Showing papers on "Efficient frontier published in 2021"

Minimax and Biobjective Portfolio Selection Based on Collaborative Neurodynamic Optimization

Abstract: Portfolio selection is one of the important issues in financial investments. This article is concerned with portfolio selection based on collaborative neurodynamic optimization. The classic Markowitz mean–variance (MV) framework and its variant mean conditional value-at-risk (CVaR) are formulated as minimax and biobjective portfolio selection problems. Neurodynamic approaches are then applied for solving these optimization problems. For each of the problems, multiple neural networks work collaboratively to characterize the efficient frontier by means of particle swarm optimization (PSO)-based weight optimization. Experimental results with stock data from four major markets show the performance and characteristics of the collaborative neurodynamic approaches to the portfolio optimization problems.

Bayesian mean–variance analysis: optimal portfolio selection under parameter uncertainty

Abstract: The paper solves the problem of optimal portfolio choice when the parameters of the asset returns distribution, for example the mean vector and the covariance matrix, are unknown and have to be est...

Mean–Variance Portfolio Selection Under Volterra Heston Model

Abstract: Motivated by empirical evidence for rough volatility models, this paper investigates continuous-time mean–variance (MV) portfolio selection under the Volterra Heston model. Due to the non-Markovian and non-semimartingale nature of the model, classic stochastic optimal control frameworks are not directly applicable to the associated optimization problem. By constructing an auxiliary stochastic process, we obtain the optimal investment strategy, which depends on the solution to a Riccati–Volterra equation. The MV efficient frontier is shown to maintain a quadratic curve. Numerical studies show that both roughness and volatility of volatility materially affect the optimal strategy.

Cryptocurrency Portfolio Selection—A Multicriteria Approach

Abstract: This paper proposes the PROMETHEE II based multicriteria approach for cryptocurrency portfolio selection. Such an approach allows considering a number of variables important for cryptocurrencies rather than limiting them to the commonly employed return and risk. The proposed multiobjective decision making model gives the best cryptocurrency portfolio considering the daily return, standard deviation, value-at-risk, conditional value-at-risk, volume, market capitalization and attractiveness of nine cryptocurrencies from January 2017 to February 2020. The optimal portfolios are calculated at the first of each month by taking the previous 6 months of daily data for the calculations yielding with 32 optimal portfolios in 32 successive months. The out-of-sample performances of the proposed model are compared with five commonly used optimal portfolio models, i.e., naive portfolio, two mean-variance models (in the middle and at the end of the efficient frontier), maximum Sharpe ratio and the middle of the mean-CVaR (conditional value-at-risk) efficient frontier, based on the average return, standard deviation and VaR (value-at-risk) of the returns in the next 30 days and the return in the next trading day for all portfolios on 32 dates. The proposed model wins against all other models according to all observed indicators, with the winnings spanning from 50% up to 94%, proving the benefits of employing more criteria and the appropriate multicriteria approach in the cryptocurrency portfolio selection process.

Optimal mean-variance reinsurance in a financial market with stochastic rate of return

Abstract: In this paper, we investigate the optimal investment and reinsurance strategies for a mean-variance insurer when the surplus process is represented by a Cramer-Lundberg model. It is assumed that the instantaneous rate of investment return is stochastic and follows an Ornstein-Uhlenbeck (OU) process, which could describe the features of bull and bear markets. To solve the mean-variance optimization problem, we adopt a backward stochastic differential equation (BSDE) approach and derive explicit expressions for both the efficient strategy and efficient frontier. Finally, numerical examples are presented to illustrate our results.

