Showing papers on "Efficient frontier published in 2011"

An Analytic Derivation of the Efficient Portfolio Frontier

Abstract: The characteristics of the mean-variance, efficient portfolio frontier have been discussed at length in the literature. However, for more than three assets, the general approach has been to display qualitative results in terms of graphs. In this paper, the efficient portfolio frontiers are derived explicitly, and the characteristics claimed for these frontiers are verified. The most important implication derived from these characteristics, the separation theorem, is stated and proved in the context of a mutual fund theorem. It is shown that under certain conditions, the classic graphical technique for deriving the efficient portfolio frontier is incorrect.

Fallacy of the Log-Normal Approximation to Optimal Portfolio Decision-Making Over Many Periods

Abstract: The fallacy that a many-period expected-utility maximizer should maximize (a) the expected logarithm of portfolio outcomes or (b) the expected average compound return of his portfolio is now understood to rest upon a fallacious use of the Law of Large Numbers . This paper exposes a more subtle fallacy based upon a fallacious use of the Central-Limit Theorem . While the properly normalized product of independent random variables does asymptotically approach a log-normal distribution under proper assumptions, it involves a fallacious manipulation of double limits to infer from this that a maximizer of expected utility after many periods will get a useful approximation to his optimal policy by calculating an efficiency frontier based upon (a) the expected log of wealth outcomes and its variance or (b) the expected average compound return and its variance. Expected utilities calculated from the surrogate log-normal function differ systematically from the correct expected utilities calculated from the true probability distribution. A new concept of ‘initial wealth equivalent’ provides a transitive ordering of portfolios that illuminates commonly held confusions. A non-fallacious application of the log-normal limit and its associated mean-variance efficiency frontier is established for a limit where any fixed horizon period is subdivided into ever more independent sub-intervals. Strong mutual-fund Separation Theorems are then shown to be asymptotically valid.

Dynamic Portfolio Selection Methods for Power Generation Assets

Abstract: In this paper we start off by reviewing the literature on how to extend the mean-variance portfolio model to multi-stage portfolio problems. We then apply a multi-period portfolio selection model to power generation assets, which is based on a reallocation methodology with scenario tree. Two solution approaches are used: the multi-period rebalancing model and the global solution one. These approaches are contrasted with the efficient frontier obtained for a "buy-and-hold policy", thus helping to illustrate the effect of portfolio dynamization. The study covers all major electricity generation technologies in Germany and investigates the impact of offshore wind and solar power plants on existing power generation portfolios. We find that solar power technology has a positive impact on the efficiency of the portfolios, and the analysis underlines the advantages of using a multi-period rebalancing model for decision-making.

Why Does an Equal-Weighted Portfolio Outperform Value- and Price-Weighted Portfolios?

Abstract: We compare the performance of equal-, value-, and price-weighted portfolios of stocks in the major U.S. equity indices over the last four decades. We nd that the equal-weighted portfolio with monthly rebalancing outperforms the value- and price-weighted portfolios in terms of total mean return, four factor alpha, Sharpe ratio, and certainty-equivalent return, even though the equal-weighted portfolio has greater portfolio risk. The total return of the equal-weighted portfolio exceeds that of the value- and price-weighted because the equal-weighted portfolio has both a higher return for bearing systematic risk and a higher alpha when using the fourfactor model. The nonparametric test of Patton and Timmermann (2009) indicates that the dierences in the total return of the equal-weighted portfolio and the valueand price-weighted portfolios is monotonically related to size, price, liquidity and idiosyncratic volatility; the relation with reversal is not monotonic, although the equal-weighted portfolio strongly outperforms the value- and price-weighted portfolios for the deciles with the lowest and the highest reversal characteristic. The higher systematic return of the equal-weighted portfolio arises from its higher exposure to the market, size, and value factors. The higher alpha of the equal-weighted portfolio arises from the monthly rebalancing required to maintain equal weights, which is implicitly a contrarian strategy that exploits reversal; thus, alpha depends only on the rebalancing frequency and not on the choice of initial weights.

Risk and Return Analysis on Performance of the Islamic mutual funds: Evidence from Malaysia*

Abstract: The study used monthly aggregate returns to evaluate performance of the mutual funds for the Islamic and Conventional portfolios in Malaysia, from 1996 to 2009. The evidence from aggregate returns of the 128 Islamic mutual funds and 350 Conventional mutual funds, consists of 160 observations denoted that both portfolios have performed better than the market portfolio within the period. However, the result has shown on average the Islamic portfolio provides slightly less returns relative to the Conventional counterparts. The result revealed a statistically significant difference between the standard deviation of the portfolios, indicating that the Islamic portfolio is riskier than the Conventional portfolio. The results also revealed that both Islamic and Conventional portfolios were depended on the market portfolio of which the former portfolio was closely mirrored to the market movement in relation to the latter portfolio.

