Related papers: Asymptotic distribution of the Markowitz portfolio
We show that the Markowitz portfolio is a scalar multiple of another portfolio which replaces the covariance with the second moment matrix, via simple application of the Sherman-Morrison identity. Moreover it is shown that when using…
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…
We consider the problem of portfolio selection within the classical Markowitz mean-variance framework, reformulated as a constrained least-squares regression problem. We propose to add to the objective function a penalty proportional to the…
This paper studies a robust continuous-time Markowitz portfolio selection pro\-blem where the model uncertainty carries on the covariance matrix of multiple risky assets. This problem is formulated into a min-max mean-variance problem over…
Asymptotic distribution for the proportional covariance model under multivariate normal distributions is derived. To this end, the parametrization of the common covariance matrix by its Cholesky root is adopted. The derivations are made in…
We revisit Markowitz's mean-variance portfolio selection model by considering a distributionally robust version, where the region of distributional uncertainty is around the empirical measure and the discrepancy between probability measures…
We study the Markowitz portfolio selection problem with unknown drift vector in the multidimensional framework. The prior belief on the uncertain expected rate of return is modeled by an arbitrary probability law, and a Bayesian approach…
Since Markowitz's mean-variance framework, optimizing a portfolio that maximizes the profit and minimizes the risk has been ubiquitous in the financial industry. Initially, profit and risk were measured by the first two moments of the…
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…
Markowitz mean-variance portfolios with sample mean and covariance as input parameters feature numerous issues in practice. They perform poorly out of sample due to estimation error, they experience extreme weights together with high…
Traditional Markowitz portfolio optimization constrains daily portfolio variance to a target value, optimising returns, Sharpe or variance within this constraint. However, this approach overlooks the relationship between variance at…
More than seventy years ago Harry Markowitz formulated portfolio construction as an optimization problem that trades off expected return and risk, defined as the standard deviation of the portfolio returns. Since then the method has been…
We introduce a universal framework for mean-covariance robust risk measurement and portfolio optimization. We model uncertainty in terms of the Gelbrich distance on the mean-covariance space, along with prior structural information about…
We describe a procedure to perform approximate inference on the achieved signal-noise ratio of the Markowitz Portfolio under Gaussian i.i.d. returns. The procedure relies on a statistic similar to the Sharpe Ratio Information Criterion.…
Entropy based ideas find wide-ranging applications in finance for calibrating models of portfolio risk as well as options pricing. The abstracted problem, extensively studied in the literature, corresponds to finding a probability measure…
The aggregation of individual risks in large credit and insurance portfolios is guided by diversification and the law of large numbers, which formalizes the convergence of sample averages to their means. At the same time, regulatory capital…
We derive properties of the cdf of random variables defined as saddle-type points of real valued continuous stochastic processes. This facilitates the derivation of the first-order asymptotic properties of tests for stochastic spanning…
Inhomogeneous phase-type (IPH) distributions extend classical phase-type models by allowing transition intensities to vary over time, offering greater flexibility for modeling heavy-tailed or time-dependent absorption phenomena. We focus on…
We estimate the global minimum variance (GMV) portfolio in the high-dimensional case using results from random matrix theory. This approach leads to a shrinkage-type estimator which is distribution-free and it is optimal in the sense of…
We study statistical inference and distributionally robust solution methods for stochastic optimization problems, focusing on confidence intervals for optimal values and solutions that achieve exact coverage asymptotically. We develop a…