Showing papers on "Efficient frontier published in 2005"
Posted Content•
TL;DR: In this paper, the authors present a method of calculating a portfolio that gives the optimal value-at-risk (VAR) among those which yield at least some specified expected return.
Abstract: Value-at-Risk (VAR) is an important and widely used measure of the extent to which a given portfolio is subject to risk present in financial markets. In this paper, we present a method of calculating a portfolio that gives the optimal VAR among those which yield at least some specified expected return. This method allows us to calculate the mean-VAR-efficient frontier. The method is based on the approximation of historical VAR by smoothed VAR (SVAR), which filters out local irregular behavior of the historical VAR function. Moreover, we compare VAR as a risk measure to other well-known measures of risk, such as conditional value-at risk (CVAR) and the standard deviation. We show that the resulting efficient frontiers are quite different. An investor who wants to controls his or her VAR should not look at portfolios lying on other than the VAR efficient frontier, although the calculation of this frontier is algorithmically more complex than other frontiers. We support this conjecture by presenting the results of a large-scale experiment with a representative selection of stock and bond indices from developed and emerging markets that involved the computation of many thousand VAR-optimal portfolios.
293 citations
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TL;DR: In this article, a continuous-time mean-variance portfolio selection problem is studied where all the market coefficients are random and the wealth process under any admissible trading strategy is not allowed to be below zero at any time.
Abstract: A continuous-time mean-variance portfolio selection problem is studied where all the market coefficients are random and the wealth process under any admissible trading strategy is not allowed to be below zero at any time. The trading strategy under consideration is defined in terms of the dollar amounts, rather than the proportions of wealth, allocated in individual stocks. The problem is completely solved using a decomposition approach. Specifically, a (constrained) variance minimizing problem is formulated and its feasibility is characterized. Then, after a system of equations for two Lagrange multipliers is solved, variance minimizing portfolios are derived as the replicating portfolios of some contingent claims, and the variance minimizing frontier is obtained. Finally, the efficient frontier is identified as an appropriate portion of the variance minimizing frontier after the monotonicity of the minimum variance on the expected terminal wealth over this portion is proved and all the efficient portfolios are found. In the special case where the market coefficients are deterministic, efficient portfolios are explicitly expressed as feedback of the current wealth, and the efficient frontier is represented by parameterized equations. Our results indicate that the efficient policy for a mean-variance investor is simply to purchase a European put option that is chosen, according to his or her risk preferences, from a particular class of options.
293 citations
TL;DR: In this article, a continuous-time mean-variance portfolio selection problem is studied where all the market coefficients are random and the wealth process under any admissible trading strategy is not allowed to be below zero at any time.
Abstract: A continuous-time mean-variance portfolio selection problem is studied where all the market coefficients are random and the wealth process under any admissible trading strategy is not allowed to be below zero at any time. The trading strategy under consideration is defined in terms of the dollar amounts, rather than the proportions of wealth, allocated in individual stocks. The problem is completely solved using a decomposition approach. Specifically, a (constrained) variance minimizing problem is formulated and its feasibility is characterized. Then, after a system of equations for two Lagrange multipliers is solved, variance minimizing portfolios are derived as the replicating portfolios of some contingent claims, and the variance minimizing frontier is obtained. Finally, the efficient frontier is identified as an appropriate portion of the variance minimizing frontier after the monotonicity of the minimum variance on the expected terminal wealth over this portion is proved and all the efficient portfolios are found. In the special case where the market coefficients are deterministic, efficient portfolios are explicitly expressed as feedback of the current wealth, and the efficient frontier is represented by parameterized equations. Our results indicate that the efficient policy for a mean-variance investor is simply to purchase a European put option that is chosen, according to his or her risk preferences, from a particular class of options.
291 citations
TL;DR: In this article, the authors proposed a nonparametric estimator of the efficient frontier, which is based on conditional quantiles of an appropriate distribution associated with the production process and provided the statistical theory of the obtained estimators.
