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This chapter presents the portfolio optimization problem formulated as a multi-criteria mixed integer program. Weighting and lexicographic approach are proposed. The portfolio selection problem considered is based on a single-period model of investment. An extension of the Markowitz portfolio optimization model is considered, in which the variance has been replaced with the Value-at-Risk (VaR). The VaR is a quantile of the return distribution function. In the classical Markowitz approach, future returns are random variables controlled by such parameters as the portfolio efficiency, which is measured by the expectation, whereas risk is calculated by the standard deviation. As a result, the classical problem is formulated as a quadratic program with continuous variables and some side constraints. The objective of the problem considered in this chapter is to allocate wealth on different securities to maximize the weighted difference of the portfolio expected return and the threshold of the probability that the return is less than a required level. The auxiliary objectives are minimization of risk probability of portfolio loss and minimization of the number of security types in portfolio. The four types of decision variables are introduced in the model: a continuous wealth allocation variable that represents the percentage of wealth allocated to each asset, a continuous variable that prevents the probability that return of investment is not less than required level, a binary selection variable that prevents the choice of portfolios whose VaR is below the minimized threshold, and a binary selection variable that represents choice of stocks in which capital should be invested. The results of some computational experiments with the mixed integer programming approach modeled on a real data from the Warsaw Stock Exchange are reported.

This study aims to propose the Shapley value that originates from the game theory to quantify the relative risk of a security in an optimal portfolio.

Systematic risk as expressed by the relative covariance of stock returns to market returns is an essential measure in pricing risky securities. Although very much in use, the concept has become marginalized in recent years because of the difficulties that arise estimating beta. The idea is that portfolios can be viewed as cooperative games played by assets aiming at minimizing risk. With the Shapley value, investors can calculate the exact contribution of each risky asset to the joint payoff. For a portfolio of three stocks, this study exemplifies the Shapley value when risk is minimized regardless of portfolio return.

This study computes the Shapley value of stocks and indices for optimal mean-variance portfolios by using daily returns for the years 2016–2019. This results in the risk attributes allocated to securities in optimal portfolios. The Shapley values are analyzed and compared to the standard beta estimates to determine the ranking of assets with respect to pertinent risk and return.

An alternative approach to value risk and return in optimal portfolios is presented in this study. The logic and the mechanics of Shapley value theory in portfolio analysis have been explained, and its advantages relative to standard beta analysis are presented. Hence, financial analysts when adding or removing specific assets from present positions will have the true and exact impact of their actions by using the Shapley value instead of the beta.

When computing the Shapley value, portfolio risk is decomposed exactly among its assets because it considers all possible coalitions of portfolios. In that sense, financial analysts when adding or removing specific securities from present holdings will be able to predict the true and exact impact of their transactions by using the Shapley value instead of the beta. The main implication for investors is that risk is ultimately priced relative to their holdings. This prevents the subjective mispricing of securities, as standard beta is not used and might allow investors to gain from arbitrage conditions.

The logic and the methodology of Shapley value theory in portfolio analysis have been explained as an alternative to value risk and return in optimal portfolios by presenting its advantages relative to standard beta analysis. The conclusion is that the Shapley value theory contributes much more financial optimization than to standard systematic risk analysis because it enables looking at the contribution of each security to all possible coalitions of portfolios.

This study aims to assess the relationship between cash management and fund performance in index fund portfolios.

Using a sample of 104 index mutual funds that track the Standard and Poor 500 stock market index from January 1999 to December 2016, the authors employ quintile portfolios and different regression models to assess the differences in risk-adjusted monthly returns experienced by index funds managing different cash levels in their portfolios. To ensure the robustness of the results, different sub-periods and market states are considered in the analyses as well as other exogenous factors and fund characteristics affecting the level of portfolio cash holdings and index fund performance.

Results show that index funds holding higher levels of cash and cash equivalents performed significantly worse than their low-cash counterparts. This evidence remains even after considering different sub-periods and bullish and bearish market conditions and controlling for fund expenses and other variables that could drive this cash-performance relationship.

This study expands the extant literature analyzing cash management in the mutual fund industry. More specifically, the analyses focus on index fund portfolios that replicate a specific benchmark, given that their performance differences should not be related to the market evolution but to the factors derived from the fund management and other exogenous issues. These findings are of interest to managers and investors willing to improve their risk-adjusted returns while investing as diversified as a stock market index.

El objetivo de este estudio es analizar la relación existente entre la gestión de efectivo y el desempeño consiguiente en las carteras de fondos de inversión indexados.

