/sell) cross each other as strategies are combined in a portfolio. Then portfolio…
Designing an optimum portfolio for allocating suitable weights to its constituent assets so that the return and risk associated with the portfolio are optimized is a computationally hard problem. The seminal work of Markowitz that attempted…