Abstract: In frontier analysis, most of the nonparametric approaches (free disposal hull [FDH], data envelopment analysis [DEA]) are based on envelopment ideas, and their statistical theory is now mostly available. However, by construction, they are very sensitive to outliers. Recently, a robust nonparametric estimator has been suggested by Cazals, Florens, and Simar (2002, Journal of Econometrics 1, 1–25). In place of estimating the full frontier, they propose rather to estimate an expected frontier of order m. Similarly, we construct a new nonparametric estimator of the efficient frontier. It is based on conditional quantiles of an appropriate distribution associated with the production process. We show how these quantiles are interesting in efficiency analysis. We provide the statistical theory of the obtained estimators. We illustrate with some simulated examples and a frontier analysis of French post offices, showing the advantage of our estimators compared with the estimators of the expected maximal output frontiers of order m.We thank J.P. Florens for helpful discussions and C. Cazals for providing the post office data set. We also are very grateful to the referees for useful suggestions.
282 citations
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TL;DR: A nonparametric efficiency measurement approach for the static portfolio selection problem in mean-variance-skewness space that permits to differentiate between portfolio efficiency and allocative efficiency, and a convexity efficiency component related to the difference between the primal, nonconvex approach and the dual, convex approach.
Abstract: This paper proposes a nonparametric efficiency measurement approach for the static portfolio selection problem in mean-variance-skewness space. A shortage function is defined that looks for possible increases in return and skewness and decreases in variance. Global optimality is guaranteed for the resulting optimal portfolios. We also establish a link to a proper indirect mean-variance-skewness utility function. For computational reasons, the optimal portfolios resulting from this dual approach are only locally optimal. This framework permits to differentiate between portfolio efficiency and allocative efficiency, and a convexity efficiency component related to the difference between the primal, non-convex approach and the dual, convex approach. Furthermore, in principle, information can be retrieved about the revealed risk aversion and prudence of investors. An empirical section on a small sample of assets serves as an illustration.
152 citations
TL;DR: This paper is devoted to the study of a stochastic linear-quadratic optimal control problem where the control variable is constrained in a cone, and all the coefficients of the problem are random processes.
Abstract: This paper is devoted to the study of a stochastic linear-quadratic (LQ) optimal control problem where the control variable is constrained in a cone, and all the coefficients of the problem are random processes. Employing Tanaka's formula, optimal control and optimal cost are explicitly obtained via solutions to two extended stochastic Riccati equations (ESREs). The ESREs, introduced for the first time in this paper, are highly nonlinear backward stochastic differential equations (BSDEs), whose solvability is proved based on a truncation function technique and Kobylanski's results. The general results obtained are then applied to a mean-variance portfolio selection problem for a financial market with random appreciation and volatility rates, and with short-selling prohibited. Feasibility of the problem is characterized, and efficient portfolios and efficient frontier are presented in closed forms.
105 citations
Posted Content•
TL;DR: In this paper, the authors consider classes of reward-risk optimization problems that arise from different choices of reward and risk measures and present an algorithm based on a sequence of convex feasibility problems for the general quasi-concave ratio problem.
Abstract: We consider classes of reward-risk optimization problems that arise from different choices of reward and risk measures In certain examples the generic problem reduces to linear or quadratic programming problems We state an algorithm based on a sequence of convex feasibility problems for the general quasi-concave ratio problem We also consider reward-risk ratios that are appropriate in particular for non-normal assets return distributions and are not quasi-concave
86 citations
TL;DR: Important properties of the mean–absolute deviation (MAD) portfolio optimization model, which was introduced in 1990 to cope with very large–scale portfolio optimization problems, are surveyed.
Abstract: We will survey important properties of the mean–absolute deviation (MAD) portfolio optimization model, which was introduced in 1990 to cope with very large–scale portfolio optimization problems. MAD model has been used for solving huge portfolio optimization models including internationally diversified investment model, long-term ALM model, mortgage–backed security portfolio optimization model. Also, the MAD model enjoys several nice theoretical properties. In particular, all CAPM type relations for mean–variance model hold for the MAD model as well. Further, the MAD model is more compatible to the fundamental principle of rational decision making.
82 citations
01 Jan 2005
TL;DR: This dissertation describes a way to stably calibrate GH distributions for a wider range of parameters than has previously been reported and develops a version of the EM algorithm for calibrating GH distributions, which enables for the first time certain GH distributions to be used in modeling contexts when previously they have been numerically intractable.
Abstract: The distributions of many financial quantities are well-known to have heavy tails, exhibit skewness, and have other non-Gaussian characteristics. In this dissertation we study an especially promising family: the multivariate generalized hyperbolic distributions (GH). This family includes and generalizes the familiar Gaussian and Student t distributions, and the so-called skewed t distributions, among many others.