Utilizando una muestra de 104 fondos que replican el índice bursátil Standard and Poor's 500 desde enero de 1999 hasta diciembre de 2016, se emplean carteras hipotéticas que invierten en fondos similares y diferentes análisis de regresión para analizar las diferencias en las rentabilidades ajustadas mensuales entre fondos indexados que gestionan diferentes niveles de efectivo en sus carteras. Por motivos de robustez, se tienen en cuenta diversos subperiodos y estados de mercado, así como otros factores exógenos y características de los fondos que afectan tanto al nivel de efectivo mantenido en la cartera indexada como al desempeño de la misma.

Los resultados muestran que los fondos indexados que gestionan niveles de efectivo más elevados experimentan un desempeño significativamente menor que otros fondos comparables que mantienen menores porcentajes de efectivo en sus carteras de inversión. Se obtiene una evidencia similar tras considerar diferentes subperiodos y momentos alcistas y bajistas de mercado, así como al considerar los gastos propios de cada fondo y otras variables que podrían afectar esta relación entre el rendimiento y el efectivo gestionado.

Este estudio contribuye a la literatura existente que analiza la gestión de efectivo en la industria de fondos de inversión. Más específicamente, los análisis se centran en carteras de fondos que replican un índice bursátil específico, dado que las diferencias en sus rendimientos en este tipo de fondos no deberían originarse por la evolución del mercado, sino a causa de factores relacionados con la gestión de sus carteras y otros componentes exógenos al índice bursátil. Estos hallazgos son de interés para gestores e inversores que pretendan mejorar sus rentabilidades ajustadas al invertir mediante una estrategia tan diversificada como un índice bursátil.

This paper aims to propose two portfolio selection models with hesitant value-at-risk (HVaR) – HVaR fuzzy portfolio selection model (HVaR-FPSM) and HVaR-score fuzzy portfolio selection model (HVaR-S-FPSM) – to help investors solve the problem that how bad a portfolio can be under probabilistic hesitant fuzzy environment.

It is strictly proved that the higher the probability threshold, the higher the HVaR in HVaR-S-FPSM. Numerical examples and a case study are used to illustrate the steps of building the proposed models and the importance of the HVaR and score constraint. In case study, the authors conduct a sensitivity analysis and compare the proposed models with decision-making models and hesitant fuzzy portfolio models.

The score constraint can make sure that the portfolio selected is profitable, but will not cause the HVaR to decrease dramatically. The investment proportions of stocks are mainly affected by their HVaRs, which is consistent with the fact that the stock having good performance is usually desirable in portfolio selection. The HVaR-S-FPSM can find portfolios with higher HVaR than each single stock and has little sacrifice of extreme returns.

This paper fulfills a need to construct portfolio selection models with HVaR under probabilistic hesitant fuzzy environment. As a downside risk, the HVaR is more consistent with investors’ intuitions about risks. Moreover, the score constraint makes sure that undesirable portfolios will not be selected.

The purpose of the study is to examine overreaction effect in the Chinese stock market after the global financial crisis (GFC) of 2007 for all the stocks listed in Shanghai Stock Exchange (SSE) Composite 50 index.

To capture overreaction effect in the stock listed at SSE 50 Index, a time series analysis of average cumulative abnormal return within a unified framework is applied for the period of January 2009 to December 2015. From these loser and winner portfolios, contrarian strategy is applied to build arbitrage portfolio, which is the difference of mean reversions between loser and winner portfolios. The portfolio construction is based on a 12-month formation period and 6-month testing period for intermediate-term analysis and. for short-term analysis, 6 month formation and 3 month testing periods. The authors also applied regression analysis to test a return reversal effect for the sampled period.

Results show that contrarian strategy yields positive excess returns for the arbitrage portfolio for most of the testing periods. The intermediate baseline case shows the arbitrage portfolio producing an average excess return of 14.1%, while even the short-term one produces 4%, which is statistically significant at the 5% level. The study finds asymmetrical overreactions in the SSE especially for loser portfolios. The biggest winner and loser portfolios follow the mean reversal effect. Moreover, before-after test for the biggest winner and loser portfolios shows that the losers recovered and beat the market immediately.

The study could benefit government, policy makers and regulators by studying how presence of more individual investors than institutional investors of China stock market leads to more irrational decisions giving rise to volatility. The regulators could build favourable policies for institutional investors to give them incentive to invest more than individual investors through which market volatility could be controlled.

This research contributes to market behaviour research, showing how working under hypotheses of overreaction; gains can be made with contrarian investment strategy through arbitrage portfolios. The authors provide specific additional support for the short and medium-term overreaction in the SSE for the period 2009–2015 using regression analysis.

This research contributes to market behaviour research, showing how working under hypotheses of overreaction; gains can be made with contrarian investment strategy through arbitrage portfolios. We provide specific additional support for the short and medium-term overreaction in the SSE for the period 2009–2015 using regression analysis.