The Efficiency of Real-World Bargaining: Evidence from Wholesale Used-Auto Auctions

Abstract: This study empirically quantifies the efficiency of a real-world bargaining game with two-sided incomplete information. Myerson and Satterthwaite (1983) and Williams (1987) derived the theoretical ex-ante efficient frontier for bilateral trade under two-sided uncertainty and demonstrated that it falls short of ex-post efficiency, but little is known about how well bargaining performs in practice. Using about 265,000 sequences of a game of alternating-offer bargaining following an ascending auction in the wholesale used-car industry, this study estimates (or bounds) distributions of buyer and seller values and evaluates where realized bargaining outcomes lie relative to efficient outcomes. Results demonstrate that the ex-ante and ex-post efficient outcomes are close to one another, but that the real bargaining falls short of both, suggesting that the bargaining is indeed inefficient but that this inefficiency is not solely due to the information constraints highlighted in Myerson and Satterthwaite (1983). Quantitatively, findings indicate that over one-half of failed negotiations are cases where gains from trade exist, leading an efficiency loss of 12–23% of the available gains from trade.

A stochastic approximation method for approximating the efficient frontier of chance-constrained nonlinear programs

Abstract: We propose a stochastic approximation method for approximating the efficient frontier of chance-constrained nonlinear programs. Our approach is based on a bi-objective viewpoint of chance-constrained programs that seeks solutions on the efficient frontier of optimal objective value versus risk of constraints violation. To this end, we construct a reformulated problem whose objective is to minimize the probability of constraints violation subject to deterministic convex constraints (which includes a bound on the objective function value). We adapt existing smoothing-based approaches for chance-constrained problems to derive a convergent sequence of smooth approximations of our reformulated problem, and apply a projected stochastic subgradient algorithm to solve it. In contrast with exterior sampling-based approaches (such as sample average approximation) that approximate the original chance-constrained program with one having finite support, our proposal converges to stationary solutions of a smooth approximation of the original problem, thereby avoiding poor local solutions that may be an artefact of a fixed sample. Our proposal also includes a tailored implementation of the smoothing-based approach that chooses key algorithmic parameters based on problem data. Computational results on four test problems from the literature indicate that our proposed approach can efficiently determine good approximations of the efficient frontier.

A comparison on particle swarm optimization and genetic algorithm performances in deriving the efficient frontier of stocks portfolios based on a mean‐lower partial moment model

Abstract: In this paper, a portfolio optimization model on the basis of the risk measure of lower partial moment of the first order is discussed. Two meta‐heuristic methods of particle swarm optimization and genetic algorithm performances are applied and compared from different aspects to derive the stocks portfolios efficient frontier. The data belongs to the monthly returns of 20 randomly selected and approved stocks in the New York Stock Exchange for the financial period of 2005–2011. The results prove that both algorithms are quite efficient in solving the mean‐lower partial moment of the first order model with the particle swarm optimization being superior.

Portfolio optimization of financial commodities with energy futures.

Abstract: The recent growth in economic and financial markets has brought the focus on energy derivatives as an alternative investment class for investors, financial analysts, and portfolio managers. The financial modeling and risk management of portfolios using the energy derivatives instrument is a requirement and challenge for researchers in the field. The energy and other commodity futures force the expert investors to investigate the broader investment spectrum and consequently diversify their portfolios using the futures instruments. Going beyond the conventional portfolios and developing out-of-the-box strategies that comply with the changing financial and economic advancements are the keys to long-term sustainability in the financial world. This study investigates the impact of diversification with five energy futures from January 2011 to July 2020 on three traditional commodity futures portfolios. The results show that diversification increased the returns while simultaneously reducing the portfolio volatility in all portfolios. The diversified portfolios provided higher returns than the traditional portfolios for the same level of risk. This study also revealed that the results might improve when a short position in the futures contracts is allowed. Moreover, we conclude that adding multiple energy futures in a portfolio provides enhanced diversification results, whereas the WTI crude oil futures fail to diversify any portfolio considered in the study.

