Showing papers on "Efficient frontier published in 2006"

Minimum-Variance Portfolios in the U.S. Equity Market

Abstract: In the minimum-variance portfolio, far to the left on the efficient frontier, security weights are independent of expected security returns. Portfolios can be constructed using only the estimated security covariance matrix, without reference to equilibrium expected or actively forecasted returns. Empirical results illustrate the practical value of large-scale numerical optimizations using return-based covariance matrix estimation methodologies, providing new perspective on the factor characteristics of low-volatility portfolios. Optimizations that go back to 1968 reveal that the long-only minimum-variance portfolio has about three-fourths the realized risk of the capitalization-weighted market portfolio, with higher average returns.

Incorporating estimation errors into portfolio selection: Robust portfolio construction

Abstract: The authors explore the negative effect that estimation error has on mean-variance optimal portfolios. It is shown that asset weights in mean-variance optimal portfolios are very sensitive to slight changes in input parameters. This instability is magnified by the presence of constrains that asset managers typically impose on their portfolios. The authors propose to use robust mean variance, a new technique which is based on robust optimisation, a deterministic framework designed to explicitly consider parameter uncertainty in optimisation problems. Alternative uncertainty regions that create a less conservative robust problem are introduced. In fact, the authors' proposed approach does not assume that all estimation errors will negatively affect the portfolios, as is the case in traditional robust optimisation, but rather that there are as many errors with negative consequences as there are errors with positive consequences. The authors demonstrate through extensive computational experiments that portfolios generated with their proposed robust mean variance methodolgy typically outperform traditional mean variance portfolios in a variety of investment scenarios. Additionally, robust mean variance portfolios are usually less sensitive to input parameters.

Bank efficiency: The role of bank strategy and local market conditions

Abstract: In this paper we focus on the assumption of a common efficient frontier when performing an efficiency study for the banking sector. The fact that environmental factors that are not appropriately controlled may easily bias efficiency estimates. First, we estimate a common cost and profit frontier. In this first stage, as an innovation to the literature, we use exogenously computed input prices rather than the normally used endogenous input prices. Second, we regress the estimated inefficiencies on a set of a bank’s strategic choices, local banking market variables, and local (regional) macro variables. For the analysis, we use a unique dataset of 401 largely independent cooperative local banks in the Netherlands for the years 1998 and 1999. Our results show that the use of exogenous input prices rather than endogenous input prices is particularly important for the cost frontier as the spread in cost inefficiencies becomes larger and more plausible. Our second stage results suggest that most of the estimated inefficiency indeed is managerial (X-) inefficiency. Environmental factors do play a role, but only to a limited extent.

Asset and liability management under a continuous-time mean–variance optimization framework

Abstract: Asset and liability (AL) management under the mean–variance criteria refers to an optimization problem that maximizes the expected final surplus subject to a given variance of the final surplus or, equivalently, minimizes the variance of the final surplus subject to a given expected final surplus. We employ stochastic optimal control theory to analytically solve the AL management problem in a continuous-time setting. More specifically, we derive both the optimal policy and the mean–variance efficient frontier by a stochastic linear quadratic control framework. Then, the quality of the derived optimal AL management policy is examined by comparing it with those in the literature. We further discuss consequences of a discrepancy in objectives between equity holders and investors of a mutual fund. Finally, the optimal funding ratio, i.e., the wealth-to-liability ratio, is determined.

A benchmark approach to finance

Abstract: This paper derives a unified framework for portfolio optimization, derivative pricing, financial modeling, and risk measurement. It is based on the natural assumption that investors prefer more rather than less, in the sense that given two portfolios with the same diffusion coefficient value, the one with the higher drift is preferred. Each such investor is shown to hold an efficient portfolio in the sense of Markowitz with units in the market portfolio and the savings account. The market portfolio of investable wealth is shown to equal a combination of the growth optimal portfolio (GOP) and the savings account. In this setup the capital asset pricing model follows without the use of expected utility functions, Markovianity, or equilibrium assumptions. The expected increase of the discounted value of the GOP is shown to coincide with the expected increase of its discounted underlying value. The discounted GOP has the dynamics of a time transformed squared Bessel process of dimension four. The time transformation is given by the discounted underlying value of the GOP. The squared volatility of the GOP equals the discounted GOP drift, when expressed in units of the discounted GOP. Risk-neutral derivative pricing and actuarial pricing are generalized by the fair pricing concept, which uses the GOP as numeraire and the real-world probability measure as pricing measure. An equivalent risk-neutral martingale measure does not exist under the derived minimal market model.

