Outliers,GARCH-type models and risk measures: A comparison of several approaches

In this paper we focus on the impact of additive outliers (level and volatility) on the calculation of risk measures, such as minimum capital risk requirements. Through simulation and empirical studies, we compare six alternative proposals that are used in the literature to reduce the effects of outliers in the estimation of risk measures when using GARCH-type models. The methods are based on [1] correcting for significant outliers, [2] accommodating outliers using complex (e.g. fat-tail) distributions and [3] accounting for outlier effects by robust estimation. The main conclusions of the simulation study are that the presence of outliers bias these risk measures, being the proposal by Grané and Veiga (2010) that providing the highest bias reduction. From the out-of-sample results for four international stock market indexes we found weak evidence that more complex models (specification and error distribution) perform better in estimating the minimum capital risk requirements during the last global financial crisis.     

How Crashes Develop: Intradaily Volatility and Crash Evolution

This paper explores whether affine models with volatility jumps estimated on intradaily S&P 500 futures data over 1983 to 2008 can capture major daily outliers such as the 1987 stock market crash. Intradaily jumps in futures prices are typically small; self‐exciting but short‐lived volatility spikes capture intradaily and daily returns better. Multifactor models of the evolution of diffusive variance and jump intensities improve fits substantially, including out‐of‐sample over 2009 to 2016. The models capture reasonably well the conditional distributions of daily returns and realized variance outliers, but underpredict realized variance inliers. I also examine option pricing implications.     

A Test for Symmetry with Leptokurtic Financial Data

Most of the tests for symmetry are developed under the (implicitor explicit) null hypothesis of normal distribution. As is wellknown, many financial data exhibit fat tails, and thereforecommonly used tests for symmetry (such as the standard test based on sample skewness) are not valid fortesting the symmetry of leptokurtic financial data. In particular,the test uses third moment, which may not be robust in presence of gross outliers. In this article wepropose a simple test for symmetry based on the Pearson typeIV family of distributions, which take account of leptokurtosisexplicitly. Our test is based on a function that is boundedover the real line, and we expect it to be more well behavedthan the test based on sample skewness (third moment). Resultsfrom our Monte Carlo study reveal that the suggested test performsvery well in finite samples both in terms of size and power.Simulation results also support our conjecture of the teststo be well behaved and robust to excess kurtosis. We apply thetest to some selected individual stock return data to illustrateits usefulness.     

Hidden Markov models with t components. Increased persistence and other aspects

Hidden Markov models have been applied in many different fields, including econometrics and finance. However, the lion's share of the investigated models concerns Markovian mixtures of Gaussian distributions. We present an extension to conditional t-distributions, including models with unequal distribution types in different states. It is shown that the extended models, on the one hand, reproduce various stylized facts of daily returns better than the common Gaussian model. On the other hand, robustness to outliers and persistence of the visited states increases significantly.     

The use of least median of squares in the estimation of land value equations

Ordinary least squares (OLS) regression is relatively sensitive to the presence of outliers in a data set. In this paper, a robust estimation method, least median of squares (LMS) is used to identify outliers in land value data. Once the outliers are identified, are the land value equations re-estimated. The results show that a few observations can have a significant effect on the estimated coefficients. Finally, the observations which were identified as outliers were examined in more detail. One cause of outliers is an omitted variable. In this case, a large fraction of the outliers were found to be observations with high development potential.     

Robust estimation of historical volatility and correlations in risk management

Financial time series have two features which, in many cases, prevent the use of conventional estimators of volatilities and correlations: leptokurtotic distributions and contamination of data with outliers. Other techniques are required to achieve stable and accurate results. In this paper, we review robust estimators for volatilities and correlations and identify those best suited for use in risk management. The selection criteria were that the estimator should be stable to both fractionally small departures for all data points (fat tails), and to fractionally large departures for a small number of data points (outliers). Since risk management typically deals with thousands of time series at once, another major requirement was the independence of the approach of any manual correction or data pre-processing. We recommend using volatility t-estimators, for which we derived the estimation error formula for the case when the exact shape of the data distribution is unknown. A convenient robust estimator for correlations is Kendall's tau, whose drawback is that it does not guarantee the positivity of the correlation matrix. We chose to use geometric optimization that overcomes this problem by finding the closest correlation matrix to a given matrix in terms of the Hadamard norm. We propose the weights for the norm and demonstrate the efficiency of the algorithm on large-scale problems.     

Ratio Analysis Using Rank Transformation

This paper presents an alternate method for transforming financial ratios. Ratios are ranked and scaled into a uniform distribution with boundaries between 0 and 1. Conceptually, we suggest that this method solves a number of methodological problems associated with ratios, including constrained choice of regression models, ratio outliers, negative ratios, and non-normal distributions. Scaled ranks of financial ratios are also conceptually appealing because they appear to capture comparative ordinal data about cross-sectional relationships between firms.The study empirically tests scaled rank transformations by examining the association of the transformations with stock returns. Results show that models using relative ranked accounting ratios have more explanatory and predictive power than untransformed, log-transformed and square-root transformed ratios.     