The primary obstacle to the applications of such distributions is the numerical difficulty of calibrating the distributional parameters to the data. In this dissertation we describe a way to stably calibrate GH distributions for a wider range of parameters than has previously been reported. In particular, we develop a version of the EM algorithm for calibrating GH distributions. This is a modification of methods proposed in McNeil, Frey, and Embrechts (2005), and generalizes the algorithm of Protassov (2004). Our algorithm extends the stability of the calibration procedure to a wide range of parameters, now including parameter values that maximize log-likelihood for our real market data sets. This allows for the first time certain GH distributions to be used in modeling contexts when previously they have been numerically intractable.
Our algorithm enables us to make new uses of GH distributions in three financial applications. First, we forecast univariate Value-at-Risk (VaR) for stock index returns, and we show in out-of-sample backtesting that the GH distributions outperform the Gaussian distribution. Second, we calculate an efficient frontier for equity portfolio optimization under the skewed-t distribution and using Expected Shortfall as the risk measure. Here, we show that the Gaussian efficient frontier is actually unreachable if returns are skewed t distributed. Third, we build an intensity-based model to price Basket Credit Default Swaps by calibrating the skewed t distribution directly, without the need to separately calibrate the skewed t copula. To our knowledge this is the first use of the skewed t distribution in portfolio optimization and in portfolio credit risk.
82 citations
TL;DR: The admissible efficient portfolio model is proposed under the assumption that the expected return and risk of asset have admissible errors with general investment constraints.
79 citations
TL;DR: In this paper, the mean-Gini (MG) efficient portfolio frontier is derived for U.S. classes of assets and analyzed analytically by restricting asset distributions, showing that MG is more diversified than MV.
Abstract: A main advantage of the mean-variance (MV) portfolio frontier is its simplicity and ease of derivation. A major shortcoming, however, lies in its familiar restrictions, such as the quadraticity of preferences or the normality of distributions. As a workable alternative to MV, we present the mean-Gini (MG) efficient portfolio frontier. Using an optimization algorithm, we compute MG and mean-extended Gini (MEG) efficient frontiers and compare the results with the MV frontier. MEG allows for the explicit introduction of risk aversion in building the efficient frontier. For U.S. classes of assets, MG and MEG efficient portfolios constructed using Ibbotson (2000) monthly returns appear to be more diversified than MV portfolios. When short sales are allowed, distinct investor risk aversions lead to different patterns of portfolio diversification, a result that is less obvious when short sales are foreclosed. Furthermore, we derive analytically the MG efficient portfolio frontier by restricting asset distributions. The MG frontier derivation is identical in structure to that of the MV efficient frontier derivation. The penalty paid for simplifying the search for the MG efficient frontier is the loss of some information about the distribution of assets.
12 Dec 2005
TL;DR: This work introduces a powerful hybrid multiobjective optimization approach that combines evolutionary computation with linear programming to simultaneously maximize these return measures, minimize these risk measures, and identify the efficient frontier of portfolios that satisfy all constraints.
Abstract: A principal challenge in modern computational finance is efficient portfolio design - portfolio optimization followed by decision-making. Optimization based on even the widely used Markowitz two-objective mean-variance approach becomes computationally challenging for real-life portfolios. Practical portfolio design introduces further complexity as it requires the optimization of multiple return and risk measures subject to a variety of risk and regulatory constraints. Further, some of these measures may be nonlinear and nonconvex, presenting a daunting challenge to conventional optimization approaches. We introduce a powerful hybrid multiobjective optimization approach that combines evolutionary computation with linear programming to simultaneously maximize these return measures, minimize these risk measures, and identify the efficient frontier of portfolios that satisfy all constraints. We also present a novel interactive graphical decision-making method that allows the decision-maker to quickly down-select to a small subset of efficient portfolios. The approach has been tested on real-life portfolios with hundreds to thousands of assets, and is currently being used for investment decision-making in industry.
TL;DR: In this paper, a stochastic programming model for portfolio selection is proposed, in which the portfolio semivariance is the objective function to be minimized subject to standard parametric constraints, leading to the mean-semivariance efficient frontier.
