Markowitz Theory Research Articles

Mixed time scale strategy in portfolio management

The fluctuation in the prices in a stock market can be separated into two time scales: a long term trend guided by financial principles and a short term trend governed by the specific trading mechanisms used. We proposed a mixed strategy for managing stock portfolios in which the long term trend is tracked by Markowitz's theory of mean variance analysis, and the short term fluctuation in stock price is monitored by a trading threshold. This strategy is tested in a two-stock portfolio formed from twenty four selected stocks in the Hang Seng Index from July 10 2007 to July 21 2009, which covers the financial Tsunami in 2008. In our mixed strategy, the test is based on a periodic trading with a period of ten trading days. At the beginning of each trading period, a two-stock portfolio that has the optimal Sharpe ratio among all the possible combination of 24 chosen stocks from the Hang Seng Index is selected using mean variance analysis. This is accomplished through a two steps process that involves a maximization of the Sharpe ratio for each pair with an implementation of the worst scenario hypothesis and a threshold that control the activation of trading. Then we examine the price fluctuation of the chosen stocks to determine the trading action. A trading threshold is proposed to facilitate the trading decision so as to ensure that the price of the selected portfolio will likely follow a rising trend on the decision day. The yield of the portfolio based on this mixed strategy is compared to the Hang Seng Index and the averaged price of the 24 stocks over the same period. The results show that this strategy of portfolio management yields a factor of 1.6 of the initial value, whereas the corresponding yield of the Hang Seng Index is a decrease in value by a factor of 0.8. Over the period of two years for the comparison, the investment using our mixed strategy in portfolio management maintains a positive return for a wide range of trading threshold, from a few days to one month. Our choice of a trading period of 10days reduces the transaction frequency in order to avoid the penalty of transaction fee. Our strategy therefore allows higher flexibility in the trading scheme for investors of different trading habits. An important observation of our strategy is that it preserves the assets over the Tsunami in 2008, which is important to conservative investors who prefer protection in the worst situation.

An approach to portfolio selection using an ARX predictor for securities’ risk and return

It is well known that every investment carries a risk associated, and depending on the type of investment, it can be very risky; for instance, securities. However, Markowitz proposed a methodology to minimize the risk of a portfolio through securities diversification. The selection of the securities is a choice of the investor, who counts with several technical analyzes to estimate investment’s returns and risks. This paper presents an autoregressive exogenous (ARX) predictor model to provide the risk and return of some Brazilian securities – negotiated at the Brazilian stock market, BOVESPA – to select the best portfolio, herein understood as the one with minimum expected risk. The ARX predictor succeeded in predicting expected returns and risks of the securities, which resulted in an effective portfolio. Additionally the Markowitz theory was confirmed, showing that diversification reduces the risk of a portfolio.

The role of portfolio diversification in the hotel industry

PurposeThe purpose of this paper is to study whether geographic and sector diversification allow for a significant reduction in the risk exposure of a portfolio of hotel investments in one of the major tourist markets, the Italian market.Design/methodology/approachThis paper evaluates the benefits related to a Markowitz diversification approach for the construction of a specialised portfolio in the hotel real estate market. The portfolio analysis considers the degree of efficiency of each portfolio, the type of diversification adopted by a more efficient portfolio, the persistence of results over time and the impact of diversification constraints.FindingsThe results demonstrate that, while standard geographic and sector diversification allow for good results, the more efficient portfolios are more concentrated. The trade‐off is worse if some concentration constraints are established, but the portfolios identified are characterised by higher performance persistence.Research limitations/implicationsThe analysis only considers high‐quality hotels in the Italian market. Unfortunately, some information on costs is not as detailed as would be desired. The availability of a more complete database could increase the significance of the results obtained.Practical implicationsThe results are relevant for constructing all hotels' portfolios, like those managed by a real estate fund manager, in order to define the type and degree of diversification that allow for minimal risk exposure.Originality/valueThis paper is the first to apply the Markowitz theory to the Italian hotel industry in order to identify the best diversification criteria.

