Skewness Of Returns Research Articles

Non-Normality and Risk in Developing Asian Markets

This paper examines whether additional risk factors such as the variance, skewness, and coskewness of returns offer an appropriate explanation of company returns in less developed capital markets. Arguments for considering some additional factors in pricing models to better deal with such situations are presented. Using individual company returns from a range of developing Asian capital markets, empirical tests examine the importance of these extra risk factors. Results indicate that both individually and when in combination, variance and coskewness are significantly related to returns in these markets. Skewness is less consistently important. Robustness tests confirm that these measures tend not to capture size or book to market factors.

An Interest Rate Tree Driven by a Lévy Process

The lognormal diffusion process is mathematically tractable and incorporates the kind of continuous random evolution of the price by small increments that seems to characterize most security prices. But market microstructure studies have shown that a lognormal diffusion does not describe very well price formation at the shortest intervals. This is especially true of short-term bond returns. Bond price changes are mostly small, but the tails of the distribution are fatter than the lognormal allows and occasional non-diffusive jumps do seem to occur. Also, the intervals between price changes vary considerably in length. Alternative distributions have been proposed, but they do not have the convenient mathematical properties of the lognormal, so implementation can be challenging. Hainaut and MacGilchrist propose using the normal inverse Gaussian (NIG) distribution that arises from a particular Levy process and develop a lattice implementation for pricing. A pentanomial tree incorporates the NIG by matching its first four moments. In a simulation exercise, the NIG consistently outperforms the lognormal, largely due to its ability to capture skewness in returns.

Skewness in hedge funds returns: classical skewness coefficients vs Azzalini's skewness parameter

PurposeRecent literature discusses the persistence of skewness and tail risk in hedge fund returns. The aim of this paper is to suggest an alternative skewness measure, Azzalini's skewness parameter delta, which is derived as the normalized shape parameter from the skew‐normal distribution. The paper seeks to analyze the characteristics of this skewness measure compared with other indicators of skewness and to employ it in some typical risk and performance measurements.Design/methodology/approachThe paper first provides an overview of the skew‐normal distribution and its mathematical formulation. Then it presents some empirical estimations of the skew‐normal distribution for hedge fund returns and discusses the characteristics of using delta with respect to classical skewness coefficients. Finally, it illustrates how delta can be used in risk management and in a performance measurement context.FindingsThe results highlight the advantages of Azzalini's skewness parameter delta, especially with regard to its interpretation. Delta has a limpid financial interpretation as a skewness shock on normally distributed returns. The paper also derives some important characteristics of delta, including that it is more stable than other measures of skewness and inversely related to popular risk measures such as the value‐at‐risk (VaR) and the conditional value‐at‐risk (CVaR).Originality/valueThe contribution of the paper is to apply the skew‐normal distribution to a large sample of hedge fund returns. It also illustrates that using Azzalini's skewness parameter delta as a skewness measure has some advantages over classical skewness coefficients. The use of the skew‐normal and related distributions is a relatively new, but growing, field in finance and not much has been published on the topic. Skewness itself, however, has been the subject of a great deal of research. Therefore, the results contribute to three fields of research: skewed distributions, risk measurement, and hedge fund performance.

On the Relation between EGARCH Idiosyncratic Volatility and Expected Stock Returns

A spurious positive relation between EGARCH estimates of expected month t idiosyncratic volatility and month t stock returns arises when the month t return is included in the estimation of model parameters. We illustrate via simulations that this look-ahead bias is problematic for empirically observed degrees of stock return skewness and typical monthly return time series lengths. Moreover, the empirical idiosyncratic-return relation becomes negligible when expected month t idiosyncratic volatility is estimated using returns only upto month t-1.

