Markowitz Efficient Frontier Research Articles

Построение границы Марковица методом кусочно-нелинейной аппроксимации

В работе изложен подход к осуществлению аппроксимации границы допустимого множества портфелей в координатах (доходность, СКО). Авторы показали, что гиперболический вид границы Марковица строго соблюдается лишь для областей, удаленных от оси симметрии гиперболы. Авторы представили вывод функциональной зависимости СКО от доходности портфеля в явном виде. Так как область кривой вблизи оси симметрии может быть описана гиперболой только при нарастании погрешности, предложено на этом участке аппроксимировать ее кубической параболой. Таким образом, реализуется подход к оценке границы Марковица посредством построения кусочно-нелинейной функции.

An Application of Portfolio Theory and the Efficient Frontier Concept to the Risk-Return Decisions of Beothuk Hunter-Fisher-Gatherers

This paper proposes the use of the Markowitz efficient frontier from academic finance as a way of understanding the resource choices of indigenous Beothuk hunter-fisher-gatherers in eighteenth-century Newfoundland.

An Introduction to Resampled Efficiency

Resampled Efficiency provides the solution to using uncertain information in portfolio optimization. The proper purpose of investment advice is to improve a client’s portfolio in terms of maximizing return for an appropriate level of risk. Asset management techniques for optimizing the investment value of forecasts of return and risk have been available for fifty years. Markowitz provides the classic definition of optimality: a portfolio is risk-return efficient if no other portfolio has higher expected return for a given level of risk or less risk for a given level of expected return. The set of all portfolios that are risk-return efficient are said to form the Markowitz efficient frontier. Markowitz also developed mathematical methods for solving the risk-return optimization problem.

Markowitz efficiency and size effect: evidence from the UK stock market

Academics and practitioners have frequently debated the relationship between market capitalization and expected return. We apply the Markowitz efficient frontier approach to develop a portfolio performance measure that compares the return of a portfolio to its optimal return, using data from the UK stock market over the period 1985–2012. Our results show that there is a negative relationship between portfolio size and portfolio return during the period under study. When comparing actual portfolio return with achievable return for the same level of risk, we find that as the portfolio size expands, underperformance of the portfolio increases, i.e. the larger the portfolio size, the greater the underperformance. This indicates that Markowitz efficiency is difficult to achieve, particularly in large portfolios. Changing model parameters leads to alternative efficient frontiers that impact upon the measurement of performance. However, the use of alternative efficient frontiers does not affect our result of the size effect on the relative performance of portfolios. Our study shows that the size effect is present over the full period. Our findings also suggest that the excess returns found in small portfolios are likely to be associated with higher levels of diversifiable risk in comparison with larger portfolios. Furthermore, in contrast to other studies, we find no evidence to support the size reversal effect in the data.

Diversification in Portfolio Risk Management:The Case of the UAE Financial Market

The paper looks at the existence of portfolio risk management for the UAE Financial Market. The research methodology centers on applying Modern Portfolio Theory, with particular emphasis on the Markowitz Efficient Frontier, Minimum Variance Analysis, and Portfolio Optimization. The data is essentially based on the top performing sectors of the UAE economy, and twenty key companies are chosen from each sector to test for diversification. Key findings suggest that the risk of the portfolio is lower than the weighted risk of the twenty individual stocks, i.e. efficient diversification can be achieved.

Government intervention in Russian bourse: a case of financial contagion

PurposeIn September‐October 2008 the Russian stock markets came under severe strain amidst the global financial crisis. During this time the Russian government intervened several times to halt the trade to impede the continuous slide. The government justified its actions owing to the argument that the crisis was due to a trickledown effect from the financial crisis in the USA and the other developed markets. The purpose of this paper is to put to test the government's claim by exploring the level of integration between Russia and the USA and European equity markets.Design/methodology/approachThe study employs Markov Regime Switching Model for tracking structural breaks in the time series. This method divides the data into three periods, i.e. pre crisis, during crisis and post crisis. Next the Multivariate GARCH‐DCC model technique is used to establish the time varying linkages in order to verify the contagion effect. In the final step the Markowitz mean‐variance framework is used to position each individual index portfolio with respect to the efficient frontier to analyze the impact of crisis as well as Russian government intervention.FindingsThe findings suggest that the Russian equity market is weakly integrated with US and strongly integrated with European markets. The results correspond to the underlying financial and economic linkages between Russia, the US and Europe. When examined in a portfolio setup, the results show sudden fall in correlation among the Russian, US and European equity markets suggesting weak linkages among these markets. Finally, the Markowitz Efficient frontier indicates dramatic rise in volatility on the day intervention began and ended which signifies the increased uncertainty among the investors owing to Russian government ad hoc interventions.Originality/valueThe paper attempts to examine the Russian government intervention in the backdrop of financial crisis 2008 and concludes that the government intervention essentially increased the uncertainty in the local as well as international markets. Therefore, it is essential that the government should avoid direct intervention in its stock market.

