Related papers: Robustifying Markowitz
Markowitz's optimal portfolio relies on the accurate estimation of correlations between asset returns, a difficult problem when the number of observations is not much larger than the number of assets. Using powerful results from random…
The signal-noise ratio of a portfolio of p assets, its expected return divided by its risk, is couched as an estimation problem on the sphere. When the portfolio is built using noisy data, the expected value of the signal-noise ratio is…
Robust estimation for modern portfolio selection on a large set of assets becomes more important due to large deviation of empirical inference on big data. We propose a distributionally robust methodology for high-dimensional mean-variance…
Shorting for hedging exposes to risk when the market dynamics is uncertain. Managing uncertainty and risk exposure is key in portfolio management practice. This paper develops a robust framework for dynamic minimum-variance hedging that…
The asymptotic distribution of the Markowitz portfolio is derived, for the general case (assuming fourth moments of returns exist), and for the case of multivariate normal returns. The derivation allows for inference which is robust to…
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…
We introduce a covariance matrix estimator that both takes into account the heteroskedasticity of financial returns (by using an exponentially weighted moving average) and reduces the effective dimensionality of the estimation (and hence…
The mean and variance of portfolio returns are the standard quantities to measure the expected return and risk of a portfolio. Efficient portfolios that provide optimal trade-offs between mean and variance warrant consideration. To express…
The popularity of modern portfolio theory has decreased among practitioners because of its unfavorable out-of-sample performance. Estimation errors tend to affect the optimal weight calculation noticeably, especially when a large number of…
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…
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…
The portfolio optimisation problem, first raised by Harry Markowitz in 1952, has been a fundamental and central topic to understanding the stock market and making decisions. There has been plenty of works contributing to development of the…
With the good development in the financial industry, the market starts to catch people's eyes, not only by the diversified investing choices ranging from bonds and stocks to futures and options but also by the general "high-risk,…
The Markowitz model is still the cornerstone of modern portfolio theory. In particular, when focusing on the minimum-variance portfolio, the covariance matrix or better its inverse, the so-called precision matrix, is the only input…
Utility and risk are two often competing measurements on the investment success. We show that efficient trade-off between these two measurements for investment portfolios happens, in general, on a convex curve in the two dimensional space…
We first study the properties of solutions of quadratic programs with linear equality constraints whose parameters are estimated from data in the high-dimensional setting where p, the number of variables in the problem, is of the same order…
A continuous-time Markowitz's mean-variance portfolio selection problem is studied in a market with one stock, one bond, and proportional transaction costs. This is a singular stochastic control problem,inherently in a finite time horizon.…
Under losses which are potentially heavy-tailed, we consider the task of minimizing sums of the loss mean and standard deviation, without trying to accurately estimate the variance. By modifying a technique for variance-free robust mean…
In this paper we apply a heuristic method based on artificial neural networks in order to trace out the efficient frontier associated to the portfolio selection problem. We consider a generalization of the standard Markowitz mean-variance…
We present an exact algorithm for mean-risk optimization subject to a budget constraint, where decision variables may be continuous or integer. The risk is measured by the covariance matrix and weighted by an arbitrary monotone function,…