We consider the problem related to the estimation of parametric models in the presence of outliers. The maximum likelihood estimator is often used to find parameter values. However, it is highly sensitive to abnormal points. In this regard, the weighted trimmed likelihood estimator (WTLE) has been introduced as a robust alternative. We present a new scheme for automatically computing the trimming parameter and weights of the WTLE. The method is illustrated by applying it to the standard GARCH model. We compare the approach with other recently introduced robust GARCH estimators through an extensive simulation study.

The generalized lambda distribution (GLD) is a versatile distribution that can accommodate a wide range of shapes, including fat-tailed and asymmetric distributions. It is defined by its quantile function. We introduce a more intuitive parameterization of the GLD that expresses the location and scale parameters directly as the median and inter-quartile range of the distribution. The remaining two shape parameters characterize the asymmetry and steepness of the distribution respectively. This is in contrasts to the previous parameterizations where the asymmetry and steepness are described by the combination of the two tail indices. The estimation of the GLD parameters is notoriously difficult. With our parameterization, the fitting of the GLD to empirical data can be reduced to a two-parameter estimation problem where the location and scale parameters are estimated by their robust sample estimators. This approach also works when the moments of the GLD do not exist. Moreover, the new parameterization can be used to compare data sets in a convenient asymmetry and steepness shape plot. In this paper, we derive the new formulation, as well as the conditions of the various distribution shape regions and moment conditions. We illustrate the use of the asymmetry and steepness shape plot by comparing equities from the NASDAQ-100 stock index.

We consider the problem related to the estimation of parametric models in the presence of outliers. The maximum likelihood estimator is often used to find parameter values. However, it is highly sensitive to abnormal points. In this regard, the weighted trimmed likelihood estimator (WTLE) has been introduced as a robust alternative. We present a new scheme for automatically computing the trimming parameter and weights of the WTLE. The method is illustrated by applying it to the standard GARCH model. We compare the approach with other recently introduced robust GARCH estimators through an extensive simulation study.

We consider the use of the generalized lambda distribution (GLD) family as a flexible distribution with which to model financial data sets. The GLD can assume distributions with a large range of shapes. Analysts can therefore work with a single distribution to model almost any class of financial assets, rather than needing several. This becomes especially useful in the estimation of risk measures, where the choice of the distribution is crucial for accuracy. We introduce a new parameterization of the GLD, wherein the location and scale parameters are directly expressed as the median and interquartile range of the distribution. The two remaining parameters characterize the asymmetry and steepness of the distribution. Conditions are given for the existence of its moments, and for it to have the appropriate support. The tail behavior is also studied. The new parameterization brings a clearer interpretation of the parameters, whereby the distribution's asymmetry can be more readily distinguished from its steepness. This is in contrast to current parameterizations of the GLD, where the asymmetry and steepness are simultaneously described by a combination of the tail indices. Moreover, the new parameterization can be used to compare data sets in a convenient asymmetry and steepness shape plot.

The management of time and holidays can prove crucial in applications that rely on his- torical data. A typical example is the aggregation of a data set recorded in different time zones and under different daylight saving time rules. Be- sides the time zone conversion function, which is well supported by default classes in R, one might need functions to handle special days or holi- days. In this respect, the package timeDate en- hances default date-time classes in R and brings new functionalities to time zone management and the creation of holiday calendars.

Generalized autoregressive heteroskedasticity (GARCH) models are widely used to reproduce stylized facts of financial time series and today play an essential role in risk management and volatility forecasting. But despite extensive research, problems are still encountered during parameter estimation in the presence of outliers. Here we show how this limitation can be overcome by applying the robust weighted trimmed likelihood estimator (WTLE) to the standard GARCH model. We suggest a fast implementation and explain how the additional robust parameter can be automatically estimated. We compare our approach with other recently introduced robust GARCH estimators and show through the results of an extensive simulation study that the proposed estimator provides robust and reliable estimates with a small computation cost. Moreover, the proposed fully automatic method for selecting the trimming parameter obviates the tedious fine tuning process required by other models to obtain a “robust” parameter, which may be appreciated by practitioners.

