Portfolio Optimization Process Research Articles

Improved Hedge Fund Portfolio Optimization Using 2-Step Covariance Matrix and Fund Transaction Costs

This study focuses on fund portfolio investments in the Chinese market. The application of classic portfolio optimization methods encounters several issues when applied to fund portfolios. For example, issues such as the non-normal distribution of returns on funds or fund portfolios, turnover rate limitations in fund investments, and liquidity constraints of fund assets, which can lead to transaction costs and opportunity costs, are prevalent challenges. The existence of these issues can compromise the effectiveness of classic portfolio optimization methods like Mean-Variance Optimization. This may result in a reduction of accuracy in determining the portfolios optimal weights, a deviation of actual trading results from the models optimal expectation, and may even render the optimal weights impractical in real-world scenarios. To address these challenges, this paper integrates the 2-Step covariance matrix method (2-Step method) and the measurement of fund transaction costs into the portfolio optimization process. The paper finds that the 2-Step method, compared to the baseline, can indeed improve the risk-return indicators of the potimal fund portfolio. The inclusion of the transaction cost can effectively control the turnover frequency of the portfolio. Even after accounting for these costs, the 2-Step method continues to exhibit a significant improvement effect compared to the baseline.

Portfolio Optimization Using Markowitz Model on Sri-Kehati Index

This thesis investigates the portfolio optimization process using the Markowitz model on the SRI-KEHATI index, an esteemed sustainable investment index. The study aims to explore the potential advantages of incorporating environmental, social, and governance (ESG) factors into portfolio construction. By leveraging historical financial data and reliable ESG metrics, this research develops optimized portfolios that strike a balance between risk and return while adhering to the sustainability criteria of the SRIKEHATI index. The methodology encompasses the collection of credible ESG data and financial information for the constituents of the SRIKEHATI index. The Markowitz model is subsequently employed to analyze the risk and return characteristics of each asset within the portfolio. Through the application of optimization algorithms, the study seeks to identify the optimal asset allocation that maximizes risk-adjusted returns, taking into account the ESG criteria outlined by the SRI-KEHATI index. The outcomes of this research provide valuable insights into the effectiveness of portfolio optimization techniques within the realm of sustainable investing. By considering both financial metrics and ESG factors, investors can construct portfolios that align with their sustainability objectives while optimizing risk and return. The findings shed light on the performance of the optimized portfolios and compare them with conventional approaches, thereby demonstrating the potential benefits of integrating ESG considerations into portfolio decision-making. Additionally, this study examines the practical implications associated with implementing sustainable portfolio strategies based on the SRI-KEHATI index. Overall, this thesis contributes to the expanding body of knowledge on sustainable investing and portfolio optimization, specifically focusing on the SRI-KEHATI index. It provides valuable insights for investors, asset managers, and policymakers interested in sustainable investment strategies. Furthermore, it offers a framework for incorporating ESG considerations into the portfolio construction process using the Markowitz model, thereby aiding in the development of more robust and sustainable investment portfolios.

Real-Time Portfolio Management System Utilizing Machine Learning Techniques

There are 1641 companies listed on the National Stock Exchange of India. It is undoubtedly infeasible for a retail investor to invest in all the stocks. It is a well-known fact that the portfolio’s return is an average return of all its constituent stocks, and risk will be less than or equal to the maximum risk of all the portfolio components. This paper is unique as it elaborates on the entire portfolio selection, optimization, and management process. Portfolio selection is accomplished through the K-Means algorithm. Optimization is achieved utilizing the genetic algorithm, and a sliding window is applied for portfolio management. Four different ways of portfolio calculation, namely, equally-weighted portfolio, global minimum variance portfolio, market cap-weighted portfolio, and maximum Sharpe ratio portfolio, are applied. The results depict that all three optimized portfolios outperform the Nifty index. The dataset for the study is obtained from globaldatafeeds.in.

