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PortfolioOptimisers.jl
  • Portfolio optimisation library in Julia
  • Capability Catalogue
  • User Guide
    • Introduction to the user guide
    • Data and priors
    • Optimisers
    • Risk measures
    • Constraints and costs
    • Validation and tuning
    • Post-processing
    • Choosing a strategy
    • The point-in-time universe
    • The online walk-forward
    • Online portfolio selection
  • Examples
    • Examples introduction
      • Getting started: a simple MeanRisk optimisation
      • Data preprocessing and the ingestion layer
      • Asset pre-selection
      • Expected returns estimation
      • Covariance estimation
      • Higher moment estimation
      • Factor priors
      • Black-Litterman
      • Advanced Black-Litterman variants
      • Entropy pooling
      • Opinion pooling
      • Uncertainty sets
      • Windowed moment estimators
      • ℓ1 uncertainty sets: the quintile and 1/N portfolios
      • MeanRisk objectives
      • Efficient frontier
      • Pareto surface
      • Multiple risk measures
      • OWA risk measures
      • BrownianDistanceVariance and VarianceSkewKurtosis
      • Drawdown risk measures
      • Tail risk measures that weight the worst losses more than CVaR
      • Risk budgeting
      • Risk contribution
      • Clustering optimisers
      • Clustering optimisers with mixed risks and constraints
      • Meta-optimisers
      • Subset resampling and cross-validation
      • Near optimal centering
      • Feature matrices as a distance source
      • Clustering on a fundamentals panel
      • Online portfolio selection
      • Budget constraints
      • Linear and group constraints
      • Cardinality and threshold
      • Phylogeny and centrality constraints
      • Turnover and tracking
      • Fees and net returns
      • Regularisation
      • Nested clustered optimisation with layered constraints and fees
      • Custom objectives and constraints
      • Factor exposure constraints
      • Cross validation
      • Hyperparameter tuning
      • Pipelines
      • Time-dependent constraints
      • Train/test splitting
      • Time-dependent optimisers
      • Calibrated risk measures: a rule in place of a number
      • Weight drift and held weights: reading a backtest as a fund holds it
      • The online walk-forward: one estimator, updated fold by fold
      • Finite allocation
      • Plotting and reporting
      • Performance attribution and post-optimisation diagnostics
      • Profile: retail, daily
      • Profile: desk, monthly
      • Profile: institutional
      • Profile: factor-views desk
      • Cross-sectional factor model, end to end
      • Cross-sectional factor model through a Pipeline
      • Reading a return forecast before an optimiser sees it
      • Observed factors, from raw prices to a cross-validated portfolio
  • API introduction
  • Type hierarchy
  • Public API
        • Tables
        • Arg data and moments
        • Arg priors and uncertainty sets
        • Arg phylogeny and constraints
        • Arg risk measures and costs
        • Arg optimisation
        • Field dict
        • Validations and returns
        • Math data and moments
        • Math priors and networks
        • Math risk and optimisation
        • Math online selection
        • References
      • Type roots
      • Pretty show
      • Scoped config
      • Preferences
      • Messages
      • Errors
      • Type aliases
      • Observation weights
      • Assertions
      • Vec scalar
      • Norm error
      • Kappa log
      • Partial fit
      • Online (a)
      • Online (b)
      • Coverage Policy
      • Returns Source
      • Operators
      • Array views
      • Type utilities
      • Factory
      • Propagatable
      • Forward properties
      • Vector to scalar measures
      • Mean test
      • Mean test draws
      • Asset Panel
      • Asset Panel builder
      • Listing Span
      • Preprocessing
      • Panel views
      • Prices result
      • Price ingestion
      • Price gap fill
      • Price filters
      • Returns result
      • Prices to returns
      • Train/test split
      • Base asset selection
      • Cross-sectional transforms
      • Feature selector
      • Panel data frame
      • Returns buffer state
      • Preprocessing partial fit
      • Asset panel concat
      • Panel field values
      • Asset panel summary
      • Panel round trip
      • Posdef matrix
      • Denoise
      • Detone
      • Matrix processing
      • Matrix square root
      • Base moments
      • Simple expected returns
      • Covariance
      • Simple variance
        • Gerber covariance
        • Smyth-Broby Covariance
        • Gerber IQ covariance (a)
        • Gerber IQ covariance (b)
      • Distance Covariance