Downside Loss Aversion and Portfolio Management

Abstract: Downside loss-averse preferences have seen a resurgence in the portfolio management literature. This is due to the increasing use of derivatives in managing equity portfolios and the increased use of quantitative techniques for bond portfolio management. We employ the lower partial moment as a risk measure for downside loss aversion and compare mean-variance (M-V) and mean-lower partial moment (M-LPM) optimal portfolios under nonnormal asset return distributions. When asset returns are nearly normally distributed, there is little difference between the optimal M-V and M-LPM portfolios. When asset returns are nonnormal with large left tails, we document significant differences in M-V and M-LPM optimal portfolios. This observation is consistent with industry usage of M-V theory for equity portfolios but not for fixed-income portfolios.

Master funds in portfolio analysis with general deviation measures

Abstract: Generalized measures of deviation are considered as substitutes for standard deviation in a framework like that of classical portfolio theory for coping with the uncertainty inherent in achieving rates of return beyond the risk-free rate. Such measures, derived for example from conditional value-at-risk and its variants, can reflect the different attitudes of different classes of investors. They lead nonetheless to generalized one-fund theorems in which a more customized version of portfolio optimization is the aim, rather than the idea that a single “master fund” might arise from market equilibrium and serve the interests of all investors. The results that are obtained cover discrete distributions along with continuous distributions. They are applicable therefore to portfolios involving derivatives, which create jumps in distribution functions at specific gain or loss values, well as to financial models involving finitely many scenarios. Furthermore, they deal rigorously with issues that come up at that level of generality, but have not received adequate attention, including possible lack of differentiability of the deviation expression with respect to the portfolio weights, and the potential nonuniqueness of optimal weights. The results also address in detail the phenomenon that if the risk-free rate lies above a certain threshold, the usually envisioned master fund must be replaced by one of alternative type, representing a “net short position” instead of a “net long position” in the risky instruments. For nonsymmetric deviation measures, the second type need not just be the reverse of the first type, and there can sometimes even be an interval for the risk-free rate in which no master fund of either type exists. A notion of basic fund, in place of master fund, is brought in to get around this difficulty and serve as a single guide to optimality regardless of such circumstances.

Has Monetary Policy Become More Efficient? A Cross-Country Analysis

Abstract: Over the past twenty years, macroeconomic performance has improved in industrialized and developing countries alike. In a broad cross-section of countries inflation volatility has fallen markedly while output variability has either fallen or risen only slightly. This increased stability can be attributed to either: 1) more efficient policymaking by the monetary authority, 2) a reduction in the variability of the aggregate supply shocks, or 3) changes in the structure of the economy. In this paper we develop a method for measuring changes in performance, and allocate the source of performance changes to these two factors. Our technique involves estimating movements toward an inflation and output variability efficiency frontier, and shifts in the frontier itself. We study the change from the 1980s to the 1990s in the macroeconomic performance of 24 countries and find that, for most of the analyzed countries, more efficient policy has been the driving force behind improved macroeconomic performance.

Mean-variance trade-offs in supply contracts

Abstract: We study the trade-offs faced by a manufacturer signing a portfolio of long-term contracts with its suppliers and having access to a spot market. The manufacturer incurs inventory risk when purchasing too many contracts and spot price risk when buying too few. We quantify these risks for a single selling period by studying the profit mean and variance for a given portfolio of option contracts. We characterize the set of efficient portfolios that the manufacturer must hold in order to obtain dominating mean-variance pairs. Among these, we emphasize the maximum expectation portfolio, obtained by solving the classical newsvendor problem, and the corresponding minimum variance portfolio. We show that the upper-level sets of a mean-variance utility function are connected. Hence, a greedy method will find the portfolios on the efficient frontier. Finally, we provide a comparison with standard hedging strategies and show that the approximation associated with financial hedging can be relatively inaccurate. © 2006 Wiley Periodicals, Inc. Naval Research Logistics 2006

