Time Series Of Returns Research Articles

Inference of Binary Regime Models with Jump Discontinuities

Identifying the instances of jumps in a discrete-time-series sample of a jump diffusion model is a challenging task. We have developed a novel statistical technique for jump detection and volatility estimation in a return time series data using a threshold method. The consistency of the volatility estimator has been obtained. Since we have derived the threshold and the volatility estimator simultaneously by solving an implicit equation, we have obtained unprecedented accuracy across a wide range of parameter values. Using this method, the increments attributed to jumps have been removed from a large collection of historical data of Indian sectorial indices. Subsequently, we have tested the presence of regime-switching dynamics in the volatility coefficient using a new discriminating statistic. The statistic has been shown to be sensitive to the transition kernel of the regime-switching model. We perform the testing using Bootstrap method and find a clear indication of presence of multiple regimes of volatility in the data. A link to all Python codes is given in the conclusion. The methodology is suitable for analyzing high frequency data and may be applied for algorithmic trading.

Asset pricing anomalies: Liquidity risk hedgers or liquidity risk spreaders?

We capture two distinct investing preferences – hedging against aggregate liquidity risk or betting on it – in the cross-section of stock returns. A three-factor model underpinned by exposures to changes in market liquidity, isolating two alternating patterns, is developed. Our results can be summarized in the following ways: one, the improved performance of recent asset-pricing models is driven by factors that mimic liquidity risk hedging and are linked to cross-sectional mispricing. Two, our model outperforms competing models in explaining time-series return variation across market states. Three, our parsimonious model enables an understanding of diverging return premia in the cross-section. Four, the estimated risk premiums in our model correspond to theoretical, economic, and statistical restrictions holistically across varied and complex anomaly structures. In this respect, the performance of the proposed model is even better than the risk premiums on factors in the model that have the largest cross-sectional r-squared values.

Manager characteristics: Predicting fund performance

A great deal of research effort has sought to understand whether fund managers have skill. However, most of this research draws inferences from fund returns attributable to funds that may have been managed by many different managers over the years. In this paper we focus on the fund manager. We put together a comprehensive data base of manager returns, including a time series of managers' career returns, concatenating performance from the different funds that a manager may have managed over time. We relate these returns to the characteristics of the managers as we seek to understand whether these characteristics have an impact on: manager skill; manager style; and on performance persistence.

Analysis of the cryptocurrency market using different prototype-based clustering techniques

Since the emergence of Bitcoin, cryptocurrencies have grown significantly, not only in terms of capitalization but also in number. Consequently, the cryptocurrency market can be a conducive arena for investors, as it offers many opportunities. However, it is difficult to understand. This study aims to describe, summarize, and segment the main trends of the entire cryptocurrency market in 2018, using data analysis tools. Accordingly, we propose a new clustering-based methodology that provides complementary views of the financial behavior of cryptocurrencies, and one that looks for associations between the clustering results, and other factors that are not involved in clustering. Particularly, the methodology involves applying three different partitional clustering algorithms, where each of them use a different representation for cryptocurrencies, namely, yearly mean, and standard deviation of the returns, distribution of returns that have not been applied to financial markets previously, and the time series of returns. Because each representation provides a different outlook of the market, we also examine the integration of the three clustering results, to obtain a fine-grained analysis of the main trends of the market. In conclusion, we analyze the association of the clustering results with other descriptive features of cryptocurrencies, including the age, technological attributes, and financial ratios derived from them. This will help to enhance the profiling of the clusters with additional descriptive insights, and to find associations with other variables. Consequently, this study describes the whole market based on graphical information, and a scalable methodology that can be reproduced by investors who want to understand the main trends in the market quickly, and those that look for cryptocurrencies with different financial performance.In our analysis of the 2018 and 2019 for extended period, we found that the market can be typically segmented in few clusters (five or less), and even considering the intersections, the 6 more populations account for 75% of the market. Regarding the associations between the clusters and descriptive features, we find associations between some clusters with volume, market capitalization, and some financial ratios, which could be explored in future research.

Exact Elliptical Distributions for Models of Conditionally Random Financial Volatility

Assuming the time series of random returns to be jointly elliptical, we derive a relationship between its conditional variance and the probability density function of the conditioning set. In the case that such a relationship is linear in a quadratic form for of the conditioning variables, we show that the probability density function of the conditioning variables is multivariate t. This result is then applied to models of conditionally random volatility and used to derive exact results for the GARCH(p,q) class of processes previously thought to be intractable.