Return Distributions and Improved Tests of Asset Pricing Models

We compare and contrast some existing ordinary least squares(OLS)- and generalized method of moments (GMM)-based tests ofasset pricing models with a new more general test. This newtest is valid under the assumption that returns are ellipticallydistributed, a necessary and sufficient assumption of the linearcapital asset pricing model (CAPM). This new test fails to rejectthe CAPM on a dataset of stocks sorted by market valuations,whereas similar tests constructed from OLS and GMM estimationmethods reject the linear CAPM. We also find that outliers reducethe OLS-estimated mispricing of the linear CAPM on monthly returnssorted by previous performance, that is, momentum. Monte Carloevidence supports superior size and power properties of thenew test relative to OLS- and GMM-based tests.     

Identifying and treating outliers in finance

Outliers represent a fundamental challenge in the empirical finance research. We investigate whether the routine techniques used in finance research to identify and treat outliers are appropriate for the data structures we observe in practice. Specifically, we propose a multivariate identification strategy that can effectively detect outliers. We also introduce an estimator that minimizes the bias outliers caused in both cross‐sectional and panel regressions and provide outlier mitigation guidance. Using replications of four recently published studies in premier finance journals, we show how adjusting for multivariate outliers can lead to significantly different results.     

Analysis of earnings management influence on the investment efficiency of listed Chinese companies

This study examines the “EM (earnings management) and excess investment hypothesis,” which posits that upward EM increases investment spending. Two types of EM proxies and two types of investment proxies are calculated to ensure the robustness of results. The two types of EM proxies are case studies (firms with three fraudulent activities) and econometric estimation of regression residuals (of revenues and accrual functions). The two investment proxies are industry-adjusted investment and investment function residuals. Considering that outliers are common in panel data but are often ignored in estimation, the aforementioned proxies are determined with and without considering the outliers using listed companies in China from 1998 to 2010. Empirical results demonstrate that the hypothesis is supported when the outliers are considered, whereas the opposite result is obtained when the outliers are not considered. The analysis and findings of this study indicate that considering the influence of the outliers is crucial to support the hypothesis.     

Divergence of Cash Flow and Voting Rights,Opacity, and Stock Price Crash Risk: International Evidence

This study investigates whether and how the deviation of cash flow rights (ownership) from voting rights (control), or simply the ownership‐control wedge, influences the likelihood that extreme negative outliers occur in stock return distributions, which we refer to as stock price crash risk. We do so using a comprehensive panel data set of firms with a dual‐class share structure from 20 countries around the world for the period of 1995–2007. We predict and find that opaque firms with a large wedge are more crash prone than opaque firms with a small wedge. In addition, we predict and find that the positive relation between the wedge and crash risk is less pronounced for firms with more effective external monitoring and for firms with greater growth opportunities. The results of this study are broadly consistent with Jin and Myers’s theory that agency costs, combined with opacity, exacerbate stock price crash risk.     

Outlier analysis and mortality forecasting: The United Kingdom and Scandinavian countries

The Lee-Carter model and its variants have been extensively employed by actuaries, demographers, and many others to forecast age-specific mortality. In this study, we use mortality data from England and Wales, and four Scandinavian countries to perform time-series outlier analysis of the key component of the Lee-Carter model – the mortality index. We begin by employing a systematic outlier detection process to ascertain the timing, magnitude, and persistence of any outliers present in historical mortality trends. We then try to match the identified outliers with imperative events that could possibly justify the vacillations in human mortality levels. At the same time, we adjust the effect of the outliers for model re-estimation. A new iterative model re-estimation method is proposed to reduce the chance of erroneous model specification. The empirical results indicate that the outlier-adjusted model could achieve more efficient forecasts of variables such as death rates and life expectancies. Finally, we point out that the Lee-Carter forecasts are especially vulnerable to outliers near the forecast origin, and discuss the potential limitations of the application of the Lee-Carter model to mortality forecasting.     

Financial Development and Economic Growth: Do Outliers Matter?

This study examines the effect of outliers on causal relationship between financial development and economic growth using 48 countries from 1988 to 2014. The dynamic panel model of Levine, Loayza, and Beck (2000) is used to examine this issue. We propose a novel approach by combining the least square dummy variable correction method (LSDVC) to remove the estimates bias in the dynamic panel model and the least trimmed squares (LTS) to control outlier influence. The combination of these two methods is referred to as LSDVC + LTS. Our results show a counter-intuitive evidence that bank development negatively affects economic growth when the outlier influence is ignored. This counter-intuitive evidence holds even when the conventional winsorization method is used to control the outliers. However, bank development exhibits a positive influence on economic growth once the proposed approach LSDVC + LTS is adopted. Also, stock market development exhibits a positive effect on economic growth regardless of the outliers.     

Seasonality in outliers of daily stock returns: A tail that wags the dog?