Multi-moment Asset Allocation and Pricing Models

Abstract: About the Contributors. Preface. 1. Theoretical Foundations of Asset Allocations and Pricing Models with Higher-order Moments (Emmanuel Jurczenko and Bertrand Maillet). 2. On certain Geometric Aspects of Portfolio Optimisation with Higher Moments (Gustavo Athayde and Renato Flores). 3. Hedge Funds portfolio Selection with Higher-order Moments: A Non-parametric Mean-Variance-Skewness-Kurtosis Efficient Frontier (Emmanuel Jurczenko, Bertrand Maillet and Paul Merlin). 4. Higher Order Moments and Beyond (Luisa Tibiletti). 5. Gram-Charlier Expansions and Portfolio Selection in Non Gaussian Universes (Francois Desmoulins-Lebeault). 6. The Four-moment Capital Asset Pricing Model: between Asset Pricing and Asset Allocation (Emmanuel Jurczenko and Bertrand Maillet). 7. Multi-Moments Method For Portfolio Management: Generalized Capital Asset Pricing Model in Homogeneous and Heterogeneous Markets (Yannick Malevergne and Didier Sornette). 8. Modeling the Dynamics of Conditional Dependency Between Financial Series (Eric Jondeau and Michael Rockinger). 9. A Test of the Homogeneity of Asset Pricing Models (Giovanni Barone-Adesi, Patrick Gagliardini and Giovanni Urga). Index.

Efficient frontiers for electricity procurement by an LDC with multiple purchase options

Abstract: In meeting its retail sales obligations, management of a local distribution company (LDC) must determine the extent to which it should rely on spot markets, forward contracts, and the increasingly popular long-term tolling agreements under which it pays a fee to reserve generator capacity. We address these issues by solving a mathematical programming model to derive the efficient frontier that summarizes the optimal tradeoffs available to the LDC between procurement risk and expected cost. To illustrate the approach, we estimate the expected procurement costs and associated variances that proxy for risk through a spot-price regression for the spot-purchase alternative and a variable-cost regression for the tolling-agreement alternative. The estimated regressions yield the estimates required to determine the efficient frontier. We develop several such frontiers under alternative assumptions as to the forward-contract price and the tolling agreement's capacity payment, and discuss the implications of our results for LDC management.

Portfolio optimization in stochastic markets

Abstract: We consider a multiperiod mean-variance model where the model parameters change according to a stochastic market. The mean vector and covariance matrix of the random returns of risky assets all depend on the state of the market during any period where the market process is assumed to follow a Markov chain. Dynamic programming is used to solve an auxiliary problem which, in turn, gives the efficient frontier of the mean-variance formulation. An explicit expression is obtained for the efficient frontier and an illustrative example is given to demonstrate the application of the procedure.

Continuous-time mean-variance efficiency: the 80% rule

Abstract: This paper studies a continuous-time market where an agent, having specified an investment horizon and a targeted terminal mean return, seeks to minimize the variance of the return. The optimal portfolio of such a problem is called mean-variance efficient a la Markowitz. It is shown that, when the market coefficients are deterministic functions of time, a mean-variance efficient portfolio realizes the (discounted) targeted return on or before the terminal date with a probability greater than 0.8072. This number is universal irrespective of the market parameters, the targeted return and the length of the investment horizon.

Portfolio selection with a drawdown constraint

Abstract: When identifying optimal portfolios, practitioners often impose a drawdown constraint. This constraint is even explicit in some money management contracts such as the one recently involving Merrill Lynch’ management of Unilever’s pension fund. In this setting, we provide a characterization of optimal portfolios using mean–variance analysis. In the absence of a benchmark, we find that while the constraint typically decreases the optimal portfolio’s standard deviation, the constrained optimal portfolio can be notably mean–variance inefficient . In the presence of a benchmark such as in the Merrill Lynch–Unilever contract, we find that the constraint increases the optimal portfolio’s standard deviation and tracking error volatility. Thus, the constraint negatively affects a portfolio manager’s ability to track a benchmark.