Dynamic portfolio optimization with inverse covariance clustering

Market conditions change continuously. However, in portfolio investment strategies, it is hard to account for this intrinsic non-stationarity. In this paper, we propose to address this issue by using the Inverse Covariance Clustering (ICC) method to identify inherent market states and then integrate such states into a dynamic portfolio optimization process. Extensive experiments across three different markets, NASDAQ, FTSE and HS300, over a period of ten years, demonstrate the advantages of our proposed algorithm, termed Inverse Covariance Clustering-Portfolio Optimization (ICC-PO). The core of the ICC-PO methodology concerns the identification and clustering of market states from the analytics of past data and the forecasting of the future market state. It is therefore agnostic to the specific portfolio optimization method of choice. By applying the same portfolio optimization technique on a ICC temporal cluster, instead of the whole train period, we show that one can generate portfolios with substantially higher Sharpe Ratios, which are statistically more robust and resilient with great reductions in the maximum loss in extreme situations. This is shown to be consistent across markets, periods, optimization methods and selection of portfolio assets.

Kako kombinovati srpski indeks akcija sa plemenitim metalima u multivarijantnom Markowitz portfoliu

This paper aims to determine how to combine the Serbian stock index, BELEXline, with four precious metals - gold, silver, platinum and palladium, in order to minimize risk. In the process of portfolio construction, we use the theoretical concept of Markowitz. In particular, we first determine a portfolio of five assets, then exclude an asset with the lowest share and repeat the procedure till we reach a portfolio of two assets. In this way, we construct four portfolios of five, four, three and two assets. In the five-asset portfolio, the portfolio optimization process determines a zero share of silver, because silver bears the highest risk of all other portfolio instruments. This, also, means that five and four-asset portfolios have the same characteristics. On the other hand, in the three-asset portfolio, which contains the Serbian index, gold and platinum, we find a higher share of platinum, compared to the five-asset portfolio, because platinum has a higher negative correlation with BELEXline, vis-à-vis gold-BELEXline pair. Two-asset portfolio, which includes only the index and gold, has a higher risk in the amount of 5% and 4%, in relation to the four and three-asset counterparts. The general conclusion is that a three-asset portfolio is the best one, since it has slightly higher risk than a five or four-asset portfolio, but it has lower transaction cost because it includes only three instruments.

Dynamic Portfolio Optimization with Inverse Covariance Clustering

Market conditions change continuously. However, in portfolio's investment strategies, it is hard to account for this intrinsic non-stationarity. In this paper, we propose to address this issue by using the Inverse Covariance Clustering (ICC) method to identify inherent market states and then integrate such states into a dynamic portfolio optimization process. Extensive experiments across three different markets, NASDAQ, FTSE and HS300, over a period of ten years, demonstrate the advantages of our proposed algorithm, termed Inverse Covariance Clustering-Portfolio Optimization (ICC-PO). The core of the ICC-PO methodology concerns the identification and clustering of market states from the analytics of past data and the forecasting of the future market state. It is therefore agnostic to the specific portfolio optimization method of choice. By applying the same portfolio optimization technique on a ICC temporal cluster, instead of the whole train period, we show that one can generate portfolios with substantially higher Sharpe Ratios, which are statistically more robust and resilient with great reductions in maximum loss in extreme situations. This is shown to be consistent across markets, periods, optimization methods and selection of portfolio assets.

Portfolio allocation under asymmetric dependence in asset returns using local Gaussian correlations

It is well known that there are asymmetric dependence structures between financial returns. This paper describes a portfolio selection method rooted in the classical mean–variance framework that incorporates such asymmetric dependency structures using a nonparametric measure of local dependence, the local Gaussian correlation (LGC). It is shown that the portfolio optimization process for financial returns with asymmetric dependence structures is straightforward using local covariance matrices. The new method is shown to outperform the equally weighted (“1/N”) portfolio and the classical Markowitz portfolio when applied to historical data on six assets.

