Related papers: Introducing Variety in Risk Management
It is shown that the axioms for coherent risk measures imply that whenever there is an asset in a portfolio that dominates the others in a given sample (which happens with finite probability even for large samples), then this portfolio…
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,…
High precision analytical approximation is proposed for variance-covariance based risk allocation in a portfolio of risky assets. A general case of a single-period multi-factor Merton-type model with stochastic recovery is considered. The…
Parametric statistical methods play a central role in analyzing risk through its underlying frequency and severity components. Given the wide availability of numerical algorithms and high-speed computers, researchers and practitioners often…
In economics, insurance and finance, value at risk (VaR) is a widely used measure of the risk of loss on a specific portfolio of financial assets. For a given portfolio, time horizon, and probability $\alpha$, the $100\alpha\%$ VaR is…
The downside risk of a portfolio of (equity)assets is generally substantially higher than the downside risk of its components. In particular in times of crises when assets tend to have high correlation, the understanding of this difference…
We propose a definition of diversification as a binary relationship between financial portfolios. According to it, a convex linear combination of several risk positions with some weights is considered to be less risky than the probabilistic…
Measures of risk concentration and their asymptotic behavior for portfolios with heavy-tailed risk factors is of interest in risk management. Second order regular variation is a structural assumption often imposed on such risk factors to…
Multivariate probability density functions of returns are constructed in order to model the empirical behavior of returns in a financial time series. They describe the well-established deviations from the Gaussian random walk, such as an…
Estimating the covariance of asset returns, i.e., the risk model, is a key component of financial portfolio construction and evaluation. Most risk modeling approaches produce a factor model that decomposes the asset variability into two…
A new framework for portfolio diversification is introduced which goes beyond the classical mean-variance approach and portfolio allocation strategies such as risk parity. It is based on a novel concept called portfolio dimensionality that…
Portfolio diversification, traditionally measured through asset correlations and volatilitybased metrics, is fundamental to managing financial risk. However, existing diversification metrics often overlook non-numerical relationships…
The conventional wisdom of mean-variance (MV) portfolio theory asserts that the nature of the relationship between risk and diversification is a decreasing asymptotic function, with the asymptote approximating the level of portfolio…
The fundamental principle in Modern Portfolio Theory (MPT) is based on the quantification of the portfolio's risk related to performance. Although MPT has made huge impacts on the investment world and prompted the success and prevalence of…
The risk of financial positions is measured by the minimum amount of capital to raise and invest in eligible portfolios of traded assets in order to meet a prescribed acceptability constraint. We investigate nondegeneracy, finiteness and…
Factor models have become a common and valued tool for understanding the risks associated with an investing strategy. In this report we describe Exabel's factor model, we quantify the fraction of the variability of the returns explained by…
This article develops the theory of risk budgeting portfolios, when we would like to impose weight constraints. It appears that the mathematical problem is more complex than the traditional risk budgeting problem. The formulation of the…
Risk diversification is one of the dominant concerns for portfolio managers. Various portfolio constructions have been proposed to minimize the risk of the portfolio under some constrains including expected returns. We propose a portfolio…
We introduce a faithful representation of the heavy tail multivariate distribution of asset returns, as parsimonous as the Gaussian framework. Using calculation techniques of functional integration and Feynman diagrams borrowed from…
The so-called risk diversification principle is analyzed, showing that its convenience depends on individual characteristics of the risks involved and the dependence relationship among them. ----- Se analiza el principio de…