Abstract: An ongoing stream in financial analysis proposes mean‐semivariance in place of mean‐variance as an alternative approach to portfolio selection, since segments of investors are more averse to returns below the mean value than to deviations above and below the mean value. Accordingly, this paper searches for a stochastic programming model in which the portfolio semivariance is the objective function to be minimized subject to standard parametric constraints, which leads to the mean‐semivariance efficient frontier. The proposed model relies on an empirically tested basis, say, portfolio diversification and the empirical validity of Sharpe's beta regression equation relating each asset return to the market. From this basis, the portfolio semivariance matrix form is strictly mathematically derived, thus an operational quadratic objective function is obtained without resorting to heuristics. Ease of computation is highlighted by a numerical example, which allows one to compare the results from the proposed mean...
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TL;DR: In this article, two additional models, (i) maximin, and (ii) minimization of mean absolute deviation, were proposed to examine to what extent all three formulations provide similar portfolios.
Abstract: The classical Quadratic Programming (QP) formulation of the well-known portfolio selection problem has traditionally been regarded as cumbersome and time consuming. This paper formulates two additional models, (i) maximin, and (ii) minimization of mean absolute deviation. Data from 67 securities over 48 months are used to examine to what extent all three formulations provide similar portfolios. As expected, the maximin formulation yields the highest return and risk, while the QP formulation provides the lowest risk and return, which also creates the efficient frontier. The minimization of mean absolute deviation is close to the QP formulation. When the expected returns are confronted with the true ones at the end of a six months period, the maximin portfolios seem to be the most robust of all.
TL;DR: The proposed Constant Returns to Scale approach has two interesting features: (a) the sequence of targets ends in the efficient frontier and (b) the final, efficient target is generally closer to the original unit than the one-step projection is.
Abstract: Data Envelopment Analysis (DEA) can be used for assessing the relative efficiency of a number of operating units, finding, for each inefficient unit, a target operating point lying on the efficient frontier Most DEA models project an inefficient unit onto a most distant target, which makes its attainment more difficult In this paper, we advocate determining a sequence of targets, each one within an appropriate, short distance of the preceding The proposed Constant Returns to Scale approach has two interesting features: (a) the sequence of targets ends in the efficient frontier and (b) the final, efficient target is generally closer to the original unit than the one-step projection is
TL;DR: A context-dependent DEA is presented which measures the relative attractiveness of libraries on a specific performance level against libraries exhibiting poorer performance and provides finer DEA results with respect to the performance of all DMUs.
Abstract: Data envelopment analysis (DEA) identifies an empirical efficient frontier of a set of peer decision making units (DMUs) with multiple inputs and outputs. The efficient frontier is characterized by the DMUs with an unity efficiency score. The performance of inefficient DMUs is characterized with respect to the identified efficient frontier. If the performance of inefficient DMUs deteriorates or improves (up to the frontier), the efficient DMUs still have an unity efficiency score. However, the performance of DMUs may be influenced by the context — e.g. a product may appear attractive against a background of less attractive alternatives and unattractive when compared to more attractive alternatives. With an application to Tokyo public libraries, the current paper presents and demonstrates a context-dependent DEA which measures the relative attractiveness of libraries on a specific performance level against libraries exhibiting poorer performance. The set of libraries are grouped into different levels of efficient frontiers. Each efficient frontier (on a specific performance level) is then used as evaluation context for the relative attractiveness. The performance of the efficient libraries changes as the inefficient libraries change their performance. The context-dependent DEA can also be used to differentiate the performance of efficient DMUs. The context-dependent DEA provides finer DEA results with respect to the performance of all DMUs.
TL;DR: A method is introduced for identifying efficient frontier and efficient DMUs in data envelopment analysis for identifying efficiency scores of decision making units (DMUs).
TL;DR: In this paper, a new portfolio theory is proposed, which takes into account the non-Gaussian properties of asset returns, quantified by the so-called moments and cumulants of its distribution of returns.
Abstract: A new portfolio theory takes into account the non-Gaussian properties of asset returns. The non-Gaussian properties of a portfolio are quantified by the so-called moments and cumulants of its distribution of returns. Generalizing the concept of efficient frontiers, the non-Gaussian efficient frontier depends on the chosen risk measure, corresponding to different orders or combinations of centered moments or cumulants. These extended formulas let investors analyze the conditions under which it is possible to have one9s cake and eat it too, in order to construct a portfolio with both higher return and fewer major risks.
TL;DR: In this article, the authors analyzed performance and portfolio choice of banks' investments across business units using methodologies developed mainly for equity investments, and found that there are gains to diversification and that risk adjusted performance is mostly consistent with optimal portfolio choice.