Superstar effects on royalty income in a performing rights organization

This paper examines the economic accomplishments of individual members in a Performing Rights Organization (PRO), sometimes referred to as a Performing Rights Society. Today, there is the growing importance of intellectual property and copyright protection for authors and creators of literary, dramatic, musical, artistic and other intellectual works. The digital age has placed added pressure on songwriters, lyricists and composers in their ability to derive economic benefits from their intellectual creativity in the form of a copyright. Copyright laws protect and enable the creation of music by allowing authors and composers to license the control and use of their creations, and receive compensation in the form of royalty payments for their work. The PROs license, collect and distribute royalty payments for non-dramatic public performances of copyrighted musical works created and owned by its members or affiliates. In this paper, skewness and heavy tail of returns in the form of member royalty payments are estimated using the skew-normal and skew-t distributions in a parametric approach. We found strong evidence of the so-called ‘superstar effect’ in which the average royalty payment made by a PRO is still dominated by extreme outcomes, and relatively few members earned a substantial share of royalty payments from blockbuster hits that have endured over time. There is little evidence of smaller niche members dominating or replacing the ‘superstars.’ Economists and others will benefit from this empirical study which emphasizes a new understanding of the music industry from a PRO, member royalty payment and performance copyright perspective.

Multi-objective mean–variance–skewness model for generation portfolio allocation in electricity markets

This paper proposes an approach for generation portfolio allocation based on mean–variance–skewness (MVS) model which is an extension of the classical mean–variance (MV) portfolio theory, to deal with assets whose return distribution is non-normal. The MVS model allocates portfolios optimally by considering the maximization of both the expected return and skewness of portfolio return while simultaneously minimizing the risk. Since, it is competing and conflicting non-smooth multi-objective optimization problem, this paper employed a multi-objective particle swarm optimization (MOPSO) based meta-heuristic technique to provide Pareto-optimal solution in a single simulation run. Using a case study of the PJM electricity market, the performance of the MVS portfolio theory based method and the classical MV method is compared. It has been found that the MVS portfolio theory based method can provide significantly better portfolios in the situation where non-normally distributed assets exist for trading.

Skewness in Stock Returns: Reconciling the Evidence on Firm versus Aggregate Returns

Aggregate stock market returns display negative skewness. Firm-level stock returns display positive skewness. The large literature that tries to explain the first stylized fact ignores the second. This paper provides a unified theory that reconciles the two facts by explicitly modeling firm-level heterogeneity. I build a stationary asset pricing model of firm announcement events where firm returns display positive skewness. I then show that cross-sectional heterogeneity in firm announcement events can lead to negative skewness in aggregate returns. I provide evidence consistent with the model predictions.

Impact of Skewness on the Performance of Optimal Portfolios

The global minimum variance portfolio (GMVP) plays an important role in the Markowitz's mean-variance analysis. The usual assumption for studying the GMVP is the normality which is a symmetric model. In this paper, we study the influence of the skewness on the distributional properties of the estimated weights of optimal portfolios and on the corresponding inference procedures derived for the optimal portfolio weights assuming that the asset returns are normally distributed. It is shown that even a simple form of the skewness in the asset returns can dramatically influence the performance of optimal portfolios. In the empirical study, we apply our results to the real data of several stocks included into the Dow Jones index.

Forward-Looking Market Risk Premium

A method for computing forward-looking market risk premium is developed in this paper. We first derive a theoretical expression that links forward-looking risk premium to investors' risk aversion and forward-looking volatility, skewness, and kurtosis of cumulative return. In addition, investors' risk aversion is theoretically linked to volatility spread, defined as the gap between the risk-neutral volatility deduced from option data and the physical return volatility exhibited by return data. The volatility spread formula serves as the basis for using the generalized method of moments to estimate investors' risk aversion. We adopt the generalized autoregressive conditional heteroskedasticity model for the physical return process and estimate the model using the S&P 500 daily index returns and then deduce the forward-looking variance, skewness, and kurtosis of the corresponding cumulative return. The forward-looking risk premiums are estimated monthly over the sample period of 2001–2010, and all are found to be positive. Furthermore, two asset pricing tests are conducted. First, change in forward-looking risk premiums is negatively related to the S&P 500 holding period return, reflecting that an increase in discount rate reduces current stock prices. Second, market illiquidity positively affects forward-looking risk premium, indicating that forward-looking risk premium contains an illiquidity risk premium component. Data, as supplemental material, are available at http://dx.doi.org/10.1287/mnsc.2013.1758 This paper was accepted by Wei Jiang, finance.

