Variance Portfolio Research Articles

A Hierarchical Approach to a Tri-Objective Portfolio Optimization Problem Considering an ESG Index

Traditional portfolio construction primarily revolves around a bi-objective approach, focusing on minimizing portfolio variance while maximizing expected returns. However, this approach leaves out other objectives that could interest decision makers. In this work, we incorporate an extra objective, namely the environmental, social, and governance index (ESG), as a secondary objective. This addition empowers investors to customize their portfolios by defining explicit trade-off thresholds between expected returns and risk, considering the ESG index. To achieve this goal, we make use of external archiving techniques and evolutionary algorithms. In particular, we first find approximate solutions to the bi-objective problem; then, we look for efficient solutions for ESG. We tested our approach with data on the Dow Jones, S&P500, and Nasdaq100 from Yahoo Finance. The results show that the proposed methodology can identify portfolios with good returns and risks considering ESG.

The Effects of the Introduction of Volume-Based Liquidity Constraints in Portfolio Optimization with Alternative Investments

Recently, liquidity issues in financial markets and portfolio asset management have attracted much attention among investors and scholars, fuelling a stream of research devoted to exploring the role of liquidity in investment decisions. In this paper, we aim to investigate the effects of introducing liquidity in portfolio optimization problems. For this purpose, first we consider three volume-based liquidity measures proposed in the literature and we build a new one particularly suited to portfolio optimization. Secondly, we formulate an extended version of the Markowitz portfolio selection problem, named mean–variance–liquidity, wherein the goal is to minimize the portfolio variance subject to the usual constraint on the expected portfolio return and an additional constraint on the portfolio liquidity. Thirdly, we consider a sensitivity analysis, with the aim to assess the trade-offs between liquidity and return, on the one hand, and between liquidity and risk, on the other hand. In the second part of the paper, the portfolio optimization framework is applied to a dataset of US ETFs comprising both standard and alternative, often illiquid, investments. The analysis is carried out with all the liquidity measures considered, allowing us to shed light on the relationships among risk, return and liquidity. Finally, we study the effects of the introduction of a Bitcoin ETF, as an asset with an extremely high expected return and risk.

Portofolio Management with Markowitz Model to Determine Optimal Investment Values

Investment is a commitment to a number of funds or other resources made at this time with the aim of obtaining a number of benefits in the future. Investments can be channeled through several instruments, such as deposits, gold, property, stocks, and many more. With the various types of investments that exist today, the difficulty of finding an investment cannot be an obstacle. In investment, the appropriate allocation of funds can be an important factor in obtaining profits. By using the correct method, the risk factors that may occur can be minimized as well as possible. The method that can be used in determining funds in investment activities is using the Markowitz Model. Then, the author initiates a method for optimizing assets using the Markowitz method. In this research, used data from 10 stocks in Indonesia PANI, CLEO, DSSA, UNIC, ADRO, CITA, CAKK, TPIA, MYOR, ANTM. Then, the stocks will be arranged optimally portfolio. The optimal investment weight obtained for stocks from January 1, 2019 to December 31, 2023 using the Markowitz model, each share weighting namely 7,6% PANI, 18,05% CLEO, 8,48% DSSA, 16,902% UNIC, 12,471% ADRO, 10,496% CITA, 7,246% CAKK, 12,946% TPIA, 5,877% MYOR, and 0,464% ANTM company stocks and provide a portfolio ratio of 5.694581 which can also be interpreted that the optimal return ratio profit is 5.694581 times greater than the possible loss or portfolio variance.

To hedge or not to hedge? Cryptocurrencies, gold and oil against stock market risk

The article aims to determine whether any hedging strategy against stock market risk, performed using instruments popular in the literature (gold, cryptocurrencies and oil), can beat index futures. As a hedging strategy, we understand a pair-wise portfolio consisting of a long position in stocks and a short position in a hedging instrument put together to minimise the portfolio variance. As a benchmark, we analyse optimal and naive hedging strategies with futures contracts. We demonstrate that, regardless of the stock market, the best hedging strategy focused on variance minimisation requires using index futures. Both strategies: the optimisation-based one and the naive one, beat the dynamic strategies utilising the remaining hedging assets. Therefore, from a risk-minimisation point of view, investors have no motivation to implement cryptocurrencies, gold or oil in hedging strategy against stock market risk. The results are robust with respect to hedging against tail risk.

Partial index tracking enhanced mean–variance portfolio

AbstractEstimation constitutes a major challenge in the implementation of mean–variance portfolios. To overcome this, we propose a partial index‐tracking strategy that aims to mitigate estimation error ex‐ante. Theoretically, we minimize the mean‐squared error of the proposed strategy by shrinking the portfolio variance to its tracking error. Using an empirical design with over 50 years of data, our paper makes two important observations. First, we show that our proposed approach is consistent with both linear and non‐linear shrinkage strategies in terms of robustness. Second, the proposed decision rule leads to a lower out‐of‐sample tracking error. Our findings, overall, stress the appeal of partial index tracking not only in terms of shrinkage (robustness) but also in terms of relative performance.

