Olivier Ledoit Homepage

I straddle the frontier between academic finance and quantitative trading. On the academic side, I taught option pricing, empirical finance, and statistical arbitrage at UCLA Anderson School of Management, and quantitative asset management at HEC (Hautes Etudes Commerciales) in France. On the trading side, I went from Vice-President to Director to Managing Director at Credit Suisse in London. I am best-known for my work with large-dimensional covariance matrices.

Education: BSc in engineering from Ecole Polytechnique in France, MSc in economics and statistics from ENSAE (Ecole Nationale de la Statistique et de l'Administration Economique), and PhD in finance from MIT Sloan School of Management. Currently involved with the Department of Economics at the University of Zurich (Switzerland), and with US quantitative hedge fund AlphaCrest Capital Management. A short CV is here, and my official University of Zurich webpage is there.


Over 25 years, I published 26 papers, totaling 658 pages (not including online supplements and official computer code), which would be the size of a very thick book. These 26 papers together gathered more than 9,500 citations. My research can be divided between large-dimensional covariance matrices (19 papers), and collateral interests (7 papers). 

Large-dimensional covariance matrices

The covariance matrix is one of the two most important object in multivariate statistics. Its standard estimator, the sample covariance matrix, breaks down when the dimension of the matrix is large. My long-term co-author Michael Wolf and I had a vision that that the problem could be fixed by using an equation from quantum physics invented in 1955 by Eugene Wigner (Nobel Prize 1963), and extended by Vladimir Marchenko and Leonid Pastur in 1967. Between our vision and successful delivery lied an arduous path that required a lot of intellectual effort and cumulative creativity over decades. This long journey is documented by a series of 19 publications in peer-reviewed academic journals over a time span of 19 years, listed below in chronological order:

  1. Olivier Ledoit and Michael Wolf (2002) "Some hypothesis tests for the covariance matrix when the dimension is large compared to the sample size"Annals of Statistics 30(4):1081-1102 
  2. Olivier Ledoit, Pedro Santa-Clara and Michael Wolf (2003) "Flexible multivariate GARCH modeling with an application to international stock markets" Review of Economics and Statistics 85(3):735-747
  3. Olivier Ledoit and Michael Wolf (2003) "Improved estimation of the covariance matrix of stock returns with an application to portfolio selection" Journal of Empirical Finance 10(5):603-621
  4. Olivier Ledoit and Michael Wolf (2004) "Honey, I shrunk the sample covariance matrix" Journal of Portfolio Management 30(4):110-119
  5. Olivier Ledoit and Michael Wolf (2004) "A well-conditioned estimator for large-dimensional covariance matrices" Journal of Multivariate Analysis 88(2):365-411
  6. Olivier Ledoit and Sandrine Peche (2011) "Eigenvectors of some large sample covariance matrix ensembles" Probability Theory and Related Fields 151:233-264
  7. Olivier Ledoit and Michael Wolf (2012) "Nonlinear shrinkage estimation of large-dimensional covariance matrices" Annals of Statistics 40(2):1024-1060
  8. David R. Bell, Olivier Ledoit and Michael Wolf (2014) "A new portfolio formation approach to mispricing of marketing performance indicators: An application to customer satisfaction" Customer Needs and Solutions 1(4):263-276
  9. Olivier Ledoit and Michael Wolf (2015) "Spectrum estimation: A unified framework for covariance matrix estimation and PCA in large dimensions" Journal of Multivariate Analysis 139:360-384
  10. Olivier Ledoit and Michael Wolf (2017) "Numerical implementation of the QuEST function" Computational Statistics & Data Analysis 115:199-223
  11. Olivier Ledoit and Michael Wolf (2018) "Nonlinear shrinkage of the covariance matrix for portfolio selection: Markowitz meets Goldilocks" Review of Financial Studies 30(12):4349-4388
  12. Olivier Ledoit and Michael Wolf (2018) "Optimal estimation of a large-dimensional covariance matrix under Stein's loss" Bernoulli 24(4B):3791-3832
  13. Robert F. Engle [Nobel Prize 2003], Olivier Ledoit and Michael Wolf (2019) "Large dynamic covariance matrices" Journal of Business & Economic Statistics 37(2):363-375
  14. Olivier Ledoit, Michael Wolf and Zhao Zhao (2019) "Efficient sorting: A more powerful test for cross-sectional anomalies" Journal of Financial Econometrics 17(4):645-686
  15. Olivier Ledoit and Michael Wolf (2020) "The power of (non-)linear shrinking: A review and guide to covariance matrix estimation" Journal of Financial Econometrics nbaa007
  16. Olivier Ledoit and Michael Wolf (2020) "Analytical nonlinear shrinkage of large-dimensional covariance matrices" Annals of Statistics 48(5):3043-3065
  17. Gianluca De Nard, Olivier Ledoit and Michael Wolf (2021) "Factor models for portfolio selection in large dimensions: The good, the better and the ugly" Journal of Financial Econometrics 19(2):236-257
  18. Zhao Zhao, Olivier Ledoit and Hui Jiang (2021) "Risk reduction and efficiency increase in large portfolios: Gross-exposure constraints and shrinkage of the covariance Matrix" Journal of Financial Econometrics nbab001
  19. Olivier Ledoit and Michael Wolf (2021) "Shrinkage estimation of large covariance matrices: Keep it simple, statistician?" Journal of Multivariate Analysis 186:104796
Within this long list of articles, we can single out the review paper (#15) as being the best introduction to our lifetime research contributions, the linear shrinkage paper (#5) as the simplest and most impactful across at least ten different scientific fields, and our latest Annals paper (#16) as the most perfected realization of our initial vision, which circles back to the ground-breaking work on shrinkage by the late Charles Stein. Other giants on whose shoulders we stand include Harry Markowitz (Nobel Prize 1990), who put the covariance matrix front-and-center in financial economics, and Zhidong Bai and Jack Silverstein, who provided the technical foundations on which we built our edifice.

Now anybody who needs a covariance matrix can estimate it accurately, even if dimension is large.