Mean-variance Theory Research Articles

The Optimal Strategy of the Goodgrant Foundation

The Goodgrant Foundation want to help improve educational performance of undergraduates attending colleges and universities in the United States, and it maintains for five years, starting July 2016, and they wonder how to invest. To begin with, we primarily screen 7804 school samples and elect 2977 relatively excellent schools. Investors are divided into three categories according to their attitude towards the risk (risk preference, risk neutral and risk aversion). The optimal investment plan of risk preference, risk neutral, and the risk aversion investments are 54 schools, 93 schools, and 95 schools respectively by the means of technique of Markowitz mean-variance theory.

Portfolio diversification opportunities across stock markets of Asian tigers, Thailand and India: a vector autoregression approach

This paper explores the possibility of the creation of a collective investment vehicle that replicates the equity indices of South Korea, Taiwan, Hong Kong, Singapore, Thailand and India. To begin with, a portfolio of these indices was created using the mean variance theory. Thereafter vector autoregression was applied to examine the dynamic linkages among these markets. Since the trading hours of these markets overlap and there is no a priori for specifying how shock transmits among them, Granger causality test was applied to ascertain which markets are influential to decide the ordering of the VAR approach. The results of variance decomposition show that the impact of these markets on each other is not much and is limited to a range of 5-6%. Impulse response graphs confirm no clear leading markets among the chosen six and the transmission of shock from one market to other disappears in 2-3 days.

Portfolio diversification opportunities across stock markets of Asian tigers, Thailand and India: a vector autoregression approach

This paper explores the possibility of the creation of a collective investment vehicle that replicates the equity indices of South Korea, Taiwan, Hong Kong, Singapore, Thailand and India. To begin with, a portfolio of these indices was created using the mean variance theory. Thereafter vector autoregression was applied to examine the dynamic linkages among these markets. Since the trading hours of these markets overlap and there is no a priori for specifying how shock transmits among them, Granger causality test was applied to ascertain which markets are influential to decide the ordering of the VAR approach. The results of variance decomposition show that the impact of these markets on each other is not much and is limited to a range of 5-6%. Impulse response graphs confirm no clear leading markets among the chosen six and the transmission of shock from one market to other disappears in 2-3 days.

Last-Train Timetabling under Transfer Demand Uncertainty: Mean-Variance Model and Heuristic Solution

Traditional models of timetable generation for last trains do not account for the fact that decision-maker (DM) often incorporates transfer demand variability within his/her decision-making process. This study aims to develop such a model with particular consideration of the decision-makers’ risk preferences in subway systems under uncertainty. First, we formulate an optimization model for last-train timetabling based on mean-variance (MV) theory that explicitly considers two significant factors including the number of successful transfer passengers and the running time of last trains. Then, we add the mean-variance risk measure into the model to generate timetables by adjusting the last trains’ departure times and running times for each line. Furthermore, we normalize two heterogeneous terms of the risk measure to provide assistance in getting reasonable results. Due to the complexity of MV model, we design a tabu search (TS) algorithm with specifically designed operators to solve the proposed timetabling problem. Through computational experiments involving the Beijing subway system, we demonstrate the computational efficiency of the proposed MV model and the heuristic approach.

Managing Portfolio Diversity within the Mean Variance Theory

It is well documented that the classical mean variance theory (MVT) may yield portfolios (MVTP) that are highly concentrated and/or are outperformed by equal weight portfolios (EWP). In this work, it is proposed to expand the MVT minimizing utility function with diversity booster DB = δ∑_(i=1)^N=w_i^2 where wi are portfolio weights; ∑_(i=1)^N=w_i = 1. DB decreases with growing number of non-zero weights and has a minimum when all weights are equal (wi = 1/N). At high δ, DB becomes the dominant term in the utility function and yields EWP. For performance analysis, portfolio constructed with 12 major US equity ETFs is considered. Out-of-sample performance of maximum Sharpe portfolios is tested using statistics of bootstrapped Sharpe ratios for monthly rebalancing periods. It is found that for the three-year calibrating window the diversified MVT portfolio (DMVTP) outperformed both MVTP and EWP in 2012 - 2015. While the MVTP weights were highly concentrated and had sharp jumps between rebalancing periods, the DMVTP weights slowly changed with time.

Optimal portfolios with downside risk

Markowitz optimal portfolio theory (Markowitz 1987), also known as the Mean-Variance theory, has had a tremendous impact and hundreds of papers are devoted to this topic. This theory addresses the ...

