A novel portfolio selection model in a hybrid uncertain environment

Stochastic Orderings represent a relevant approach in portfolio selection for various reasons. Firstly, Stochastic Ordering are theoretically justified by Expected Utility theory. Typically, investors are classified according to their attitude toward risk. For each class of investors then, it is possible to define stochastic orderings coherent with investors' preference. Secondly, Stochastic Orderings are flexible enough to allow different definitions of efficiency suitable for each category of investors. This Thesis proposes several applications of Stochastic Orderings to portfolio selection problems. In the first chapter, an analysis of the relationship between Second order of Stochastic Dominance efficient set and Mean Variance Efficient Frontier is proposed. Not only 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 of Stochastic Dominance. Based on this fact, the chapter concludes proposing dominating strategies 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 non satiable, nor risk averting nor risk seeking, an extension of 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, to test for portfolio efficiency with respect a general stochastic ordering. Both the analysis of efficiency for Second order of Stochastic Dominance and behavioral finance, questioned the validity of highly diversified choices. For this reason, this thesis concludes 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 show how Risk Diversification based strategies perform under periods of financial distress.

We propose a numerical optimization approach that can be used to solve portfolio selection problems including several assets and involving objective functions from cumulative prospect theory (CPT). Implementing the suggested algorithm, we compare asset allocations that are derived for CPT based on two different methods: maximizing CPT along the mean–variance efficient frontier so that simple mean–variance algorithms can be used, and maximizing CPT without this restriction. According to the theoretical literature, with normally distributed returns and unlimited short sales, these two approaches lead to the same optimal solutions. We find that for empirical finite discrete distributions obtained via sampling and subsequent clustering from a normal distribution, the difference between the two approaches remains negligible even if short sales are restricted. However, if standard asset allocation data for pension funds is considered, the difference is considerable. Moreover, for certain types of derivatives, such as call options, the restriction of asset allocations to the mean–variance efficient frontier produces sizable losses in various respects, including decreases in expected returns and expected utility. We are able to explain these differences by CPT’s preference for positive skewness, which is not accounted for by optimizing CPT along the mean–variance efficient frontier.

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

PurposeThe purpose of this paper is to develop a prescriptive portfolio selection (PPS) model based on a compromise between the idea of “fast” and “slow” thinking proposed by Kahneman.Design/methodology/approach“Fast” thinking is effortless and comfortable for investors, while “slow” thinking may result in better performance. These two systems are related to the first two types of analysis in the decision theory: descriptive, normative and prescriptive analysis. However, to compromise between “fast” and “slow” thinking, “overconfidence” is used as a weighting parameter. A case study including a sample of 161 active investors in Tehran Stock Exchange (TSE) is provided. Moreover, the feasibility and optimality of the model are discussed.FindingsResults show that the PPS recommendations are efficient with a shift from the mean-variance efficient frontier; investors prefer PPS portfolios over the advisor recommendations; and investors have no significant preference between PPS and their own expectations.Research limitations/implicationsTwo assumptions of this study include: first, investors follow their “fast” system of thinking by themselves. Second, the investors’ “slow” system of thinking is represented by advisor recommendations which are simple expected value of risk and return. Therefore, considering these two assumptions for any application is the main limitation of this study. Moreover, the authors did not have access to more investors in TSE or other financial markets.Originality/valueThis is the first study that includes overconfidence in modeling portfolio selection for the purpose of achieving a portfolio that has a reasonable performance and one that investors are comfortable with.

One way to form an optimal stock portfolio is to use the mean-variance efficient frontier (MVEF) method. However, the MVEF method is susceptible to changes in input. An optimal stock portfolio formation method has been developed to overcome this problem, known as the Resampled Efficient Frontier (REF) method. The REF method is a refinement of the MVEF method. REF is done by generating data repeatedly using the Montecarlo simulation. The parameters needed to form a stock portfolio using REF are the average input return μ and the covariance variance matrix Σ. The calculation results show that the weight of the REF portfolio is not negative (there is no short selling strategy). The Sharpe ratio of the REF portfolio is also higher than the MVEF. A larger Sharpe ratio indicates that the REF portfolio has a better performance compared to MVEF. However, empirically based on a case study simulation, the MVEF method experienced a smaller loss compared to the REF method.

