This article discusses and investigates the quality of hedge fund databases. The main goal of this article is to increase awareness of the practical limitations of hedge fund data and devise a tool for the quantification of financial data quality. The accuracy of hedge fund return data is taken for granted in most empirical studies. It is shown, however, that hedge fund return time series often exhibit peculiar and most likely “man-made” patterns, which are worth examining. A statistical testing methodology that can detect these patterns is developed. Based on these tests, a data quality score for rating hedge funds and, more generally, hedge fund databases is devised. An empirical study is conducted to show how this data quality score can be used when exploring a hedge fund database. This can confirm many of the insights by Liang [2003] concerning the quality of hedge fund return data using a different methodology. In a final step the authors attempt to estimate the impact of imperfect data on performance measurement by defining a “data quality bias.” TOPICS:Real assets/alternative investments/private equity, quantitative methods, performance measurement

This paper studies the quasi-maximum-likelihood estimator (QMLE) in a general conditionally heteroscedastic time series model of multiplicative form X-t = sigma(t)Z(t), where the unobservable volatility sigma(t) is a parametric function of (Xt-1,..., Xt-p, sigma(t-1),..., sigma(t-q)) for some p, q >= 0, and (Z(t)) is standardized i.i.d. noise. We assume that these models are solutions to stochastic recurrence equations which satisfy a contraction (random Lipschitz coefficient) property. These assumptions are satisfied for the popular GARCH, asymmetric GARCH and exponential GARCH processes. Exploiting the contraction property, we give conditions for the existence and uniqueness of a strictly stationary solution (X-t) to the stochastic recurrence equation and establish consistency and asymptotic normality of the QMLE. We also discuss the problem of invertibility of such time series models.

In this paper we study the asymptotic behavior of the Gaussian quasi maximum likelihood estimator of a stationary GARCH process with heavy-tailed innovations. This means that the innovations are regularly varying with index alpha is an element of (2, 4). Then, in particular, the marginal distribution of the GARCH process has infinite fourth moment and standard asymptotic theory with normal limits and root n-rates breaks down. This was recently observed by Hall and Yao [Econometrica 71 (2003) 285-317]. It is the aim of this paper to indicate that the limit theory for the parameter estimators in the heavy-tailed case nevertheless very much parallels the normal asymptotic theory. In the light-tailed case, the limit theory is based on the CLT for stationary ergodic finite variance martingale difference sequences. In the heavy-tailed case such a general result does not exist, but an analogous result with infinite variance stable limits can be shown to hold under certain mixing conditions which are satisfied for GARCH processes. It is the aim of the paper to give a general structural result for infinite variance limits which can also be applied in situations more general than GARCH.

This paper studies the quasi-maximum-likelihood estimator (QMLE) in a general conditionally heteroscedastic time series model of multiplicative form Xt = σtZt , where the unobservable volatility σt is a parametric function of (Xt−1, . . . ,Xt−p,σt−1, . . . , σt−q) for some p,q ≥ 0, and (Zt ) is standardized i.i.d. noise. We assume that these models are solutions to stochastic recurrence equations which satisfy a contraction (random Lipschitz coefficient) property. These assumptions are satisfied for the popular GARCH, asymmetric GARCH and exponential GARCH processes. Exploiting the contraction property, we give conditions for the existence and uniqueness of a strictly stationary solution (Xt ) to the stochastic recurrence equation and establish consistency and asymptotic normality of the QMLE. We also discuss the problem of invertibility of such time series models.