Portfolio management with semi-parametric bootstrapping

Estimation risk is an important topic within the area of risk management. Uncertainties regarding parameter estimates carry on to the final statistical product, such as investment strategies, and need to be estimated and accounted for. Unless the exact expressions for the estimators’ variances are known, the product’s variability will be assessed through bootstrap techniques. The present paper addresses this issue, proposing a semi-parametric bootstrap method for reproducing the data, a method which parametrically takes care of all marginal characteristics of the returns data, and also takes care of the dependence structure existing in the data, in a very simple and clever non-parametric way. The technique is applied to the problem of assessing the variability of the Markowitz-efficient frontier. Simulation experiments are conducted to assess the out-of-sample forecasting usefulness of the semi-parametric bootstrap methodology.

Bootstrap Simulations for Finance Portfolio

In this paper we present Markowitz finance portfolio theory and efficient frontier with no bootstrap simulation , with single ordinary bootstrap and finally with double bootstrap simulation and we conclude that there are significant differences between those estimations. We prefer bootstrap simulation and especially double bootstrap as with this procedure we have the ability to reduce the number of the assets in our portfolio and to choose the most profitable of them. We apply the above methodologies in ten stocks of Athens Stock Exchange Market

Analysis of Kelly-optimal portfolios

We investigate the use of Kelly's strategy in the construction of an optimal portfolio of assets. For lognormally distributed asset returns, we derive approximate analytical results for the optimal investment fractions in various settings. We show that when mean returns and volatilities of the assets are small and there is no risk-free asset, the Kelly-optimal portfolio lies on Markowitz Efficient Frontier. Since in the investigated case the Kelly approach forbids short positions and borrowing, often only a small fraction of the available assets is included in the Kelly-optimal portfolio. This phenomenon, that we call condensation, is studied analytically in various model scenarios.

Dotted Representations of Mean-Variance Efficient Frontiers and their Computation

This paper is about dotted representations of efficient frontiers. Dotted representations, as in portfolio selection, can often be the most practical way of communicating an efficient frontier. The most popular method is to minimize variance subject to fixed levels of expected return. However, even when the fixed levels are evenly dispersed, one can not count on the resulting dots being evenly dispersed. Another method uses fixed values of a risk tolerance parameter, but with this method the resulting dots are even less controllable. In this paper we develop a third approach applicable to what we call Markowitz problems (mean-variance problems with all linear constraints). The approach utilizes the results of algorithms that can compute all hyperbolic segments of a Markowitz efficient frontier. Then the approach can place dots on the hyperbolic segments of the efficient frontier in a variety ways including equally spaced. The advantage of the approach is the speed at which dotted representations can be produced and modified, particularly on large applications.