Abstract: This paper analyzes performance and portfolio choice of banks’ investments across business units using methodologies developed mainly for equity investments. The backgrounds to the paper are major recent developments in the financial services industry, mainly consolidation in the banking industry that raised the issue of efficiency gains due to diversification. The paper focuses on banks in Israel as an extended case study, using the fact that Israeli banks have operated as (limited) universal banks for a long time. The results suggest that there are gains to diversification and that risk adjusted performance is mostly consistent with optimal portfolio choice. Most of the previous research in this area has been done in the US. These studies necessarily focused on hypothetical combinations of different business activities because of the legal limits on US banks. Thus this paper adds to the literature both by examining actual combinations and looking at another country.
Journal Article•
TL;DR: In this paper, a mean-CVaR optimal combined bidding model is built by considering the risk and expected revenue rate synthetically, based on the proposed model, the efficient frontier and the electricity allocation ratio for the power suppliers in four markets, such as annual contract market, monthly contract market and day-ahead market, were calculated.
Abstract: In electricity market, the different markets have different price fluctuation and stochastic changing characteristics of revenue rate. To obtain the maximum annual profits and the minimum risk value, the power suppliers should allocate the bidding electricity to each market reasonably. Using the risk management theory in financial research field for reference, taking the conditional value at risk (CVaR) as risk measurement index, a novel Mean-CVaR optimal combined bidding model is built by considering the risk and expected revenue rate synthetically. Based on the proposed model, the efficient frontier and the electricity allocation ratio for the power suppliers in four markets, such as annual contract market, monthly contract market, day-ahead market and spot market are calculated. The calculation results show that the proposed model can truly reflect the essential characters of the market risk facing the power suppliers and guarantee the power suppliers to obtain the expected profits at the minimum CVaR risk level. So it provides the power suppliers a new way for bidding decision-making and risk valuation.
TL;DR: In this paper, the authors present an analysis of the efficiency frontier, formed by a set of efficient portfolios corresponding to a parameterized class of utility functions, and develop a procedure for testing the separability of this frontier into K independent funds.
TL;DR: In this article, the impact of the stochastic evolution of the active membership population on the mismatch between assets and liabilities of a defined benefit pension scheme was investigated and the trade-off between risk and cost of contribution strategies was formulated using a constrained nonlinear programming approach.
Abstract: This paper focuses on the impact of the stochastic evolution of the active membership population on the mismatch between assets and liabilities of a defined benefit pension scheme. Classical results in the actuarial literature on pension plan population theory have been extended to the stochastic case. The paper formulates the trade-off between risk and cost of contribution strategies. Then, using a constrained nonlinear programming approach, optimal contributions strategies have been derived and the trade-off solved by means of identifying an efficient frontier. Finally, a numerical application has been carried out, showing the inefficiency of certain classical normal cost methods.
TL;DR: In this article, the authors introduce the concept of product performance from the perspective of customers, which is measured as a ratio of outputs that customers obtain from a product relative to inputs that customers have to spend for purchasing and using the product.
Abstract: This study introduces the concept of product performance from the perspective of customers. Product performance is measured as a ratio of outputs that customers obtain from a product relative to inputs that customers have to spend for purchasing and using the product. The output side is modelled by a set of customer-relevant parameters such as technical performance attributes but also non-functional benefits and brand strength; the input side reflects user costs. More than 60% of the cars in this study are rated as efficient and obtain the maximum efficiency value of unity. They form the efficient frontier of the compact car market representing a reference function for performance evaluation. Using a super-efficiency model, it is possible to differentiate the efficient products that are left with a score of 100% by standard efficiency models. Our approach is relevant for companies because implications for product design and market segmentation can be derived.
22 Jun 2005
TL;DR: In this paper, the possibilistic mean-variance model of portfolio selection is presented under the assumption that the returns of assets are fuzzy numbers, which can better integrate the experts' knowledge and the managers' subjective opinions to compare with conventional probabilistic mean -variance methodology.
Abstract: There are many non-probabilistic factors that affect the financial markets. In this paper, the possibilistic mean-variance model of portfolio selection is presented under the assumption that the returns of assets are fuzzy numbers, which can better integrate the experts' knowledge and the managers' subjective opinions to compare with conventional probabilistic mean-variance methodology. The possibilistic efficient frontier is derived explicitly when short sales are not allowed on all risky assets and a risk-free asset.
