Do average higher moments predict aggregate returns in emerging stock markets?

PurposeIt has been demonstrated in the US market that expected market excess returns can be predicted using the average higher-order moments of all firms. This study aims to empirically test this theory in emerging markets.Design/methodology/approachTwo measures of average higher moments have been used (equal-weighted and value-weighted) along with the market moments to predict subsequent aggregate excess returns using the linear as well as the quantile regression model.FindingsThe authors report that both equal-weighted skewness and kurtosis significantly predict subsequent market returns in two countries, while value-weighted average skewness and kurtosis are significant in predicting returns in four out of nine sample markets. The results for quantile regression show that the relationship between the risk variable and aggregate returns varies along the spectrum of conditional quantiles.Originality/valueThis is the first study that investigates the impact of third and fourth higher-order average realized moments on the predictability of subsequent aggregate excess returns in the MSCI Asian emerging stock markets. This study is also the first to analyze the sensitivity of future market returns over various quantiles.

Entropy Balancing for Continuous Treatments

Interest in evaluating the effects of continuous treatments has been on the rise recently. To facilitate the estimation of causal effects in this setting, the present paper introduces entropy balancing for continuous treatments (EBCT) – an intuitive and user-friendly automated covariate balancing scheme – by extending the original entropy balancing methodology of Hainmueller, J. 2012. “Entropy Balancing for Causal Effects: A Multivariate Reweighting Method to Produce Balanced Samples in Observational Studies.” Political Analysis 20 (1): 25–46. In order to estimate balancing weights, the proposed approach solves a globally convex constrained optimization problem, allowing for computationally efficient software implementation. EBCT weights reliably eradicate Pearson correlations between covariates (and their transformations) and the continuous treatment variable. As uncorrelatedness may not be sufficient to guarantee consistent estimates of dose–response functions, EBCT also allows to render higher moments of the treatment variable uncorrelated with covariates to mitigate this issue. Empirical Monte-Carlo simulations suggest that treatment effect estimates using EBCT display favorable properties in terms of bias and root mean squared error, especially when balance on higher moments of the treatment variable is sought. These properties make EBCT an attractive method for the evaluation of continuous treatments. Software implementation is available for Stata and R.

The space $D$ in several variables: random variables and higher moments

We study the Banach space $D([0,1]^m)$ of functions of several variables that are (in a certain sense) right-continuous with left limits, and extend several results previously known for the standard case $m=1$. We give, for example, a description of the dual space, and we show that a bounded multilinear form always is measurable with respect to the $\sigma$-field generated by the point evaluations. These results are used to study random functions in the space. (I.e., random elements of the space.) In particular, we give results on existence of moments (in different senses) of such random functions, and we give an application to the Zolotarev distance between two such random functions.

Taylor’s law of fluctuation scaling for semivariances and higher moments of heavy-tailed data

We generalize Taylor’s law for the variance of light-tailed distributions to many sample statistics of heavy-tailed distributions with tail index α in (0, 1), which have infinite mean. We show that, as the sample size increases, the sample upper and lower semivariances, the sample higher moments, the skewness, and the kurtosis of a random sample from such a law increase asymptotically in direct proportion to a power of the sample mean. Specifically, the lower sample semivariance asymptotically scales in proportion to the sample mean raised to the power 2, while the upper sample semivariance asymptotically scales in proportion to the sample mean raised to the power (2−α)/(1−α)>2. The local upper sample semivariance (counting only observations that exceed the sample mean) asymptotically scales in proportion to the sample mean raised to the power (2−α2)/(1−α). These and additional scaling laws characterize the asymptotic behavior of commonly used measures of the risk-adjusted performance of investments, such as the Sortino ratio, the Sharpe ratio, the Omega index, the upside potential ratio, and the Farinelli–Tibiletti ratio, when returns follow a heavy-tailed nonnegative distribution. Such power-law scaling relationships are known in ecology as Taylor’s law and in physics as fluctuation scaling. We find the asymptotic distribution and moments of the number of observations exceeding the sample mean. We propose estimators of α based on these scaling laws and the number of observations exceeding the sample mean and compare these estimators with some prior estimators of α.

On The Randomized Schmitter Problem

We revisit the classical Schmitter problem in ruin theory and consider it for randomly chosen initial surplus level U. We show that the computational simplification that is obtained for exponentially distributed U allows to connect the problem to m-convex ordering, from which simple and sharp analytical bounds for the ruin probability are obtained, both for the original (but randomized) problem and for extensions involving higher moments. In addition, we show that the solution to the classical problem with deterministic initial surplus level can conveniently be approximated via Erlang(k)-distributed U for sufficiently large k, utilizing the computational advantages of the advocated randomization approach.

