Markowitz's Modern Portfolio Theory Research Articles

Portfolio optimization in the stock market under disruptions: Real case studies of COVID-19 pandemic and currency risk

The connection between risk and return is a critical concept in finance. Investors who take on more risk can earn higher returns. Disruptions are part of market risks, also known as systematic risks. Due to political and macroeconomic risks, their effects on the entire economic market, or a significant portion of its sectors, are not negligible. Among these sectors, the stock market is essential as a basis of the economy. The point is that the consequences of all disruptions are not merely unpleasant for companies. They may affect corporate profitability both negatively and positively. Hence, investors who trace companies' news and fundamental conditions react, and the closing price probably encounters volatility. Therefore, the common trend of several stocks may fluctuate. This research investigates how investors in the stock market should form their investment portfolio to see the minor losses when disruptions occur and take advantage of the potential provided profitability by turning threats into opportunities. A three-step framework is presented to achieve this goal. A prerequisite for this framework is the collection of relevant data. Ten stocks from distinct industries of the Securities and Exchange Organization of Iran are chosen for the examination. In the first step, multi-variate regression analysis categorizes selected stocks into the most and the least affected groups. At the same time, a comprehensive technical analysis is involved in this step. Then, in the second step, three well-known machine learning techniques, namely, stacked long short-term memory (Stacked LSTM), autoregressive integrated moving average (ARIMA), and Prophet, are compared from the point of view of predicting future closed prices of selected stocks. The method with the most minor statistical error in forecasting, i.e., root mean squared error (RMSE) and validation loss, estimates the next month's closed prices. Finally, based on the predicted closed prices, the third step empowers the investor to optimize their portfolio in different scenarios, containing various investment weights on the two obtained groups of the first step, using the Markowitz Modern Portfolio Theory. The COVID-19 pandemic and currency risk are the two examined real case studies to validate the proposed methodology. Numerical results based on the Sharp Ratio show the superiority of investing 75 percent of an asset in the most affected stocks and the rest in the least affected stocks in the case of a pandemic and vice versa for the case of currency risk, which reveals that according to the unique features of disruptions investors can benefit from both categories of stocks.

Propose an Optimum Stocks Portfolio Using Markowitz Modern Portfolio Theory in Educational Endowment Fund Management (Case Study of XYZ Institution)

XYZ institution is a Public Service Agency in Educational Sector, focused on giving the scholarship in master and doctoral programs level domestically and abroad, also in many affiliated researchers funding programs. The effect of granting scholarships and research funding produces an extraordinary output for the country. It was successfully increased the quality level of education in Indonesian society, also with the Indonesian Human Development Index. With a great accumulated amount of asset under management in fiscal year 2023, XYZ institution have a really big opportunity to maximize the investment return and give all Indonesia’s citizens an equal chance of pursuing the higher education. Markowitz Modern Portfolio Theory (MPT) is utilized to construct an optimal stocks portfolio for XYZ institution. The proposed stocks portfolio seeks to find a combination between high-growth stocks that have the potential to increase in value and stable dividend-paying stocks that provide income stability. The goal is to maximize the overall investment portfolio returns while taking its risk tolerance and investing objectives into consideration. Diversification was done by investing in a diverse range of companies across sectors and asset classes, reducing exposure to single asset risk. The proposed optimum investment portfolio provides XYZ institution a diversified allocation of assets, consisting of a portion in Time Deposits at 36,68%, Government Bonds at 34,10%, Corporate Bonds at 27,21%, and Stocks at 2%, which is constructed in a form of Aggressive Strategy, Moderate Strategy, and Defensive Strategy. The stocks selection resulting the best five stocks composition in Moderate Strategy which consist of BBNI at 20,17%, BJBR at 19,54%, PTBA at 20,15%, ADRO at 19,67%, and INDF at 20,47%, projected could give a return contribution at 6,60% with the lowest given risk of 26,83% from the stocks portfolio and could generate a 7,15% to the overall investment portfolio return.