      • Lower Tail Dependence Covariance
      • Rank covariance
      • Histogram
      • Mutual info covariance
      • Denoise covariance
      • Detone covariance
      • Processed covariance
      • PortfolioOptimisersCovariance
      • Shrunk Expected Returns
      • Equilibrium expected returns
      • Excess expected returns
      • Coskewness
      • Cokurtosis
      • Base regression
        • Stepwise Regression
        • Dimension reduction regression
      • Implied Volatility
      • Correlation covariance
      • Abstract covariance variance
      • Standard deviation expected returns
        • Windowed expected returns
        • Windowed covariance
        • Windowed variance
        • Windowed Coskewness
        • Windowed Cokurtosis
        • Windowed preamble
      • Median expected returns
      • Custom value expected returns
        • Exp weighted expected returns
        • Exp weighted variance
        • Exp weighted covariance
        • Exp weighted centring
        • Regime adjusted exp weighted variance
        • Regime adjusted exp weighted covariance (a)
        • Regime adjusted exp weighted covariance (b)
        • Mahalanobis regime bias
        • HAC row kernel
        • Regime switches
        • Estimated regime bias
        • Estimated Mahalanobis bias
        • Mahalanobis level closure
      • Higher-Moment Partial Fit
        • Cross-Sectional Regression
        • Cross-Sectional Weights
        • Cross-Sectional Factor Model
          • Base descriptor
          • Panel Field Descriptors
          • Lag Descriptors
          • EW mean descriptors
          • EW volatility descriptors
          • EW beta descriptors (a)
          • EW beta descriptors (b)
          • Rolling Descriptors
          • Base exposure
          • Composite Exposure
          • Derived Exposure
          • One-Hot Exposure
          • Constant Exposure
          • Exposure Neutralisation
          • Observed Exposure
        • Factor Family Basis
        • Factor Family Basis Transforms
          • Base Return Forecast
          • Descriptor Scores
          • Custom Value Return Forecast
          • Fixed Weighted Return Forecast
          • Exp weighted Return Forecast
          • Target Return Forecast
          • Forecast Evaluation
          • Forecast History
          • Forecast Information Coefficient
          • Forecast Portfolios
          • Forecast Factor Correlation
          • Forecast Forward Windows
          • Forecast Calibration
          • Forecast Summary
          • Target Return Forecast Step
        • Cross-Sectional Regression Diagnostics
        • Cross-Sectional Exposure Diagnostics
        • Factor Model Summary
        • Cross-Sectional Idiosyncratic Diagnostics
        • Cross-Sectional Exposure IC
      • Coverage Universe
      • Price-level expected returns
      • Composite price-level statistics
      • Rank-one covariance
      • Geodesic shrinkage covariance
      • Base Distance
      • Distance
      • Distance distance
      • Similarity
      • Feature Distance
      • Feature distance active rows
    • JuMP model optimisation
      • Base Phylogeny
      • Clusters
      • Hierarchical
      • Non hierarchical clustering
      • Phylogeny
        • DBHT
        • PMFG
        • Graph Traversal
        • Clique Hierarchy
        • Bubble Tree
        • DBHT Dendrogram
        • DBHT Clustering
      • LoGo
        • Minimum Spanning Tree
        • Network Estimator
        • Network Graph
        • Separation
        • Centrality
        • Centrality Polarity
        • Centrality Estimator
        • Centrality Queries
      • Phylogeny Clustering
      • Phylogeny Matrix
      • Asset Phylogeny
      • Base Constraint Generation
      • Linear constraint generation (a)
      • Linear constraint generation (b)
      • Risk budget constraint generation
      • Phylogeny constraint generation
      • Weight bounds constraint generation
      • Asset sets matrix
      • Threshold constraint generation
      • Exposure constraint generation
      • Cross-Sectional Factor Axis
      • Base Prior
      • Empirical Prior
      • Factor Prior
      • High Order Prior
        • Black-Litterman Views Generation
        • Black-Litterman Prior
        • Bayesian Black-Litterman Prior
        • Factor Black-Litterman Prior
        • Augmented Black-Litterman Prior
          • Entropy pooling algorithms
          • Entropy pooling mean views
          • Entropy pooling view types
          • Entropy pooling solvers
          • Entropy pooling moment views
          • Entropy pooling tail view solve
        • Meucci entropy pooling Prior
        • Entropy pooling Prior (a)
        • Entropy pooling Prior (b)
        • Entropy pooling Prior (c)
      • Opinion pooling Prior
      • High order factor Prior estimator