Reinforcement learning in individual pension system: the case of Turkey

Purpose- How individuals make saving/investment decisions and they are subject to learning processes are important questions in economics. Behavioral economics and finance literature tell us that individuals can deviate from bayesian decisions and the personal experiences can be effective in decision making. “Reinforcement learning” provides a framework for individual investors who are weighing on strategies successful and avoid strategies unsuccessful in which they experience. In this study, we investigate the effect of past experiences on individuals' retirement savings/investment decisions and whether individual investors are reinforcement learner. For this purpose, we examine individual contracts in the annual micro panel dataset obtained from the Pension Monitoring Center in Individual Pension System in Turkey. Methodology- Essentially, we assume that individuals' retirement saving/investment decisions are influenced by returns and variances (represents the risk level) of their avaliable portfolio as well as their time horizon, spending habits, retirement goals, risk tolerance and demographic characteristics. In this context, we estimate a linear model by including returns and variances in order to investigate how much sensitive individual investors are to returns and variances of their portfolio. Moreover, we add lagged returns and variances to our econometric setup to examine whether they are reinforcement learner. After that, we conduct a before-after analysis by looking at the dataset from 3-year window to analyze the impact of the 2013 state subsidy reform on reinforcement learning of individual investors. Findings- Similar to individuals' age, gender and education level, portfolio returns and variances also have a statistically significant effect on the contributions paid. Increases in portfolio returns affect the contributions paid positively, while increases in portfolio variance affect it negatively. As an indicator of reinforcement learning, respectively, lagged returns and variances have a significant positive and negative effect like the same year returns and variances of individual investors. According to this result, individual investors weigh on successful strategies and avoid unsuccessful strategies they have experienced. Increases in variances and lagged variances of individuals' portfolios have a larger negative effect compared to returns. Additionally, looking at the 3-year window, we report that the reinforcement learning of individual investors has strengthened after the 2013 state subsidy reform. Conclusion- We show that individual investors in IPS in Turkey exhibit reinforcement learning when making retirement savings/investment decisions. High return or low variance obtained in previous periods causes individuals to pay more contributions paid in the next period. This result reveals that individuals benefit from their past experiences when making logical and optimized decisions based on their avaliable knowledge and expectations. The 25% state subsidy in 2013 caused individual portfolio returns to increase and variances to decrease. With these effects, we report that reinforcement learning has become stronger after 2013. Keywords: Reinforcement learning, decision-making, pension savings, personal finance, retirement policies JEL Codes: D80, D70, H3, D14, J26

Is gold a safe haven for the U.S. dollar during extreme conditions?

This paper examines whether gold can act as a hedge/safe-haven asset for the U.S. dollar exchange rate risk against a broad range of currencies. Findings imply the important exchange rate hedging role of gold. Moreover, gold acts as a safe-haven asset during the COVID-19 pandemic and the Russia-Ukraine war for some exchange rate pairs examined. Analysis of gold-currency portfolios reveals that including an optimized amount of gold reduces portfolio variance during the COVID period but produces mixed findings during the war. These findings are robust against additional tests accounting for different holding periods for gold and asymmetries in the relationship between gold and exchange rate returns. Our results offer important implications for international investors and policymakers concerned with the U.S. dollar's exchange rate risk.

Gold, crude oil, and cryptocurrencies versus stock index futures: An analysis of hedging strategies in global stock markets

The study aims to verify the hedging ability of gold, cryptocurrencies, and crude oil to serve as hedging instruments against stock market risk. We compare the hedging effectiveness of these popular assets with stock index futures contracts. As a hedging strategy, we understand a pair-wise portfolio consisting of a long position in stocks and a short position in a hedging instrument put together to minimize the portfolio variance. We conclude that hedging strategies using stock index futures contracts provide an efficient hedging mechanism for investors aiming to protect their stock portfolios. Unlike stock index futures contracts, the effectiveness of hedging with gold, crude oil, and cryptocurrencies is low in most sub-periods. Hence, from a risk minimization perspective, investors have no incentive to implement gold, cryptocurrencies, or crude oil in hedging strategy against stock market risk.