Maximum Drawdown Distributions: The Cross-Asset Dimension

Potential severe drawdowns are a central concern of investors and pose a risk often inadequately considered in the risk profiling or portfolio optimization process. In this article, conditional expected drawdowns are extended from a multi-asset perspective by introducing the conditional expected cross-maximum drawdown measure. The dimensions of magnitude and time are combined to describe tail risk dynamics across asset classes. Beyond extending the risk analytics toolbox, approaches are introduced to explicitly and computational efficiently incorporate this perspective in the optimization process. This puts investors in the position to significantly improve the tails of the maximum drawdown distribution of their strategic asset allocation. <b>Key Findings</b> ▪ The understanding of maximum drawdown distributions is extended from a multi-asset perspective to address a central concern of investors. ▪ A framework to estimate and analyze the dynamics across asset classes is established by using the introduced risk measure and bootstrapping simulations. ▪ Applications in portfolio optimization highlight the fact that investors can significantly increase resilience and improve the risk-adjusted returns of their strategic asset allocation.

Robust conditional expectation reward–risk performance measures

In this paper, we develop robust portfolio optimization models for conditional expectation type reward–risk performance measures that significantly improve upon conventional portfolio selection techniques. In particular, we directly address estimation error in the portfolio optimization process by adopting a robust optimization method that is typically used with conventional robust statistical estimation techniques. Alongside this robust optimization, we propose the use of an early-warning system based on moving averages to predict market crises. Empirical analyses based on the US stock market validate the proposed robust approaches and highlight the implications of financial crises for portfolio selection problems. The results confirm that the proposed robust portfolio optimization models substantially improve upon their conventional counterparts for out-of-sample portfolios, providing valuable managerial insights.

Black–Litterman and Beyond: The Bayesian Paradigm in Investment Management

The Black–Litterman model is one of the most popular models in quantitative finance, with numerous theoretical and practical achievements. From the standpoint of investment theory, the Black–Litterman model allows seamless incorporation of Bayesian statistics into the portfolio optimization process. From a practical standpoint, it provides portfolio managers with a structured approach to express subjective views, thereby freeing their investment processes from a total reliance on backward-looking historical data. In this article, the authors provide an overview of the original Black–Litterman model and its various extensions and enhancements addressing issues in real-world trading and investment management. <b>TOPICS:</b>Statistical methods, portfolio construction, performance measurement <b>Key Findings</b> ▪ The authors provide an overview of the original Black–Litterman model and its various extensions and enhancements, addressing issues in real-world trading and investment management. ▪ Many important practical considerations in implementing the Black-Litterman model are discussed including choice of priors, view generation, and transaction costs. ▪ Particular emphasis is given to the extensions of the Black-Litterman model of significant practical relevance to today’s investors such as factor models, model misspecification, non-normality, and multiperiod portfolio optimization.

When Ignorance Is Not Bliss: An Empirical Analysis of Subtier Supply Network Structure on Firm Risk

Using a multitier mapping of supply-chain relationships constructed from granular global, firm-to-firm supplier–customer linkages data, we quantify the degree of financial risk propagation from the supply network beyond firms’ direct supply-chain connections and isolate structural network properties serving as significant moderators of risk propagation. We first document a baseline fact: a significant proportion of tier-2 suppliers are shared by tier-1 suppliers. We then construct two simple metrics to capture the degree of tier-2 sharing and disentangle its effect from tier-2 suppliers’ own risks. We show that the focal firms’ risk levels are significantly related to the proportion of shared tier-2 suppliers in their supply network, and the effect becomes monotonically stronger as their tier-2 suppliers become more highly shared. Finally, we uncover causal relationships behind these associations using a new source of exogenous, idiosyncratic risk events in an event study setting. We show that, as tier-2 suppliers are impacted by these events, focal firms experience negative abnormal returns, the magnitude of which is significantly larger when the impacted tier-2 suppliers are more heavily shared. Overall, our study uncovers the subtier network structure as an important risk source for the focal firm, with the degree of tier-2 sharing as the main moderator. Our results also provide the microfoundation for a common structure in idiosyncratic risks and suggest the importance of incorporating the effect of subtier supply network structure in the portfolio-optimization process. This paper was accepted by Vishal Gaur, operations management.

