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.
Research
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:
- 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
- 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
- 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
- Olivier Ledoit and Michael Wolf (2004) "Honey, I shrunk
the sample covariance matrix" Journal
of Portfolio Management 30(4):110-119
- Olivier Ledoit and Michael Wolf (2004) "A
well-conditioned estimator for large-dimensional covariance
matrices" Journal
of Multivariate Analysis 88(2):365-411
- Olivier Ledoit and Sandrine
Peche (2011) "Eigenvectors of
some large sample covariance matrix ensembles" Probability
Theory and Related Fields 151:233-264
- Olivier Ledoit and Michael Wolf (2012) "Nonlinear
shrinkage estimation of large-dimensional covariance matrices"
Annals of Statistics 40(2):1024-1060
- 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
- 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
- Olivier Ledoit and Michael Wolf (2017) "Numerical
implementation of the QuEST function" Computational
Statistics & Data Analysis 115:199-223
+ Matlab code
- 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
- 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)
- 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
- 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
- Olivier Ledoit and Michael Wolf (2020) "Analytical
nonlinear shrinkage of large-dimensional covariance matrices"
Annals of Statistics 48(5):3043-3065
- 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
- Olivier Ledoit and Michael Wolf (2021) "Shrinkage
estimation of large covariance matrices: Keep it simple,
statistician?" Journal of Multivariate Analysis
186:104796
- 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
- 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
- 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:
- 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
- Anders Johansen, Didier
Sornette
and Olivier Ledoit (1999) "Predicting
financial crashes using discrete scale invariance" Journal
of Risk 1(4):5-32
- Antonio E.
Bernardo and Olivier Ledoit (2000) "Gain, loss, and
asset pricing" Journal of Political Economy 108(1):144-172
- Anders Johansen, Olivier Ledoit and Didier Sornette (2000) "Crashes
as critical points" International
Journal of Theoretical and Applied Finance 3(2):219-255
- 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
- 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
- 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.