Offering a unifying theoretical perspective not readily available in any other text, this innovative guide to econometrics uses simple geometrical arguments to develop students' intuitive understanding of basic and advanced topics, emphasizing throughout the practical applications of modern theory and nonlinear techniques of estimation. One theme of the text is the use of artificial regressions for estimation, reference, and specification testing of nonlinear models, including diagnostic tests for parameter constancy, serial correlation, heteroscedasticity, and other types of mis-specification. Explaining how estimates can be obtained and tests can be carried out, the authors go beyond a mere algebraic description to one that can be easily translated into the commands of a standard econometric software package. Covering an unprecedented range of problems with a consistent emphasis on those that arise in applied work, this accessible and coherent guide to the most vital topics in econometrics today is indispensable for advanced students of econometrics and students of statistics interested in regression and related topics. It will also suit practising econometricians who want to update their skills. Flexibly designed to accommodate a variety of course levels, it offers both complete coverage of the basic material and separate chapters on areas of specialized interest.

Estimation and Inference in Econometrics

Economics and Information Theory

Giventhegrowingneedformanagingfinancialrisk,riskpredictionplaysanincreasing roleinbankingandfinance.Inthisstudywecomparetheout-of-sampleperformance of existing methods and some new models for predicting value-at-risk (VaR) in a univariate context. Using more than 30 years of the daily return data on the NASDAQ Composite Index, we find that most approaches perform inadequately, although several models are acceptable under current regulatory assessment rules for model adequacy. A hybrid method, combining a heavy-tailed generalized autoregressive conditionally heteroskedastic (GARCH) filter with an extreme value theory-based approach, performs best overall, closely followed by a variant on a filtered historical simulation, and a new model based on heteroskedastic mixture distributions. Conditional autoregressive VaR (CAViaR) models perform inadequately, though an extension to a particular CAViaR model is shown to outperform the others.

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Value-at-Risk Prediction: A Comparison of Alternative Strategies

We propose a new measure of risk, based entirely on downward moves measured using high frequency data. Realised semivariances are shown to have important predictive qualities for future market volatility. The theory of these new measures is spelt out, drawing on some new results from probability theory.

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Measuring downside risk-realised semivariance.

In this paper we examine and summarize properties of several well-known risk measures that can be used in the framework of setting solvency capital requirements for a risky business. Special attention is given to the class of (concave) distortion risk measures. We investigate the relationship between these risk measures and theories of choice under risk. Furthermore we consider the problem of how to evaluate risk measures for sums of non-independent random variables. Approximations for such sums, based on the concept of comonotonicity, are proposed. Several examples are provided to illustrate properties or to prove that certain properties do not hold. Although the paper contains several new results, it is written as an overview and pedagogical introduction to the subject of risk measurement. The paper is an extended version of Dhaene et al. (2003).

https://papers.ssrn.com/sol3/Delivery.cfm?abstractid=892185

Risk Measures and Comonotonicity: A Review

We examine two performance measures advocated for asymmetric return distributions: the Sortino ratio—originally introduced by Sortino and Price (Sortino F and Price L 1994 J. Investing 59–65)—and a measure based on power utility introduced in Leland (Leland H 1999 Financial Analysts J. 27–36). In particular, we investigate the role of the maximum principle in this context, and assess the conditions under which the measures satisfy it. Our results add further motivation for the use of a modified Sortino ratio, by placing it on a sound theoretical foundation. In this light, we discuss its relative merits compared with alternative approaches.

On the foundation of performance measures under asymmetric returns

Recalling the class of risk measures introduced by Stone [1973], the authors survey measures from different academic disciplines—including psychology, operations research, management science, economics, and finance—that have been introduced since 1973. We introduce a general class of risk measures that extends Stone's class to include these new measures. Finally, we give four axioms that describe necessary attributes of a good financial risk measure and show which of the measures surveyed satisfy these. We demonstrate that all measures that satisfy our axioms, as well as those that do not but are commonly used in finance, belong to our new generalized class.

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An Extended Family of Financial-Risk Measures

Using both industry-specific data on 55 US industry sectors and an extensive range of macroeconomic variables, the authors compare the performance of nearest neighbour algorithms, OLS, and a number of two-stage models based on these two methods, when forecasting industry returns. As industry returns are a relatively under-researched area in the Finance literature, we also give a brief review of the existing theories as part motivation for our specific choice of variables, which are commonly employed by asset managers in practice. Performance is measured by the Information Coefficient (IC), which is defined as the average correlation between the 55 forecasted returns and the realised returns across industries over time. Due to transaction costs, investors and asset managers typically want a steady outperformance over time. Hence, the volatility of IC is taken into account through the application of “Sharpe Ratios”. We find that two-stage procedures mixing industry-specific information with macroeconomic indicators generally outperform both the stand-alone nearest neighbour algorithms and time-series based OLS macroeconomic models.

Evaluating the Performance of Nearest Neighbour Algorithms when Forecasting US Industry Returns

By formulating a nested test of the asymmetric response model of Bawa, Brown, and Klein (1981), the mean-lower partial moment CAPM (LPMCAPM) of Bawa and Lindenberg (1977) and the mean-variance CAPM of Sharpe (1963, 1964), Lintner (1965) and Mossin (1969), this paper investigates the relative merits of symmetric and asymmetric risk measures using UK equity data for differently sized companies and at different frequencies. Our analysis shows that, when equity returns are not normal - which is the case for most daily and weekly returns, and for a large portion of smaller firms - the CAPM is rejected in 30%-50% of cases, and the optimal choice of alternative model is LPM-CAPM in over two thirds of these. These, and our further results, have strong consequences for the accurate measurement of equity risk, performance and prices, as downside and/or asymmetric risk measures often outperform the traditional CAPM framework, thus rendering it’s related and widely-used current approaches sub-optimal for some company sizes/data frequency combinations.

On empirical risk measurement with asymmetric returns data

This paper reviews and extends definitions and properties of the three classical performance statistics (the Sharpe Ratio, the Treynor Index, and Jensen's Alpha) by locating them in a more general framework: the Asymmetric Response Mode. This allows various notions of beta, which can be related to downside risk, to be employed, and includes, as special cases, a market timing model and the mean-variance CAPM. Due to the general lack of data on fund performance in practice, our emphasis is on small sample analysis where possible. We illustrate our results empirically using data on 15 U.S.-based emerging markets investment funds.

Christian S. Pedersen

Papers

On the foundation of performance measures under asymmetric returns

An Extended Family of Financial-Risk Measures

Evaluating the Performance of Nearest Neighbour Algorithms when Forecasting US Industry Returns

On empirical risk measurement with asymmetric returns data

Small Sample Analysis of Performance Measures in the Asymmetric Response Model