Complex system properties in the spreading of COVID-19 pandemic

The objective of the present study was to show that the spread of the COVID-19 pandemic around the world shows complex system properties such as lognormal laws, temporal fluctuation scaling, and time correlation. First, the daily cumulative number of confirmed cases and deaths is distributed among countries as lognormals such that the time series exhibit a temporal fluctuation scaling. Second, the daily return time series of cases and deaths per day have associated Levy stable distributions and they have time correlation. The idea was to draw attention to the fact that the spread of the COVID-19 pandemic can be seen as a complex system, and, thus, contribute to the identification of the structural properties of this system, which is relevant as it is expected that future stochastic models describing the spread of the COVID-19 pandemic from a microscopic dynamics perspective should be able to explain the emergence of the structural properties identified here.

Top-bottom investing skill and the fund alpha in Indian mutual fund industry: an empirical investigation

PurposeMutual funds are the second most preferred investment option in India and have garnered considerable research interest. The focus of Indian studies thus far has been restricted to the bottom-up approach of investing which rewards a fund manager for picking winner stocks and generates superior returns. While changing portfolio allocation as per varying macro-trends has been instrumental in generating superior returns, it has not been given the desired attention. This study addresses this important research gap.Design/methodology/approachThe authors analyze the industry selection ability of the fund manager on a robust sample by decomposing alpha into alpha due to industry selection and alpha attributable to stock selection. Alpha estimates are computed on a robust sample of 34 open-ended Indian equity mutual funds for a 10-year duration 2011–2020 using three base models of asset pricing – single-factor, four-factor and five-factor alpha under panel data methodology.FindingsThe study leads us to four major findings. One, industry selection explains more than two-fifth of the alpha both in cross-section and time series of returns; two, industry selection exhibits persistence for more than four quarters across asset pricing model; third, younger funds have level playing when alpha from picking right industries is concerned; four, broad industry allocation continues to explain superior returns as sector allocation undergoes consolidation during ongoing COVID-19 pandemic and funds increase exposure to defensive stocks, consistent with folio allocations as per macroeconomic conditions.Research limitations/implicationsThe authors find strong evidence of persistence in the case of alpha attributable to the industry selection component, and the findings are consistent with the persistence results reported in the empirical literature. While some funds excel in stock-picking skills and others excel in picking the right industries, both skills together make for winner funds that attract larger investor flows as investors chase superior performance. The authors also find no evidence of diseconomies of scale in the case of industry allocation alpha generated by the fund managers.Practical implicationsThe results suggest a fresh approach for investors while making mutual fund investment decisions; the investors can achieve superior returns by assessing industry selection skills as it tends to provide a more holistic picture concerning a perennial question – why some funds outperform and continue to contribute to investor's wealth?Social implicationsMutual funds have become a favored investment option for Indian investors more so as a disciplined investment option owing to dismal financial literacy rates. The study throws light on a relatively unaddressed dimension of choosing winner funds. The significance of right sector allocation assumed even more significance with the onset of the pandemic which lends further credence to the findings of the study.Originality/valueResearch has been conducted on secondary data extracted from a well-cited database for Indian mutual funds. Empirical analysis and conclusion drawn are based on authentic statistical analysis and adds to the existing literature.

Adaptive Seriational Risk Parity and Other Extensions for Heuristic Portfolio Construction Using Machine Learning and Graph Theory

In this article, the authors present a conceptual framework named <i>adaptive seriational risk parity</i> (ASRP) to extend hierarchical risk parity (HRP) as an asset allocation heuristic. The first step of HRP (quasi-diagonalization), determining the hierarchy of assets, is required for the actual allocation done in the second step (recursive bisectioning). In the original HRP scheme, this hierarchy is found using single-linkage hierarchical clustering of the correlation matrix, which is a static tree-based method. The authors compare the performance of the standard HRP with other static and adaptive tree-based methods, as well as seriation-based methods that do not rely on trees. Seriation is a broader concept allowing reordering of the rows or columns of a matrix to best express similarities between the elements. Each discussed variation leads to a different time series reflecting portfolio performance using a 20-year backtest of a multi-asset futures universe. Unsupervised learningbased on these time-series creates a taxonomy that groups the strategies in high correspondence to the construction hierarchy of the various types of ASRP. Performance analysis of the variations shows that most of the static tree-based alternatives to HRP outperform the single-linkage clustering used in HRP on a risk-adjusted basis. Adaptive tree methods show mixed results, and most generic seriation-based approaches underperform. <b>Key Findings</b> ▪ The authors introduce the <i>adaptive seriational risk parity</i> (ASRP) framework as a hierarchy of decisions to implement the quasi-diagonalization step of hierarchical risk parity (HRP) with seriation-based and tree-based variations as alternatives to single linkage. Tree-based variations are further separated in static and adaptive versions. Altogether, 57 variations are discussed and connected to the literature. ▪ Backtests of the 57 different HRP-type asset allocation variations applied to a multi-asset futures universe lead to a correlation matrix of the resulting 57 portfolio return time series. This portfolio return correlation matrix can be visualized as a dendrogram using single-linkage clustering. The correlation hierarchy reflected by the dendrogram is similar to the construction hierarchy of the quasi-diagonalization step. Most seriation-based strategies seem to underperform HRP on a risk-adjusted basis. Most static tree-based variations outperform HRP, whereas adaptive tree-based methods show mixed results. ▪ The presented variations fit into a triple artificial intelligence approach to connect synthetic data generation with explainable machine learning. This approach generates synthetic market data in the first step. The second step applies an HRP-type portfolio allocation approach as discussed in this article. The third step uses a model-agnostic explanation such as the SHAP framework to explain the resulting performance with features of the synthetic market data and with model selection in the second step.