The squares of a GARCH(p, q) process satisfy an ARMA equation with white noise innovations and parameters which are derived from the GARCH model. Moreover, the noise sequence of this ARMA process constitutes a strongly mixing stationary process with geometric rate. These properties suggest to apply classical estimation theory for stationary ARMA processes.We focus on the Whittle estimator for the parameters of the resulting ARMA model. Giraitis and Robinson (2000) show in this context that the Whittle estimator is strongly consistent and asymptotically normal provided the process has finite 8th moment marginal distribution. We focus on the GARCH(l,l) case when the 8th moment is infinite. This case corresponds to various real-life log-return series of financial data. We show that the Whittle estimator is consistent as long as the 4th moment is finite and inconsistent when the 4th moment is infinite. Moreover, in the finite 4th moment case rates of convergence of the Whittle estimator to the true parameter are the slower, the fatter the tail of the distribution.These findings are in contrast to ARMA processes with iid innovations. Indeed, in the latter case it was shown by Mikosch et at. (1995) that the rate of convergence of the Whittle estimator to the true parameter is the faster, the fatter the tails of the innovations distribution. Thus the analogy between a squared GARCH process and an ARMA process is misleading insofar that one of the classical estimation techniques, Whittle estimation, does not yield the expected analogy of the asymptotic behavior of the estimators. (C) 2002 Elsevier Science B.V. All rights reserved.

Modern risk management calls for an understanding of stochastic dependence going beyond simple linear correlation. This article deals with the static (nontime- dependent) case and emphasizes the copula representation of dependence for a random vector. Linear correlation is a natural dependence measure for multivariate normally, and more generally, elliptically distributed risks but other dependence concepts like comonotonicity and rank correlation should also be understood by the risk management practitioner. Using counterexamples the falsity of some commonly held views on correlation is demonstrated; in general, these fallacies arise from the naive assumption that dependence properties of the elliptical world also hold in the non-elliptical world. In particular, the problem of finding multivariate models which are consistent with prespecified marginal distributions and correlations is addressed. Pitfalls are highlighted and simulation algorithms avoiding these problems are constructed.

Correlation is a mine eld for the unwary. One does not have to search far in the literature of nancial risk management to nd misunderstanding and confusion. This is worrying since correlation is a central technical idea in nance. Correlation lies at the heart of the capital asset pricing model (CAPM) and the arbitrage pricing theory (APT), where its use as a measure of dependence between nancial instruments is essentially founded on an assumption of multivariate normally distributed returns. Increasingly, however, correlation is being used as a dependence measure in general risk management, often in areas where the assumption of multivariate normal risks is completely untenable such as credit risk. In using correlation as an all-purpose dependence measure and transferring CAPM thinking to general risk management, many integrated risk management systems are being built on shaky foundations. This article will tell you when it is safe and unproblematic to use correlation in the way that you imagine you can use it, and when you should take care. In particular it will tell you about two fallacies that have claimed many victims. These traps are known to statisticians, but not, we suggest, to the general correlation-using public. We will help you avoid these pitfalls and introduce an alternative approach to understanding and modelling dependency copulas. The recognition that correlation is often an satisfactory measure of dependence in nancial risk management is not in itself new. For instance, Blyth (1996) and Shaw (1997) have made the point that (linear) correlation cannot capture the non-linear dependence relationships that exist between many real world risk factors. We believe this point is worth repeating and amplifying; our aim is to provide theoretical clari cation of some of the important and often subtle issues surrounding correlation. To keep things simple we consider only the static case. That is, we consider a vector of dependent risks (X1; : : : ; Xn) 0 at a xed point in time. We do not consider serial correlation within or cross correlation between stochastic processes (see Boyer, Gibson, and Loretan (1999) in this context). Nor do we consider the statistical estimation of correlation, which is fraught with diAEculty. In this paper we do not go this far because enough can go wrong in the static case to ll an entire book.

This article will tell you when it is safe and unproblematic to use correlation in the way that you imagine you can use it, and when you should take care. In particular it will tell you about two fallacies that have claimed many victims. These traps are known to statisticians, but not, we suggest, to the general correlation-using public. We will help you avoid these pitfalls and introduce an alternative approach to understanding and modelling dependency - copulas.

This paper gives a survey on equity factor modeling and how it relates to other risk modeling techniques. The theory is illustrated by means of an empirical study.