Static Mean-Variance Analysis with Uncertain Time Horizon

Abstract: We generalize Markowitz analysis to the situations involving an uncertain exit time. Our approach preserves the form of the original problem in that an investor minimizes portfolio variance for a given level of the expected return. However, inputs are now given by the generalized expressions for mean and variance-covariance matrix involving moments of the random exit time in addition to the conditional moments of asset returns. Although efficient frontiers in the generalized and the standard Markowitz case may coincide under certain conditions, we demonstrate that, by means of an example, in general that is not true. In particular, portfolios efficient in the standard Markowitz sense can be inefficient in the generalized sense and vice versa. As a result, an investor facing an uncertain time horizon and investing as if her time of exit is certain would in general make suboptimal portfolio allocation decisions. Numerical simulations show that a significant efficiency loss can be induced by an improper use of standard mean-variance analysis when time horizon is uncertain.

Finding the efficient frontier of a bi-criteria, spatially explicit, harvest scheduling problem

Abstract: This article evaluates the performance of five traditional methods and one new method of generating the efficient frontier for a bi-criteria, spatially explicit harvest scheduling problem. The problem is to find all possible efficient solutions, thus defining the trade-offs between two objectives: (1) maximizing the net present value of the forest and (2) maximizing the minimum area over the planning horizon in large, mature forest patches. The methods for generating the efficient frontier were tested using a hypothetical forest consisting of 50 stands. The methods were compared based on the number of efficient solutions each method can identify and on how quickly the solutions were identified. The potential to generalize these algorithms to 3- or n-criteria cases is also assessed. Three of the traditional approaches, the - constraining; the triangles method, the decomposition algorithm based on the Tchebycheff metric; and the new, proposed method are capable of generating all or most of the efficient solutions. However, the triangles and the new method far outperformed the other approaches in terms of solution time. The new method, called alpha-delta, appears to be the simplest to generalize to the tri-criteria case. FOR .S CI. 52(1):93-107.

Efficient electricity portfolios for Switzerland and the United States

Abstract: This study applies financial portfolio theory to determine efficient electricity-generating technology mixes for Switzerland and the United States. Expected returns are given by the (negative of the) rate of increase of power generation cost. Volatility of returns relates to the standard deviation of the cost increase associated with the portfolio, which contains Nuclear, Run of river, Storage hydro and Solar in the case of Switzerland, and Coal, Nuclear, Gas, Oil, and Wind in the case of the United States. Since shocks in generation costs are found to be correlated, the seemingly unrelated regression estimation (SURE) method is applied for filtering out the systematic component of the covariance matrix of the cost changes. Results suggest that at observed generation costs in 2003, the maximum expected return (MER) portfolio for Switzerland would call for a shift towards Nuclear and Solar, and therefore away from Run of river and Storage hydro. By way of contrast, the minimum variance (MV) portfolio mainly contains Nuclear power and Storage hydro. The 2003 MER portfolio for the United States contains Coal generated electricity and Wind, while the MV alternative combines Coal, Nuclear, Oil and Wind. Interestingly, Gas does not play any role in the determination of efficient electricity portfolios in the United States.

Portfolio Optimization: New Capabilities and Future Methods

Abstract: This paper addresses the problem of portfolio selection in finance. In many cases, currently available software to compute the efficient frontier runs into difficulty in problems with more than about 600 securities. To proceed beyond this size, it is often necessary to modify the problem in which case there is typically a loss of information. In this paper, we discuss a computer capability that can exactly compute mean-variance efficient frontiers of problems with up to 2,000 securities in very reasonable time (even if a problem’s covariance matrix is 100% dense). The paper also discusses an augmentation to the theory of portfolio selection that allows multiple objectives (such as dividends, liquidity, social responsibility, amount invested in R&D, and so forth) to be incorporated into the portfolio selection process. In such problems, the efficient set is no longer a “frontier,” but is now best described as a “surface” with the interesting property that it is composed of platelets (like on the back of a turtle). Moreover, the computer capability that can compute the exact efficient frontier of a mean-variance problem with up to 2,000 securities also has, after additional coding, the ability to compute exactly all platelets of the efficient surface of a tri-criterion portfolio problem with up to 400 securities.