Benefit and Risk Balance Optimization for Stochastic Hydropower Scheduling

Limited by inflow forecasting methods, the forecasting results are so unreliable that we have to take their uncertainty and risk into account when incorporating stochastic inflow into reservoir operation. Especially in the electricity market, punishment often happens when the hydropower station does not perform as planned. Therefore, focusing on the risk of power generation, a benefit and risk balance optimization model (BRM) which takes stochastic inflow as the major risk factor is proposed for stochastic hydropower scheduling. The mean-variance theory is firstly introduced into the optimal dispatching of hydropower station, and a variational risk coefficient is employed to give service to managers’ subjective preferences. Then, the multi-period stochastic inflow is simulated by multi-layer scenario tree. Moreover, a specific scenario reduction and reconstruction method is put forward to reduce branches and computing time accordingly. Finally, the proposed model is applied to the Three Gorges Reservoir (TGR) in China for constructing a weekly generation scheduling in falling stage. Compared to deterministic dynamic programming (DDP) and stochastic dynamic programming (SDP), BRM achieves more satisfactory performance. Moreover, the tradeoffs for risk-averse decision makers are discussed, and an efficient curve about benefit and risk is formed to help make decision.

A TEST OF SECOND-ORDER STOCHASTIC DOMINANCE WITH DIFFERENT WEIGHTING METHODS: EVIDENCE FROM BIST-30 and DJIA

Portfolio optimization is one of the most important steps in asset allocation procedure. Having optimized portfolios with Markowitz Mean-Variance, recently Stochastic Dominance method is taking place as a preliminary test in efficient asset allocation procedure. In some studies, it is even used as an alternative method to replace mean-variance theory in portfolio selection. In this research, distribution-based Stochastic Dominance method applied to discover the dominant individual stocks of DJIA and BIST-30 indices. We conducted Second-order Stochastic Dominance (SSD) method with various weighting logic Equal, Simple and Logarithmic. This paper concerns about two concepts; firstly, investigating market efficiency with SSD in one emerging and one developed market, Borsa Istanbul and New York Stock Exchange, respectively. Secondly, the impact of different weighting methods in dominant portfolios. Results illustrate that, there are differences in dominant portfolios with various weighting methods. Further, NYSE seems more efficient market than BIST.

When Behavioral Portfolio Theory meets Markowitz theory

The Behavioral Portfolio Theory (BPT) developed by Shefrin and Statman (2000) is often set against Markowitz's (1952) Mean Variance Theory (MVT). In this paper, we compare the asset allocations generated by BPT and MVT without restrictions. Using U.S. stock prices from the CRSP database for the 1995–2011 period, this paper is the first study that empirically determines the BPT optimal portfolio. We show that Shefrin and Statman's (2000) optimal portfolio is Mean Variance (MV) efficient in more than 70% of cases. However, our results also indicate that the BPT portfolio exhibits a high level of risk, high returns and positively skewed returns. We show that the risk aversion coefficient of the BPT portfolio is up to 10 times lower than the risk aversion degree shown by typical MV investors. Even if the asset allocations may coincide, typical MV investors will not usually select the BPT optimal portfolios. These results underline that MVT and BPT cannot be used interchangeably.

Naïve versus Mean-Variance Diversification in Indian Capital Markets

Markowitz’s mean-variance efficiency theory brought tremendous opportunities for portfolio managers, as now they are able to understand deeply the relationship between expected risk and return of the portfolios. Several models were developed based on mean-variance framework, but all of them suffered on account of either parameter estimation problem or psychological biasness in favour of simple portfolio strategies like naïve diversification. Much of the research evidence has proved that naïve diversification has either outperformed or not significantly underperformed as compared to mean-variance framework. In the present study, we compared the mean-variant efficient portfolios with stock portfolios on the basis of naïve diversification for the 15-year period and across all market capitalisation stock sets. Performance-wise naïve diversified portfolios dominated, although not statistically, the mean-variant portfolios especially in mid cap and small cap stock sets. Similar results were obtained for return per unit of risk. The study adds the role played by market capitalisation in already existing literature on naïve diversification.

A robust decision-making approach for p-hub median location problems based on two-stage stochastic programming and mean-variance theory: a real case study

The stochastic location-allocation p-hub median problems are related to long-term decisions made in risky situations. Due to the importance of this type of problems in real-world applications, the authors were motivated to propose an approach to obtain more reliable policies in stochastic environments considering the decision makers’ preferences. Therefore, a systematic approach to make robust decisions for the single location-allocation p-hub median problem based on mean-variance theory and two-stage stochastic programming was developed. The approach involves three main phases, namely location modeling, risk modeling, and decision making, each including several steps. In the first phase, the pertinent location-allocation model of the problem is developed in the form of a two-stage stochastic model based on its deterministic version. A risk measure, based on total cost function and mean-variance theory, is derived in the second phase. Furthermore, two heterogeneous terms of the risk measure have been normalized and an innovative procedure has been proposed to significantly improve the calculation efficiency. In the third phase, the Pareto solution is obtained, the frontier curve is depicted to determine the decision maker’s risk aversion coefficient, and a robust policy is obtained through optimization based on decision makers’ preferences. Finally, a case study of an automobile part distribution system with stochastic demand is described to further illustrate our risk management and analysis approach.

