Research

Here is a list of papers that have been accepted by peer-reviewed academic journals. One of my specialties is the estimation of large dimensional covariance matrices. At the bottom of the abstract you will be able to download the Acrobat PDF version of the full paper, which can be viewed by using the free Acrobat Reader from the Adobe website. 


Publications

  1. "Nonlinear shrinkage estimation of large-dimensional covariance matrices", co-authored with Michael Wolf, Annals of Statistics, Volume 40, Number 2, April 2012, pages 1024-1060. This marks the beginning of a new era in our research on large-dimensional covariance matrix estimation. We are now able to shrink each sample eigenvalue individually, instead of applying the same shrinkage intensity towards the cross-sectional mean as in linear shrinkage. Given that the problem of eigenvalues shrinkage is intrinsically nonlinear, this constitutes a substantive improvement and should be considered state-of-the-art. Abstract and paper.

  2. "Robust Structure Without Predictability: The 'Compass Rose' Pattern of the Stock Market", co-authored with Timothy Falcon Crack, Journal of Finance, Volume 51, Number 2, June 1996, pages 751-762. This paper unearths a striking pattern that was overlooked in a figure chosen to illustrate... the absence of patterns in stock returns, in the classic MBA textbook Principles of Corporate Finance by Brealey and Myers. The 6th edition has been modified with our pattern (see Figure 13.2). Abstract and paper.

  3. "Some Hypothesis Tests for the Covariance Matrix When the Dimension Is Large Compared to the Sample Size", co-authored with Michael Wolf, Annals of Statistics, Volume 30, Number 4, August 2002, pages 1081-1102. This is a pure statistics paper that examines the robustness of standard tests of the covariance matrix in large dimensions. The standard test for sphericity is shown to be robust, and we show how the standard test statistic for equality must be modified in order to be made robust. Abstract and paper.

  4. "Gain, Loss and Asset Pricing", co-authored with Antonio Bernardo, Journal of Political Economy, Volume 108, Number 1, February 2001, pages 144-172. We develop a measure of attractiveness for risky investments, called the gain-loss ratio. It constitutes an improvement over the widely used Sharpe ratio. The problem with the Sharpe ratio is that it penalizes upside risk, which is irrational because everyone likes investments with higher chance of upside. The advantage of the gain-loss ratio is that it penalizes only downside risk (losses) and rewards all upside potential (gains). In addition, the gain-loss ratio integrates itself perfectly well within the framework of Arrow-Debreu state prices, which forms the cornerstone of modern microeconomic theory. Abstract and paper.

  5. "Eigenvectors of some large sample covariance matrix ensembles", co-authored with Sandrine Péché,Probability Theory and Related Fields, Volume 151, no. 1-2, pages 233-264. This is a paper in pure Probability Theory that lays the foundation for subsequent statistical work. In particular, it nails down the (average) location of the eigenvectors of the sample covariance matrix under large-dimensional asymptotics, i.e., when the number of observations and the number of variables go to infinity together. The main theoretical contribution of the paper is a generalization of the well-known Marchenko-Pastur equation. We also pave the way for a new generation of improved estimators of the covariance matrix and its inverse. Abstract and paper

  6. "A Well-Conditioned Estimator for Large-Dimensional Covariance Matrices", co-authored with Michael Wolf, Journal of Multivariate Analysis, Volume 88, Issue 2, February 2004, pages 365-411. This paper introduces an estimator of the covariance matrix that is more accurate than the sample covariance matrix. Furthermore, it is guaranteed to be invertible even when dimension exceeds sample size. Abstract, paper and programming code.

  7. "Improved Estimation of the Covariance Matrix of Stock Returns With an Application to Portfolio Selection", co-authored with Michael Wolf, Journal of Empirical Finance, Volume 10, Issue 5, December 2003, pages 603-621. This paper shows how to shrink optimally the sample covariance matrix towards any structured target. The structure chosen here is a one-factor market model covariance matrix. The resulting estimator constitutes an attractive alternative to multi-factor models for the covariance matrix of stock returns. Abstract, paper and programming code.

  8. "Using Central Limit Theorems for Dependent Data", co-authored with Timothy Falcon Crack, Journal of Financial Education, Volume 36, nos. 1/2 (Spring/Summer 2010). This is a Financial Education paper that teaches Doctoral Students how to apply Central Limit Theorems when data are dependent - a pervasive case in Finance. We provide a step-by-step derivation of the asymptotic distribution of the sample variance of a Gaussian AR(1) process. Abstract and paper

  9. "Robust performance hypothesis testing with the Sharpe ratio", co-authored with Michael Wolf, Journal of Empirical Finance, Volume 15, Issue 5, December 2008, pages 850-859. This paper shows how to test the hypothesis that a portfolio, fund or trading strategy has higher Sharpe ratio than another, when returns have fat tails and/or are serially dependent. Abstract, paper and programming code.

  10. "Flexible Multivariate GARCH Modeling With an Application to International Stock Markets", co-authored with Pedro Santa-Clara and Michael Wolf, Review of Economics and Statistics, Volume 85, Issue 3, August 2003, pages 735-747. This paper gives a flexible method to estimate time-varying volatilities and correlations. It is important because volatilities and correlations are known to vary rapidly through time, especially during crises, when it is the most critical to have an accurate and up-to-date covariance matrix for risk management and risk measurement purposes. This is the first paper to propose a computationally feasible estimation method for the (diagonal) Multivariate GARCH(1,1) model without imposing arbitrary restrictions. The resulting covariance matrix is guaranteed to be positive definite, which is necessary for portfolio optimization. Abstract, paper and programming code

  11. "Honey, I Shrunk the Sample Covariance Matrix", co-authored with Michael Wolf, Journal of Portfolio Management, Volume 31, Number 1, Fall 2004. This is a paper for practitioners showing how to shrink optimally the sample covariance matrix towards the constant-correlation covariance matrix. The resulting estimator improves the out-of-sample performance of portfolio managers. Abstract, paper and programming code.

  12. "Crashes as Critical Points", co-authored with Anders Johansen and Didier Sornette, International Journal of Theoretical and Applied Finance, Volume 3, Number 2, April 2000, pages 219-255. Abstract and paper.

  13. "Predicting Financial Crashes using Discrete Scale Invariance", co-authored with Anders Johansen and Didier Sornette, Journal of Risk, Volume 1, Number 4, Summer 1999, pages 5-32.  In this article and the one above, we present a theoretical model of financial markets with traders imitating one another. This model implies that a speculative bubble will display an oscillating pattern whose frequency accelerates, building up to a crash. An analysis of major crashes including the crashes of 1929 and 1987 confirms our hypothesis by showing the presence of accelerating oscillations before the date of the crash. Abstract and paper.

  14. "Robust performance hypothesis testing with the variance", co-authored with Michael Wolf, Wilmott Magazine, Issue 55, September 2011, pages 86-89. This paper shows how to test the hypothesis that a portfolio, fund or trading strategy has lower volatility than another, when returns have fat tails and/or are serially dependent. Abstract, paper and programming code.


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