      • Asset Panel Estimators
      • Base cross-sectional factor Prior
      • Cross-Sectional Factor Prior
      • Prior partial fit
      • Prior expected returns
      • Low-dimension ensemble prior
      • Cross-Sectional Prior Fold
      • Cross-Sectional Forecast History Carry
      • Cross-Sectional Calibration Rules
      • Cross-Sectional Carry Histories
      • Prior Scenarios
      • Prior Returns Source
      • Base Uncertainty Sets
      • Delta Uncertainty Sets
      • Normal Uncertainty Sets
      • Bootstrap Uncertainty Sets
      • L1 uncertainty sets
      • Calibration Rules
      • Compact Uncertainty Sets
      • Norm-Ball Uncertainty Sets
      • Orthogonal Uncertainty Sets
      • Compact Radius Rules
    • Turnover
    • Fees
    • Net returns drawdowns
    • Tracking
      • Base Risk Measures
      • Variance
      • Moment Risk Measures
      • Kurtosis
      • Negative Skewness
        • X at Risk
        • Conditional X at Risk
        • Entropic X at Risk
        • Relativistic X at Risk
        • Power Norm X at Risk
      • OWA risk measures (a)
      • OWA risk measures (b)
      • Average Drawdown
      • Ulcer Index
      • Maximum Drawdown
      • Brownian Distance Variance
      • Worst Realisation
      • No Risk
      • Range
      • Turnover risk measure
      • Tracking risk measure
      • Variance Skew Kurtosis
      • Generic Value at Risk Range
      • Ratio Risk Measure
      • Equal Risk Measure
      • Median Absolute Deviation Risk
      • Non-Optimisation Risk Measures
      • Adjust Risk Contributions
      • Expected Risk
      • Risk Measure Tools
        • Optimisation types
        • Pipe routing
        • Time-dependent
        • Weight finalisers
        • Investable universe
        • Panel collapse
        • Result investable view
        • Base Cross Validation (a)
        • Base Cross Validation (b)
        • KFold
        • Combinatorial
        • WalkForward
        • Multiple randomised
        • Validation
        • Scoring
        • Optimisation Cross Validation
        • Base search cross validation
        • Grid search cross validation
        • Randomised search cross validation
        • Online fold loop
        • Covariance Forecast Evaluation
        • Covariance forecast summary
        • Resume
        • Log-wealth regret
      • Naive optimisation
        • Base clustering optimisation
        • Hierarchical Risk Parity
        • Schur Complement Hierarchical Risk Parity
        • Hierarchical Equal Risk Contribution
          • JuMP optimisation types
          • JuMP model accessors
          • JuMP model state
          • Frontier sweep
          • JuMP model setup
          • MIP indicators
            • Return estimators
            • Objective functions
            • Return constraints
          • Budget Constraints
          • Weight Constraints
          • SDP Constraints
          • Integer Phylogeny Constraints
          • Cardinality Constraints
          • Threshold Constraints
          • Turnover Constraints
          • Fees Constraints
          • Tracking Error Constraints
          • Regularisation Constraints
          • Weight norm constraints
        • JuMP Optimiser (a)
        • JuMP Optimiser (b)
        • Mean Risk
        • Factor risk contribution
        • Near optimal centering (a)
        • Near optimal centering (b)
        • Risk budgeting
        • Relaxed risk budgeting
          • Base Risk Constraints
          • Variance Constraints
          • Moment risk measure constraints
          • Kurtosis Constraints
          • Negative Skewness Constraints
            • XatRisk Constraints
            • Conditional XatRisk Constraints
            • Entropic XatRisk Constraints
            • Relativistic XatRisk Constraints
            • Power-Norm XatRisk Constraints
          • OWA risk measures constraints
          • Average Drawdown Constraints
          • Ulcer Index Constraints
          • Maximum Drawdown Constraints
          • Brownian Distance Variance Constraints
          • Worst Realisation Constraints
          • No Risk Constraints
          • Range Constraints
          • Turnover Risk Measure Constraints
          • Tracking Risk Measure Constraints
          • Variance Skew Kurtosis Constraints
          • Generic Value at Risk Range Constraints
        • Base meta optimisation
        • Nested Clustered
        • Stacking
        • Subset resampling
        • Base finite allocation
        • Discrete finite allocation
        • Greedy finite allocation
      • Risk measure compatibility
      • Online optimisation
        • Base Online Portfolio Selection
        • Online Selection Rules
        • Online Portfolio Selection
        • Programme Allocation Set
        • Forecast rules
        • Second set rules