Markowitz's Mean-Variance Asset–Liability Management with Regime Switching: A Multi-Period Model

Abstract: This paper considers an optimal portfolio selection problem under Markowitz's mean-variance portfolio selection problem in a multi-period regime-switching model. We assume that there are n + 1 securities in the market. Given an economic state which is modelled by a finite state Markov chain, the return of each security at a fixed time point is a random variable. The return random variables may be different if the economic state is changed even for the same security at the same time point. We start our analysis from the no-liability case, in the spirit of Li and Ng (2000), both the optimal investment strategy and the efficient frontier are derived. Then we add uncontrollable liability into the model. By direct comparison with the no-liability case, the optimal strategy can be derived explicitly.

Mean–variance portfolio optimization when means and covariances are unknown

Abstract: Markowitz’s celebrated mean–variance portfolio optimization theory assumes that the means and covariances of the underlying asset returns are known. In practice, they are unknown and have to be estimated from historical data. Plugging the estimates into the efficient frontier that assumes known parameters has led to portfolios that may perform poorly and have counter-intuitive asset allocation weights; this has been referred to as the “Markowitz optimization enigma.” After reviewing different approaches in the literature to address these difficulties, we explain the root cause of the enigma and propose a new approach to resolve it. Not only is the new approach shown to provide substantial improvements over previous methods, but it also allows flexible modeling to incorporate dynamic features and fundamental analysis of the training sample of historical data, as illustrated in simulation and empirical studies.

A General Test for SSD Portfolio Efficiency

Abstract: We develop a Linear Programming test to analyze if a given investment portfolio is efficient in terms of second-order stochastic dominance relative to all possible portfolios formed from a set of base assets. The test has a convenient Linear Programming structure. In case of efficiency, the primal model identifies a subgradient vector of a utility function that rationalizes the evaluated portfolio. In case of inefficiency, the dual model identifies a second, efficient portfolio that dominates the evaluated portfolio. The test gives a general necessary and sufficient condition, and can deal with general linear portfolio restrictions, inefficiency degree measures, and scenarios with unequal probabilities. We also develop a compact version of the test that substantially reduces computational burden at the cost of losing information about the dual dominating portfolio in case of inefficiency. An application to US investment benchmark data qualifies a broad stock market index as inefficient, and suggests that no risk-averse investor would hold the market index in the face of attractive premiums offered by some more concentrated investment portfolios.

Multi-period mean-variance portfolio selection with Markov regime switching and uncertain time-horizon

Abstract: This paper investigates a multi-period mean-variance portfolio selection with regime switching and uncertain exit time. The returns of assets all depend on the states of the stochastic market which are assumed to follow a discrete-time Markov chain. The authors derive the optimal strategy and the efficient frontier of the model in closed-form. Some results in the existing literature are obtained as special cases of our results.

Portfolio Risk in Multiple Frequencies

Abstract: Portfolio risk, introduced by Markowitz in 1952, and defined as the standard deviation of the portfolio return, is an important metric in the Modern Portfolio Theory (MPT). A popular method for portfolio selection is to manage the risk and return of a portfolio according to the cross-correlations of returns for various financial assets. In a real world scenario, estimated empirical financial correlation matrix contains significant level of intrinsic noise that needs to be filtered prior to risk calculations. In this paper, we present basic concepts of risk engineering in finance applications. Then, we extend our discussion to the eigenfiltering of measurement noise for hedged portfolios. Moreover, we extend risk measurement methods for trading in multiple frequencies. Finally, three novel risk management methods are proposed as an independent overlay of the underlying investment decision mechanism, i.e. the trading strategy. We highlight performance and merit of the risk engineering techniques introduced by presenting the back-testing results of an investment strategy for the stocks listed in the NASDAQ 100 index. It is shown in the paper that managing portfolio risk more intelligently may offer advantages for improved return on investment.