Patent•
21 Jun 2005
TL;DR: In this article, a mean-variance efficient frontier is calculated based on input data characterizing the defined expected return and the defined standard deviation of return of each of the plurality of assets of an optimal portfolio.
Abstract: A computer-implemented method and computer program product for selecting a portfolio weight (subject to specified constraints) for each of a plurality of assets of an optimal portfolio. A mean-variance efficient frontier is calculated based on input data characterizing the defined expected return and the defined standard deviation of return of each of the plurality of assets. Multiple sets of optimization inputs are drawn from a distribution of simulated optimization inputs consistent with the defined expected return, the defined standard deviation of return of each of the plurality of assets and then a simulated mean-variance efficient frontier is computed for each set of optimization inputs. A meta-resampled efficient frontier is determined as a statistical mean of associated portfolios among the simulated mean-variance efficient frontiers, and a portfolio weight is selected for each asset from the meta-resampled efficient frontier according to a specified investment objective. The number of simulations and the number of simulation periods is determined on the basis of a specified level of forecast certainty.
TL;DR: An improved aggregated ratio model is established to better comprehend the inner relationship between the two methods, and an inference that the observed DMU is ratio efficient if and only if it is CCR efficient is proposed.
Abstract: This paper proposes an aggregated ratio analysis model which can be utilized to evaluate relative efficiency of decision making units (DMUs). We show that our proposed ratio model is equivalent to the CCR DEA model. This equivalence property offers a great deal of opportunities for DEA to be interpreted and applied in different ways. Our model also offers an insight into the frontier analysis. Whether a DMU is on the frontier or efficient frontier can be informed by using our aggregated ratio analysis. Several results developed in the paper are coincident with that in the literature.
TL;DR: In this article, a mean-variance-skewness portfolio optimization model is proposed, which can be used for constructing a portfolio when the asset returns follow skewed distribution.
Abstract: We will show that a mean-variance-skewness portfolio optimization model, a direct extension of the classical mean-variance model can be solved exactly and fast by using the state-of-the-art integer programming approach. This implies that we can now calculate a portfolio with maximal expected utility for any decreasing risk averse utility function. Also, we will show that this model can be used as a practical tool for constructing a portfolio when the asset returns follow skewed distribution. As an example, we apply this model to construct an index plus alpha portfolio.
TL;DR: In this article, the authors developed a new theory of portfolio and risk based on incremental entropy and Markowitz's theory, which emphasizes that there is an objectively optimal portfolio for given probability of returns.
Abstract: Purpose – To develop a new theory of portfolio and risk based on incremental entropy and Markowitz's theory.Design/methodology/approach – Replacing 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.Findings – The 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/value – This 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.
Journal Article•
TL;DR: In this article, the authors studied a multi-period portfolio optimization problem with uncertain exit time and obtained the optimal investment strategy and the analytical expression of efficient frontier by applying the dynamic programming principle.
Abstract: The paper studies a multi_period portfolio optimization problem with uncertain exit time. With the assumption that the exit time is a random variable obeying some distribution this problem of uncertain exit time is translated into a determinate horizon one. Then the classical methods can be used to solve this model. By applying the dynamic programming principle we obtain the optimal investment strategy and the analytical expression of efficient frontier. Through an example we also prove that this paper is an extension to determinate horizon case and that the optimal investment strategy is affected by the distribution of exit time.
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TL;DR: In this paper, the authors proposed a new method based on the large deviations theory to select an optimal investment for a large portfolio such that the risk, defined as the probability that the portfolio return underperforms an investable benchmark, is minimal.
Abstract: In this study, we propose a new method based on the large deviations theory to select an optimal investment for a large portfolio such that the risk, which is defined as the probability that the portfolio return underperforms an investable benchmark, is minimal. As a particular case, we examine the effect of two types of asymmetric dependence; 1) asymmetry in a portfolio return distribution, and 2) asymmetric dependence between asset returns, on the optimal portfolio invested in two risky assets. Furthermore, since our analysis is based on a parametric framework, this allows us to formulate a close-form relationship between the measures of correlation and the optimal portfolio. Finally, we calibrate our method with equity data, namely S&P 500 and Bangkok SET. The empirical evidences confirm that there is a significant impact of asymmetric dependence on optimal portfolio and risk.