Modelization and Calibration of the Power-Law Distribution in Stock Market by Maximization of Varma Entropy

Proper description of the return distribution is crucial for investment practitioners. The underestimation of the tail risk may lead to severe consequences, even for assets with moderate fluctuations. However, many empirical studies found that the distribution tails of many financial assets drop off more slowly than the Gaussian distributions. Therefore, we intend to model and calibrate the heavy tails observed in financial fluctuations in this study. By maximizing the Varma entropy with value-at-risk and expected shortfall constraints, we obtain the probability distribution of stock return and observe that the tail of stock return distribution is a power law. Since the variance of the real stock portfolio may be a random variable, using the mean-VaR-ES constraints to maximize the Varma entropy effectively avoids the problem of assuming that the variance is a constant value under the traditional mean-variance constraint. Therefore, the deduced theoretical model would be more consistent with the real market. Using high-frequency data from China’s stock markets, we calibrate our theoretical model and give the concrete form of probability density distribution p(x) for different time intervals. The calibration results show that the tail of the stock return distribution is a power law with most of the power-law orders between −2 and −7. We prove the robustness of our results by calibrating the Varma entropy for S&P 500 of the USA stock market and different stock market indices in China’s A-share market. Our research’s findings not only offer a theoretical perspective for researchers but also give investing professionals a theoretical foundation on which to base their decisions.

Forecasting portfolio variance: a new decomposition approach

Forecasting portfolio variance: a new decomposition approach

Economic evaluation of dynamic hedging strategies using high-frequency data

This paper assesses the value of volatility timing when high-frequency data are available for measuring the realized hedged portfolio variance. We derive an analytical solution to estimate the performance fee for switching from static to dynamic generalized autoregressive conditional heteroskedasticity (GARCH) strategies. We find that the benefits depend on the realized hedged portfolio variances and the risk aversion level of the hedger. We use data from US equity indices to demonstrate that the switching can benefit hedgers, even after the transaction costs are accounted for. Hedgers with higher levels of risk aversion can benefit more from implementing the volatility-timing strategy.

APPLICATION OF THE MARKOWITZ MODEL AND INDEXMODEL IN REAL STOCK MARKETS

The complete Markowitz Model and the Index Model have a wide range of applications for portfolios in the stockmarket, and in this paper, we want to apply these two models in a realistic stock market. In this paper, ten stocksbelonging to different industries and the S&P 500 equity index are selected as a portfolio, and the 1-month Fed Fundsrate is chosen as the risk-free rate. Through proper data aggregation and processing, we calculate the weights ofeach stock in the portfolio in the case of minimal portfolio variance and maximal Sharpe ratio under five additionalconstraints using the complete Markowitz Model and the Index Model, respectively. Finally, we can calculate theminimal variance frontier, efficient frontier, inefficient frontier, and capital allocation line under each constraint, plottedusing the Solver Table in Excel

Optimal futures hedging by using realized semicovariances: The information contained in signed high‐frequency returns

AbstractThis paper proposes a realized semicovariance‐based generalized autoregressive conditional heteroskedasticity (GARCH) model for optimal futures hedging in which realized semicovariances are computed from signed high‐frequency returns. The model enables flexible, continuous leverage for equity indices and exhibits stronger responses to jointly negative return shocks than do traditional threshold‐based asymmetric GARCH models. Our results indicate that the proposed model outperforms simpler models in model fit, covariance prediction, and portfolio variance reduction and can help achieve pronounced economic gains for hedgers. The findings demonstrate that signed high‐frequency returns contain valuable information for explaining covariance asymmetries and provide managerial implications for market participants to improve risk management.

Semi-Metric Portfolio Optimization: A New Algorithm Reducing Simultaneous Asset Shocks

This paper proposes a new method for financial portfolio optimization based on reducing simultaneous asset shocks across a collection of assets. This may be understood as an alternative approach to risk reduction in a portfolio based on a new mathematical quantity. First, we apply recently introduced semi-metrics between finite sets to determine the distance between time series’ structural breaks. Then, we build on the classical portfolio optimization theory of Markowitz and use this distance between asset structural breaks for our penalty function, rather than portfolio variance. Our experiments are promising: on synthetic data, we show that our proposed method does indeed diversify among time series with highly similar structural breaks and enjoys advantages over existing metrics between sets. On real data, experiments illustrate that our proposed optimization method performs well relative to nine other commonly used options, producing the second-highest returns, the lowest volatility, and second-lowest drawdown. The main implication for this method in portfolio management is reducing simultaneous asset shocks and potentially sharp associated drawdowns during periods of highly similar structural breaks, such as a market crisis. Our method adds to a considerable literature of portfolio optimization techniques in econometrics and could complement these via portfolio averaging.

Filtering time-dependent covariance matrices using time-independent eigenvalues

We propose a data-driven, model-free, way to reduce the noise of covariance matrices of time-varying systems. If the true covariance matrix is time-invariant, non-linear shrinkage of the eigenvalues is known to yield the optimal estimator for large matrices. Such a method outputs eigenvalues that are highly dependent on the inputs, as common sense suggests. When the covariance matrix is time-dependent, we show that it is generally better to use the set of eigenvalues that encode the average influence of the future on present eigenvalues resulting in a set of time-independent average eigenvalues. This situation is widespread in nature, one example being financial markets, where non-linear shrinkage remains the gold-standard filtering method. Our approach outperforms non-linear shrinkage both for the Frobenius norm distance, which is the typical loss function used for covariance filtering and for financial portfolio variance minimization, which makes our method generically relevant to many problems of multivariate inference. Further analysis of financial data suggests that the expected overlap between past eigenvectors and future ones is systematically overestimated by methods designed for constant covariances matrices. Our method takes a simple empirical average of the eigenvector overlap matrix, which is enough to outperform non-linear shrinkage.