An adaptive network based fuzzy inference system-genetic algorithm clustering ensemble algorithm for performance assessment and improvement of conventional power plants

Abstract: Performance measurement and assessment are fundamental to management planning and control activities of complex systems such as conventional power plants. They have received considerable attention by both management practitioners and theorists. There has been several efficiency frontier analysis methods reported in the literature. However, each of these methodologies has its strength and weakness. This study proposes a non-parametric efficiency frontier analysis methods based on adaptive network based fuzzy inference system (ANFIS) and genetic algorithm clustering ensemble (GACE) for performance assessment and improvement of conventional power plants. The proposed ANFIS-GA algorithm is capable to find a stochastic frontier based on a set of input-output observational data and do not require explicit assumptions about the functional structure of the stochastic frontier. Furthermore, it uses a similar approach to econometric methods for calculating the efficiency scores. Moreover, the effect of the return to scale of a power plant on its efficiency is included and the unit used for the correction is selected by notice of its scale. GACE is used to cluster power plants to increase homogeneousness. The proposed approach is applied to a set of actual conventional power plants to show its applicability and superiority. The superiority and advantages of the proposed algorithm are shown by comparing its results against ANN Fuzzy C-means Algorithm and conventional econometric method.

Advances in Portfolio Construction and Implementation

Abstract: A review of portfolio planning: models and systems Generalised mean variance analysis and robust portfolio diversification Portfolio construction from mandate to stock weight: a practitioner's perspective Enhanced indexation Portfolio management under taxes Using genetic algorithms to construct portfolios Near-uniformly distributed, stochastically generated portfolios Modelling directional hedge funds mean, variance and correlation with tracker funds Integrating market and credit risk in fixed income portfolios Incorporating skewness and kurtosis in portfolio optimization: a multidimensional efficient set Balancing growth and shortfall probability in continuous time active portfolio management Assessing the merits of risk-based optimisation for portfolio concentration The mean-downside risk portfolio frontier: a non-parametric approach Some exact results for portfolio estimators in the two-period capital market model optimal asset allocation for endowments: a large deviations approach Methods of relative portfolio optimization Predicting portfolio returns using exact efficient set distributors

Comparative issues in large-scale mean-variance efficient frontier computation

Abstract: One of the functions of a portfolio management system is to return quickly an efficient frontier. However, in the large-scale problems (1000 to 3000 securities) that are beginning to appear with greater frequency, the task of computing the mean-variance efficient frontier, even when all constraints are linear, can range from the significant to the prohibitive. For ease of reference, we call mean-variance problems with all linear constraints Markowitz problems. With little on the time to compute a Markowitz-problem efficient frontier in the literature, we conduct experiments that involve varying problem sizes, methods employed, and optimizers used to present an overall picture of the situation and establish benchmarks in the large-scale arena. One of the conclusions of the experiments is the superiority of the class of techniques that would fall under the title of parametric quadratic programming.

Mean--variance portfolio optimization when means and covariances are unknown

Abstract: Markowitz's celebrated mean--variance portfolio optimization theory assumes that the means and covariances of the underlying asset returns are known. In practice, they are unknown and have to be estimated from historical data. Plugging the estimates into the efficient frontier that assumes known parameters has led to portfolios that may perform poorly and have counter-intuitive asset allocation weights; this has been referred to as the "Markowitz optimization enigma." After reviewing different approaches in the literature to address these difficulties, we explain the root cause of the enigma and propose a new approach to resolve it. Not only is the new approach shown to provide substantial improvements over previous methods, but it also allows flexible modeling to incorporate dynamic features and fundamental analysis of the training sample of historical data, as illustrated in simulation and empirical studies.

Portfolios for Investors Who Want to Reach TheirGoals While Staying on the Mean–Variance Efficient Frontier

Abstract: How can investors construct portfolios that help them reach their goals, such as a comfortable retirement for themselves, a bequest for their children, and college education for their grandchildren? Are such portfolios on the mean–variance efficient frontier? How can advisors discuss investment risk with clients whose risk tolerance varies by goal—low for retirement and higher for bequests? These are the questions answered in this article The authors show that advisors can help clients construct portfolios that take clients to their goals while also leaving them on the mean–variance efficient frontier

Emergency Medicine: An Operations Management View

Abstract: Operations management (OM) is the science of understanding and improving business processes For the emergency department (ED), OM principles can be used to reduce and alleviate the effects of crowding A fundamental principle of OM is the waiting time formula, which has clear implications in the ED given that waiting time is fundamental to patient-centered emergency care The waiting time formula consists of the activity time (how long it takes to complete a process), the utilization rate (the proportion of time a particular resource such a staff is working), and two measures of variation: the variation in patient interarrival times and the variation in patient processing times Understanding the waiting time formula is important because it presents the fundamental parameters that can be managed to reduce waiting times and length of stay An additional useful OM principle that is applicable to the ED is the efficient frontier The efficient frontier compares the performance of EDs with respect to two dimensions: responsiveness (ie, 1/wait time) and utilization rates Some EDs may be "on the frontier," maximizing their responsiveness at their given utilization rates However, most EDs likely have opportunities to move toward the frontier Increasing capacity is a movement along the frontier and to truly move toward the frontier (ie, improving responsiveness at a fixed capacity), we articulate three possible options: eliminating waste, reducing variability, or increasing flexibility When conceptualizing ED crowding interventions, these are the major strategies to consider