Sparse index clones via the sorted ℓ1-Norm

Index tracking and hedge fund replication aim at cloning the return time series properties of a given benchmark, by either using only a subset of its original constituents or by a set of risk factors. In this paper, we propose a model that relies on the Sorted Penalized Estimator, called SLOPE, for index tracking and hedge fund replication. We show that SLOPE is capable of not only providing sparsity, but also to form groups among assets depending on their partial correlation with the index or the hedge fund return times series. The grouping structure can then be exploited to create individual investment strategies that allow building portfolios with a smaller number of active positions, but still comparable tracking properties. Considering equity index data and hedge fund returns, we discuss the real-world properties of SLOPE based approaches with respect to state-of-the art approaches.

Clustering high‐frequency financial time series based on information theory

AbstractClustering large financial time series data enables pattern extraction that facilitates risk management. The knowledge gathered from unsupervised learning is useful for improving portfolio optimization and making stock trading recommendations. Most methods available in the literature for clustering financial time series are based on exploiting linear relationships between time series. However, prices of different assets (stocks) may have non‐linear relationships which may be quantified using information based measures such as mutual information (MI). To estimate the empirical mutual information between time series of stock returns, we employ a novel kernel density estimator (KDE) based jackknife mutual information estimation (JMI), and compare it with the widely‐used binning method. We then propose an average distance gradient change algorithm and an algorithm based on the average silhouette criterion that use pairwise and groupwise MI of high‐frequency financial stock returns. Through numerical studies, we provide insights into the impact of the clustering on asset allocation and risk management based on the nonlinear information structure of the US stock market.

Determination of Risk Value Using the ARMA-GJR-GARCH Model on BCA Stocks and BNI Stocks

Stocks are common investments that are in great demand by investors. Stocks are also an investment instrument that provides returns but tends to be riskier. The return time series is easier to handle than the price time series. In investment activities, there are the most important components, namely volatility and risk. All financial evaluations require accurate volatility predictions. Volatility is identical to the conditional standard deviation of stock price returns. The most frequently used risk calculation is Value-at-Risk (VaR). Mathematical models can be used to predict future stock prices, the model that will be used is the Glosten Jagannathan Runkle-generalized autoregressive conditional heteroscedastic (GJR-GARCH) model. The purpose of this study was to determine the value of the risk obtained by using the time series model. GJR-GARCH is a development of GARCH by including the leverage effect. The effect of leverage is related to the concept of asymmetry. Asymmetry generally arises because of the difference between price changes and value volatility. The method used in this study is a literature and experimental study through secondary data simulations in the form of daily data from BCA shares and BNI shares. Data processing by looking at the heteroscedasticity of the data, then continued by using the GARCH model and seeing whether there is an asymmetry in the data. If there is an asymmetric effect on the processed data, then it is continued by using the GJR-GARCH model. The results obtained on the two stocks can be explained that the analyzed stock has a stock return volatility value for the leverage effect because the GJR-GARCH coefficient value is &gt; 0. So, the risk value obtained by using VaR measurements on BCA stocks is 0.047247 and on BNI stocks. is 0.037355. Therefore, the ARMA-GJR-GARCH model is good for determining the value of stock risk using VaR.

Using Triples to Assess Symmetry Under Weak Dependence

ABSTRACT The problem of assessing symmetry about an unspecified center of the one-dimensional marginal distribution of a strictly stationary random process is considered. A well-known U-statistic based on data triples is used to detect deviations from symmetry, allowing the underlying process to satisfy suitable mixing or near-epoch dependence conditions. We suggest using subsampling for inference on the target parameter, establish the asymptotic validity of the method in our setting, and discuss data-driven rules for selecting the size of subsamples. The small-sample properties of the proposed inferential procedures are examined by means of Monte Carlo simulations. Applications to time series of output growth and stock returns are also presented.