Asset allocation

Purpose – The purpose of this paper is to conceptualise a workable strategic asset allocation (SAA) model, given the data paucity problem, and involve an ex ante framework that is distributional free. Design/methodology/approach – The SAA model is developed within a semi‐quantitative and expert‐based framework – the analytic hierarchy process (AHP) – and not a purely time‐series one. It is developed on the basis of consensus by a group of real estate investment experts, who agree on a fixed investment time horizon so that the time factor is disregarded as a variant. The SAA becomes the interface around which a set of tactical bands is imposed, subject to the Markowitz mean‐variance optimisation, and utilizing the total‐return data set of the Jones Lang LaSalle Real Estate Intelligence Service‐Asia. The lower and upper limits of the tactical bands represent the cyclical attractiveness of the various Asian office markets as growth and value‐added markets Findings – The SAA‐AHP model robustly reflects expert judgement among a cohesive group of real estate investment experts, with regard to a Pan‐Asia office market portfolio of eight major Asian cities. Through pair‐wise comparisons and subject to consistency checks in terms of the consistency ratio of <0.10, then the comparative expert assessment of the macro‐economic and the real estate specific factors driving individual Asian real estate markets, would be consistent (i.e. non conflicting). Then the total weighted evaluations of individual markets are derived and deployed as the SAA portfolio mix. This portfolio mix thus becomes the appropriate interface, around which the tactical asset allocation (TAA) is developed within defined tactical bands. These bands must be in line with the underlying Asian real estate market analysis and their cyclical positions. The TAA is obtained through the Markowitz mean‐variance portfolio optimisation, with the objective of locating the optimally efficient TAA on the Markowitz efficient frontier, under a maximising risk‐adjusted‐return Sharpe ratio. Originality/value – The SAA‐AHP model is reliant on an ex ante assessment of alternative asset allocation strategies on the basis of expert judgement of the macroeconomic environment and the Asian office markets. It is an appropriate SAA alternative to one based on the typical economic‐sized indicators, for example, the urban GDP.

An artificial intelligence approach to portfolio selection and management

This research addresses an important problem in finance, which is the portfolio selection and management problem. Modern portfolio theory and Markowitz efficient frontier start with a set of assets (securities) and generate an optimal weight combination for the optimal risky portfolio that lies on the efficient frontier. The current research work takes a step back, to identify which assets should be selected, in the first place, from a pool of available assets, and a step forward, to try to predict the expected returns for a better utilisation of the Markowitz efficient frontier. Artificial intelligence (AI) techniques are widely used in various fields of finance, which motivated the use of these techniques to find a quantitative and systematic method to construct an optimal portfolio. The genetic algorithms technique (GAs) is one of the AI techniques being successfully used to solve complex optimisation problems. GAs are deployed in this research to select the optimal portfolio based on maximising a composite objective function that maximises return, minimises risk and minimises cross-correlation between assets in the candidate portfolio. GAs are tested on two stock markets, the US stock market, represented by a pool of 40 US companies, and the Egyptian stock market, represented by a pool of 37 actively transacted companies. In both markets the generated optimal portfolio based on genetic algorithms was able to provide higher risk adjusted returns than the market index, in both the training period and the testing period. The neural networks technique is used to provide a better estimate for expected returns than the conventional historical average. It was found that, even in bearish market periods, the optimally selected portfolio, which was weekly managed using neural networks, was able to generate positive returns utilising the Markowitz efficient frontier. The research result has demonstrated the usefulness of applying the proposed AI approach represented by genetic algorithms and neural networks in active portfolio selection and management.

Single-Period Markowitz Portfolio Selection, Performance Gauging, and Duality: A Variation on the Luenberger Shortage Function

The Markowitz portfolio theory (Ref. 1) has stimulated research into the efficiency of portfolio management. This paper studies existing nonparametric efficiency measurement approaches for single-period portfolio selection from a theoretical perspective and generalizes currently used efficiency measures into the full mean-variance space. We introduce the efficiency improvement possibility function (a variation on the shortage function), study its axiomatic properties in the context of the Markowitz efficient frontier, and establish a link to the indirect mean-variance utility function. This framework allows distinguishing between portfolio efficiency and allocative efficiency; furthermore, it permits retrieving information about the revealed risk aversion of investors. The efficiency improvement possibility function provides a more general framework for gauging the efficiency of portfolio management using nonparametric frontier envelopment methods based on quadratic optimization.

Point of View The Problem of Indoor Mold for Portfolio and Property Managers

Executive Summary. Recent stock market volatility and low interest rates have renewed interest in income / dividend producing investments. Previous research has studied the inclusion of public real estate or private real estate in a mixed-asset portfolio, but only one study has included both (with constraints). This study analyzes the inclusion of both public and private real estate in a mixed-asset portfolio using the mean / variance Markowitz efficient frontier methodology unconstrained. The 5-, 10-, 15- and 25-year results show that both public and private real estate can improve efficient frontiers substantially and may command a larger allocation than currently used.