Hedge Fund Performance Using Scaled Sharpe And Treynor Measures

The Sharpe ratio is widely used as a performance measure for traditional (i.e., long only) investment funds, but because it is based on mean-variance theory, it only considers the first two moments of a return distribution. It is, therefore, not suited for evaluating funds characterised by complex, asymmetric, highly-skewed return distributions such as hedge funds. It is also susceptible to manipulation and estimation error. These drawbacks have demonstrated the need for new and additional fund performance metrics. The monthly returns of 184 international long/short (equity) hedge funds from four geographical investment mandates were examined over an 11-year period.This study contributes to recent research on alternative performance measures to the Sharpe ratio and specifically assesses whether a scaled-version of the classic Sharpe ratio should augment the use of the Sharpe ratio when evaluating hedge fund risk and in the investment decision-making process. A scaled Treynor ratio is also compared to the traditional Treynor ratio. The classic and scaled versions of the Sharpe and Treynor ratios were estimated on a 36-month rolling basis to ascertain whether the scaled ratios do indeed provide useful additional information to investors to that provided solely by the classic, non-scaled ratios.

The Bias Ratio As A Hedge Fund Fraud Indicator: An Empirical Performance Study Under Different Economic Conditions

The Sharpe ratio is widely used as a performance evaluation measure for traditional (i.e., long only) investment funds as well as less-conventional funds such as hedge funds. Based on mean-variance theory, the Sharpe ratio only considers the first two moments of return distributions, so hedge funds characterised by complex, asymmetric, highly-skewed returns with non-negligible higher moments may be misdiagnosed in terms of performance. The Sharpe ratio is also susceptible to manipulation and estimation error. These drawbacks have demonstrated the need for augmented measures, or, in some cases, replacement fund performance metrics. Over the period January 2000 to December 2011 the monthly returns of 184 international long/short (equity) hedge funds with investment mandates that span the geographical areas of North America, Europe, and Asia were examined. This study compares results obtained using the Sharpe ratio (in which returns are assumed to be serially uncorrelated) with those obtained using a technique which does account for serial return correlation. Standard techniques for annualising Sharpe ratios, based on monthly estimators, do not account for serial return correlation this study compares Sharpe ratio results obtained using a technique which accounts for serial return correlation. In addition, this study assess whether the Bias ratio supplements the Sharpe ratio in the evaluation of hedge fund risk and thus in the investment decision-making process. The Bias and Sharpe ratios were estimated on a rolling basis to ascertain whether the Bias ratio does indeed provide useful additional information to investors to that provided solely by the Sharpe ratio.

Hedge Fund Performance Evaluation Using The Sharpe And Omega Ratios

The Sharpe ratio is widely used as a performance evaluation measure for traditional (i.e., long only) investment funds as well as less-conventional funds such as hedge funds. Based on mean-variance theory, the Sharpe ratio only considers the first two moments of return distributions, so hedge funds characterised by asymmetric, highly-skewed returns with non-negligible higher moments may be misdiagnosed in terms of performance. The Sharpe ratio is also susceptible to manipulation and estimation error. These drawbacks have demonstrated the need for augmented measures, or, in some cases, replacement fund performance metrics. Over the period January 2000 to December 2011 the monthly returns of 184 international long/short (equity) hedge funds with geographical investment mandates spanning North America, Europe, and Asia were examined. This study compares results obtained using the Sharpe ratio (in which returns are assumed to be serially uncorrelated) with those obtained using a technique which does account for serial return correlation. Standard techniques for annualising Sharpe ratios, based on monthly estimators, do not account for this effect. In addition, this study assesses whether the Omega ratio supplements the Sharpe Ratio in the evaluation of hedge fund risk and thus in the investment decision-making process. The Omega and Sharpe ratios were estimated on a rolling basis to ascertain whether the Omega ratio does indeed provide useful additional information to investors to that provided by the Sharpe ratio alone.