Analysis of Life Extension Performance Metrics for Optimal Management of Offshore Wind Assets

Abstract The main objective of this study is to develop an optimal life extension management strategy for ageing offshore wind farms. Finding the appropriate performance metric for an operation is essential for a durable, reliable, and profitable offshore wind farm operation. To this end, the key metrics to evaluate the life extension performance of an offshore wind farm are investigated. The mean value and the standard deviation of each performance metric are calculated using a probabilistic techno-economic assessment framework for a single offshore wind asset, which is later extended to evaluate the whole offshore wind farm by the multi-asset portfolio optimization. In this regard, the Markowitz modern portfolio theory is applied to estimate a risk-adjusted return parameter, the Sharpe ratio of the overall portfolio of offshore wind assets. Later on, the key performance metrics are compared to identify the most suitable metrics at different stages of life extension, and a further discussion is given for different offshore wind farm sizes. Moreover, the optimal management strategy, which maximizes the Sharpe ratio of the overall offshore wind farm, is analyzed using one of the key performance metrics under optimistic, moderate, and pessimistic scenarios. Finally, the optimal allocation (portfolio) of offshore wind assets attained based on the mean-variance optimization is presented for the different stages of the life extension of the offshore wind farms accounting for the uncertainty propagation during the life extension.

Fast Quadratic Programming for Mean-Variance Portfolio Optimization

In this paper, a vectorized quadratic convex optimization algorithm based on Matlab's quadprog built-in function is proposed. We target specifically a classic problem confronted by portfolio analysts, that of optimizing asset allocation when choosing among several asset classes, in the context of Markowitz's modern portfolio theory. Simulating return trajectories for several asset classes, we formulate the optimization routine in such a way that is able to handle multiple scenarios at the same time, instead of on a one-by-one basis, reducing computational times significantly, without introducing observable estimation errors. A sensitivity analysis is offered with respect to the optimal batch size.

A Study on Factors Influencing Mutual Fund Portfolio Performance

Mutual fund portfolio managers do not always meet performance expectations, resulting in loss of capital reserves. Out of 3,612 U.S. based open-ended mutual funds, the risk-adjusted performance of 2,890 (80%) failed to meet the S&P 500 performance between the year 2006 to 2016. Grounded in Markowitz's modern portfolio theory, this correlational study examined the relationship between mutual fund class type, portfolio turnover, fund longevity, management turnover, and annual fund risk-adjusted performance. Archival data were collected from 88 U.S. based equity mutual funds companies. The results of the multiple regression analysis indicated the model as a whole was able to significantly predict annual fund risk-adjusted performance for the 5-year period ending 2016, F (4, 83) = 3.581, p = .010, R2 = .147. In the final model, mutual fund class type and portfolio turnover were statistically significant with mutual fund class type (ß= .249, t = 2.302, p = .024) accounting for a higher contribution to the model than portfolio turnover (ß = .238, t = 2.312, p = .023).

A polynomial goal programming model for portfolio optimization based on entropy and higher moments

Portfolio selection is a critical factor in investment. Having considered a number of risky assets, fund managers must choose the optimum portfolio. Stock values can be affected by different types of events such as governmental crises, economic turmoil and industrial improvements. Due to the vague nature of these events, it is difficult to estimate the future value of stocks. However, Markowitz's Modern portfolio theory, which is principally focused on portfolio risk, has introduced a novel model for stock diversification. According to this approach, an investor can decrease portfolio risk basically by holding mixtures of assets that are not highly positively correlated. Meanwhile, an efficient portfolio can only be obtained by focusing on return and risk simultaneously. When the normality assumption of return series of assets are not valid, higher moments can also be added to ensure the efficiency of the Markowitz model. In this study, a new approach for polynomial goal programming which is based on a mean-variance-skewness-kurtosis-entropy model is proposed. Two real data sets were used in experiments to verify the effectiveness of the proposed model. Based on a variety of portfolio optimization model, the out-of-sample performance of two entropy measures- Shannon entropy and Gini-Simpson entropy- were compared in the portfolio selection. The results indicate that the proposed approach is well-suited especially for portfolio models with higher moments.