Public and Private Real Estate in a Mixed-Asset Portfolio

Executive Summary. Recent stock market volatility and low interest rates have renewed interest in income / dividend producing investments. Previous research has studied the inclusion of public real estate or private real estate in a mixed-asset portfolio, but only one study has included both (with constraints). This study analyzes the inclusion of both public and private real estate in a mixed-asset portfolio using the mean / variance Markowitz efficient frontier methodology unconstrained. The 5-, 10-, 15- and 25-year results show that both public and private real estate can improve efficient frontiers substantially and may command a larger allocation than currently used.

The monetary appreciation of paintings: from realism to Magritte

This study investigates how investments in painted arts compare to those in stocks in terms of risk return trade off using Sharpe and Treynor ratios and Markowitz efficient frontiers. A large database was analysed consisting of more than 10500 auction prices of Belgian painted art over the period 1970-1997. Hedonic art returns are influenced by auction location and auction house, current of art, painters’ reputation, medium, signature and painting size. Surrealism and luminism were the most popular currents of art (in monetary terms), while expressionism and symbolism gained (financial) esteem. This study concludes that art investments underperform equity market investments due to high riskiness, transaction costs, capital gains, resale rights, and insurance premia. In addition, the Markowitz efficient frontier shows limited diversification potential for art.

Alternative Investments in the Institutional Portfolio

This study provides an update of an earlier analysis (Schneeweis and Spurgin, [1999]) of the risk and return benefits of various hedge funds and managed futures investments as stand-alone investments or as part of an investor9s diversified stock/bond portfolio. Both traditional Markowitz efficient frontiers with and without investment restrictions as well as the risk and return performance of portfolios constructed from adding alternative investments to established U.S. stock and bond portfolios are evaluated. The Markowitz efficient frontier determination is conducted using alternative methods of risk and return forecasting including 1) historical returns, and 2) the construction of ex ante return forecasts in which expected returns are based on their historical return to risk relationship; that is, ex ante return forecasts are constructed from cross-sectional OLS regressions of historical return on historical variance and are used as inputs into the Markowitz portfolio optimization model. The latter approach reduces the impact of historically high (low) abnormal returns from influencing the allocation process.

Optimal Diversification: Is It Really Worthwhile?

Executive Summary. Recent research has demonstrated that the Markowitz efficient frontier is fuzzy and may consist of many statistically indistinguishable frontiers. Therefore, it opens the possibility that an efficient portfolio developed by mean-variance analysis may not be any more efficient than a naively diversified portfolio. Using an efficiency test developed by Gibbons, Ross, and Shanken (1989), we find evidence to support that an efficient portfolio is statistically more efficient than a corresponding naively diversified portfolio when the portfolio formation period is the same as the period used for testing the efficiency difference. However, no evidence is found to support that an efficient portfolio is statistically more efficient than a corresponding naively diversified portfolio when the portfolio formation period differs from the test period. Thus, in practical terms, efficient portfolios may not be superior to naively diversified portfolios in a statistical sense.

Regional Economic Diversification and Efficiency: Baumol’s Likely Lower Confidence Limit Measure of Risk

In this paper we argue that the appropriate concept of regional economic efficiency is Baumol’s lower confidence limit criteria. This implies a substantially reduced subset of the usual Markowitz efficient frontier. We examine this proposition in the context of a tractable equilibrium model with a data set for the province of Saskatchewan. We conclude that the Baumol efficiency criteria suggest maintaining substantial levels of activity in the high-risk, but higher-return, resource sectors of the economy. The results suggest that the cost of stability could be high, in terms of per capita income, if this economy were to diversify too far from its resource-based comparative advantage.

Conditional heteroscedasticity and real estate in diversified portfolios: an application of the QTARCH methodology

Recent empirical and theoretical studies have shown the necessity of including real estate in diversified portfolios. In this paper we present one of the latest developed autoregressive conditional heteroscedasticity models (QTARCH) and, using 52 years of Swiss data, we investigate the ability of this class of models to forecast conditional means and variances of portfolios containing only stocks and bonds, and portfolios containing real estate also. The analysis is done in a Markowitz efficient frontier framework. We find that if a simple QTARCH model had been used with our data, the portfolio's risk would have been significantly reduced. It is also shown that even when the QTARCH methodology is applied, including real estate in diversified portfolios is still justified. Furthermore, three years of out-of-sample performances of the model are extremely convincing.