Moments Of Return Distribution Research Articles

Higher Moments Actually Matter: Spillover Approach for Case of CESEE Stock Markets

The interconnectedness of stock markets is an important topic in empirical research, as spillovers on financial markets matter for asset pricing, portfolio allocation, financial stability, and risk management. This research focuses on all four moments of return distributions on stock markets and their spillovers between CESEE (Central, Eastern, and South-Eastern Europe) stock markets. Higher moments analysis needs to be explored more deeply, but can provide detailed insights into distribution shifts of market returns due to shocks in other markets. This research fills such a gap in the literature by estimating spillover effects between the four moments of stock market return distributions. Based on data from January 2013 to September 2022, the VAR (vector autoregression) model is estimated for individual moments across stock markets as a base for the calculation of spillover indices. The main findings indicate that it is difficult to track all the spillovers at once as the net emitter of shocks to one or other of the countries involved often change to being a net receiver and vice versa. Moreover, higher moments spillovers matter for individual markets, which has important implications for dynamic portfolio selection.

Mental accounts with horizon and asymmetry preferences

This paper extends mental accounting theory with an investment horizon and asymmetric trade-off between extreme gains and losses. This horizon-asymmetry mental accounting (HAMA) framework widens the spectrum of investors’ optimal portfolio choices considerably. Risk aversion, implied from the mean-variance portfolio theory, and the bond-to-stock ratio decline with the investment horizon. HAMA investors with a large gain–loss asymmetry trade-off are more concerned about skewness and kurtosis rather than variance. To apply the model to United States stock data, we develop a parsimonious semi-parametric version of HAMA that relies on the moments of return distributions. The analysis of optimal portfolios shows that investors who care significantly about upside potential hold asymmetric, leptokurtic, and less diversified allocations.

Proper use of the modified Sharpe ratios in performance measurement: rearranging the Cornish Fisher expansion

Performance analysis is a key process in finance to evaluate or compare investment opportunities, allocations, or management. The classical method is to compute the market or sub-market returns and volatilities, and then calculate the standard performance measure, namely, the Sharpe ratio. This measure is based on the first two moments of a return distribution. Therefore, a significant weakness of this method is that it implicitly assumes that the distribution is Gaussian (if it is not Gaussian, the approach may lead to a bad fit). In fact, risk comes from not only volatility, but also from higher moments of distribution such as skewness and kurtosis. The standard method to resolve this issue is to use the modified Sharpe ratio; this method replaces the classical Sharpe ratio volatility with the value at risk. The latter is computed using the Cornish Fisher expansion, a tool based on the first four moments of return distribution. This methodology, however, may present a major pitfall: in some cases, quantile functions do not stay monotone. In this paper, we show how this tool can be used effectively through a specific procedure, rearrangement. We compare various metrics using rank correlation, and demonstrate how and in which cases the proposed procedure delivers ranking different from the standard Sharpe ratio ranking. Furthermore, we show how our technique offers better distribution approximations and is therefore a more useful performance metric. Institutional investors may find the technique proposed here useful in that it allows for considering non-normality in performance analysis.

Establishing the risk denominator in a Sharpe ratio framework for share selection from a momentum investment strategy approach

Background: Based on the static mean-variance portfolio optimisation theory, investors will choose the portfolio with the highest Sharpe ratio to achieve a higher expected utility. However, the traditional Sharpe ratio only accounts for the first two moments of return distributions, which can lead to false portfolio performance diagnostics with the presence of asymmetric, highly skewed returns. Aim: With many criticising the standard deviation's applicability and with no consensus on the ascendency of which other risk denominator to consult, this study contributes to the literature by validating the importance of consulting value-at-risk as the more commendable risk denominators for the Johannesburg Stock Exchange. Method: These results were derived from a novel index approach that produces a comprehensive risk-adjusted performance evaluation score. Results: Of the 24 Sharpe ratio variations under evaluation, this study identified the value-at-risk Sharpe ratio as the better variation, which led to more profi table share selections for long-only portfolios from a one-year and five-year momentum investment strategy perspective. However, the attributes of adjusting for skewness and kurtosis exhibited more promise from a three-year momentum investment strategy perspective. Conclusion: The results highlighted the ability to outperform the market, which further emphasised the importance of active portfolio management. However, the results also conrfimed that active and more passive equity portfolio managers will have to consult different Sharpe ratio variations to enhance the ability to outperform the market and a buy-and-hold strategy.