Developments in Multi-Attribute Portfolio Selection

Abstract: In this paper we reconcile why it is possible that people in finance view conventional portfolio selection as a single criterion problem and people in multiple criteria optimization view it as a bi-criterion problem. We then show how, for more complex investors, the theory of mean-variance portfolio selection can be extended to include additional objectives such as dividends, liquidity, turnover, number of securities in a portfolio, and so forth. This is followed by a discussion of the nature of the nondominated sets of multiple objective portfolio selection problems and developments underway for the solution of such problems.

Efficient Electricity Portfolios for Switzerland and the United States

Abstract: This study applies financial portfolio theory to determine efficient electricity-generating technology mixes for Switzerland and the United States. Expected returns are given by the (negative of the) rate of increase of power generation cost. Volatility of returns relates to the standard deviation of the cost increase associated with the portfolio, which contains Nuclear, Run of river, Storage hydro and Solar in the case of Switzerland, and Coal, Nuclear, Gas, Oil, and Wind in the case of the United States. Since shocks in generation costs are found to be correlated, the seemingly unrelated regression estimation (SURE) method is applied for filtering out the systematic component of the covariance matrix of the cost changes. Results suggest that at observed generation costs in 2003, the maximum expected return (MER) portfolio for Switzerland would call for a shift towards Nuclear and Solar, and therefore away from Run of river and Storage hydro. By way of contrast, the minimum variance (MV) portfolio mainly contains Nuclear power and Storage hydro. The 2003 MER portfolio for the United States contains Coal generated electricity and Wind, while the MV alternative combines Coal, Nuclear, Oil and Wind. Interestingly, Gas does not play any role in the determination of efficient electricity portfolios in the United States.

Bond Portfolio Optimization: A Risk-Return Approach

Abstract: In this article, the authors apply Markowitz’s approach of portfolio selection to government bond portfolios. As a main feature of the analysis, the term structure models is used to estimate expected returns, return variances, and covariances of different bonds. The authors’ empirical study for the German market shows that a small number of risky bonds is sufficient to reach very promising predicted risk-return profiles. If the number of risky bonds in the portfolio is not too large and the term structure model does not contain more than two factors, these predictions are confirmed by the realized risk-return profiles.

Determining portfolio performance measures by weight-based action detection

Abstract: A portfolio-analysis tool receives data that describe an actual portfolio. It computes from those data the returns or other performance measures of hypothetical portfolios whose holdings are drawn from the assets that the actual portfolio held during some period. Among the purposes of doing so is to detect biases made in investment-portfolio actions of the type taken, for instance, to accommodate cash inflows and withdrawals. For that purpose, differences between the hypothetical portfolio and the actual portfolio are so made as to offset portfolio actions identified by finding differences between the weights that positions actually exhibit and the weights they would result from return only. Returns for the hypothetical portfolio are computed by calculating an offset return incrementally, one such offset at a time, and then computing the hypothetical portfolio's return as the sum of quantities proportional to the offset return and that of the actual portfolio.

A Note on the Mean-Variance Analysis of Self-Financing Portfolios

Abstract: This paper extends the work of Korkie and Turtle (2002) by first proving that the traditional estimate for the optimal return of self-financing portfolios always over-estimates from its theoretic value. To circumvent the problem, we develop a Bootstrap estimate for the optimal return of self-financing portfolios and prove that this estimate is consistent with its counterpart parameter. We further demonstrate the superiority of our proposed estimate over the traditional estimate by simulation.