We document significant intra-year seasonality in outliers of S&P500 daily rates of return. Controlling for outliers in dummy regressions reveals that both the January and Monday effects turn from insignificant to highly significant. Mean daily return on January doubles and becomes significantly higher than all other months of the year, and Monday's mean return turns significantly positive and higher than other days of the week. The recently documented Halloween effect turns significant only after controlling for outliers as June, August, and September turn out to be months with remarkably low rates of returns. Being random, outliers cannot serve as instrumental variables for designing trading rules, yet, their impact on options pricing through the increase in volatility, may be applied for profitable options strategies.     

Interval Estimation of Actuarial Risk Measures

Abstract

This article investigates performance of interval estimators of various actuarial risk measures. We consider the following risk measures: proportional hazards transform (PHT), Wang transform (WT), value-at-risk (VaR), and conditional tail expectation (CTE). Confidence intervals for these measures are constructed by applying nonparametric approaches (empirical and bootstrap), the strict parametric approach (based on the maximum likelihood estimators), and robust parametric procedures (based on trimmed means).

Using Monte Carlo simulations, we compare the average lengths and proportions of coverage (of the true measure) of the intervals under two data-generating scenarios: “clean” data and “contaminated” data. In the “clean” case, data sets are generated by the following (similar shape) parametric families: exponential, Pareto, and lognormal. Parameters of these distributions are selected so that all three families are equally risky with respect to a fixed risk measure. In the “contaminated” case, the “clean” data sets from these distributions are mixed with a small fraction of unusual observations (outliers). It is found that approximate knowledge of the underlying distribution combined with a sufficiently robust estimator (designed for that distribution) yields intervals with satisfactory performance under both scenarios.     

Unveiling the embedded coherence in divergent performance rankings

This paper focuses on analyzing functional relationships among performance measures, centered on the adjusted differential risk premium between the asset and the benchmark and on Sharpe-1994 ratio. First, we develop a risk normalization procedure for variance and Aumann–Serrano riskiness which turns contradictory rankings into coherent ones, and combines the effects of correlation and outliers into the analysis. On this basis, we deduce functional connections among performance measures, arriving at a new indicator which expresses performance as the addition of three effects due to Sharpe ratio, correlation and outliers. We show it is a strictly increasing function of Homm–Pigorsch ratio.     

Bootstrapping a distance test for stochastic dominance analysis

A major impediment to measuring portfolio performance under stochastic dominance has been the lack of test statistics for orders of stochastic dominance above first degree. In this article, the Bootstrap method, introduced by Efron (1979), is used to estimate critical values for distance statistics in order to test the null hypothesis of no dominance, under second- and third-degree stochastic dominance, for several samples of stock returns. These test statistics, suggested by Whitmore (1978), are analogous to the Kolmogorov-Smirnov distance statistics that can be used to test for first-degree stochastic dominance. Stochastic dominance is shown to accurately assess portfolio performance of sample distributions when the population distributions are controlled and Bootstrap statistics are employed in the analysis. In addition, second- and third-degree stochastic dominance analysis of the smallfirm January anomaly indicates that, over the 23-year time period 1964 to 1986, small firms statistically dominate a diversified market index in only one calendar year.     

Unit roots and infrequent large shocks: new international evidence on output

The nature and magnitude of the economic shocks that have affected the per capita GDP of 16 OECD countries are analyzed over a long period using the outlier method. Strong proof of infrequent large permanent and transitory shocks were found, essentially resulting from the two major wars in the twentieth century, the recession in the 1920s, the Great Depression, among others. We also examine the nature of the output trend by combining different tests of non-stationarity on different GDP series corrected by the outliers detected. It is shown that the per capita GDP series cannot reject the unit root hypothesis in 13 of the 16 countries examined. No conclusion could be drawn for the other countries because the test results were contradictory.     

A Robustification of the Chain-Ladder Method

Abstract

In a non-life insurance business an insurer often needs to build up a reserve to able to meet his or her future obligations arising from incurred but not reported completely claims. To forecast these claims reserves, a simple but generally accepted algorithm is the classical chain-ladder method. Recent research essentially focused on the underlying model for the claims reserves to come to appropriate bounds for the estimates of future claims reserves. Our research concentrates on scenarios with outlying data. On closer examination it is demonstrated that the forecasts for future claims reserves are very dependent on outlying observations. The paper focuses on two approaches to robustify the chain-ladder method: the first method detects and adjusts the outlying values, whereas the second method is based on a robust generalized linear model technique. In this way insurers will be able to find a reserve that is similar to the reserve they would have found if the data contained no outliers. Because the robust method flags the outliers, it is possible to examine these observations for further examination. For obtaining the corresponding standard errors the bootstrapping technique is applied. The robust chain-ladder method is applied to several run-off triangles with and without outliers, showing its excellent performance.     

Distribution of parallel exchange rates in African countries

This paper investigates the distribution of parallel exchange rates in African countries using exploratory data analysis techniques and model fitting. Stable laws are fitted to empirical distributions using the maximum likelihood estimation method. Empirical evidence supports the stable hypothesis these distributions are positively skewed and have tails that are much heavier than Gaussian counterparts. The stable hypothesis is further supported by the “converging variance test,” which suggests that these distributions have infinite variance.