A portfolio selection model with return as triangular intuitionistic fuzzy number is developed in this study to assess and select portfolios on China Stock Exchange. Although the portfolio selection has been widely investigated, and most studies have regarded return and risk as the main decisive criteria, there are many uncertainties in the financial market, such as social, political and human psychological factors, which makes it difficult for us to describe the risks in line with empirical evidence. To fill this gap, first, a literature review was conducted to clarify the current situation and shortcomings of portfolio selection. Second, the triangular intuitionistic fuzzy number was used to fuzzify the coefficients of the objective function and the constraints in the portfolio model. Third, the triangular intuitionistic fuzzy number model was transformed into a linear programming model by using the selected exact ranking function, and the model was solved by MATLAB. Finally, the historical monthly returns of 10 stocks in China’s Stock Exchange from December 2017 to November 2020, lasting 36 months, were selected to demonstrate the model. The results indicate that the portfolio selection model with triangular intuitionistic fuzzy number can better meet the uncertainty of the real securities market, and more reasonable investment decision guidance can be provided for investors. Besides, the limitations of this study are pointed out, and implications and directions for future research are discussed.

Deals with a continuous-time version of the Markowitz mean-variance portfolio selection problem. The proposed model is concerned with a basket of securities consisting of one bank account and multiple stocks. One distinct feature of the model is that the market parameters, including the bank interest rate and the appreciation and volatility rates of the stocks, depend on the market mode that switches between a finite number of states. It is assumed that the random regime switching is independent of the random sources that drive the stock prices. Although the model is more realistic and takes into account possible random volatility, it essentially renders the underlying market incomplete. We use a Markov-chain modulated diffusion formulation to model the problem. By using techniques of stochastic linear-quadratic control, we obtain mean-variance efficient portfolios and efficient frontiers in explicitly closed forms, based on solutions of two systems of linear ordinary differential equations. We also address related issues such as minimum variance portfolio and mutual fund theorem. The results are notably different from those for the case when there is no regime switching. Nonetheless, if the interest rate is independent of the Markov chain and is deterministic, then the results exhibit (rather unexpected) similarity to their no-regime-switching counterparts, even if the stocks appreciation and volatility rates are Markov-modulated.

Structural reliability analysis with fuzzy random variables using error principle

In order to study the effect of different risk measures on the efficient portfolios (frontier) while properly describing the characteristic of return distributions in the stock market, it is assumed in this paper that the joint return distribution of risky assets obeys the multivariate t-distribution. Under the mean-risk analysis framework, the interrelationship of efficient portfolios (frontier) based on risk measures such as variance, value at risk (VaR), and expected shortfall (ES) is analyzed and compared. It is proved that, when there is no riskless asset in the market, the efficient frontier under VaR or ES is a subset of the mean-variance (MV) efficient frontier, and the efficient portfolios under VaR or ES are also MV efficient; when there exists a riskless asset in the market, a portfolio is MV efficient if and only if it is a VaR or ES efficient portfolio. The obtained results gener alize relevant conclusions about investment theory, and can better guide investors to make their investment decision.

Any given set of asset parameters yields a specific mean–variance optimal tangency portfolio. Yet, when the number of assets is large, there are some general characteristics of optimal portfolios that hold ‘almost surely’. This paper investigates these characteristics. We analytically show that the proportion of assets held short converges to 50% as the number of assets grows. This is a fundamental and robust property of mean–variance optimal portfolios, and it does not depend on the parameter estimation method, the investment horizon, or on a special covariance structure. While it is known that optimal portfolios may all have positive weights in some special situations (e.g. uncorrelated assets), the analysis shows that these cases occupy a zero measure in the parameter space, and therefore should not be expected to be observed empirically. Thus, our analysis offers a general explanation for the empirical finding of many short positions in optimal portfolios.