Quintile regression based approach for dynamical VaR and CVaR forecasting using metalog distribution

The paper proposes a new method of dynamic VaR and CVaR (ES) risk measures forecasting. Quantile linear GARCH model is chosen as the main forecasting model for time series quantiles. To build a forecast, the values of quantiles are approximated by the metalog distribution, which makes it possible to use analytical formulas to evaluate risk measures. The method of VaR and CVaR forecasting is formulated as a step-by-step algorithm. At the first stage, an initial model is built to obtain variance estimates. The predicted variance values obtained from the constructed model are used at the second stage to find the QLGARCH model coefficients by solving the minimization problem. At the third stage, the QLGARCH models are estimated on a non uniform quantile grid. The obtained predicted values of quantiles are used to estimate the approximating metalog distribution. The investigated theory is applied to VaR and CVaR forecasting for time series of daily log return of the DJI index.

Debt-by-Price Ratio, End-of-Year Economic Growth, and Long-Term Prediction of Stock Returns

With the prominent role of government debt in economic growth in recent decades, one would expect that government debt alongside economic growth to be a risk factor priced in the time series of stock returns. In this paper, this idea is investigated by applying a nonparametric model, namely, a local-linear kernel smoother with the aim of forecasting long-term stock returns where the model and smoothing parameters are chosen by cross-validation. While a wide range of predictive variables are examined, we find that our newly introduced debt-by-price ratio and the third to fourth quarter economic growth are robust predictors of stock returns, beating the well-known predictive variables in the literature by a significant difference. The combination of these two covariates can explain almost 30% variation of stock returns at a one-year horizon. This is very crucial considering the difficulty in capturing even a small proportion of movements in stock returns.

Good volatility, bad volatility, and time series return predictability

We propose a least squares estimator weighted by a combination of lagged realized semivariances related to positive and negative returns (WLS-CRS) and use univariate models alone and in combination to reveal significant return predictability. For an investor with a mean-variance preference who allocates a portfolio based on an equal-weighted combination of WLS-CRS model forecasts, the annual certainty equivalent return is 242.8 basis points higher than that received by an investor whose portfolio is allocated based on historical average forecasts. In forecasting stock returns, WLS-CRS estimates outperform the popular ordinary least squares estimates in both statistical and economic evaluation frameworks. WLS-CRS also outperforms estimators based on least squares weighted by lagged realized volatility. We further demonstrate the dominant role of negative return semivariance in improved forecasting performance. Our main findings hold through several robustness checks, including alternative validation samples, different risk aversion coefficients, and various forecast combinations.

Pairs Trading via Unsupervised Learning

This paper develops a pairs trading strategy via unsupervised learning. Unlike conventional pairs trading strategies that identify pairs based on return time series, we identify pairs by incorporating firm characteristics as well as price information. Firm characteristics are revealed to provide important information for pair identification and significantly improve the performance of the pairs trading strategy. Applied to the US stock market from January 1980 to December 2020, the long-short portfolio constructed via the agglomerative clustering earns a statistically significant annualized mean return of 24.8% and a Sharpe ratio of 2.69. The strategy remains profitable after accounting for transaction costs and removing stocks below 20% NYSE-size quantile. A host of robustness tests confirm that the results are not driven by data snooping.

A Cryptocurrency Risk–Return Analysis for Bull and Bear Regimes

In this article, the authors develop a new analytical lens through which to examine the risk–return profiles of bitcoin, litecoin, ripple, and ethereum. Their focus is to understand better the price behavior of individual cryptocurrencies and their influence on one another. To achieve this, they segment each cryptocurrency’s time series of returns into disparate bull and bear regimes. They then examine the nature and extent of overlap between these regimes and whether they change over time. They also collect and plot several indicative distributed-denial-of-service attacks against the time series to investigate their possible impact on regime change episodes. Their findings shed light on previously unexplored systemic risk indicators within the cryptomarket as a whole and on the relationship between specific cryptocurrency pairs. These findings enhance the risk management toolkit for investors by revealing potential price behavior contagion patterns between cryptocurrencies pertinent to blended portfolio management. Furthermore, the authors’ approach serves as a blueprint for additional research into regime-type overlap within the cryptomarket. TOPICS:Real assets/alternative investments/private equity, exchanges/markets/clearinghouses, financial crises and financial market history Key Findings ▪ Periods of overlapping regimes increase over time. The increase indicates a rise in cryptomarket systemic risk and an associated reduction in the diversification value of a blended portfolio of cryptocurrencies. ▪ Bitcoin exhibits the most favorable risk measures across both bull and bear regimes, including the lowest proclivity for extreme events during bear regimes. In contrast, ripple displays the overall riskiest profile across both regime types. ▪ Bitcoin’s regime type has the most meaningful impact on the risk–return profile of other cryptocurrencies, namely, litecoin and ripple. However, this relationship does not hold in reverse, a likely consequence of bitcoin’s market dominance and relative maturity.