The Rank-Size Rule and Challenges in Diversifying Commercial Real Estate Portfolios

The strategy of geographically diversifying a portfolio of commercial real estate assets is an intuitive approach for risk management. However, due to high concentrations of these assets in major metropolitan areas, investors may face additional constraints in the portfolio optimization process. The rank-size rule, a log-linear relationship between city rank and size, provides one of the greatest empirical regularities in regional science. As such, it serves as a possible theoretical guide to the weights given to properties by location in a commercial real estate portfolio. This paper sets forth some ideas relating to the concentration side of portfolio variance and the limiting effect that large concentrations may have on the ability to diversify risk. Two variants of the rank-size relationship – the Zipf distribution and the parabolic fractal distribution – are fitted to a variety of datasets to provide a sense of the degree of concentration in the commercial real estate industry. These empirical findings suggest the presence of limitations to geographical diversification that have varying degrees of severity across different property types or sectors of the commercial real estate market.

Incorporating environmental and social considerations into the portfolio optimization process

Over the last years, more and more companies face increased pressure by the public to provide information on how they perform on environmental, social and governance (ESG) issues. However, so far a very small number of studies have investigated optimal ways to construct socially responsible portfolios, either in the sense of the screening criteria used to narrow the investment universe, or the optimization process employed to determine the asset proportions. This study covers this gap by introducing an algorithm that first performs a screening to eliminate stocks from the investment universe that do not respect the imposed ESG constraint and then on the ESG compliant universe the portfolio optimization is performed. The novelty of the proposed approach lies in the fact that all underlying functionality of the algorithm, including the screening procedure and the imposed constraints, is facilitated seamlessly through a novel solution representation. Three multiobjective evolutionary algorithms have been adapted to work well with the proposed solution representation and the imposed constraints. The study by utilizing data from the FTSE-100 corporate social responsibility index finds that investors that are concerned about the environmental and social impact of their investments that must be ready to sacrifice a part of their welfare by selecting combinations of assets that provide subordinate return and risk combinations, compared to the available investment opportunities.

Revisiting Fama–French factors' predictability with Bayesian modelling and copula‐based portfolio optimization

AbstractThis study is investigating the predictability of the five Fama–French factors and explores their optimal portfolio allocation for factor investing during 2000–2017. Firstly, we forecast each factor with a pool of linear and nonlinear models. Next, the individual forecasts are combined through dynamic model averaging, and their performance is benchmarked by the best performing individual predictor and other forecast combination techniques. Finally, we use the generalized autoregressive score model and the skewedtcopula method to estimate the correlation of assets. The generalized autoregressive score performance is also compared with other traditional approaches such as dynamic conditional correlation model and asymmetric dynamic conditional correlation. The performance of the constructed portfolios is assessed through traditional metrics and ratios accounting for the conditional value‐at‐risk and the conditional diversification benefits approach. Our results show that combining Bayesian forecast combinations with copulas is leading to significant improvements in the portfolio optimization process, and forecasting covariance accounting for asymmetric dependence between the factors adds diversification benefits to the obtained portfolios.

Neural network copula portfolio optimization for exchange traded funds

This paper attempts to investigate if adopting accurate forecasts from Neural Network (NN) models can lead to statistical and economically significant benefits in portfolio management decisions. In order to achieve that, three NNs, namely the Multi-Layer Perceptron, Recurrent Neural Network and the Psi Sigma Network (PSN), are applied to the task of forecasting the daily returns of three Exchange Traded Funds (ETFs). The statistical and trading performance of the NNs is benchmarked with the traditional Autoregressive Moving Average models. Next, a novel dynamic asymmetric copula model (NNC) is introduced in order to capture the dependence structure across ETF returns. Based on the above, weekly re-balanced portfolios are obtained and compared using the traditional mean–variance and the mean–CVaR portfolio optimization approach. In terms of the results, PSN outperforms all models in statistical and trading terms. Additionally, the asymmetric skewed t copula statistically outperforms symmetric copulas when it comes to modelling ETF returns dependence. The proposed NNC model leads to significant improvements in the portfolio optimization process, while forecasting covariance accounting for asymmetric dependence between the ETFs also improves the performance of obtained portfolios.