Equilibrium investment strategy for a DC pension plan with learning about stock return predictability

Abstract: This paper investigates a time-consistent investment strategy under the mean-variance criterion for an investor who accumulates retirement savings through a defined contribution (DC) pension plan with stock and bond investment opportunities. The expected return rate on the stock is modulated by an unobservable predictor which follows a mean-reverting stochastic process. The evolution of the instantaneous interest rate is described by the Vasicek model. In addition, the contribution rate of the DC pension plan is stochastic and correlated with financial risks coming from the stochastic interest rate and stock price. In a game theoretic framework, we derive a closed-form equilibrium investment strategy and corresponding equilibrium value function for the mean-variance criterion by adopting the filtering technique and the stochastic control method. Furthermore, we provide an equilibrium investment strategy and equilibrium value function when the expected return rate of the stock is completely observable. Finally, some numerical examples are presented to demonstrate the sensitivity analysis of the equilibrium investment strategy and equilibrium efficient frontier. Numerical analysis confirms that there is non-negligible information loss on the equilibrium investment strategy and equilibrium value function due to partial observation in the stock price dynamics.

How inefficient is an inefficient credit process? An analysis of the Italian banking system

Abstract: Purpose – The paper aims to disentangle the physiological credit risk from the credit risk coming from the inefficient screening and monitoring management process. The analysis is conducted on a sample of 338 Italian banks–56 joint-stock banks (SpA), 23 cooperative banks (Popolari) and 259 mutual banks (BCCs)–over the time period 2006–2017. Design/methodology/approach – The authors use the maximum likelihood method to estimate the efficient frontier, as a set of best management credit practices, which minimises the credit risk defined on the basis of the level of loans granted, the technical structure of the loan portfolio (such as credit lines, mortgages, consumer loans and other technical loan categories) and the interest rate charges. Findings – The empirical results show that the increase in non-performing loans (NPLs) is related both to the severe and protracted recession in Italy, which significantly reduced borrowers’ capacity to service their debt, and to other factors, such as banks’ lending monitoring policies with limited capacity to work-out defaulted loans. Originality/value – The authors propose a new approach to the study of the performance of the credit process. With the stochastic frontier, the physiological credit risk, assumed by the bank according to its lending activity and management choices, is separated from the credit risk resulting from an inefficient management of the screening and monitoring process. In addition, the authors analyse the determinants of the excess of NPLs. This aspect is considered particularly original because the scientific contributions which consider the causes of NPLs have largely focused on the level of NPLs not considering the physiological part, linked to the structure of the bank’s loan portfolio and its operational strategy and therefore not compressible and in any case not attributable to mismanagement or moral hazard.

Risk-aversion in data envelopment analysis models with diversification

Abstract: We deal with data envelopment analysis models with diversification which can identify investment opportunities efficient with respect to several inputs and outputs represented by risk and return measures. Moreover, they enable to project the inefficient investment opportunity to the efficient frontier and suggest how to revise its structure. However, the current DEA models does not take into account the individual risk aversion of a particular investor. We will introduce several approaches based on the spectral risk measures which deal with this drawback. These approaches are then compared in the empirical study. Note that all considered models as well as risk aversion are consistent with the second order stochastic dominance.

Essays on Stochastic Orderings in Portfolio Selection

Abstract: Stochastic Ordering represents a relevant approach in portfolio selection for various reasons. Firstly, stochastic ordering is theoretically justified by expected utility theory. Typically, investors are classified according to their attitude towards risk. For each class of investors then, it is possible to define stochastic orderings coherent with their risk preference. Secondly, stochastic ordering is flexible enough to allow different definitions of efficiency suitable for each category of investors. This thesis proposes several applications of stochastic ordering to portfolio selection problems. In the first chapter, an analysis of the relationship between second order stochastic dominance efficient sets and the mean variance efficient frontier is proposed. Not only do the two sets differ under many aspects, but the global minimum variance portfolio and other mean variance efficient portfolios are dominated in the sense of second order stochastic dominance. Based on this fact, the chapter proposes some dominating strategies that are able to outperform the global minimum variance portfolio. In the second chapter, starting from recent findings in the literature, that address the behavior of investors as neither non-satiable, nor risk averse or risk seeking, an extension of the classic definition of stochastic dominance efficiency linked to behavioral finance is given. In particular, investors' behavior changes according to market conditions. The last part of the chapter presents a methodology, based on estimation function theory, that allows to test for portfolio efficiency with respect to a general stochastic ordering. Both the analysis of efficiency for second order of stochastic dominance and behavioral finance, questions the validity of highly diversified choices. For this reason, this thesis continues the analysis by introducing risk diversification measures, a new class of functional quantifying the amount of idiosyncratic risk diversified among the assets in a portfolio. The mean risk diversification efficient frontier is introduced, along with the concept of mean risk diversification efficiency. The empirical analysis describes the relationship between risk aversion, risk diversification and classic diversification, and shows how risk diversification based strategies perform under periods of financial distress.