Realized volatility with stochastic sampling

A central limit theorem for the realized volatility of a one-dimensional continuous semimartingale based on a general stochastic sampling scheme is proved. The asymptotic distribution depends on the sampling scheme, which is written explicitly in terms of the asymptotic skewness and kurtosis of returns. Conditions for the central limit theorem to hold are examined for several concrete examples of schemes. Lower bounds for mean squared error and for asymptotic conditional variance are given, which are attained by using a specific sampling scheme.

Robust Estimation of Hedge Fund Performance

Returns of hedge funds generally exhibit non-normality. It is well documented that if asset returns have systematic skewness, expected returns should include rewards for accepting this risk. This skewness risk premium should be controlled for in any estimate of performance. To investigate this issue we specify the Residual Augmented Least Squares (RALS) estimator, designed to exploit non-normality in a time series’ distribution. Specifying a linear factor model, we provide robust estimates of hedge fund performance, demonstrating the increase in efficiency of RALS relative to OLS estimation. Our evidence suggests that measuring performance using OLS alphas is inefficient, understating the performance of some hedge funds and overstating the performance of others. We then examine the source of the OLS mispricing. We find that the level of mispricing is positively related to estimates of skewness in the historical fund returns. We conclude that when estimated by OLS the performance of managers who pursue a strategy exhibiting positive skewness is understated and those whose strategy exhibits negative skewness is overstated. Estimation by RALS overcomes this. Our findings are robust to the biases in hedge fund databases.

Optimal Portfolio Selection with a Shortfall Probability Constraint: Evidence from Alternative Distribution Functions

We propose a new approach to optimal portfolio selection in a downside risk framework that allocates assets by maximizing expected return subject to a shortfall probability constraint, reflecting the typical desire of a risk-averse investor to limit the maximum likely loss. Our empirical results indicate that the loss-averse portfolio outperforms the widely-used mean-variance approach based on the cumulative cash values, geometric mean returns, and average risk-adjusted returns. We also evaluate the relative performance of the loss-averse portfolio with normal, symmetric thin-tailed, symmetric fat-tailed, and skewed fat-tailed return distributions in terms of average return, average risk, and average risk-adjusted return.

Resisting the Manipulation of Performance Metrics: An Empirical Analysis of The Manipulation-Proof Performance Measure

Performance manipulation can make a fund more attractive to investors and, more seriously, managers can intentionally misreport returns to enhance performance scores. This paper empirically investigates whether the manipulation-proof performance measure derived by Goetzmann et al. (2007) really is impervious to performance anipulation, using TASS hedge fund data, which have very skewed and fat-tailed return distributions. This article determines that the MPPM can evaluate performance more correctly than other measures. At application level, we propose the Doubt Ratio (DR), a new simple measure to detect funds that might have been manipulated or whose returns were intentionally smoothed, as in Madoff’s case. Our findings will help investors select funds and financial supervisors filter out funds for further investigation.

Skewness in Stock Returns, Periodic Cash Payouts, and Investor Heterogeneity

This paper analyzes the asset pricing implications of periodic cash payouts within the context of a stationary rational expectations model with heterogeneous investors. The periodicity of cash payouts provides a natural motivation for time-varying conditional volatility in stock returns. I show that the unconditional distribution of returns is a mixture of normals distribution, which has non-trivial skewness properties. I examine how conditional volatility, trading volume and skewness in stock returns are related to information dispersion and liquidity in the stock market. The model provides a rationale for why firm returns have positive skewness while market returns have negative skewness.

Static portfolio choice under Cumulative Prospect Theory

We derive the optimal portfolio choice for an investor who behaves according to Cumulative Prospect Theory (CPT). The study is done in a one-period economy with one risk-free asset and one risky asset, and the reference point corresponds to the terminal wealth arising when the entire initial wealth is invested into the risk-free asset. When it exists, the optimal holding is a function of a generalized Omega measure of the distribution of the excess return on the risky asset over the risk-free rate. It conceptually resembles Merton’s optimal holding for a CRRA expected-utility maximizer. We derive some properties of the optimal holding and illustrate our results using a simple example where the excess return has a skew-normal distribution. In particular, we show how a CPT investor is highly sensitive to the skewness of the excess return on the risky asset. In the model we adopt, with a piecewise-power value function with different shape parameters, loss aversion might be violated for reasons that are now well-understood in the literature. Nevertheless, we argue that this violation is acceptable.