Does Behavioral Portfolio Theory Support Markowitz Theory? Evidence from French Data

Does Behavioral Portfolio Theory Support Markowitz Theory? Evidence from French Data

Finansinio sverto naudojimas aktyviai valdant investicijų portfelį

The analysis of the portfolio theories was carried out in the article. H. Markowitz theory of an optimal portfolio formation was briefly described, the process of the portfolio selection was discussed, the basic corrections, improvements, development and application of the theory suggested by the scientists were named. With reference to the literature analysis the most suitable portfolio theory was chosen for further development, aiming at the application of the theory to active portfolio management using the financial leverage. The basic limitations of the chosen theory were evaluated in order to apply it to the subject of research, specific development solutions were suggested and, on the grounds of them, the adjusted efficient set was proposed. An empirical research was carried out, validating the expedience of the financial leverage usage when actively managing the investment portfolio, and evaluating the intensity of the financial leverage usage. Built on the results of the research,the efficient set which was suggested in the theoretical-hypothetical part of the study was adjusted.

Markowitz meets Talmud: A combination of sophisticated and naive diversification strategies

The modern portfolio theory pioneered by Markowitz (1952) is widely used in practice and extensively taught to MBAs. However, the estimated Markowitz portfolio rule and most of its extensions not only underperform the naive 1/ N rule (that invests equally across N assets) in simulations, but also lose money on a risk-adjusted basis in many real data sets. In this paper, we propose an optimal combination of the naive 1/ N rule with one of the four sophisticated strategies—the Markowitz rule, the Jorion (1986) rule, the MacKinlay and Pástor (2000) rule, and the Kan and Zhou (2007) rule—as a way to improve performance. We find that the combined rules not only have a significant impact in improving the sophisticated strategies, but also outperform the 1/ N rule in most scenarios. Since the combinations are theory-based, our study may be interpreted as reaffirming the usefulness of the Markowitz theory in practice.

Optimization Stock Portfolio With Mean-Variance and Linear Programming: Case In Indonesia Stock Market

It is observed that the number of Indonesia’s domestic investor who involved in the stock exchange is very less compare to its total number of population (only about 0.1%). As a result, Indonesia Stock Exchange (IDX) is highly affected by foreign investor that can threat the economy. Domestic investor tends to invest in risk-free asset such as deposit in the bank since they are not familiar yet with the stock market and anxious about the risk (risk-averse type of investor). Therefore, it is important to educate domestic investor to involve in the stock exchange. Investing in portfolio of stock is one of the best choices for risk-averse investor (such as Indonesia domestic investor) since it offers lower risk for a given level of return. This paper studies the optimization of Indonesian stock portfolio. The data is the historical return of 10 stocks of LQ 45 for 5 time series (January 2004 – December 2008). It will be focus on selecting stocks into a portfolio, setting 10 of stock portfolios using mean variance method combining with the linear programming (solver). Furthermore, based on Efficient Frontier concept and Sharpe measurement, there will be one stock portfolio picked as an optimum Portfolio (Namely Portfolio G). Then, Performance of portfolio G will be evaluated by using Sharpe, Treynor and Jensen Measurement to show whether the return of Portfolio G exceeds the market return. This paper also illustrates how the stock composition of the Optimum Portfolio (G) succeeds to predict the portfolio return in the future (5th January – 3rd April 2009). The result of the study observed that optimization portfolio using Mean-Variance (consistent with Markowitz theory) combine with linear programming can be applied into Indonesia stock’s portfolio. All the measurements (Sharpe, Jensen, and Treynor) show that the portfolio G is a superior portfolio. It is also been found that the composition (weights) stocks of optimum portfolio (G) can be used to predict the forward return (5th January – 3rd April 2009). It is shown that the stock portfolio return of 5th January – 3rd April 2009) has exceeded the market return for the same period of time based on Sharpe and Treynor measurement.

Long-term uncertainty evaluation of pool electricity markets

Abstract Pool electricity markets are cleared under the strong assumption of having a perfectly known future; in real life, this is anything but true. The inability to predict the random parameters of the supply and the demand function introduces risk into the market clearing process. Therefore, the main interest is to minimize such risk by means of a trade-off of the mean and the variance of the social cost function. This paper considers random variations on the levels and on the slopes of the quadratic supply and demand functions. Correlation is considered between the corresponding coefficients of the supply and demand curves. By means of the mean–variance Markowitz theory, the risk introduced by these random variations is analyzed. A comprehensive analysis on the effects that the mean–variance Markowitz theory has on the nodal spot prices and on the point-elasticities of the supply and demand curves is made. The non-linear optimization model presented in this paper is validated through a three-, a six-, and a 21-node system.