Financial Markets Linkages Via Higher Moments: A Realized Spill-Over Approach

We examine the linkages both within and between stock and foreign exchange (FX) markets via three higher moments of return distributions (volatility, skewness and kurtosis). We find FX market linkages (in the 2nd and 4th moments) are relatively more prominent in developed markets. Cross-asset markets in emerging countries are more likely to be negatively linked through the 3rd moment but they are positively associated via the 2nd and 4th moments in developed markets indicating common concerns regarding tail risks in the former. Finally, cross-asset market linkages are of a similar magnitude to intra-asset-market linkages within emerging markets but the latter is relatively stronger in developed markets.

The Bias Ratio As A Hedge Fund Fraud Indicator: An Empirical Performance Study Under Different Economic Conditions

The Sharpe ratio is widely used as a performance evaluation measure for traditional (i.e., long only) investment funds as well as less-conventional funds such as hedge funds. Based on mean-variance theory, the Sharpe ratio only considers the first two moments of return distributions, so hedge funds characterised by complex, asymmetric, highly-skewed returns with non-negligible higher moments may be misdiagnosed in terms of performance. The Sharpe ratio is also susceptible to manipulation and estimation error. These drawbacks have demonstrated the need for augmented measures, or, in some cases, replacement fund performance metrics. Over the period January 2000 to December 2011 the monthly returns of 184 international long/short (equity) hedge funds with investment mandates that span the geographical areas of North America, Europe, and Asia were examined. This study compares results obtained using the Sharpe ratio (in which returns are assumed to be serially uncorrelated) with those obtained using a technique which does account for serial return correlation. Standard techniques for annualising Sharpe ratios, based on monthly estimators, do not account for serial return correlation this study compares Sharpe ratio results obtained using a technique which accounts for serial return correlation. In addition, this study assess whether the Bias ratio supplements the Sharpe ratio in the evaluation of hedge fund risk and thus in the investment decision-making process. The Bias and Sharpe ratios were estimated on a rolling basis to ascertain whether the Bias ratio does indeed provide useful additional information to investors to that provided solely by the Sharpe ratio.

Hedge Fund Performance Evaluation Using The Sharpe And Omega Ratios

The Sharpe ratio is widely used as a performance evaluation measure for traditional (i.e., long only) investment funds as well as less-conventional funds such as hedge funds. Based on mean-variance theory, the Sharpe ratio only considers the first two moments of return distributions, so hedge funds characterised by asymmetric, highly-skewed returns with non-negligible higher moments may be misdiagnosed in terms of performance. The Sharpe ratio is also susceptible to manipulation and estimation error. These drawbacks have demonstrated the need for augmented measures, or, in some cases, replacement fund performance metrics. Over the period January 2000 to December 2011 the monthly returns of 184 international long/short (equity) hedge funds with geographical investment mandates spanning North America, Europe, and Asia were examined. This study compares results obtained using the Sharpe ratio (in which returns are assumed to be serially uncorrelated) with those obtained using a technique which does account for serial return correlation. Standard techniques for annualising Sharpe ratios, based on monthly estimators, do not account for this effect. In addition, this study assesses whether the Omega ratio supplements the Sharpe Ratio in the evaluation of hedge fund risk and thus in the investment decision-making process. The Omega and Sharpe ratios were estimated on a rolling basis to ascertain whether the Omega ratio does indeed provide useful additional information to investors to that provided by the Sharpe ratio alone.