Hedging and value at risk: A semi‐parametric approach

AbstractThe non‐normality of financial asset returns has important implications for hedging. In particular, in contrast with the unambiguous effect that minimum‐variance hedging has on the standard deviation, it can actually increase the negative skewness and kurtosis of hedge portfolio returns. Thus, the reduction in Value at Risk (VaR) and Conditional Value at Risk (CVaR) that minimum‐variance hedging generates can be significantly lower than the reduction in standard deviation. In this study, we provide a new, semi‐parametric method of estimating minimum‐VaR and minimum‐CVaR hedge ratios based on the Cornish‐Fisher expansion of the quantile of the hedged portfolio return distribution. Using spot and futures returns for the FTSE 100, FTSE 250, and FTSE Small Cap equity indices, the Euro/US Dollar exchange rate, and Brent crude oil, we find that the semiparametric approach is superior to the standard minimum‐variance approach, and to the nonparametric approach of Harris and Shen (2006). In particular, it provides a greater reduction in both negative skewness and excess kurtosis, and consequently generates hedge portfolios that in most cases have lower VaR and CVaR. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 30:780–794, 2010

Using Relative Returns to Accommodate Fat-Tailed Innovations in Processes and Option Pricing

The canonical process used to described financial time series is based on a logarithmic random walk.Adding fat tail distributions for the innovations in this framework creates fundamental inconsistencies, essentially related to a diverging integral.We propose to use geometric processes and relative returns instead. This change solves four problems related to (1) the (infinite) values of statistical quantities for processes with fat-tail innovations, (2) the robustness of computations when dealing with large events (genuine or noise), (3) the negative skewness of returns in stocks, and (4) the pricing of options with heteroskedasticity and fat-tails. The mathematical properties of geometric processes is explored for set-ups of increasing complexity. The European option pricing framework is modified to use geometric processes for the underlying, allowing to incorporate naturally fat-tail innovations.

Incorporating Liquidity Risk in Value-at-Risk Based on Liquidity Adjusted Returns

In this paper, based on Acharya and Pedersen’s overlapping generation model, we show that liquidity risk could influence the market risk forecasting through at least two ways. Then we argue that traditional liquidity adjusted VaR measure, the simply adding of the two risk measure, would underestimate the risk. Hence another approach, by modeling the liquidity adjusted returns (LAr) directly, was employed to incorporate liquidity risk in VaR measure in this study. Under such an approach, China’s stock market is specifically studied. We estimate the one-day-ahead “standard” VaR and liquidity adjusted VaR by forming a skewed Student’s t AR-GJR model to capture the asymmetric effect, non-normality and excess skewness of return, illiquidity and LAr. The empirical results support our theoretical arguments very well. We find that for the most illiquidity portfolio, liquidity risk represents more than 22% of total risk. We also find that simply adding of the two risk measure would underestimate the risk. The accuracy testing show that our approach is more accurate than the method of simply adding.

The Pricing of Volatility and Skewness: A New Interpretation

Investors who perceive themselves to possess superior security selection skill will be want to invest more heavily in securities with highly volatile and skewed returns, because it is among those securities that the largest winners can generally be found. If fundamental investors overestimate, or oversell, their skill, the result will be the relative overpricing of highly volatile and skewed securities. This article develops a simple model that draws out the implications of the foregoing observation. The implications of that model are consistent with recent empirical work which points to the overpricing of highly volatile and skewed securities.

Modelling skewness and elongation in financial returns: the case of exchange-traded funds

Recent studies have documented the importance of asymmetry and tail-fatness of returns on portfolio-choice, asset-pricing, value-at-risk and option-valuation models. This article explores the nature of skewness and elongation in daily Exchange-traded Fund (ETF) return distributions using g, h and (g × h) distributions. These exploratory data analytic techniques of Tukey (1977) reveal patterns that are hidden from a cursory glance at conventional measures for skewness and elongation. The g, h and (g × h) distributions provide parameter estimates that indicate substantial variation in skewness and elongation for individual ETFs; nonetheless, some trends are discovered when the funds are grouped by fund size and style of investing. Monte Carlo simulations suggest that these exploratory techniques are able to capture patterns found in commonly used Generalized Autoregressive Conditional Heteroskedasticity (GARCH) family of models.