On the diversification of portfolios of risky assets

Abstract: We introduce a measure of diversification for portfolios comprising d risky assets. This measure relates the smallest possible return variance among these d assets to the overall portfolio return variance, yielding the portion of non-diversifiable risk. In the context of normally distributed asset returns, its estimator and finite-sample properties are explored when being applied to the trivial asset allocation strategy. An overview of different previous approaches towards the measurement of diversification is provided, and the shortcomings of some of these approaches are illustrated. A categorization of tests regarding the portfolio return variance is given, especially for comparing naively allocated with minimum-variance portfolios. The empirical part of this work is carried out on monthly return data for the S&P500 constituents, with a return history spanning the last five decades. When measuring the diversification of naively allocated 40-asset portfolios, the average degree of diversification barely exceeds 60%. This result indicates that - for the mutual fund manager as well as for the private investor - well-founded selection of assets indeed leads to better portfolio diversification than naive allocation does.

Using Industry Momentum to Improve Portfolio Performance

Abstract: Minimum-variance portfolios, which ignore the mean and focus on the (co)variances of asset returns, outperform mean-variance approaches in out-of-sample tests. Despite these promising results, minimum-variance policies fail to deliver a superior performance compared with the simple 1/N rule. In this paper, we propose a parametric portfolio policy that uses industry return momentum to improve portfolio performance. Our portfolio policies outperform a broad selection of established portfolio strategies in terms of Sharpe ratio and certainty equivalent returns. The proposed policies are particularly suitable for investors because portfolio turnover is only moderately increased compared to standard minimum-variance portfolios.

A new IPSO-SA approach for cardinality constrained portfolio optimization

Abstract: Article history: Received 1 October 2010 Received in revised form 7 January 2011 Accepted 10 January 2011 Available online 14 January 2011 The problem of portfolio optimization has always been a key concern for investors. This paper addresses a realistic portfolio optimization problem with floor, ceiling, and cardinality constraints. This problem is a mixed integer quadratic programming where traditional optimization methods fail to find the optimal solution, efficiently. The present paper develops a new hybrid approach based on an improved particle swarm optimization (PSO) and a modified simulated annealing (SA) to find the cardinality constrained efficient frontier. The proposed algorithm benefits from simple and easy characteristics of PSO with an adaptation of inertia weights and constriction factor. In addition, incorporating an SA procedure into IPSO helps escaping from local optima and improves the precision of convergence. Computational results on benchmark problems with up to 225 assets signify that our proposed algorithm exceeds not only the standard PSO but also the other heuristic algorithms previously presented to solve the cardinality constrained portfolio problem. © 2011 Growing Science Ltd. All rights reserved

Mean–Variance–Skewness–Kurtosis Approach to Portfolio Optimization: An Application in İstanbul Stock Exchange

Abstract: Portfolio optimization, the construction of the best combination of investment instruments that will meet the investors’ basic expectations under certain limitations, has an important place in the finance world. In the portfolio optimization, the Mean Variance model of Markowitz (1952) that expresses a tradeoff between return and risk for a set of portfolios, has played a critical role and affected other studies in this area. In the Mean Variance model, only the covariances between securities are considered in determining the risk of portfolios. The model is based on the assumptions that investors have a quadratic utility function and the return of the securities is distributed normally. Various studies that investigate the validity of these assumptions find evidence against them. Asset returns have significant skewness and kurtosis. In the light of these findings, it is seen that in recent years researchers use higher order of moments in the portfolio selection

A Class of Chance Constrained Multi-objective Portfolio Selection Model Under Fuzzy Random Environment

Abstract: This paper deals with a class of chance constrained portfolio selection problems in the fuzzy random decision making system. An integrated fuzzy random portfolio selection model with a chance constraint is proposed on the basis of the mean-variance model and the safety-first model. According to different definitions of chance, we consider two types of fuzzy random portfolio selection models: one is for the optimistic investors and the other is for the pessimistic investors. In order to deal with the fuzzy random models, we develop a few theorems on the variances of fuzzy random returns and the equivalent partitions of two types of chance constraints. We then transform the fuzzy random portfolio selection models into their equivalent crisp models. We further employ the e-constraint method to obtain the efficient frontier. Finally, we apply the proposed models and approaches to the Chinese stock market as an illustration.