Investment Risk and Returns: The Relationship between a Stock and an Index Using the Modern Portfolio Theory

The aim of this report is to examine investment risk and returns by looking at the relationship between a stock and an index using the Markowitz Modern Portfolio theory. Monthly Data on IBM and Dow Jones were obtained from yahoo finance for the period 1995 to 2015. A linear regression was utilized to analyze the relationship between the Dow Jones index and the IBM stock returns. The results revealed that there is a positive relationship between IBM stock returns and the Dow Jones index. In their decision making, investors and policy makers are, recommended to additionally consider the micro and macro demand and supply forces that could possibly influence ROI in other to avoid or reduce risk.

Bidding strategy for agents in multi-attribute combinatorial double auction

In a multi-attribute combinatorial double auction (MACDA), sellers and buyers’ preferences over multiple synergetic goods are best satisfied. In recent studies in MACDA, it is typically assumed that bidders must know the desired combination (and quantity) of items and the bundle price. They do not address a package combination which is the most desirable to a bidder. This study presents a new packaging model called multi-attribute combinatorial bidding (MACBID) strategy and it is used for an agent in either sellers or buyers side of MACDA. To find the combination (and quantities) of the items and the total price which best satisfy the bidder’s need, the model considers bidder’s personality, multi-unit trading item set, and preferences as well as market situation. The proposed strategy is an extension to Markowitz Modern Portfolio Theory (MPT) and Five Factor Model (FFM) of Personality. We use mkNN learning algorithm and Multi-Attribute Utility Theory (MAUT) to devise a personality-based multi-attribute combinatorial bid. A test-bed (MACDATS) is developed for evaluating MACBID. This test suite provides algorithms for generating stereotypical artificial market data as well as personality, preferences and item sets of bidders. Simulation results show that the success probability of the MACBID’s proposed bundle for selling and buying item sets are on average 50% higher and error in valuation of package attributes is 5% lower than other strategies.

Analysis of the Effects of Diversification for Dar Es Salaam Stock Exchange Optimal Portfolio

Dar es Salaam stock exchange (DSE) market is among the stock markets dealing with financial securities transactions and it operates under the brokerage system. Different individuals have little knowledge on how these stock markets operate and many of them fear to invest in stock business because they don’t have the base line of their decision especially on the risk bearings. This paper is based solely on DSE stocks data for the period of past nine years and it tries to give out the nature of return of the stocks, the effects on restrictions at the DSE stock environment to the stock returns and also it explores the effect of diversification on return and on risk (standard deviation). The study uses the classical Markowitz Modern Portfolio Theory (MPT) model in its analysis with little modification so as to meet with the DSE environment. Data from DSE was analysed by using the excel solver and its macros like the solver add – in. After the analysis it is observed that restrictions have an effect on the stock risk and return, where it reduce risk and increases return because the unconstrained frontier is greater than the constrained frontier. Moreover it is found that for the diversification to have a significant effect the stocks have to be nearly or perfectly negatively correlated.

Portfolio Optimization Problems in Different Input Data using Particle Swarm Optimization

optimization and diversification as a tool for development and understanding of financial markets have been entered in financial management topics for guide investors to make appropriate decision. Markowitz's modern portfolio theory (MPT) has been the most successful achievement in this field. Since, stock has a non-linear behavior in stock market; the need to non-linear models in order to identify the behavior of stock in relation to portfolio's optimum selection should be felt. Because of successful performance of evolutionary algorithms, these algorithms can provide suitable methods for investors. In this paper, particle swarm optimization (PSO) algorithm employed to select optimum portfolio. Proposed approach was tested on monthly and yearly data set of fifty top companies accepted in Tehran Stocks Exchange which were collected from March 2007 to September 2011. PSO performance compared with genetic algorithm (GA) and artificial bee colony algorithm (ABC) in term of Sharp ratio. The computational results show that the PSO algorithm impressively outperforms GA and ABC, and monthly data is better criterion than yearly data in portfolio selection.

