Olivier Ledoit Homepage

I operate at 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 on large-dimensional covariance matrices.

Education: BSc in engineering from Ecole Polytechnique in France, officer in the French Marine Corps (24th Regiment in Perpignan), 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, my official University of Zurich webpage is there, and I also have a Google Scholar page.


Over 25 years, I have published 27 papers, totaling over 600 pages (not including online supplements and official computer code), which would be the size of a very thick book. These 27 papers together have gathered more than 9,500 citations. My research can be divided between large-dimensional covariance matrices (20 papers), and additional interests (7 papers). 

Large-dimensional covariance matrices

Along with the mean vector, the covariance matrix is one of the two most important objects in multivariate statistics. Its standard estimator, the sample covariance matrix, breaks down when the dimension of the matrix is too 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.

In order to fulfill this vision, we had to walk an arduous path that required a lot of intellectual effort and cumulative creativity over decades. Our long journey is documented by a series of 20 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 + Matlab code
  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 + Online Supplement
  12. Olivier Ledoit and Michael Wolf (2018) "Optimal estimation of a large-dimensional covariance matrix under Stein's loss" Bernoulli 24(4B):3791-3832 + Online supplement (Mathematical proofs
  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) "Analytical nonlinear shrinkage of large-dimensional covariance matrices" Annals of Statistics 48(5):3043-3065
  16. 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
  17. Olivier Ledoit and Michael Wolf (2021) "Shrinkage estimation of large covariance matrices: Keep it simple, statistician?" Journal of Multivariate Analysis 186:104796
  18. Olivier Ledoit and Michael Wolf (Accepted 2020) "The power of (non-)linear shrinking: A review and guide to covariance matrix estimation" Journal of Financial Econometrics nbaa007
  19. Zhao Zhao, Olivier Ledoit and Hui Jiang (Accepted 2021) "Risk reduction and efficiency increase in large portfolios: Gross-exposure constraints and shrinkage of the covariance Matrix" Journal of Financial Econometrics nbab001
  20. Olivier Ledoit and Michael Wolf (Accepted 2021) "Quadratic Shrinkage for Large Covariance Matrices" Bernoulli Forthcoming
Within this long list of articles, we can highlight the review paper (#18) 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, our 2012 Annals paper (#7) as a mathematical powerhouse, and our latest Bernoulli paper (#20) 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, as well as Zhidong Bai and Jack Silverstein, who laid solid technical foundations on which we could erect our edifice.

Now anybody who needs a covariance matrix can estimate it accurately, even when dimension is large relative to sample size.

Additional Interests

My other interests around the broader field of financial economics led me to co-author seven more publications beyond the covariance matrix:
  1. Timothy Falcon Crack and Olivier Ledoit (1996) "Robust structure without predictability: the 'compass rose' pattern of the stock market" Journal of Finance 51(2):751-762
  2. Anders Johansen, Didier Sornette and Olivier Ledoit (1999) "Predicting financial crashes using discrete scale invariance" Journal of Risk 1(4):5-32
  3. Antonio E. Bernardo and Olivier Ledoit (2000) "Gain, loss, and asset pricing" Journal of Political Economy 108(1):144-172
  4. Anders Johansen, Olivier Ledoit and Didier Sornette (2000) "Crashes as critical points" International Journal of Theoretical and Applied Finance 3(2):219-255
  5. Olivier Ledoit and Michael Wolf (2008) "Robust performance hypothesis testing with the Sharpe ratio" Journal of Empirical Finance 15(5):850-859 + R code and Matlab code
  6. Timothy Falcon Crack and Olivier Ledoit (2010) "Central limit theorems when data are dependent: Addressing the pedagogical gaps" Journal of Financial Education 36(1/2):38-60
  7. Olivier Ledoit and Michael Wolf  (2011) "Robust performances hypothesis testing with the variance" Wilmott 2011(55):86-89 + R code and Matlab code
The 'compass rose' paper (listed as #21) was accepted by the Journal of Finance, the most prestigious journal in finance, even before my co-author Tim Crack and I had graduated from MIT. Article #24 is an econophysics paper prominently featured in Chapter 7 of the book The Physics of Wall Street: A Brief History of Predicting the Unpredictable. The gain-loss paper (#23) was published in the same academic journal as the famous Black-Scholes option pricing formula [the JPE, established in 1892 at the University of Chicago]; my co-author on this one, Tony Bernardo, ran his whole career at the UCLA Anderson School of Management and rose to be its Dean.