### Prof. Haim Shalit

Office Address: | Department of Economics Beer-Sheva University of the Negev P.O. Box 653 Beer-Sheva 84105, Israel |
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Tel: | +972-8-647-2299 | ||

Fax: | +972-8-647-2941 | ||

E-Mail: | shalit@bgu.ac.il |

Haim Shalit's research is directed toward the use of the mean-Gini model, the Lorenz curve, the Shapley value, and Marginal Conditional Stochastic Dominance in financial markets.

- Haim Shalit and Gleb Gertsman, “Optimizing Marginal Conditional Stochastic Dominance PortfoliosAbstract:

Marginal Conditional Stochastic Dominance (MCSD) states the probabilistic conditions under which, given a specific portfolio, one risky asset is marginally preferred to another by all risk-averse investors. Furthermore, by increasing the share of dominating assets and reducing the share of dominated assets one can improve the portfolio performance for all these investors. We use this standard MCSD model sequentially to build optimal portfolios that are then compared to the optimal portfolios obtained from Chow’s MCSD statistical test model. These portfolios are furthermore compared to the portfolios obtained from the recently developed Almost Marginal Conditional Stochastic Dominance (AMCSD) model. The AMCSD model restricts the class of risk-averse investors by not including extreme case utility functions and reducing the incidence of unrealistic behavior under uncertainty. For each model, an algorithm is developed to manage the various dynamic portfolios traded on the New York, Frankfurt, London, and Tel Aviv stock exchanges during the years 2000-2012. The results show how the various MCSD optimal portfolios provide valid investment alternatives to stochastic dominance optimization. MCSD and AMCSD investment models dramatically improve the initial portfolios and accumulate higher returns while the strategy derived from Chow’s statistical test performed poorly and did not yield any positive return.”,*The Open Journal of Economics and Finance*, Vol.2, No. 1, 2018, pp.36-44. - Frank Hespeler and Haim Shalit, “Mean-Extended Gini Portfolios: A 3D Efficient FrontierAbstract:

Using a numerical optimization technique we construct the mean-extended Gini (MEG) efficient frontier as a workable alternative to the mean-variance efficient frontier. MEG enables the introduction of specific risk aversion into portfolio selection. The resulting portfolios are stochastically dominant (SSD) for all risk-averse investors. Solving for MEG portfolios allows investors to tailor portfolios for specific risk aversion. The extended Gini which is calculated by the covariance of asset returns with a weighing function of the cumulative distribution function (CDF) of these returns. In a sample of asset returns, the CDF is estimated by ranking returns. In this case, analytical optimization techniques using continuous gradient approaches are unavailable, thus the need to develop numerical optimization techniques. In this paper we develop a numerical optimization algorithm that finds the portfolio optimal frontier for arbitrarily large sets of shares. The result is a 3-dimension MEG efficient frontier in the space formed by mean, the extended Gini, and the risk aversion coefficient.”,*Computational Economics*, Vol.51, No. 3, March 2018, pp.731-740. - Haim Shalit, “Portfolio Risk Management Using the Lorenz CurveAbstract:

This paper presents a methodology for using the Lorenz curve in financial economics. Most of the recent quantitative risk measures that abides by the rules of second-degree stochastic dominance such as Gini’s mean difference and Conditional Value-at-Risk are associated with the Lorenz curve. With financial data, the Lorenz curve is easy to calculate since it requires only sorting asset returns in ascending order. Therefore, the financial analyst can derive the statistics necessary to carry out a study of risk analysis to establish a set of efficient and most preferred portfolios by all risk-averse investors.”,*Journal of Portfolio Management*, Vol. 40, No. 3, Spring 2014, pp. 152–159. - Sergio Ortobelli, Haim Shalit, and Frank Fabozzi, “Portfolio Selection Problems Consistent with Given Preference Orderings.Abstract:

This paper theoretically and empirically investigates the connection between portfolio theory and ordering theory. In particular, we examine three different portfolio problems and the respective orderings used to rank investors’ choices: (1) risk orderings, (2) variability orderings and (3) tracking-error orderings. For each problem, we discuss the properties of the risk measures, variability measures, and tracking-error measures, as well as their consistency with investor choices. Finally, for each problem, we propose an empirical application of several admissible portfolio optimization problems using the U.S. stock market. The proposed empirical analysis permits us to evaluate the ex-post impact of the optimal choices, thereby deriving completely different investors’ preference orderings during the recent financial crisis.”,*International Journal of Theoretical & Applied Finance*, Vol. 16, No. 5, 2013. - Haim Shalit and Doron Greenberg, “Hedging with Stock Index Options: A Mean-Extended Gini ApproachAbstract:

One of the more efficient methods to hedge portfolios of securities whose put options are not traded is to use stock index options. We use the mean-extended Gini (MEG) model to derive the optimal hedge ratios for stock index options. We calculate the MEG ratios for some main stocks traded on the Tel Aviv Stock Exchange and compare them to the minimum-variance hedge ratios. Computed for specific values of risk aversion, MEG hedge ratios combine systematic risk with basis risk. Our results show that increasing the risk aversion used in the computation reduces the size of the hedge ratio, implying that less put options are needed to hedge away each and every security.”,*Journal of Mathematical Finance*, Vol. 3 No. 1, February 2013, pp. 119-129. - Haim Shalit, “Using OLS to Test for NormalityAbstract:

The OLS estimator is a weighted average of the slopes delineated by adjacent observations. These weights depend only on the independent variable. Equal weights are obtained if and only if the independent variable is normally distributed. This feature is used to develop a new test for normality which is compared to standard tests and provides better power for testing normality. ”,*Statistics & Probability Letters*, Vol.82, No 11, November 2012, pp. 2050-2058 . - Haim Shalit and Shlomo Yitzhaki, “How Does Beta Explain Stochastic Dominance Efficiency?Abstract:

Stochastic dominance rules provide necessary and sufficient conditions for characterizing efficient portfolios that suit all expected utility maximizers. For the finance practitioner, though, these conditions are not easy to apply or interpret. Portfolio selection models like the mean-variance model offer intuitive investment rules that are easy to understand, as they are based on parameters of risk and return. We present stochastic dominance rules for portfolio choices that can be interpreted in terms of simple financial concepts of systematic risk and mean return. Stochastic dominance is expressed in terms of Lorenz curves, and systematic risk is expressed in terms of Gini. To accommodate risk aversion differentials across investors, we expand the conditions using the extended Gini. ”,*Review of Quantitative Finance and Accounting*,Vol.35, No. 4, November 2010, pp. 431-444 . - Haim Shalit, “Finding Better Securities while Holding PortfoliosAbstract:

Investment managers always look for securities to improve their portfolio performance, a common mechanism being the mean-variance (MV) model. As an alternative, I propose using Marginal Conditional Stochastic Dominance (MCSD). MCSD ensures that all risk-averse investors benefit from the selection process by establishing the relative preference among stocks conditional on holding a specific portfolio. I describe the basic MCSD rules and apply them to large porfolios. The resulting preferred stocks are compared to the selection obtained using the mean-variance criterion and the CAPM.”,*Journal of Portfolio Management*, Vol. 37, No. 1, Fall 2010, pp. 31–42. - Haim Shalit and Shlomo Yitzhaki, “Capital Market Equilibrium with Heterogeneous InvestorsAbstract:

As a two-parameter model that satisfies stochastic dominance, the mean-extended Gini model is used to build efficient portfolios. The model quantifies risk aversion heterogeneity in capital markets. In a simple Edgeworth box framework, we show how capital market equilibrium is achieved for risky assets. This approach provides a richer basis for analyzing the pricing of risky assets under heterogeneous preferences. Our main results are: (1) Identical investors, who use the same statistic to represent risk, hold identical portfolios of risky assets being equal to the market portfolio; and (2) heterogeneous investors as expressed by the variance or the extended Gini hold different risky assets in portfolios, and therefore, no one must hold the market portfolio. ”,*Quantitative Finance*, Vol.9, No. 6, September 2009, pp. 757-766. - Sergio Ortobelli, Svetlozar Rachev, Haim Shalit, and Frank Fabozzi, “Orderings and Probability Functionals Consistent with PreferencesAbstract:

This paper unifies the classical theory of stochastic dominance and investor preferences with the recent literature on risk measures applied to the choice problem faced by investors. First we summarize the main stochastic dominance rules used in the finance literature. Then we discuss the connection with the theory of integral stochastic orders and we introduce orderings consistent with investors’ preferences. Thus, we classify them, distinguishing several categories of orderings associated with different classes of investors. Finally we show how we can use risk measures and orderings consistent with some preferences to determine the investors’ optimal choices. ”,*Applied Mathematical Finance*, Vol.16, No. 1, 2009, pp. 81-102. - Sergio Ortobelli, Svetlozar Rachev, Haim Shalit, and Frank Fabozzi, “Orderings and Risk Probability Functionals in Portfolio TheoryAbstract:

This paper studies and describes stochastic orderings of risk/reward positions in order to define in a natural way risk/reward measures consistent/isotonic to investors’ preferences. We begin by discussing the connection between the theory of probability metrics, risk measures, distributional moments, and stochastic orderings. Then we examine several classes of orderings which are generated by risk probability functionals. Finally, we demonstrate how further orderings could better specify the investor’s attitude toward risk. ”,*Probability and Mathematical Statistics*, Vol.28, No. 2, 2008, pp. 203-234. - Dima Alberg, Haim Shalit, and Rami Yosef, “Estimating Stock Market Volatility using Asymmetric GARCH ModelsAbstract:

A comprehensive empirical analysis of the mean return and conditional variance of Tel Aviv Stock Exchange (TASE) indices is performed using various GARCH models. The prediction performance of these conditional changing variance models is compared to newer asymmetric GJR and APARCH models. We also quantify the day-of-the-week effect and the leverage effect and test for asymmetric volatility. Our results show that the asymmetric GARCH model with fat-tailed densities improves overall estimation for measuring conditional variance. The EGARCH model using a skewed Student-t distribution is the most successful for forecasting TASE indices.”,*Applied Financial Economics*, Vol.18, No. 15, August 2008, pp. 1201- 1208. - Haim Shalit and Shlomo Yitzhaki, “The Mean-Gini Efficient Portfolio FrontierAbstract:

One 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 to 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 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. ”,*The Journal of Financial Research*, Vol. 28, No. 1, Spring 2005, pp. 59-75. - Haim Shalit and Shlomo Yitzhaki, “An Asset Allocation Puzzle: CommentAbstract:

This note looks at the rationale behind popular advice on portfolio allocation among cash, bonds, and stocks and proposes an additional solution to the asset allocation puzzle posed by Canner, Mankiw and Weil (1997) who show that popular advice contradicts financial theory. We offer a rational model based on stochastic dominance to demonstrate that most popular advice portfolios belong to the efficient set for all risk-averse investors. Hence, we cannot come to the conclusion that investment bankers are offering bad advice. On the contrary, our results show that advisors, acting as agents for numerous clients, recommend portfolios that are not inefficient for all risk- averse investors.”,*American Economic Review*, Vol. 93, No. 3, June 2003, pp. 1002-1008. - Haim Shalit and Shlomo Yitzhaki, “Estimating BetaAbstract:

