Testing for Forward Rate Unbiasedness allowing for Persistent Regressors
with Alex Maynard, Journal of Empirical Finance 12 (2005), 613-628

Abstract: Standard regressions of the spot return on the forward premium have long been known to provide a strong rejection of unbiasedness. More recent literature has emphasized the strong autocorrelation in the forward premium, which shows estimated autoregressive roots close and in some cases statistically indistinguishable from one. This has cast doubt on the finite sample accuracy of traditional tests and estimates to the extent that finite sample size distortion and bias have come to be considered as one of several possible explanations behind the forward premium puzzle. In order to pursue this possibility further, we revisit the unbiasedness hypothesis using more appropriate inference procedures. In particular, rather than relying on standard stationarity-based asymptotics, we model the forward premium as a near unit root (local to unity) process and then test unbiasedness using the bounds tests of Cavanagh et. al. (1995) which are explicitly designed to provide accurate size under near unit root assumptions. To summarize our empirical findings, confidence intervals on the largest root confirm uncertainty regarding the stationarity/nonstationarity of the forward premium. However, estimates of the error correlation suggest only modest simultaneity bias. Consequently, we can still reject unbiasedness at the five percent level, even when using appropriately sized bounds tests. This evidence tends to suggest that the forward premium puzzle is more robust than previously imagined. It would be interesting in further work to explore to what extent such conclusions extend to alternative characterizations of the persistence in the forward premium, such as long-memory and structural break models.

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A New Application of Exact Nonparametric Methods to Long-horizon Predictability Tests
with Alex Maynard, Studies in Nonlinear Dynamics & Econometrics 11(1)(2007 forthcoming)

Abstract: Empirical results from long-horizon regression tests have been influential in the finance literature. Yet, it has come to be understood that traditional long-horizon tests may be unreliable in finite samples when regressors are persistent and when the horizon is long relative to sample size. Recent research has provided valid alternative inference procedures in long-horizon regression in the case for which the regressor follows a near-unit root autoregressive process. However, in small samples, such processes may sometimes be difficult to distinguish with confidence from other persistent data generating processes, such as those displaying long-memory or structural breaks. In this paper, we demonstrate a simple means by which existing nonparametric sign and signed rank tests may be applied to provide exact inference in long-horizon predictive tests, without requiring any modelling assumptions on the regressor. Employing this robust approach, we find evidence of stock return predictability at moderate horizons using short-term interest rates, but little evidence of either short or long-run predictability using dividend-price ratios.

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Currencies Portfolio Return: A Copula Methodology
Last updated on: May 2, 2006

Abstract: This paper presents an application of copula methodology in modeling joint distributions with fat tails. Four widely established copulas are estimated and compared with the multivariate normal model. They are the Gaussian copula, the t-copula, the Gumbel copula and the mixture of Gumbel copula. We study the effect of the copula on the Value-at-Risk (VaR). Furthermore, we examine models with different portfolio weights. The results are quite informative. Copula is particularly useful in approximating the tails of portfolio returns. When we move toward the center of the joint distribution, this advantage is reduced. In addition, no uniformly best model is available when we consider different portfolio weights. This provides complementary results for other joint distribution modeling comparisons conducted in recent works and calls for more specific comparison criterion.

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Efficient Portfolio Analysis Using Distortion Risk Measures
with Christian Gourieroux, (job market paper, preliminary version)
Last updated on: Nov. 10, 2006

Abstract: We introduce nonparametric estimators of the sensitivity of distortion risk measure with respect to portfolio allocation. These estimators are used to derive the estimated efficient portfolio allocations when distortion risk measures are used to define the constraints and the objectives, to study their asymptotic distributional properties, and to construct tests for the hypothesis of portfolio efficiency.

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Sensitivity Analysis of Distortion Risk Measures
with Christian Gourieroux, (also job market paper, submitted to Insurance: Mathematics and Economics)
Last updated on: Nov. 1, 2006

Abstract: This paper provides a unified statistical framework for the analysis of distortion risk measures (DRM) and of their sensitivities with respect to parameters representing risk aversion and/or pessimism. We derive the general formula for calculating the asymptotic distribution of the nonparametric estimator of the functional distortion risk measures. Closed form expressions are provided for special examples such as VaR, Tail-VaR and Proportional Hazard distortion risk measure. Moreover, we analyze the link between Value-at-Risk and Tail-VaR and characterize the underlying distributions under which the two risk measures are linearly related through their risk levels. We apply the results to currency portfolios and observe that this linearity relationship between Value-at-Risk and Tail-VaR is a surprisingly common phenomenon for the portfolios considered.

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