Mean‐Variance Hedging for Production Planning with Multiple Products

Abstract: We study production planning in a multi‐product setting, in which demand for each product depends on multiple financial assets (such as commodities, market indices, etc). In addition to the production quantity decision at the beginning of the planning horizon, there is also a real‐time hedging decision throughout the horizon; and we optimize both decisions jointly. With a mean–variance problem formulation, we first derive the optimal hedging strategy, given the production quantities. This leads to an explicit objective function with which bounds on optimal production quantities are identified. Thus, optimization of the production policies can be readily solved numerically as a static minimization problem. This way, we are able to give a complete characterization of the mean–variance efficient frontier, and quantify the contribution of the hedging strategy by the variance reduction it achieves. Furthermore, the model and results are extended to allow dynamic production control that tracks the demand rates.

Dynamic Optimal Mean-Variance Portfolio Selection with a 3/2 Stochastic Volatility

Abstract: This paper considers a mean-variance portfolio selection problem when the stock price has a 3/2 stochastic volatility in a complete market. Specifically, we assume that the stock price and the volatility are perfectly negative correlated. By applying a backward stochastic differential equation (BSDE) approach, closed-form expressions for the statically optimal (time-inconsistent) strategy and the value function are derived. Due to time-inconsistency of mean variance criterion, a dynamic formulation of the problem is presented. We obtain the dynamically optimal (time-consistent) strategy explicitly, which is shown to keep the wealth process strictly below the target (expected terminal wealth) before the terminal time. Finally, we provide numerical studies to show the impact of main model parameters on the efficient frontier and illustrate the differences between the two optimal wealth processes.

Dynamic Optimal Mean-Variance Investment with Mispricing in the Family of 4/2 Stochastic Volatility Models

Abstract: This paper considers an optimal investment problem with mispricing in the family of 4/2 stochastic volatility models under mean–variance criterion. The financial market consists of a risk-free asset, a market index and a pair of mispriced stocks. By applying the linear–quadratic stochastic control theory and solving the corresponding Hamilton–Jacobi–Bellman equation, explicit expressions for the statically optimal (pre-commitment) strategy and the corresponding optimal value function are derived. Moreover, a necessary verification theorem was provided based on an assumption of the model parameters with the investment horizon. Due to the time-inconsistency under mean–variance criterion, we give a dynamic formulation of the problem and obtain the closed-form expression of the dynamically optimal (time-consistent) strategy. This strategy is shown to keep the wealth process strictly below the target (expected terminal wealth) before the terminal time. Results on the special case without mispricing are included. Finally, some numerical examples are given to illustrate the effects of model parameters on the efficient frontier and the difference between static and dynamic optimality.

Mean-Expectile Portfolio Selection

Abstract: We consider a mean-expectile portfolio selection problem in a continuous-time diffusion model. We exploit the close relationship between expectiles and the Omega performance measure to reformulate the problem as the maximization of the Omega measure, and show the equivalence between the two problems. After showing that the solution for the mean-expectile problem is not attainable but that the value function is finite, we modify the problem by introducing a bound on terminal wealth and obtain the solution by Lagrangian duality. The global expectile minimizing portfolio and efficient frontier with a terminal wealth bound are also discussed.

Hybrid quantum investment optimization with minimal holding period.