Polynomial goal programming and the implicit higher moment preferences of US institutional investors in hedge funds

Polynomial goal programming (PGP) is a flexible method that allows investor preferences for different moments of the return distribution of financial assets to be included in the portfolio optimization. The method is intuitive and particularly suitable for incorporating investor preferences in higher moments of the return distribution. However, until now, PGP has not been able to meet its full potential because it requires quantification of “real” preference parameters towards those moments. To date, the chosen preference parameters have been selected somewhat “arbitrarily”. Our goal is to calculate implied sets of preference parameters using investors’ choices of and the importance they attribute to risk and performance measures. We use three groups of institutional investors—pension funds, insurance companies, and endowments—and derive implied sets of preference parameters in the context of a hedge fund portfolio optimization. To determine “real” preferences for the higher moments of the portfolio return distribution, we first fit implied preference parameters so that the PGP optimal portfolio is identical to the desired hedge fund portfolio. With the obtained economically justified sets of preference parameters, the well-established PGP framework can be employed more efficiently to derive allocations that satisfy institutional investor expectations for hedge fund investments. Furthermore, the implied preference parameters enable fund of hedge fund managers and other investment managers to derive optimal portfolio allocations based on specific investor expectations. Moreover, the importance of individual moments, as well as their marginal rates of substitution, can be assessed.

Integrating analysts’ forecasts in the security screening process: empirical evidence from the Eurostoxx 50

In this article we attempt to expand the limited framework of single-objective optimization and broaden Markowitz's market standard, within which the portfolio selection problem is conventionally confronted. The typical theory's fundamental principle is that investment decisions are generally made using two criteria, corresponding to the first two moments of return distributions, namely the portfolio's expected return and variance. One heavy criticism over this pattern, which has often been addressed by both practitioners and academics, is that it fails to incorporate the whole spectrum of investors’ criteria, thus realistically express real-world investment policy statements. The proposed approach constitutes an innovative methodological framework for dealing with the security selection or screening phase, one of the most crucial stages in the portfolio management process. Our aim is to assist portfolio managers in formulating successful investment strategies, by providing them with an effective decision-making tool in order to obtain the so-called approved or authorized lists of most attractive stocks. More precisely, we exploit the decision technology of linguistic variables and we apply a state-of-the-art linguistic method. The validity of the proposed approach is finally tested through an illustrative application in one of the most popular European stock market indices, the Eurostoxx 50. The results obtained are characterized as very encouraging, since an adequate number of efficient portfolios produced by the model, appear to possess superior out-of-sample returns with respect to the underlying benchmark.

Testing weak form efficiency on the Toronto Stock Exchange

In order to test for weak form efficiency in the market a vast pool of individual stocks must be analyzed rather than a stock market index. In this paper, a model-based bootstrap is used to generate a series of simulated trials and a modified chart pattern recognition algorithm is applied to all stocks listed on the Toronto Stock Exchange (TSX). The number of patterns detected in the original price series is compared with the number of patterns found in the simulated series. By simulating the price path specific time dependencies present in real data are eliminated, making price changes purely random. Patterns, if consistently identified, carry information which adds value to the investment process, however, this informativeness does not guarantee profitability. Conclusions are drawn on the relative efficiency of some sectors of the economy. Although the null hypothesis of weak form efficiency on the TSX cannot be rejected, some sectors of the Canadian economy appear to be less efficient than others. In addition, pattern frequencies appear to be negatively dependent on the two moments of return distributions, variance and kurtosis.

IPSSIS: An integrated multicriteria decision support system for equity portfolio construction and selection

A fundamental principle of modern portfolio theory is that comparisons between portfolios are generally made using two criteria, corresponding to the first two moments of return distributions, namely the expected return and portfolio variance. According to this model and according to most of the portfolio models derived from the stochastic dominance approach, the group of portfolios open to comparisons is divided into two parts: on the one hand there are the efficient portfolios (those that are not dominated by any other portfolio in the group), and on the other, those that are dominated. In other words, these models do not solve for one optimal portfolio, but rather solve for an efficient set of portfolios, among which the investor must choose, given his preference system. One criticism over these models, which has often been addressed both by practitioners and academics, is that they fail to embody the objectives of the decision maker (DM), through the various stages of the decision process. Our purpose in this article is to present an integrated and innovative methodological approach for the construction and selection of equity portfolios, which will take into account the inherent multidimensional nature of the problem, while allowing the DM to incorporate his preferences in the decision process. The proposed approach, which grounds its basis on the field of multiple criteria decision making (MCDM) and more specifically on multiobjective mathematical programming (MMP), is implemented in the IPSSIS (Integrated Portfolio Synthesis and Selection Information System) decision support system (DSS). The validity of the proposed approach is tested through an illustrative application in the Athens Stock Exchange (ASE).

