INNOVATIONS
My
published research focuses on applying cutting edge
mathematical techniques to investment processes
(a.k.a.
Quantitative MetaStrategies),
with the purpose of providing practical
solutions to critical problems faced by financial
firms and investment managers, whether systematic or
discretionary. Some innovations I have contributed
(with my coauthors) to
the investment literature include the following.
DIAGRAM  INNOVATION  FIELD  APPLICATIONS 
The Sharpe ratio Efficient Frontier (SEF)  Portfolio Optimization  Riskadjusted capital allocation, taking into account higher moments.  
Quantum Portfolio Optimization Algorithm  Portfolio Optimization  Generalized dynamic portfolio optimization problems are intractable to modern supercomputers (NPComplete). We show how they can be reformulated as an integer optimization problem, so that quantum computers can solve them. [Link to a Bloomberg article] [Related release by Google & NASA]  
Opensource implementation of CLA  Portfolio Optimization  The first opensource Python class to implement the Critical Line Algorithm (CLA) for quadratic optimization subject to inequality constraints.  
Hierarchical Risk Parity (HRP)  Portfolio Optimization, Machine Learning  HRP portfolios address three major concerns of quadratic optimizers in general and Markowitz’s CLA in particular: Instability, concentration and opacity. Most notably, Monte Carlo experiments show that HRP portfolios deliver lower variance than CLA's outofsample, even though minimumvariance is CLA's objective function.  
NestedClustered Optimization (NCO)  Portfolio Optimization, Machine Learning  The NCO algorithm learns how to split the convex optimization problem into subproblems that can be solved robustly. The algorithm is agnostic with regards to the underlying procedure used: Markowitz, BlackLitterman, constrained optimization, etc.  
TheoryImplied Correlation Matrices (TIC)  Portfolio Optimization, Machine Learning  The TIC algorithm enables the computation of correlation matrices implied by knowledge graphs.  
TripleBarrier Labeling Method  Machine Learning  A supervised learning labeling method that is congruent with a predefined trading strategy (profittaking, stoploss, investment horizon).  
Metalabeling & Bet Sizing  Machine Learning  Metalabeling is a supervised learning labeling method that allows a secondary algorithm to predict whether a primary algorithm's bets will be successful. These predictions are useful in sizing the bets made by the primary algorithm. The combined effect is an overall improvement in F1scores, by optimally trading off some recall in exchange of higher precision.  
Uniqueness Weighting & Sequential Bootstrap  Machine Learning  A bootstrap method that controls for sample dependence, hence reducing the level of redundancy in the training set.  
KFold CV with Purging & Embargo  Machine Learning  CV method that prevents informational leakage from the testing set into the training set, due to labels overlap and serial conditionality.  
The "False Strategy" theorem 
Strategy Selection, MetaResearch 
The analytical solution to the problem of estimating the expected maximum Sharpe ratio out of N investment strategies.  
Optimal Significance Level (OSL) 
Strategy Selection, Machine Learning, MetaResearch 
OSL provides analytic estimates to Type I and Type II errors in the context of investments, and derives the familywise significance level that optimizes the performance of hypothesis tests under general assumptions.  
Combinatorial Purged CrossValidation (CPCV) 
Strategy Selection, MetaResearch, Machine Learning 
CPCV generates the precise number of combinations of training/testing sets needed to generate the desired number of PnL scenarios, while purging training observations that contain leaked information.  
Probability of Backtest Overfitting (PBO) 
Strategy Selection, MetaResearch 
Estimation of the probability that a strategy's historical simulation has been overfit, and hence it is not representative of future performance.  
Minimum Backtest Length (MinBTL)  Strategy Selection  If a researcher tries a large enough number of strategy configurations, a backtest can always be fit to any desired performance for a fixed sample length. We find that there is a minimum backtest length (MinBTL) that should be required for a given number of trials.  
The Strategy Approval Theorem (or Sharpe ratio Indifference Curve)  Strategy Selection  Determination of the space of pairs (candidate strategy’s Sharpe ratio, candidate strategy’s correlation to the approved set) for which the Sharpe ratio of the expanded approved set remains constant.  
The "Triple Penance" rule  Strategy Selection  The "Triple Penance" rule states that, under standard portfolio theory assumptions, it takes three times longer to recover from the expected maximum drawdown than the time it takes to produce it, with the same confidence level.  
Drawdownbased StopOuts under firstorder seriallycorrelated outcomes  Strategy Selection  A closedformula expression for drawdowns, in the more general case of firstorder seriallycorrelated outcomes.  
Probabilistic Sharpe Ratio (PSR)  Strategy Selection  Probability that the actual Sharpe ratio exceeds a given threshold, subject to the uncertainty added by higher moments.  