The efficient trade-off between security and cost for sea ports: a conceptual model

Sea ports around the world have had to introduce new security measures in the wake of the introduction of the International Maritime Organisation's ISPS Code, but may have been unable to establish an efficient trade-off between cost and security. This paper introduces a conceptual model that uses the Markowitz (1952) theory of portfolio selection to describe the process that ports and port terminals can follow to ensure that efficient security investment decisions are made to reduce the exposure to terrorist and other unlawful activities.

Generation and Transmission Expansion Under Risk Using Stochastic Programming

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> In this paper, a new model for generation and transmission expansion is presented. This new model considers as random events the demand, the equivalent availability of the generating plants, and the transmission capacity factor of the transmission lines. In order to incorporate these random events into an optimization model, stochastic programming and probabilistic constraints are used. A risk factor is introduced in the objective function by means of the mean-variance Markowitz theory. The solved optimization problem is a mixed integer nonlinear program. The expected value of perfect information is obtained in order to show the cost of ignoring uncertainty. The proposed model is illustrated by a six- and a 21-node network using a dc approximation. </para>

Modelling the Dynamic Dependence Structure in Multivariate Financial Time Series

Abstract. The dependence structure in multivariate financial time series is of great importance in portfolio management. By studying daily return histories of 17 exchange‐traded index funds, we identify important features of the data, and we propose two new models to capture these features. The first is an extension of the multivariate BEKK (Baba, Engle, Kraft, Kroner) model, which includes a multivariate t‐type error distribution with different degrees of freedom. We demonstrate that this error distribution is able to accommodate different levels of heavy‐tailed behaviour and thus provides a better fit than models based on a multivariate t‐with a common degree of freedom. The second model is copula based, and can be regarded as an extension of the standard and the generalized dynamic conditional correlation model [Engle, Journal of Business and Economics Statistics (2002) Vol. 17, 425–446; Cappiello et al. (2003) Working paper, UCSD] to a Student copula. Model comparison is carried out using criteria including the Akaike information criteria and Bayesian information criteria. We also evaluate the two models from an asset‐allocation perspective using a three‐asset portfolio as an example, constructing optimal portfolios based on the Markowitz theory. Our results indicate that, for our data, the proposed models both outperform the standard BEKK model, with the copula model performing better than the extension of the BEKK model.

Autocorrelation, bias and fat tails: Are hedge funds really attractive investments?

Hedge funds have become an increasingly popular investment tool in the past decade, owing to their general lack of correlation with stock and bond markets. When evaluated using the Markowitz portfolio selection theory, hedge funds appear to offer a remarkable opportunity. Yet use of the Markowitz theory neglects three important qualities of hedge funds: the existence of significant autocorrelation, bias and fat tails. Each of these three issues has been studied individually, but no literature exists in which their combined effect is considered. The purpose of the research reported here is to evaluate hedge fund performance incorporating these combined effects. The results indicate that hedge funds lose most of their attractiveness when the existence of autocorrelation, bias and fat tails is taken into account.

Theory of portfolio and risk based on incremental entropy

PurposeTo develop a new theory of portfolio and risk based on incremental entropy and Markowitz's theory.Design/methodology/approachReplacing arithmetic, the mean return adopted by M.H. Markowitz, with geometric mean return as a criterion for assessing a portfolio, one gets incremental entropy: one of the generalized entropies. It indicates that the incremental speed of capital is a more objective and testable criterion.FindingsThe difference between the new theory based on incremental entropy and Markowitz's theory is that the new theory emphasizes that there is an objectively optimal portfolio for given probability of returns.Originality/valueThis paper provides some formulas for optimizing portfolio allocations. Based on the new portfolio theory, this paper also presents a new measure of information value, analyzes the differences and similarities between this measure and K.J. Arrow's measure of information value, and discusses how to optimize forecasts with the new measure.

A geometric point of view on mean-variance models

This paper deals with the mathematics of the Markowitz theory of portfolio management. Let $E$ and $V$ be two homogeneous functions defined on ${\Bbb R}^n$, the first linear, the other positive definite quadratic. Furthermore let ${\mit\Delta}$ be a simp