This paper presents evidence that Ordinary Least Squares estimators of beta coefficients of major firms and portfolios are highly sensitive to observations of extremes in market index returns. This sensitivity is rooted in the inconsistency of the quadratic loss function in financial theory. By introducing considerations of risk aversion into the estimation procedure using alternative estimators derived from Gini measures of variability one can overcome this lack of robustness and improve the reliability of the results.”,*Review of Quantitative Finance and Accounting*, Vol. 18, No. 2, March 2002, pp. 95-118. - Russell Gregory-Allen and Haim Shalit, “The Estimation of Systematic Risk under Differentiated Risk Aversion: A Mean-Extended Gini ApproachAbstract:

This paper examines a mean-Gini model of systematic risk estimation that resolves some econometric problems with mean-variance beta estimation and allows for heterogeneous risk aversion across investors. Using the mean-extended Gini (MEG) model, we estimate systematic risks for different degrees of risk aversion. MEG betas are shown to be instrumental variable estimators that provide econometric solutions to biases generated by the estimation of mean-variance (MV) betas. When security returns are not normally distributed, MEG betas are proved to differ from MV betas. We design an econometric test that assesses whether these differences are significant. As an application using daily returns, we estimate MEG and MV betas for U.S. securities.”,*Review of Quantitative Finance and Accounting*,Vol. 12, No. 2 , March 1999, pp. 135-157. - Haim Shalit, “Mean-Gini Hedging in Futures MarketsAbstract:

The paper develops the mean-Gini hedging ratio as the regression coefficient of the spot price on a function of the futures price. These hedging ratios are compatible with expected utility maximization. With heterogeneous risk aversion across traders, different hedging ratios are obtained with the mean-extended Gini (MEG) model. When futures prices are normally distributed, the MEG hedging ratios are shown to be equal to the MV ratios. Two normality tests are used to verify this assertion. Since the MEG ratios are the instrumental variable estimators for the standard MV ratios, the hedging factors can be compared statistically by using a specification test to examine whether the difference between the two ratios is significant. By combining the normality test with the significance test, we are able to assess the importance of the MEG futures price hedging model.”,*The Journal of Futures Markets*, Vol. 15, No. 6, September 1995, pp. 617-635. - Haim Shalit, “Mean-Gini Analysis of Stochastic Externalities: the Case of Groundwater ContaminationAbstract:

The mean-Gini model is used to analyze stochastic externalities generated by agricultural production. The model addresses the problem of groundwater pollution caused by excessive fertilizer application. Inherent in the mean-Gini approach to expected utility maximization is a two-fold value: the simplicity of the two-parameter mean-variance model and satisfaction of necessary and sufficient conditions for stochastic dominance. Price and quantity policy recommendations to control externalities are formulated based upon the relative assessment of uncertainty by the regulatory authority and the farmers. Using the Gini as a measure of risk allows for the quantification of control policy measures under differentiated risk aversion and multiple sources of pollution. The model shows that when producers underestimate uncertainty, quota policies restricting fertilizer are more efficient than tax policies in reducing groundwater contamination.”,*Environmental and Resource Economics*, Vol. 6, No. 1, 1995, pp. 37-52. - Haim Shalit and Shlomo Yitzhaki, “Marginal Conditional Stochastic DominanceAbstract:

This paper introduces the concept of Marginal Conditional Stochastic Dominance (MCSD), which states the conditions under which all risk-averse individuals, when presented with a given portfolio, prefer to increase the share of one risky asset over that of another. MCSD rules also answer the question of whether all risk-averse individuals include a new asset in their portfolio when assets' returns are correlated. MCSD criteria are expressed in terms of the probability distributions of the assets and of the underlying portfolio. An empirical application of MCSD is provided using stocks traded on the New York Stock Exchange. MCSD rules are used to show that, in the long run, one cannot assert that the market portfolio is inefficient.”,*Management Science*, Vol. 40, No. 5, May 1994, pp. 670-684. - Amos Golan and Haim Shalit, “Wine Quality Differentials in Hedonic Grape PricingAbstract:

”,*Journal of Agricultural Economics*, Vol. 44, No. 2, May 1993, pp. 311-321. - Haim Shalit and Shlomo Yitzhaki, “Evaluating the Mean-Gini Approach to Portfolio SelectionAbstract:

”,*International Journal of Finance*, Vol. 1, No. 2, Spring 1989, pp. 15-31. - Yakir Plessner and Haim Shalit, “Inflation, the Level of Investment, and Interest RatesAbstract:

Using a microeconomic model, the paper examines the impact of inflation on the level of investment. In the framework of the loanable-funds market, the behavior of a typical risk averse borrower and a risk averse lender is investigated. It is shown how inflation depresses the level of activity in the loanable-funds market and under what conditions the Fisherian rule for the relation between inflation and the interest rale holds.”,*European Economic Review*, Vol. 30, No.4, December 1986, pp. 1169-1187. - Haim Shalit, “Calculating the Gini Index of Inequality for Individual DataAbstract:

”,*Oxford Bulletin of Economics and Statistics*, Vol. 47, No. 2, May 1985, pp. 185-189. - Rafi Melnick and Haim Shalit, “Estimating the Market for TomatoesAbstract:

An econometric model of the market for tomatoes in Israel is developed to take into account the distortions brought about by the marketing board and intermediaries. The existence of monopoly and monopsony power is hypothesized by analyzing the middlemen's optimal behavior. Being compelled by the marketing board to purchase all produce, wholesalers exert monopsony power by reducing quantities marketed to consumers by selling surpluses to the marketing board at the minimum price. The empirical results confirm the existence of strong monopsony power together with weak monopoly power in that market. ”,*American Journal of Agricultural Economics*, Vol. 67, No. 3, August 1985, pp. 573-582. - Haim Shalit and Shlomo Yitzhaki, “Mean-Gini, Portfolio Theory, and the Pricing of Risky AssetsAbstract:

This paper presents the mean-Gini (MG) approach to analyze risky prospects and construct optimum portfolios. The proposed method has the simplicity of a mean-variance model and the main features of stochastic dominance efficiency. Since mean-Gini is consistent with investor behavior under uncertainty for a wide class of probability distributions, Gini's mean difference is shown to be more adequate than the variance for evaluating the variability of a prospect. The MG approach is then applied to capital markets and the security valuation theorem is derived as a general relationship between average return and risk. This is further extended to include a degree of risk aversion that can be estimated from capital market data. The analysis is concluded with the concentration ratio to allow for the classification of different securities with respect to their relative riskiness.”,*Journal of Finance*, Vol. 39, No. 5, December 1984, pp. 1449-1468. - Haim Shalit, “Does it Pay to Stabilize the Price of Vegetables?: An Empirical Evaluation of Agricultural Price Policies”,
*European Review of Agricultural Economics*, Vol. 11, No. 1, 1984, pp. 1-16. - Haim Shalit and Andrew Schmitz, “Farmland Price Behavior and Credit Allocation”,
*Western Journal of Agricultural Economics*, Vol. 9, No. 2, December 1984, pp. 303-313. - Shlomo Yitzhaki and Haim Shalit, “Efficient Portfolios on the Tel-Aviv Stock ExchangeAbstract:

”,*Bank of Israel Review*, Vol. 58, August 1984, pp. 51-62, English Version August 1986. - David Bigman and Haim Shalit, “Applied Welfare Analysis for Consumers with Commodity Income”,
*De Economist*, Vol. 131, No. 1, April 1983, pp. 31-45. - Uri Regev, Haim Shalit, and A.P. Gutierrez, “On the Optimal Allocation of Pesticides with Increasing Resistance: the Case of Alfalfa WeevilAbstract:

”,*Journal of Environmental Economics and Management*, Vol. 10, No. 1, March 1983, pp. 86-100. - Haim Shalit and Andrew Schmitz, “Farmland Accumulation and PricesAbstract:

