NAG Libraries have many powerful and reliable optimizers which can be used to solve large portfolio optimization and selection problems in the financial industry. Below is an introduction into the notation and techniques used in portfolio optimization. We discuss some sample problems and present help in choosing an appropriate NAG optimizer. Finally, there is a section on handling transaction c...

This paper shows how one can use the theory of hidden Markov models for portfolio optimization. We illustrate our method by a ball and urn experiment. An application to historical data is examined.

In this work introduce an adaptive method of portfolio optimization. The basic idea is to describe essential movements of the stock price using a hidden Markov model and to calculate the optimal portfolio using a recursive algorithm. The portfolio optimization is adaptive in the sense that the standard EM–algorithm fits the model to historical data, which improves the portfolio performance.

In this tutorial paper we introduce different approaches to Markowitz portfolio optimization, and we show how to solve such problems in MATLAB, R and Python using the MOSEK optimization toolbox for MATLAB, the Rmosek package, and the MOSEK Python API, respectively. We first consider conic formulations of the basic portfolio selection problem, and we then discuss more advanced models for transac...

For determining an optimal portfolio allocation, parameters representing the underlying market – characterized by expected asset returns and the covariance matrix – are needed. Traditionally, these point estimates for the parameters are obtained from historical data samples, but as experts often have strong opinions about (some of) these values, approaches to combine sample information and expe...

We examine the issue of possible portfolio diversification benefits into seven Middle-Eastern and North African (MENA) stock markets. We take the standpoint of the world investor and we construct portfolios in international and local currencies based on five optimization models and two risk measures. We then compare the portfolio out-of-sample performance based on Sharpe and Sortino ratios thro...

We discuss a class of risk-sensitive portfolio optimization problems. We consider the portfolio optimization model investigated by Nagai in 2003. The model by its nature can include fixed income securities as well in the portfolio. Under fairly general conditions, we prove the existence of optimal portfolio in both finite and infinite horizon problems.

In this article, we apply the mean-expected tail loss (ETL) portfolio optimization to the consensus temporary earnings forecasting (CTEF) data from global equities. The time series model with multivariate normal tempered stable (MNTS) innovations is used to generate the out-of-sample scenarios for the portfolio optimization. We find that (1) the CTEF variable continues to be of value in portfol...

In this analysis of the risk and return of stocks in the United States and global markets, we apply several portfolio construction and optimization techniques to U.S. and global stock universes. We find that (1) mean-variance techniques continue to produce portfolios capable of generating excess returns above transaction costs and statistically significant asset selection, (2) optimization tech...

For institutional investors, optimizing the trade-off between risk and reward poses significant modeling and computational challenges. Notably, small errors in the estimated returns of financial assets can lead to optimized portfolios that incur far too much risk for the returns they actually deliver. Given these adverse effects, portfolio construction techniques that are based exclusively on r...