Owing to the fluctuations in the financial markets, many financial variables such as expected return, volatility, or exchange rate may occur imprecisely. But many portfolio selection models consider precise input of these values. Therefore, this paper studies a multiobjective international asset allocation problem under fuzzy environment. In our portfolio selection model, both of the return risk and the exchange risk are considered. The coefficient matrices in the objectives and constraints and the decision value are considered as fuzzy variables. The calculation of the portfolio and efficient frontier is derived by considering the exchange risk in the fuzzy environment. An empirical study is performed based on a portfolio of six securities denominated in six different currencies, i.e., USD, EUR, JPY, CNY, HKD, and GBP. The α-level closed interval portfolio [Formula: see text] and the fuzzy efficient frontier are obtained with different values of α ∈ (0, 1]. The empirical results indicate that the fuzzy asset selection method is a useful tool for dealing with the imprecise problem in the real world.

In structural reliability calculation, there are fuzzy uncertainties in the distribution parameters of random variables, which bring the problem of large computation and poor precision. In order to improve accuracy and efficiency of structural reliability, a novel structural reliability calculation method with fuzzy random variables is proposed from the perspective of perturbation principle. First, the fuzzy characteristic parameters of the structural fuzzy random variables are expressed as the sums of their true values and fuzzy perturbations. At the same time, the perturbations are equivalently selected. Second, the probability density function and the performance function are decomposed into a series of intervals under different level cut sets, and the Taylor series is expanded on the upper and lower limits of the intervals. Finally, according to the definition of structural reliability, based on the direct integration method, the sigmoid function is introduced into the reliability function to approximate the step function, and the fuzzy reliability is obtained. The simulation results show the effectiveness and accuracy of the proposed method, and it provides a feasible way for structural reliability analysis with fuzzy variables or fuzzy random variables.

The fundamental goal of portfolio optimization is to optimally allocate funds between different investment alternatives. The mean-variance (MV) methodology has become the most important quantitative tool used which considers the trade-off between risk and return. However the classical Markowitz’s MV method does not match the real world in numerous circumstances, thus researchers done are to improve and modify the MV model to represent the practicality. This paper discusses on a portfolio selection model that extends the classical Markowitz’s mean-variance model where the returns is represented by pentagonal fuzzy numbers. The concept of alpha level set is used to define the expected return and variance of fuzzy number. The proposed model gives better performance as compared to classical mean-variance model. Numerical examples are also presented to illustrate the usability of the model

Criteria, Models and Strategies in Portfolio Selection.- A Model for Portfolio Selection with Order of Expected Returns.- A Compromise Solution to Mutual Funds Portfolio Selection with Transaction Costs.- Optimal Portfolio Selection of Assets with Transaction Costs and No Short Sales.- Portfolio Frontier with Different Interest Rates for Borrowing and Lending.- Multi-period Investment.- Mean-Variance-Skewness Model for Portfolio Selection with Transaction Costs.- Capital Asset Pricing: Theory and Methodologies.- Empirical Tests of CAPM for China's Stock Markets.

This paper investigates whether Standards and Poors’ 100 stock index (henceforth, S&amp;P100) is a mean-variance efficient portfolio. In other words, the paper examines if there is any other portfolio allocation rule that provides better risk-return scenario than one that is achieved under value-weighted strategy used in S&amp;P100 index. Our results show that the realized risk of the S&amp;P100 index is not the lowest for the return at any other portfolio combinations using all stocks in index. There are other portfolio combinations that provide lower risk for the same realized rate of return. Similarly, the realized return of S&amp;P100 index is not the highest for the standard deviations at any other portfolio combinations. Based on these results, we conclude that the S&amp;P100 index may not be considered to be a mean-variance efficient portfolio.