A model of farmland accumulation is developed to study factors influencing U.S. farmland values. This model stresses the manner in which credit is allocated for land purchases. To secure necessary loans for additional land to expand farm size, the farmer provides as collateral his net accumulated wealth. Thus, land acquisitions are made to increase profits and to provide leverage for further land expansion. Besides income and consumption, the level of accumulated debt is one of the main determinants of farmland prices. Derived demand for farmland is developed, and the pricing equation for farmland is estimated as part of a structural equation model. ”,*American Journal of Agricultural Economics*, Vol. 64, No. 4, November 1982, pp. 710-719. - Andrew Schmitz, Haim Shalit, and Stephen J. Turnovsky, “Producer Welfare and the Preference for Price StabilityAbstract:

”,*American Journal of Agricultural Economics*, Vol. 63, No. 1, February 1981, pp. 157-160. - Haim Shalit, “The Democratic Provision of Public and Private Goods from Exhaustible ResourcesAbstract:

The problem of distributing exhaustible natural resources between consumption goods and environmental amenities through a voting process is analyzed. Assuming that individuals are endowed with an equal share of private goods, the method of majority decision does not always achieve a Pareto-optimal distribution. However, by means of side payments, the intensity of preferences is revealed. The voting procedure then leads to a Pareto-optimal solution which is more prone to environmental amenities than the simple method of majority decision.”,*Journal of Environmental Economics and Management*, Vol. 7, No. 2, June 1980, pp. 81-89. - Stephen J. Turnovsky, Haim Shalit, and Andrew Schmitz, “Consumer's Surplus, Price Instability, and Consumer WelfareAbstract:

This paper evaluates the benefits to consumers from price stabilization in terms of the convexity-concavity properties of the consumer's indirect utility function. It is shown that in the case where only a single commodity price is stabilized, the consumer's preference for price instability depends upon four parameters: the income elasticity of demand for the commodity, the price elasticity of demand, the share of the budget spent on the commodity, and the coefficient of relative risk aversion. All of these parameters enter in an intuitive way and the analysis includes the conventional consumer's surplus approach as a special case. The analysis is extended to consider the benefits of stabilizing an arbitrary number of commodity prices. Finally, some issues related to the choice of numeraire and certainty price in this context are discussed.”,*Econometrica*, Vol. 48, No. 1, January 1980, 135-152. - Andrew P. Gutierrez, Uri Regev, and Haim Shalit, “An Economic Optimization Model of Pesticide Resistance: Alfalfa and Egyptian Alfalfa Weevil- An Example”,
*Environmental Entomology*, Vol. 8, 1979, pp. 101-107. - Uri Regev, Haim Shalit, and Andrew P. Gutierrez, “ Economic Conflicts in Plant Protection: the Problems of Pesticide Resistance ”, Pest Management, G.A. Norton and C.S. Holling, eds.,
*Pergamon Press, Oxford, England*, 1979, pp. 281-299. - רפי מלניק וחיים שליט, ”ניתוח שוק העגבניות בישראל ואומדנו“,
*עיונים בכלכלה*, 1981, עמ'283-292. - שלמה יצחקי וחיים שליט, ”על תיקי השקעה יעילים בבורסה בתל אביב“,
*סקר בנק ישראל*, מס'58, 1984, עמ'51-62. - עמוס גולן וחיים שליט, ”תמחור הענבים על פי איכות היין“,
*, עיונים בכלכלה בעריכת איתן ברגלס ומרדכי פיין*, 1986, עמ' 225-240. - דימה אלברג, רמי יוסף וחיים שליט, ”אמידה וחיזוי תנודתיות מדדי מניות ת"א 25 ות"א 100“,
*רבעון לבנקאות*, מס' 164, יוני 2008, עמ' 77-93. - Haim Shalit, “The Shapley Value Decomposition of Optimal PortfoliosAbstract:

Investors want to be able to evaluate the true and complete risk of the financial assets they hold in a portfolio. Yet, the current analytic methods provide only partial risk measures. In a different approach, by viewing a portfolio of securities as a cooperative game played by the assets that minimize portfolio risk, investors can calculate the exact value each security contributes to the common payoff of the game. This is known as the Shapley value. It is determined by computing the contribution of each asset to the portfolio risk, by looking at all the possible coalitions in which the risky asset would participate. I develop this concept in order to decompose the risk of mean-variance optimal portfolios and mean-Gini portfolios. This decomposition lets us better rank of risky assets by their comprehensive contribution to the risk of optimal portfolios. Such a procedure allows investors to make unbiased and true decisions when they analyze the inherent risk of their holdings. In an application, the Shapley value is calculated for asset allocation and for portfolios of individual securities. The empirical results are contrary to some of the findings of conventional wisdom and beta analysis.”, 2017. - Frank Hespeler and Haim Shalit, “Mean-Extended Gini Portfolios: The Ultimate FrontierAbstract:

Using numerical optimization techniques we construct the mean-extended Gini (MEG) efficient frontier as a workable alternative to the mean-variance efficient frontier. The MEG model enables the introduction of specific risk aversion in portfolio selection and thus offers an alternative approach for calculating efficient portfolios and pricing risky assets. The resulting portfolios are stochastically dominant (SSD) for all risk-averse investors. Solving for MEG portfolios allows investors to construct efficient portfolios that are tailored to specific risk requisites. As a measure of risk, the model uses the extended Gini which is calculated by the covariance of asset returns with a weighing function of the cumulative distribution function (CDF) of these returns. Efficient MEG portfolios are obtained by minimizing the extended Gini of portfolio returns subject to a required mean return constraint. In a sample of asset returns, the CDF is estimated by ranking the returns. In this case analytical optimization techniques using continuous gradient approaches are unavailable, thus the need to develop numerical optimization techniques. In this paper we solve for MEG efficient portfolios expanding spreadsheet (Excel) techniques. In addition, using Mathematica software we develop a numerical optimization algorithm that finds the portfolio optimal frontier for arbitrarily large sets of shares. The result is a 3-dimension MEG efficient frontier in the mean, the extended Gini, and the risk aversion coefficient space.”, 2016. - Gleb Gertsman and Haim Shalit, “Optimizing MCSD PortfoliosAbstract:

Marginal Conditional Stochastic Dominance (MCSD) states the probabilistic conditions under which, given a specific portfolio, one risky asset is marginally preferred to another by all risk-averse investors. Furthermore, by increasing the share of dominating assets and reducing the share of dominated assets one can improve the portfolio performance for all these investors. We use this standard MCSD model sequentially to build optimal portfolios that are then compared to the optimal portfolios obtained from Chow’s MCSD statistical test model. These portfolios are furthermore compared to the portfolios obtained from the recently developed Almost Marginal Conditional Stochastic Dominance (AMCSD) model. The AMCSD model restricts the class of risk-averse investors by not including extreme case utility functions and reducing the incidence of unrealistic behavior under uncertainty. For each model, an algorithm is developed to manage the various dynamic portfolios traded on the New York, Frankfurt, London, and Tel Aviv stock exchanges during the years 2000-2012. The results show how the various MCSD optimal portfolios provide valid investment alternatives to stochastic dominance optimization. MCSD and AMCSD investment models dramatically improve the initial portfolios and accumulate higher returns while the strategy derived from Chow’s statistical test performed poorly and did not yield any positive return.”, 2015. - Arie Preminger and Haim Shalit, “Normality Is a Necessary and Sufficient Condition for OLS to Yield Robust ResultsAbstract:

Yitzhaki (1996) showed that the OLS estimator is a weighted average of the slopes defined by adjacent observations. The weights depend only on the distribution of the independent variable. In this note, we show that equal weights can only be obtained if, and only if the independent variable is normally distributed. This may serve as the basis for a new test for normality.”, 2002. - Haim Shalit, “ CV”