Examining fuzzy tactical asset allocation (FTAA) as an alternative to modern portfolio theory (MPT) asset allocation for international and direct real estate investment

PurposeAlthough the modern portfolio theory (MPT) asset allocation framework can be adopted to enable decision making for international and direct real estate investing, and that many institutional investors adopt it to support their decision making, this framework can be enhanced to capture the multi‐causal factors influencing international and direct real estate investing. The purpose of this paper is to explain how a fuzzy decision‐making approach is a more intuitive, yet rigorous alternative in this regard.Design/methodology/approachThis paper is concerned with the model formation and estimation of a unique fuzzy tactical asset allocation (FTAA), which in turn comprises the FTAA flexible programming model and the FTAA robust programming model.FindingsBoth these FTAA models enhance the classical, Markowitz MPT portfolio theory on asset allocation through making it more intuitively appropriate for decision making in international and direct real estate investing.Practical implicationsThese two FTAA models achieve the benefits of intuitively greater risk diversification by city or real estate sector and enable effective risk management. These two short‐run fuzzy models would be accepted and more such models would emerge as an effective extension of quadratic programming optimization, as more computable software programs of this kind are widespread.Originality/valueFuzzy approaches to asset allocation in the short run, are limited by some drawbacks. Fuzzy models possess the common feature of converting the equality function under quadratic programming optimization into inequality functions. Such inequality optimization replaces the point solution of the MPT TAA optimization problem, obtained through the rigid intersection of all functions, via a generalized or intuitive answer over a defined space of alternatives. The product of the fuzzy process with fuzzy inputs, in the form of fuzzy outcome is in actual fact a more natural and intuitive approach to asset optimization.

Arbitrage pricing theory-based Gaussian temporal factor analysis for adaptive portfolio management

Ever since the inception of Markowitz's modern portfolio theory, static portfolio optimization techniques were gradually phased out by dynamic portfolio management due to the growth of popularity in automated trading. In view of the intensive computational needs, it is common to use machine learning approaches on Sharpe ratio maximization for implementing dynamic portfolio optimization. In the literature, return-based approaches which directly used security prices or returns to control portfolio weights were often used. Inspired by the arbitrage pricing theory (APT), some other efforts concentrate on indirect modelling using hidden factors. On the other hand, with regard to the proper risk measure in the Sharpe ratio, downside risk was considered a better substitute for variance. In this paper, we investigate how the Gaussian temporal factor analysis (TFA) technique can be used for portfolio optimization. Since TFA is based on the classical APT model and has the benefit of removing rotation indeterminacy via temporal modelling, using TFA for portfolio management allows portfolio weights to be indirectly controlled by several hidden factors. Moreover, we extend the approach to some other variants tailored for investors according to their investment objectives and degree of risk tolerance.

Modern Portfolio Theory and the prudent hermaphrodite

Summary Employment of Markowitz's Modern Portfolio Theory, economic models designed to predict the effect of variance and covariance on optimal investment allocation, may explain a wide variety of anomalies in reproductive biology. Natural selection appears to favor genetic diversity among offspring to a greater extent than is predicted by current theory. Consideration of the possible increase in fitness by reducing the covariance among offspring may help explain a variety of phenomena from multiple mating to the evolution of recombination (i.e., overcoming “the cost of meiosis”). Modern Portfolio Theory also make novel predictions as to when hermaphrodites should prefer the male vs. female role, i.e., engage in egg- vs. sperm-trading. It predicts that the sexual role with the lower variance in reproductive success will be preferred in hermaphrodites. This contradicts Bateman's principle that the male role is usually preferred due to energetic considerations but is consistent with Gillespie's principle. The available data suggest that mating hermaphrodites are risk-averse; gamete-trading whether of eggs or sperm is a strategy to reduce risk. In addition to overall variance, the skew of the distribution can be used to predict the mating systems of hermaphrodites and thus clarify the factors that are responsible for observed patterns of sex allocation and sexual conflict. The reduction of covariance among offspring may also help resolve “Williams' paradox”; that the observed distribution of dieoecy vs. simultaneous hermaphroditism in the Animal Kingdom cannot be explained by the prevailing models of the evolution of hermaphroditism.