Application of the Mean-Variance Theory and Resampling Technique for the Italian Energy Portfolio Settlement

The energy planning based on Mean - Variance theory, guides the investors in investment decisions, trying to maximize the return and minimize the risk of investment. However, this theory is based on strong hypotheses and, in addition, input data are often affected by estimation errors. Moreover, this theory determines poor diversification increasing return and risk of the portfolio, and strong variability of the outputs when inputs are varied.In the first part of the paper, the Mean - Variance theory was applied to the energy generation in Italy; in particular, the analysis was on the actual energy mix, but also assuming the use of nuclear technology and taking into account verisimilar improvement, of technologies in the future.On the other hand, in the second part of the paper, a methodology has been applied in order to limit the problems of Mean-Variance theory applied to the energy mix settlement. In particular, the input variables have been calculated using Monte Carlo simulation, in order to reduce the estimation error, and the Resampled EfficiencyTMtechnique has been applied in order to calculate the resulting new “average” efficient frontier. This methodology has been applied either not limiting or limiting the minimum and maximum percentage for every energy generation technology, in order to simulate constraints due, for example, to the technological characteristics of the plant, the availability of the sources and eventually to norms, to the territorial characteristics and to the socio-political choices. The application of Mean - Variance theory allowed to obtain energy portfolio, alternative to the actual, characterized by higher values of expected returns an lower values of risk.It was also shown that the application of the Resampled EfficiencyTMtechnique with data originated with the Monte Carlo simulation effectively tackles the problems of Mean - Variance theory; in this way, the decision maker is helped in making decisions in the energy system policy and development.Thanks to this approach, applied in particular to the Italian energy contest, it was also possible to evaluate the effectiveness of the introduced modifications to the Italian actual energy mix to achieve the 2020 European Energy Directive targets in particular concerning the reduction of CO2levels.

When Behavioral Portfolio Theory Meets Markowitz Theory

The Behavioral Portfolio Theory (BPT) developed by Shefrin and Statman (2000) is often set against Markowitz's (1952) Mean Variance Theory (MVT). In this paper, we compare the asset allocations generated by BPT and MVT without restrictions. Using U.S. stock prices from the CRSP database for the 1995-2011 period, this paper is the first study that empirically determines the BPT optimal portfolio. We show that the Shefrin and Statman's (2000) optimal portfolio is Mean Variance (MV) efficient in more than 70% of cases. However, our results also indicate that the BPT portfolio exhibits a high level of risk, high returns and positively skewed returns. We show that the risk aversion coefficient of the BPT portfolio is up to 10 times lower than the risk aversion degree shown by typical MV investors. Even if the asset allocations may coincide, typical MV investors will not usually select the BPT optimal portfolios. These results underline that MVT and BPT cannot be used interchangeably.

Empirical Research of Portfolio Selection under M-SAD Model

The mean semi-absolute deviation is the extension and development from the mean-variance theory which proposed by Markowitz. This paper studied the Mean-SAD (semi-variance deviation) model without the short selling and used the Chinese securities markets 20 stocks to test the efficient of the model. We got the conclusion that M-SAD model can effectively direct the decision in portfolio selection. Based on the result of the empirical research, the paper prospects the application of M-SAD model in our country.

Supply chain risk analysis with mean-variance models: a technical review

Pioneered by Nobel laureate Harry Markowitz in the 1950s, the mean-variance (MV) formulation is a fundamental theory for risk management in finance. Over the past decades, there is a growing popularity of applying this ground breaking theory in analyzing stochastic supply chain management problems. Nowadays, there is no doubt that the mean-variance (MV) theory is a well-proven approach for conducting risk analysis in stochastic supply chain operational models. In view of the growing importance of MV approach in supply chain management, we review a selection of related papers in the literature that focus on MV analytical models. By classifying the literature into three major areas, namely, single-echelon problems, multi-echelon supply chain problems, and supply chain problems with information updating, we derive insights into the current state of knowledge in each area and identify some associated challenges with a discussion of some specific models. We also suggest future research directions on topics such as information asymmetry, supply networks, and boundedly rational agents, etc. In conclusion, this paper provides up-to-date information which helps both academicians and practitioners to better understand the development of MV models for supply chain risk analysis.

Somatic Portfolio Theory: When Emotions Lead to Economic Efficiency

This paper offers a theoretical generalization of the mean-variance theory (MVT) by integrating the ’expected returns/risk’ rule with variables that measure emotions. We validate its accuracy using a psycho-physiological experiment with a sample of 645 individuals who were asked to take portfolio decisions in a laboratory setting. Results show that MVT frequently fails to describe investor behavior. We obtain evidence that individuals actually take efficient portfolio choices, but only when emotions are added to the equation.This paper shows that by merging theories of rational choice and evidence of emotions, the authentic human decision process can be described and predicted.

Equilibrium Pricing Extending the Mean-Variance Theory Using Weighted Possibilistic Mean of Investor’s Subjectivity

This paper proposes an extended analytical approach to developing an equilibrium pricing vector with various types of investor’s subjectivity based on extended Mean-Variance (MV) theory. Weighted fuzzy mean and variance are introduced in order to represent investor’s subjectivity numerically. Similar to the traditional MV-based equilibrium approach, the equilibrium pricing vector of the proposed model is analytically obtained in mathematical programming. A macroeconomic index based on risky assets, which provides information with respect to the soundness of the capital market with subjectivity, is also constructed.