Stochastic Portfolio Theory and Stock Market Equilibrium

HARRY MARKOWITZ [1952, 1956, 1959] developed a theory of portfolio selection based on the optimization of a quadratic function subject to linear constraints. His work led to the development of a single period equilibrium model, the SharpeLintner capital asset pricing model (CAPM) (see Sharpe [1964], Lintner [1965a, 1965b]). R. C. Merton [1973] extended the CAPM to a continuous time model using lognormal diffusion processes to represent stock price series and showed that the original conclusions continued to hold virtually without change. In this continuous time model it became possible to observe the dynamic interaction between investors' behavior and the behavior of the stocks. In fact, Rosenberg and Ohlson [1976] showed that his interaction led to internal inconsistencies in the continuous time CAPM. In this paper we analyze long term portfolio performance compatible with equilibrium constraints on global portfolio structure. We present a portfolio theory which is based on Markowitz's theory, but which emphasizes the long term performance of the portfolios in continuous time. The concept of is introduced, a quantity which measures the relative performance of a portfolio compared to that of its component stocks. The equilibrium model we present does not consider questions dealing with optimal strategies for investors, and specifically avoids all normative issues. Rather, it provides constraints on global portfolio structure based on the principle that excess growth is conserved, that the total excess growth in the market at any instant is zero. These constraints generate a distribution of portfolios in the market similar to the energy distribution in thermodynamic equilibrium. This approach provides an alternative to classical supply-demand equilibrium. We adopt some standard conventions here, but most of the results in the paper will carry over to more general settings. The assumptions we make are: (1) Each stock price follows a lognormal diffusion process with constant drift and variance parameters. The covariance parameters between stocks are constant. Stock portfolios can be represented as Ito integrals in the various stock price processes. (2) There are no transaction costs, taxes, or problems with the indivisibility of assets. (3) The number of shares of each corporation remains constant.

Putting Markowitz theory to work

Putting Markowitz theory to work

A thermal X-RAY and resistivity study of the heusler alloy Cu2NiSn

The compound Cu2NiSn was analyzed by DTA, X-ray and electrical resistivity measurements. No single-phase structure was found at room temperature. The alloy decomposes upon heating, starting at 160°, forming copper and two hcp structures. At 500° the Heusler structure is restored. Electrical resistivity results are discussed in terms of Markowitz's theory for disordered metals.

Risk, Return, and Equilibrium: A General Single-Period Theory of Asset Selection and Capital-Market Equilibrium.

Uncertainty is a major concern in financial decision-making. Financial theory contains a number of conceptual frameworks that treat the effects of uncertainty; yet no one has attempted to put forth a general treatment of portfolio risk. This book fills the theoretical gap by developing a general measure of portfolio risk and formulating a general model of asset selection in the context of market equilibrium. The author seeks to define and elucidate theoretical issues through rigorous, quantitative arguments; and critical evaluation of the basic assumptions of the model.Stone summarizes relevant aspects of the Markowitz theory of portfolio selection and presents a brief overview of the Sharpe, Lintner, and Mossin models in which asset selections are based on two parameters of choice--either mean return and variance, or mean return and standard deviation. He then generalizes these models to objective functions that are still functions of two parameters--expected return (or expected wealth), and a general measure of risk. Stone introduces a new global measure of risk, relating it to existing work in the theory of risk, and presents and compares two alternative risk-return representations of expected utility: the Generalized Markowitz Criterion (GMC) and the Two-Parameter Functional Representation (TPFR). The author provides a general analysis of asset selection and market equilibrium and examines the GMC and TPFR in greater detail. Finally, he investigates existing models of capital market equilibrium formulated by Sharpe, Lintner, and Mossin, and analyzes these models according to the previously developed general model.Mathematical analysis and logical reasoning are the basic methodological tools used in this work. The author has, however, taken care to present proofs and derivations in sufficient detail to make them easy to follow at a graduate level. Students of economics and finance (particularly those in advanced courses dealing with risk, asset selection, or capital markets) and professionals in the field will find the book rich in constructive new theoretical material.

Mathematical Programming of Portfolio Selections

The purpose of this paper is to analyze and explain, by reference to empirical data, some of the recent work done in this area by Dr. Harry Markowitz under the sponsorship of the Cowles Commission (Cowles Commission Discussion Papers in Economics Nos. 294, 2005, and 2019. Also, “Portfolio Selection,” Journal of Finance, March 1952.). This article is divided into four parts. Part I contains a heuristic introduction to the basic problem together with a mathematical statement of Markowitz's theory of portfolio selection and its basic assumptions. Part II contains a discussion of some of the problems involved in formulating probability beliefs for available investment opportunities. In Part III, the selection technique is demonstrated by application to a very simplified case, and many of the problems involved in more complex cases are brought out. The final section contains a summarization and critique of the theory, its limitations, and its possibilities as a guide to practical decision-making.