Time-varying beta risk, volatility persistence and the asymmetric impact of news: evidence from industry portfolios

This paper examines the time-varying behaviour of beta risk and degree of volatility persistence in the daily stock returns of 30 industry portfolios consisting of firms from the NYSE, AMEX and NASDAQ stock exchanges. Using an exponential ARCH (EGARCH) for this purpose, it further examines the degree to which innovations exert an asymmetric impact on the conditional second moments of return distributions for each portfolio. Findings point to significant time-dependence in returns. There is also time-dependence in beta risk for all the industry portfolios in question and, finally, it appears that industries with relatively high volatility persistence possess higher systematic risks for investors during periods of heightened aggregate stock market volatility.

Evaluating stocks in the presence of multiple criteria

A fundamental principle of modern portfolio theory is that portfolio selection decisions are generally made using two criteria, corresponding to the first two moments of return distributions, namely the expected return and portfolio variance. One criticism over this theory, which has often been addressed both by practitioners and academics, is that it fails to embody all the decision maker's (DM's) objectives, through the various stages of the decision process. The aim of this paper is to present an alternative methodological approach for modelling one of the most crucial phases of the portfolio management process, the security evaluation phase. The main characteristic of the proposed approach is that it fully takes into account the inherent multidimensional nature of the problem, while allowing the DM to incorporate his preferences in the decision process. The validity of the proposed approach is tested through an illustrative application in Athens Stock Exchange.

Do the individual moments of REIT return distributions affect institutional ownership patterns?

This paper examines the determinants of institutional investment demand for Real Estate Investment Trust (REIT) common stock. Specifically, it explores whether the demand function of institutional investors is dependent on the first four moments of the REIT returns distribution. The objective is to determine whether institutional investment decisions concerning REITs are influenced by individual stock attributes such as the mean return, standard deviation of returns, skewness of returns and kurtosis of returns. The results suggest that standard deviation plays a significant role in the institutional demand for REITs, but no significant role is found for the higher moments of the return distribution. The results also suggest institutional investment in REITs is predictable a priori using the moments of the REIT return distribution.

Stock Selection and Timing—A New Look At Market Efficiency

In this paper it is shown that stock returns do not conform to a random walk model, nor to the more general martingale model, but nevertheless the stock market is weak-form efficient. This result is not surprising when we recall that risk-averse investors are typically concerned with more than the first moment of a security return’s distribution, and market efficiency is appropriately determined in terms of (expected) utility - not profits alone. Extant tests of market efficiency have ignored this point. By examining the first two moments of return distributions, and by not assuming any form of equilibrium pricing model, we provide tests of weakform market efficiency which are more powerful than prior studies. A market is considered informationally efficient if market prices ‘fully reflect’ information. The (sub)set of information presumed to be reflected determines the particular form of market efficiency. The market is said to be efficient in the weak-forms if market prices fully reflect the past realizations of market prices. Extant tests of the weak-form of market efficiency (e.g., Fama, 1970; Fama and Blume, 1966; and Mandelbrot, 1966) examine whether information on past price movements can be exploited to enhance profit. These tests assume that investors looking to profit from ‘trend’ data are risk-neutral. However, the normative theory of portfolio selection due to Markowitz (1952), and positive theories of capital asset pricing (e.g., Sharpe, 1964) are developed assuming that investors are risk-averse, This paper fills a gap in the literature by testing the informational efficiency of the stock market by exploring whether or not gains in CXpGGtcd utility are attainable by utilizing the time series of past stock prices. In particular, since Sharpe (1963), a simple algorithm has been available for risk-averse investors to use in selecting optimal portfolios. Normative Portfolio Theory of Markowitz (1952) (N.2“) suggests the use of historical data to obtain estimates of expected return and risk, and then apply a mathematical programming algorithm to build Mean-Variance (E- V) efficient portfolios. Surprisingly, studies that have tackled the timing question have done so in a vacuum vis-B-vis optimal (E- V) portfolio selection.