Abstract: In this paper we propose a hybrid quantum-classical algorithm for dynamic portfolio optimization with minimal holding period. Our algorithm is based on sampling the near-optimal portfolios at each trading step using a quantum processor, and efficiently post-selecting to meet the minimal holding constraint. We found the optimal investment trajectory in a dataset of 50 assets spanning a 1 year trading period using the D-Wave 2000Q processor. Our method is remarkably efficient, and produces results much closer to the efficient frontier than typical portfolios. Moreover, we also show how our approach can easily produce trajectories adapted to different risk profiles, as typically offered in financial products. Our results are a clear example of how the combination of quantum and classical techniques can offer novel valuable tools to deal with real-life problems, beyond simple toy models, in current NISQ quantum processors.

Bounds on efficient outcomes for large-scale cardinality-constrained Markowitz problems

Abstract: When solving large-scale cardinality-constrained Markowitz mean–variance portfolio investment problems, exact solvers may be unable to derive some efficient portfolios, even within a reasonable time limit. In such cases, information on the distance from the best feasible solution, found before the optimization process has stopped, to the true efficient solution is unavailable. In this article, I demonstrate how to provide such information to the decision maker. I aim to use the concept of lower bounds and upper bounds on objective function values of an efficient portfolio, developed in my earlier works. I illustrate the proposed approach on a large-scale data set based upon real data. I address cases where a top-class commercial mixed-integer quadratic programming solver fails to provide efficient portfolios attempted to be derived by Chebyshev scalarization of the bi-objective optimization problem within a given time limit. In this case, I propose to transform purely technical information provided by the solver into information which can be used in navigation over the efficient frontier of the cardinality-constrained Markowitz mean–variance portfolio investment problem.

Optimal reinsurance and investment strategies for an insurer under monotone mean-variance criterion

Abstract: This paper considers the optimal investment-reinsurance problem under the monotone mean-variance preference. The monotone mean-variance preference is a monotone version of the classical mean-variance preference. First of all, we reformulate the original problem as a zero-sum stochastic differential game. Secondly, the optimal strategy and the optimal value function for the monotone mean-variance problem are derived by the approach of dynamic programming and the Hamilton-Jacobi-Bellman-Isaacs equation. Thirdly, the efficient frontier is obtained and it is proved that the optimal strategy is an efficient strategy. Finally, the continuous-time monotone capital asset pricing model is derived.

REIT Operational Efficiency: External Advisement and Management

Abstract: This paper examines the operational efficiency of equity Real Estate Investment Trusts (REITs) with respect to external advisement and management. We employ data envelopment analysis (DEA), a non-parametric statistical procedure that tests whether decision-making units are operating on their efficient frontier, to measure the relative performance of REITs before, during, and after the 2008–2010 financial crisis. Annual observations of both advising and management status of each REIT allow us to parse efficiency by these groups in various combinations. Our evidence suggests the inefficiency of externally-advised REITs has diminished in recent years, and the structure is no longer strictly inferior. External management of property operations, however, remains less efficient than self-management. General and administrative expenses, external advisory fees and property management fees are the main sources of inefficiency over the study period. In a difference-in-difference specification we find industry-wide operational efficiency was higher in the post-crisis than the pre-crisis period, indicating efficiency gains following the crisis.

Analytical Solution to A Discrete-Time Model for Dynamic Learning and Decision-Making

Abstract: Problems concerning dynamic learning and decision-making are difficult to solve, especially analytically. We study an infinite-horizon discrete-time model with a constant unknown state that has two possible values and strive to derive an analytical solution. As a special partially observable Markov decision process (POMDP), this model unifies several types of learning-and-earning problems such as sequential hypothesis testing, dynamic pricing with demand learning, and multi-armed bandits. We adopt a relatively new solution framework from the POMDP literature based on the backward construction of the efficient frontier(s) of continuation values. This framework accommodates different optimality criteria simultaneously. In the infinite-horizon setting, with the aid of a set of signal quality indices, the extreme points on the efficient frontier can be linked through a set of difference equations and solved analytically. The solution carries structural properties analogous to those obtained under continuous-time models, and it provides a useful tool for making new discoveries through discrete-time models.