Full-spectrum portfolio and diversity analysis of energy technologies

Abstract: Publisher Summary Energy diversity and security are evaluated using Stirling's Multi-criteria Diversity Analysis (MDA) as well as more classical Markowitz Mean Variance Portfolio (MVP) theory. Each of these approaches is capable of producing an Efficient Frontier (EF) that shows optimal generating mixes—those that maximize performance (i.e. minimize cost) while minimizing risk or uncertainty (i.e. maximizing diversity). MDA covers the full spectrum of “incertitude,” reaching into areas where little is known about the range of possible outcomes, let alone their probabilities. However, MDA does not exploit statistical information that is available in certain parts of the risk spectrum where historic means, variances, and co-variances of outcomes are known as well as are used to make inferences about the future. MVP operates precisely in this space, although, like other capital market models, its prescriptive value rests on the idea that the past is the best guide to the future and that. As such MVP can be blind to unforeseen events that create future structural change.

Constructing an ‘efficient frontier’ of accounting journal quality

Abstract: This paper reports the construction of an 'efficient frontier' of the perceived quality attributes of academic accounting journals. The analysis is based on perception data from two web-based surveys of Australasian and British academics. The research reported here contributes to the existing literature by augmenting the commonly supported single dimension of quality with an additional measure indicating the variation of perceptions of journal quality. The result of combining these factors is depicted diagrammatically in a manner that reflects the risk and return trade-off as conceptualised in the capital market model of an efficient frontier of investment opportunities. This conceptualisation of a 'market' for accounting research provides a context in which to highlight the complex issues facing academics in their roles as editors, researchers and authors. The analysis indicates that the perceptions of the so-called 'elite' US accounting journals have become unsettled particularly in Australasia, showing high levels of variability in perceived quality, while other traditionally highly ranked journals (ABR, AOS, CAR) have a more 'efficient' combination of high-quality ranking and lower dispersion of perceptions. The implications of these results for accounting academics in the context of what is often seen as a market for accounting research are discussed. © 2006 Elsevier Ltd. All rights reserved.

Measuring Performance Electric Power Generations Using Artificial Neural Networks and Fuzzy Clustering

Abstract: The efficiency frontier analysis has been an important approach of evaluating firms' performance in private and public sectors. There have been many efficiency frontier analysis methods reported in the literature. However, the assumptions made for each of these methods are restrictive. Each of these methodologies has its strength as well as major limitations. This study proposes a nonparametric efficiency frontier analysis method based on the adaptive neural network technique for measuring efficiency as a complementary tool for the common techniques of the efficiency studies in the previous studies. The proposed computational methods are able to find a stochastic frontier based on a set of input-output observational data and do not require explicit assumptions about the function structure of the stochastic frontier. In purposed algorithm, for calculating the efficiency scores, a similar approach to econometric methods has been used and the effect of the scale of decision making unit (DMU) on its efficiency is included and the unit used for the correction is selected by notice of its scale. For increasing homogeneousness, the algorithm is proposed that use fuzzy C-means method to cluster DMUs. An example using real data is presented for illustrative purposes. In the application to the power generation sector of Iran, we find that the neural network provide more robust results to rank decision making units than the conventional methods

Integrated approach to improving the value potential of biopharmaceutical R&D portfolios while mitigating risk

Abstract: Effective prioritisation of R&D portfolios under resource constraints is critical for biopharmaceutical companies to gain competitive advantage. This paper presents an application of a prototype software tool to assess the reward and risk associated with different drug portfolios in development. The tool adopts a hierarchical framework to incorporate the interactions between drug development activities, the available resources and databases. The valuation approach highlights the cash flow implications of diverse portfolios under uncertainty and uses efficient frontier analysis to prioritise portfolios for given constraints. A case study is presented to illustrate the application of this method where Monte Carlo simulations are used to capture the inherent uncertainties in drug development. The example addresses the portfolio management question of which antibody drug candidates to select for clinical development given finite levels of resources. The analysis highlighted the impact of different drug combinations on the expected portfolio profitability and risk. The simulation studies were used to generate efficient frontiers so as to identify the optimal portfolios at different levels of risk and budgetary constraint. This valuation method helps decision-makers to identify clearly where a company portfolio is positioned with regard to the risk-return characteristics of alternative product portfolios and hence facilitates investment decisions. Copyright © 2006 Society of Chemical Industry