Bread in Lithuanian Literature

Bread is one of the most important cultural realities distinguished by its direct and symbolic significance. In Lithuanian folklore, there are clear direct connections between bread and the most important categories of national values: diligence, thoughtfulness, responsibility, kindness, and spiritual nobility. Bread symbolises strength, mind, self-control, loyalty, kindness, and humility. It was of immense sacral importance in the lives of our ancestors: it became the central element of numerous customs of family life, calendar rituals, agrarian celebrations, and was widely featured in Lithuanian folk songs, fairy-tales, tales, and beliefs. Bread has always been an important image in Lithuanian literature. A loaf of bread, a slice of bread, daily, wholemeal bread, the bread of life, mother’s bread are traditional images of Lithuanian poetry and prose, reflecting the reality of the nation’s life and at the same time visually drawing the hierarchy of the nation’s spiritual values. In the poem Metai (The Seasons), the pioneer of Lithuanian literature Kristijonas Donelaitis gives a vivid picture of the life of the serfs of Lithuania Minor in the eighteenth century, and his characters primarily address their thanks to God for giving people bread, the greatest grace of all. Since then, images of the worshiped daily bread have become stronger in literature, pointing to its vital importance. The image of holy bread takes root in Lithuanian twentieth-century poetry, perhaps most clearly meaningful in the work by Kazys Bradūnas, one of žemininkai, or the ‘earth’ poets. In his poetry, bread is associated with the meanings of the holiness of agricultural existence. In the poet’s work, bread is an important moment in the cosmogony of the microworld, symbolising rebirth and the higher moments of an individual’s existence. Such a poetic interpretation of bread is also characteristic of Sigitas Geda’s works. In the poetry of Justinas Marcinkevičius, Janina Degutytė, Alfonsas Maldonis, and Robertas Keturakis, bread becomes an important element in the poetic programme of goodness and is associated with the artistic meanings of human spiritual nobility, inner warmth, and love. In Lithuanian literature, bread emerges both as the great manifestation of the woman in traditional Lithuanian culture (Birutė Baltrušaitytė, Vanda Juknaitė) and as a symbol of harmony in dehumanised reality (Juozas Kundrotas). One of the most striking literary transformations of the artistic image of bread is its desacralisation in the works by Valdas Gedgaudas and the group “Svetimi” (Strangers). Here bread is interpreted as a symbol of chaos and disharmony between the human and the world. Thus, one of the most important realities of Lithuanian culture, the image of bread in Lithuanian literature, is changing; it reflects the worldview of the human of the epoch and his or her spiritual orientations and attitudes.

Instance Independence of Single Layer Quantum Approximate Optimization Algorithm on Mixed-Spin Models at Infinite Size

This paper studies the application of the Quantum Approximate Optimization Algorithm (QAOA) to spin-glass models with random multi-body couplings in the limit of a large number of spins. We show that for such mixed-spin models the performance of depth 1 QAOA is independent of the specific instance in the limit of infinite sized systems and we give an explicit formula for the expected performance. We also give explicit expressions for the higher moments of the expected energy, thereby proving that the expected performance of QAOA concentrates.

Contrasting Cryptocurrencies with Other Assets: Full Distributions and the COVID Impact

We investigate any similarity and dependence based on the full distributions of cryptocurrency assets, stock indices and industry groups. We characterize full distributions with entropies to account for higher moments and non-Gaussianity of returns. Divergence and distance between distributions are measured by metric entropies, and are rigorously tested for statistical significance. We assess the stationarity and normality of assets, as well as the basic statistics of cryptocurrencies and traditional asset indices, before and after the COVID-19 pandemic outbreak. These assessments are not subjected to possible misspecifications of conditional time series models which are also examined for their own interests. We find that the NASDAQ daily return has the most similar density and co-dependence with Bitcoin daily return, generally, but after the COVID-19 outbreak in early 2020, even S&P500 daily return distribution is statistically closely dependent on, and indifferent from Bitcoin daily return. All asset distances have declined by 75% or more after the COVID-19 outbreak. We also find that the highest similarity before the COVID-19 outbreak is between Bitcoin and Coal, Steel and Mining industries, and after the COVID-19 outbreak is between Bitcoin and Business Supplies, Utilities, Tobacco Products and Restaurants, Hotels, Motels industries, compared to several others. This study shed light on examining distribution similarity and co-dependence between cryptocurrencies and other asset classes.

Optimal Portfolio Diversification via Independent Component Analysis

A natural approach to enhance portfolio diversification is to rely on factor-risk parity, which yields the portfolio whose risk is equally spread among a set of uncorrelated factors. The standard choice is to take the variance as risk measure, and the principal components (PCs) of asset returns as factors. Although PCs are unique and useful for dimension reduction, they are an arbitrary choice: any rotation of the PCs results in uncorrelated factors. This is problematic because we demonstrate that any portfolio is a factor-variance-parity portfolio for some rotation of the PCs. More importantly, choosing the PCs does not account for the higher moments of asset returns. To overcome these issues, we propose using the independent components (ICs) as factors, which are the rotation of the PCs that are maximally independent, and care about higher moments of asset returns. We demonstrate that using the IC-variance-parity portfolio helps to reduce the return kurtosis. We also show how to exploit the near independence of the ICs to parsimoniously estimate the factor-risk-parity portfolio based on value at risk. Finally, we empirically demonstrate that portfolios based on ICs outperform those based on PCs, and several state-of-the-art benchmarks.