Genetic algorithm-based portfolio optimization with higher moments in global stock markets

Markowitz’s mean–variance portfolio model is widely used in the field of investment management. The changing dynamics of markets have resulted in higher uncertainties surrounding returns. Returns have often been found to be skewed and extreme events observed to be frequent. These characteristics are measured by skewness and kurtosis, which need to be accommodated in the definition of risk. They should also be included in the portfolio optimization process. The purpose of this paper is to investigate the impact of including higher moments in the estimation of risk in the process of international portfolio diversification. Our study is based on a sample of thirty-three globally traded stock market indexes, including emerging as well as developed markets, for the period between 2000 and 2012. Our inclusion of skewness and kurtosis makes portfolio optimization a nonlinear, nonconvex and multi-objective problem; this has been solved with the use of a genetic algorithm. Empirical results demonstrate that the higher moments model outperforms the traditional mean–variance model across the time period. The results of this study may be useful to fund managers, portfolio managers and investors, aiding them in understanding the behavior of the stock market and in selecting an optimal portfolio model among various alternative portfolio models.

Value-ranked equity portfolios via entropy pooling

This paper demonstrates how to directly incorporate common value-investing ideas into the portfolio optimization process. Through minimizing the relative entropy, multiple value rankings are merged with the historical return distribution. This approach yields performance improvements from both a diversification and a predictive perspective across various international stock markets. The predictive component can be attributed to a specific value tilt of the portfolios. Increasing the confidence in the value rankings smoothly exposes a portfolio to the desired value factor.

An Application of Transaction Cost in the Portfolio Optimization Process

We propose a transaction cost analysis (TCA) portfolio optimization procedure that incorporates transaction costs directly into the problem of the objective function of portfolio optimization. The results show that a fund achieves considerably higher net returns with TCA optimization than with traditional quadratic programming methods that do not directly consider transactions costs. For a large-cap, 50-stock portfolio, the improvement in net returns was on average +4.5 bp to +8.2 bp and as high as +7.6 bp to +13.5 bp. For a large-cap, 100-stock portfolio, the improvement in net returns was on average +3.2bp to +7.0 bp and as high as +5.0 bp to +10.2 bp. These results show that a manager can start with a seemingly suboptimal or inefficient ex ante portfolio in traditional mean variance space and earn higher ex post net returns after accounting for transaction costs.

Neural Network Copula Portfolio Optimization for Exchange Traded Funds

This paper attempts to investigate if adopting accurate forecasts from Neural Network (NN) models can lead to statistical and economically significant benefits in portfolio management decisions. In order to achieve that, three NNs, namely the Multi-Layer Perceptron (MLP), Recurrent Neural Network (RNN) and the Psi Sigma Network (PSN), are applied to the task of forecasting the daily returns of three Exchange Traded Funds (ETFs). The statistical and trading performance of the NNs is benchmarked with the traditional Auto-Regressive Moving Average (ARMA) models. Next, a novel dynamic asymmetric copula model (NNC) is introduced in order to capture the dependence structure across ETF returns. Based on the above, weekly re-balanced portfolios are obtained and compared by using the traditional mean-variance and the mean-CVaR portfolio optimization approach. In terms of the results, PSN outperforms all models in statistical and trading terms. Additionally, the asymmetric skewed t copula statistically outperforms symmetric copulas when it comes to modelling ETF returns dependence. The proposed NNC model leads to significant improvements in the portfolio optimization process, while forecasting covariance accounting for asymmetric dependence between the ETFs also improves the performance of obtained portfolios.

Portfolio Blender: Blending Qualitative Expectations in Portfolio Optimization

This note presents the Blender, a concept that was developed at Unigestion by the Quantitative Research Hedge Fund Team. In the context of portfolio optimization we propose Blended portfolios as an alternative to efficient portfolios. Albeit Blended portfolios are sub-optimal in the mean-variance sense, they have the property of being less ''extreme'' in the allocations proposed. The Blender approach is also an elegant and simple way to design a portfolio optimization process which amplifies the synergy between qualitative expectations and numerical techniques. The purpose of this note is to explain, technically, the concepts that define the Blender. Although the concepts presented in this note have been implemented in the form of a Matlab class, we do not intend to explain here how to use the class.