Factor Modeling: The Benefits of Disentangling Cross-Sectionally for Explaining Stock Returns

More than three decades ago, Jacobs and Levy introduced the idea of disentangling stock returns across numerous factors. They identified the relationships between individual stock returns and firm characteristics using a cross-sectional analysis and examined the benefits of using the resulting time series of returns to the disentangled factors for return forecasting. Some years later, an alternative factor model proposed by Fama and French made use of time-series factors based on portfolio sorts (examples of these time-series factors include the return differences between small- and big-capitalization stocks and between high- and low-book-to-price stocks). Recently, Fama and French found that the cross-sectional approach using firm characteristics is better able to explain stock returns than the time-series approach based on portfolio sorts. This article compares models that use cross-sectional factors across firm characteristics with models that use time-series factors based on portfolio sorts and discusses the benefits and challenges of the cross-sectional approach for investment management. TOPICS:Factor-based models, statistical methods, security analysis and valuation, equity portfolio management Key Findings ▪ More than three decades ago, the authors pioneered a cross-sectional approach to factor modeling that disentangled the unique contributions of numerous factors to the pricing of individual stocks. ▪ A time-series approach using portfolio sorts has dominated the asset pricing literature, but cross-sectional analysis using firm characteristics has greater explanatory power for stock returns and helps practitioners address one of the most fundamental issues in investment management: understanding and predicting the returns of individual stocks. ▪ The authors revisit disentangling returns using a cross-sectional model, compare factor models using cross-sectional factors with those using time-series factors, and discuss the benefits and challenges of cross-sectional models.

Unraveling S&P500 stock volatility and networks – an encoding-and-decoding approach

Volatility is a measure of uncertainty or risk embedded within a stock's dynamics. Such risk has been received huge amounts of attention from diverse financial researchers. By following the concept of regime-switching model, we proposed a non-parametric approach, named encoding-and-decoding, to discover multiple volatility states embedded within a discrete time series of stock returns. The encoding is performed across the entire span of temporal time points for relatively extreme events with respect to a chosen quantile-based threshold. As such the return time series is transformed into Bernoulli-variable processes. In the decoding phase, we computationally seek for locations of change points via estimations based on a new searching algorithm in conjunction with the information criterion applied on the observed collection of recurrence times upon the binary process. Besides the independence required for building the Geometric distributional likelihood function, the proposed approach can functionally partition the entire return time series into a collection of homogeneous segments without any assumptions of dynamic structure and underlying distributions. In the numerical experiments, our approach is found favorably compared with parametric models like Hidden Markov Model. In the real data applications, we introduce the application of our approach in forecasting stock returns. Finally, volatility dynamic of every single stock of S&P500 is revealed, and a stock network is consequently established to represent dependency relations derived through concurrent volatility states among S&P500.

Dynamic of the States of Three Different Stock Markets from Correlation and Partial Correlation Changes

The core focus of the study is to examine financial states using index effect on stock to stock correlations of developed, developing and emerging market. The three markets such as S&P 500, KOSPI 200 and DSE are declared as developed, developing and emerging market respectively. To study the similarity between stock price changes, we calculate the time series of the daily log return. Closing stock prices of the targeted markets have been used to measure the daily return of the stocks. To analyze the market mobility, Pearson correlation coefficient, partial correlation, and index effect on stock to stock correlation techniques have been applied. The study found that the companies of developed and emerging market are more strongly correlated than those of developing market during big crash. On the other hand, developing market shows less index effect on stock correlations during crisis. Moreover, insignificant index effect has been found in emerging market during calm state. No significant effect of DSE index on stock to stock correlations in the period of global financial crisis has been observed, implying that global financial crisis did not hit to the DSE in this period. Before the market crash, the interactions between stocks became low enough which corresponds to lower value of average correlation for all types of market. Finally, the change of correlation and partial correlation can be a good indicator to identify and predict the financial states of all the markets which will further helps the stakeholders to make proper economic decisions.