Related papers: Kendall Correlation Coefficients for Portfolio Opt…
In general, underestimation of risk is something which should be avoided as far as possible. Especially in financial asset management, equity risk is typically characterized by the measure of portfolio variance, or indirectly by quantities…
Estimating the eigenvalues of a population covariance matrix from a sample covariance matrix is a problem of fundamental importance in multivariate statistics; the eigenvalues of covariance matrices play a key role in many widely…
This paper investigates the critical role of eigenalignments between the kernel matrix and learning targets in achieving robust generalization in learning problems. We establish a direct connection between generalization performance in…
We consider a portfolio allocation problem for trend following (TF) strategies on multiple correlated assets. Under simplifying assumptions of a Gaussian market and linear TF strategies, we derive analytical formulas for the mean and…
In this article, we first propose generalized row/column matrix Kendall's tau for matrix-variate observations that are ubiquitous in areas such as finance and medical imaging. For a random matrix following a matrix-variate elliptically…
Kendall's tau and conditional Kendall's tau matrices are multivariate (conditional) dependence measures between the components of a random vector. For large dimensions, available estimators are computationally expensive and can be improved…
We study a continuous-time Markowitz mean-variance portfolio selection model in which a naive agent, unaware of the underlying time-inconsistency, continuously reoptimizes over time. We define the resulting naive policies through the limit…
We consider the problem of estimating the principal components of a population correlation matrix from a limited number of measurement data. Using a combination of random matrix and information-theoretic tools, we show that all the…
Covariance estimation for matrix-valued data has received an increasing interest in applications. Unlike previous works that rely heavily on matrix normal distribution assumption and the requirement of fixed matrix size, we propose a class…
In this paper, we apply tools from the random matrix theory (RMT) to estimates of correlations across volatility of various assets in the S&P 500. The volatility inputs are estimated by modeling price fluctuations as GARCH(1,1) process. The…
The Markowitz-based portfolio selection turns to an NP-hard problem when considering cardinality constraints. In this case, existing exact solutions like quadratic programming may not be efficient to solve the problem. Many researchers,…
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.…
It has been shown that, if a model displays long-range (power-law) spatial correlations, its equal-time correlation matrix of this model will also have a power law tail in the distribution of its high-lying eigenvalues. The purpose of this…
Optimal capital allocation between different assets is an important financial problem, which is generally framed as the portfolio optimization problem. General models include the single-period and multi-period cases. The traditional…
The global minimum-variance portfolio is a typical choice for investors because of its simplicity and broad applicability. Although it requires only one input, namely the covariance matrix of asset returns, estimating the optimal solution…
This paper examines the differences in ordinal rankings obtained from a pairwise comparison matrix using the eigenvalue method and the geometric mean method. First, we introduce several propositions on the (dis)similarity of both rankings…
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…
Portfolio optimization methods suffer from a catalogue of known problems, mainly due to the facts that pair correlations of asset returns are unstable, and that extremal risk measures such as maximum drawdown are difficult to predict due to…
We show that correlation matrices with particular average and variance of the correlation coefficients have a notably restricted spectral structure. Applying geometric methods, we derive lower bounds for the largest eigenvalue and the…
It is widely recognized that when classical optimal strategies are applied with parameters estimated from data, the resulting portfolio weights are remarkably volatile and unstable over time. The predominant explanation for this is the…