Deflated Sharpe Ratio (DSR) 
Strategy Selection, MetaResearch 
When multiple trials take place, it is necessary to correct the Sharpe Ratio for selection bias under multiple testing (backtest overfitting). DSR adapts PSR to a multipletesting strategy selection setting, effectively controlling for the probability of a false discovery.  
Minimum Track Record Length (MinTRL)  Strategy Selection  For a userdefined confidence level, it computes the minimum track record length required to assess whether a Sharpe ratio estimate exceeds a certain threshold.  
Probability of Divergence (PoD)  Strategy Selection  Probability that a portfolio manager is departing from her prior track record.  
Tactical Algorithmic Factories (TAF)  Strategy Selection  It is unreasonable to expect that all investment strategies will perform equally well under all market regimes. This motivates the problem of identifying investment algorithms that are optimal for specific market regimes.  
Order Imbalance Bars (OIB)  Market Microstructure  A microstructural sampling method that synchronizes observations with the rate of arrival of informed traders.  
VolumeSynchronized Probability of Informed Trading (VPIN)  Market Microstructure  The VPIN theory provides a formal link between the probability of informed trading (PIN) and the persistency of order flow imbalances under a volume clock. This theory can be used to monitor order flow toxicity, design dynamic circuitbreakers and prevent liquidity crises like the 'flash crash'. Read a summary here.  
Bulk Volume Classification of Trading Activity (BVC)  Market Microstructure  Tickbased trade classification algorithms estimate order flow imbalance by considering the side that initiated the trade. This fails to incorporate information from passive buyers or sellers, which use resting orders, cancellations or mechanisms to hide liquidity. BVC overcomes these limitations by taking into account all sources of buying and selling pressure in evaluating order flow imbalance. In doing so, BVC contributes to achieve better forecasts of bidask spreads, highlow ranges and toxicityinduced volatility.  
The Market Maker Asymmetric Payoff Dilemma  Market Microstructure  Characterization of a liquidity provider as the seller of a realoption to be adversely selected.  
Optimal Execution Horizon (OEH)  Execution, Trading  Volume required to provide the maximum concealment of trading intentions. This execution algorithm exploits the trader's private information regarding his own trading intentions to beat constant participation rate strategies, such as TWAP or VWAP.  
Optimal Trading Strategies (OTRs)  Execution, Trading, Operations Research 
We present empirical evidence of the existence of optimal trading rules (OTRs) for the case of prices following a discrete OrnsteinUhlenbeck process, and show how they can be computed numerically. Although we do not derive a closedform solution for the calculation of OTRs, we conjecture its existence on the basis of the empirical evidence presented. 

Advanced Hedging methods (DFO, BTCD)  Portfolio Management, Trading  New hedging methods, with applications in portfolio replication, market making, portfolio construction, etc.  
Balanced Baskets (MMSC)  Portfolio Management, Trading  A new approach for the trading and hedging of risks, without requiring a change of basis. This includes MMSC, an analogue to "risk parity" in the correlation space.  
Optimal Risk Budgeting under a Finite Investment Horizon  Portfolio Management, Trading  Path of bet sizes that maximize wealth under a finite investment horizon. This risk budgeting framework is dynamic and multihorizon, providing a global optimum that beats myopic approaches such as Markowitz's meanvariance, risk parity, etc.  
Drawdown and TimeUnderWater modeling (DD, TuW)  Risk Management  Projection of the Drawdown and TimeunderWater distributions, without assuming Normality or serial independence.  
New Algorithm for the Estimation of Mixtures of Gaussians (EF3M)  Operations Research  Distribution of the parameters of a Mixture of 2 Gaussians, consistent with 4 or 5 moments. This is the solution to the "Nonic Polynomial problem" posed by Karl Pearson in the 1894 edition of the Philosophical Transactions of the Royal Society.  
Covariance Clustering Algorithm  Spectral Theory  Algorithm for reducing the dimension of a covariance matrix, without requiring a change of basis. Clusters of variables are form in such a way that, at each reduction step, the matrix's condition number is minimized.  
Stochastic Flow Diagrams (SFD)  Graph Theory, Topology  Inspired by visualization techniques à la Feynman, we introduced a new mathematical approach to represent complex systems of time series models into a single weighted digraph. SFDs add Topology to the Statistical and Econometric toolkit used by Macroeconomists.  
Kinetic Component Analysis (KCA)  Control Theory, Dynamic Systems  We introduce a statespace application that extracts the signal from a series of noisy measurements by applying a Kalman Filter on a Taylor expansion of a stochastic process. KCA presents several advantages compared to other popular noisereduction methods such as Fast Fourier Transform (FFT) or Locally Weighted Scatterplot Smoothing (LOWESS).  
Heterogeneous SEIR Response on KGroups (KSEIR)  Control Theory, Epidemiology  The celebrated epidemiology SEIR model of Kemrack and McKenrick (1927) assumes the population responds homogeneously to an outbreak. We extend the SEIR model to consider Kgroups with heterogenous response. 