The purpose of this paper is to provide a SAS program for an efficient portfolio given a short sale restriction.

We provide a 50-stock portfolio given 50 weekly stock returns. We contrast results with a 50-stock portfolio without a restriction.

We portfolio weights and utility scores for a range of returns from zero to 2.06%.

This program can be used for any sized portfolio.

This is the first SAS program for a 50-stock portfolio given return information.

Though of fairly recent origin, the capital‐asset pricing model (CAPM) is becoming a dominant influence in the analysis of financial and investment decisions. While continuing to undergo stringent theoretical and empirical examination, the demonstrable explanatory and predictive ability of the CAPM have led to its widespread recognition as the foundation of modern financial management. Though usually attributed to Sharpe, Lintner and Mossin, the origins of the CAPM can be traced back to the celebrated work of Harry Markowitz on portfolio selection.

The purpose of this paper is to investigate relative portfolio performance between sin stock returns and faith‐based returns.

Similar to Hong and Kacperczyk, Jensen's alpha was utilized to conduct tests along with three asset‐pricing models and rolling regression technique to reveal that faith‐based and sin betas move in opposite directions during most of the sample period.

Norm‐neglect was found, in that Jensen's alpha is positive and significant for the sin portfolio. Further, evidence in favor of norm‐conforming investor behavior was found, where Jensen's alpha is negative and significant for the faith‐based portfolio. These findings provide evidence that the sin portfolio outperforms the faith‐based portfolio relative to the market. A rolling regression technique reveals that faith‐based and sin betas tend to move in opposite directions during most of the sample period. The evidence suggests that faith‐based beta has an average estimated beta of one, mimicking the market. The sin portfolio, however, has an average estimated beta of one‐half. Finally, the reward‐to‐risk measure, Sharpe ratio, is statistically higher for the sin portfolio relative to the faith‐based portfolio.

This paper contributes to the literature in the following distinct ways. First, three asset‐pricing models are estimated to examine Jensen's alpha for sin and faith‐based portfolios. Second, a rolling regression procedure is used to examine the dynamic behavior relative to the market of the sin and faith‐based portfolios. Third, use is made of the Jobson and Korkie test, which allows for statistical comparisons of Sharpe ratios. Lastly, daily instead of monthly data and a different sample period are used to examine the research questions posed in this study.

Though stock portfolio return autocorrelation is well documented in the literature, its cause is still not clearly understood. Presently, evidence of private information induced stock return autocorrelation is still very limited. The difficulty in obtaining foreign country information by small investors makes the private information of institutional investors in the ADR (American Depository Receipt) market more significant and influential. As such, the ADR market provides a favorable environment for testing the effect of private information on return autocorrelation. The purpose of this paper is to address this issue.

In this paper, ADRs are sorted annually into three groups based on market equity capitalization. Within each capitalization group, ADRs are further sorted into three groups based on the fraction of shares held by institutional investors. Each ADR is assigned to one of the nine groups and group membership is rebalanced each year. The return autocorrelation of individual ADR securities and ADR portfolios for each group are then calculated.

The results demonstrate that ADR individual stock and portfolio daily return autocorrelations are positively related to institutional ownership. It is also found that other explanations, such as non‐synchronous trading, bid‐ask spread and volatility of ADR, cannot explain the positive relation between daily return autocorrelations and institutional ownership of ADR.

Since ADR market is more suitable than other markets for testing the role of private information, stronger and clearer results are got accordingly. This paper suggests that trading strategy based on private information of institutional investors can lead to stock return autocorrelation in ADR daily returns.

The purpose of this paper is to provide a quantitative methodology based on information‐gap decision theory for dealing with (true) Knightian uncertainty in the management of portfolios of assets with uncertain returns.

Portfolio managers aim to maximize returns for given levels of risk. Since future returns on assets are uncertain the expected return on a portfolio of assets can be subject to significant uncertainty. Information‐gap decision theory is used to construct portfolios that are robust against uncertainty.

Using the added dimensions of aspirational parameters and performance requirements in information‐gap theory, the paper shows that one cannot simultaneously have two robust‐optimal portfolios that outperform a specified return and a benchmark portfolio unless one of the portfolios has arbitrarily large long and short positions.

The paper has considered only one uncertainty model and two performance requirements in an information‐gap analysis over a particular time frame. Alternative uncertainty models could be introduced and benchmarking against proxy portfolios and competitors are examples of additional performance requirements that could be incorporated in an information‐gap analysis.

An additional methodology for applying information‐gap modeling to portfolio management has been provided.

This paper provides a new and novel approach for managing portfolios in the face of uncertainties in future asset returns.