Mean-variance portfolio selection with random investment horizon

<p style='text-indent:20px;'>This paper studies a continuous-time securities market where an agent, having a random investment horizon and a targeted terminal mean return, seeks to minimize the variance of a portfolio's return. Two situations are discussed, namely a deterministic time-varying density process and a stochastic density process. In contrast to [<xref ref-type="bibr" rid="b18">18</xref>], the variance of an investment portfolio is no longer minimal when all assets are invested in a risk-free security. Furthermore, the random investment horizon has a material effect on the efficient frontier. This provides some insights into the classical mutual fund theorem.</p>

Analisis Non-Hierarchical Clustering dan Lagrangean Multiplier dalam Penentuan Bobot Portofolio Optimal Saham Perbankan Indonesia

Investment banking is a financial entity. Investment banking is an important financial intermediary that is indispensable in the capital market. The increasing interest of investors in investing in the stock market has increased because the stock market offers flexible and transparent money options opportunities for risk sharing with the potential for positive returns. Every investor wants a high rate of return with a low risk value. Risk cannot be eliminated, but can be minimized. Clustering means finding and defining a number of clusters (or groups) in a data set. Grouping is done based on numerical equations or distances (dissimilarities). The k-means algorithm is a grouping algorithm based on distance. In the k-means algorithm, the smaller the distance between the samples, the higher the similarity. The k-medoids algorithm is used to find medoids in a cluster which is the center point of the cluster. The return value or commonly known as the return on the funds invested in the investment. Portfolio is a collection of several investment instruments formed with the aim of meeting investment goals. obtained 5 clusters using k-means algorithm with total of wss 23,606. The optimal portfolio weight percentage for each stock formed is BMAS (9.11%%), BANK (32.78%), ARTO (28.84%), BBYB (16.72%), and BBHI (12.54%). Furthermore, from the results of the optimization calculations that have been obtained,the expected return portfolio value is and the portfolio variance is . Investing Rp.1.000.000.000,-, then the expected return value that will be obtained when choosing this portfolio is Rp.11.094.300,-.

MEAN-VARIANCE INVESTMENT PORTFOLIO OPTIMIZATION MODEL WITHOUT RISK-FREE ASSETS IN JII70 SHARE

In investing, investors will try to limit all the risks in managing their investments. Investor strategies to minimize investment risk are diversification by forming investment portfolios, one of which is the Mean-Variance without risk-free assets. The calculation results will show the composition of the optimum portfolio return for each stock that forms the portfolio. Optimum portfolio obtained with wT = (0.39853, 0.25519, 0.13644, 0.09788, 0.11196) sequential weight composition for TLKM, KLBF, INCO, HRUM, and FILM stocks. The composition of this optimal portfolio return is ???? 0.04 with a return of 0.00209 and a portfolio variance of 0.00015. The formation of this portfolio optimization model is expected to be additional literature in optimizing the investment portfolio with the Mean-Variance.

Coherent Diversification Measures in Portfolio Theory: An Axiomatic Foundation

We provide an axiomatic foundation for the measurement of correlation diversification in a one-period portfolio model. We propose a set of eight desirable axioms for this class of diversification measures. We name the measures satisfying these axioms coherent correlation diversification measures. We study the compatibility of our axioms with rank-dependent expected utility theory. We also test them against the two most frequently used methods for measuring correlation diversification in portfolio theory: portfolio variance and the diversification ratio. Lastly, we provide an example of a functional representation of a coherent correlation diversification measure.

Mean-Variance Investment Portfolio Optimization Model Without Risk-Free Assets in Jii70 Share

In investing, investors will try to limit all the risks in managing their investments. Investor strategies to minimize investment risk are diversification by forming investment portfolios, one of which is the Mean-Variance without risk-free assets. The calculation results will show the composition of the optimum portfolio return for each stock that forms the portfolio. Optimum portfolio obtained with wT = (0.39853, 0.25519, 0.13644, 0.09788, 0.11196) sequential weight composition for TLKM, KLBF, INCO, HRUM, and FILM stocks. The composition of this optimal portfolio return is 𝜏 0.04 with a return of 0.00209 and a portfolio variance of 0.00015. The formation of this portfolio optimization model is expected to be additional literature in optimizing the investment portfolio with the Mean-Variance.