In this talk we give an overview of our current research and new tools for portfolio optimization implemented in R and Rmetrics. We present the portfolio modeling infrastructure implemented in our R packages. We summarize the many different reward-risk models that can be solved by the software, ranging from standard mean-variance portfolio optimization, shortfall risk minimization, scenario optimization, reward/risk ratio maximization, and to general non-linear risk objectives. These can be subject to box, linear, group, quadratic covariance, general non-linear and integer constraints. At the heart of this approach to compute the efficient frontier of a portfolio is the “R Optimization Infrastructure”, which is currently under active development. This includes the ROI package by the Vienna group and the Rmetrics2AMPL library, written by our group at the ETH in Zurich. We discuss the differences and similarities of the two approaches and the advantages of each for use in portfolio design. The optimized weights of portfolio that lie on the efficient frontier are neither optimally balanced nor diversified. Neither do the risk budgets or the tail dependence structure of the portfolio returns have minimum variance. We will show, from a risk point of view, what advantages an investor can achieve by investing in more risk-diversified portfolios than by investing in traditional efficient portfolios. For this, we present the implementation of new R functions to compute the hull of the feasible set, and to explore portfolios covering the whole feasible set. For each point we then compute performance and risk attributions and discuss their volatility and risk surface on top of the feasible set as a powerful graphical decision tool. For the dynamical analysis of portfolios we report on an R generator tool for creating Google motion charts. Motion charts are dynamic Flash-based animations that can be used to explore several indicators or components of a complex adaptive system and to obtain further insight on its evolution over time. As an example, we show the temporal development of the efficient frontier of a mean-variance Markowitz portfolio. Besides allowing us to explore risk and reward dynamically, this approach also gives an insight into the co-movement of performance and risk attributions. In addition to the frontier chart, we can use line and bar charts in order to compare and better assess alternative investment decisions. Würtz, D., Chalabi, Y., Chen, W., and Ellis, A. (2009). Portfolio Optimization with R/Rmetrics. Rmetrics Association & Finance Online, Zurich, 1 ________________________________________________________ In collaboration with Yohan Chalabi*, Andrew Ellis** and Sebastián Pérez Saaibi* edition. *ETH Zürich, **Finance Online GmbH Zürich Invited Talk presented at the ”The R User Conference 2010”, July 20-23 National Institute of Standards and Technology (NIST), Gaithersburg, Maryland, USA

Time and date management plays an essential role in financial applications with data recorded in different time zones. In this talk, we describe the concepts and methods behind the S4 classes timeDate and timeSeries used in the Rmetrics packages for financial data with time and holiday management. In particular, we will explore how timeDate (Wurtz and Chalabi, 2009a) allows mixing data collected in different time zones and with different daylight saving time rules (DST). Selected examples will be provided to show its functionality and advantages compared to the other time and date classes. Typical use cases are the management of business holidays or selection of the last working day in a month. The second part of the presentation will focus on the enhanced implementation of the timeSeries class in the package timeSeries (Wurtz and Chalabi, 2009b), which is extremely fast. It represents a good example of how to implement an efficient S4 class. Examples will be provided to demonstrate how to use the timeSeries class. Finally, we will also discuss recent and future development directions of the timeDate and timeSeries packages.

We investigate the generalized lambda distribution with infinite support as an alternative distribution for modeling financial return series with power law tails. We derive expressions for the distribution, for random number generation, and for financial risk measures including value at risk, expected shortfall and tail indices. We introduce a new robust moment approach for the estimation of the distribution parameters based on the median, interquartile range, Bowley’s skewness and Moors’ kurtosis. In addition using a Monte Carlo approach we explore the use of several estimation approaches including maximum log likelihood, maximum product spacing, goodness of fit testing, and histogram binning. A new four-parameter parameterization allows an intuitive interpretation based on the asymmetry and the tail behaviour of the distribution. We also introduce a new method of obtaining parameter estimates in which the data is standardized to have zero median and unit interquartile range and then a generalized lambda distribution with zero median and unit interquartile range is fitted to the data. This reduces the number of parameters to two allowing for more efficient parameter estimation.