        • Mirror descent
        • Follow the leader
        • Adaptive optimistic
        • Meta-learning
        • Allocation risk ceiling
        • Allocation Set programme
        • Sparse portfolio algorithms
      • Projection weight finalisers
    • Expected Returns
      • Factor attribution
      • Factor attribution realised
      • Factor attribution realised methods
    • Asset selection
      • Base Pipeline
      • Step execution
      • Pipeline
      • Prediction CV
      • Search cross-validation
      • Online Pipeline
    • Plotting
    • Aliases
  • Private API
        • Tables: private API
        • Arg data and moments: private API
        • Arg priors and uncertainty sets: private API
        • Arg phylogeny and constraints: private API
        • Arg risk measures and costs: private API
        • Arg optimisation: private API
        • Field dict: private API
        • Validations and returns: private API
        • Math data and moments: private API
        • Math priors and networks: private API
        • Math risk and optimisation: private API
        • Math online selection: private API
        • References: private API
      • Type roots: private API
      • Pretty show: private API
      • Scoped config: private API
      • Preferences: private API
      • Messages: private API
      • Errors: private API
      • Type aliases: private API
      • Observation weights: private API
      • Assertions: private API
      • Vec scalar: private API
      • Norm error: private API
      • Kappa log: private API
      • Partial fit: private API
      • Online (a): private API
      • Online (b): private API
      • Coverage Policy: private API
      • Returns Source: private API
      • Operators: private API
      • Array views: private API
      • Type utilities: private API
      • Factory: private API
      • Propagatable: private API
      • Forward properties: private API
      • Vector to scalar measures: private API
      • Mean test: private API
      • Mean test draws: private API
      • Asset Panel: private API
      • Asset Panel builder: private API
      • Listing Span: private API
      • Preprocessing: private API
      • Panel views: private API
      • Prices result: private API
      • Price ingestion: private API
      • Price gap fill: private API
      • Price filters: private API
      • Returns result: private API
      • Prices to returns: private API
      • Train/test split: private API
      • Base asset selection: private API
      • Cross-sectional transforms: private API
      • Feature selector: private API
      • Panel data frame: private API
      • Returns buffer state: private API
      • Preprocessing partial fit: private API
      • Asset panel concat: private API
      • Panel field values: private API
      • Asset panel summary: private API
      • Panel round trip: private API
      • Posdef matrix: private API
      • Denoise: private API
      • Detone: private API
      • Matrix processing: private API
      • Matrix square root: private API
      • Base moments: private API
      • Simple expected returns: private API
      • Covariance: private API
      • Simple variance: private API
        • Gerber covariance: private API
        • Smyth-Broby Covariance: private API
        • Gerber IQ covariance (a): private API
        • Gerber IQ covariance (b): private API
      • Distance Covariance: private API
      • Lower Tail Dependence Covariance: private API
      • Rank covariance: private API
      • Histogram: private API
      • Mutual info covariance: private API
      • Denoise covariance: private API
      • Detone covariance: private API
      • Processed covariance: private API
      • PortfolioOptimisersCovariance: private API
      • Shrunk Expected Returns: private API
      • Equilibrium expected returns: private API
      • Excess expected returns: private API
      • Coskewness: private API
      • Cokurtosis: private API
      • Base regression: private API
        • Stepwise Regression: private API
        • Dimension reduction regression: private API
      • Implied Volatility: private API
      • Correlation covariance: private API
      • Abstract covariance variance: private API
      • Standard deviation expected returns: private API
        • Windowed expected returns: private API
        • Windowed covariance: private API
        • Windowed variance: private API
        • Windowed Coskewness: private API
        • Windowed Cokurtosis: private API
        • Windowed preamble: private API
      • Median expected returns: private API
      • Custom value expected returns: private API
        • Exp weighted expected returns: private API
        • Exp weighted variance: private API
        • Exp weighted covariance: private API
        • Exp weighted centring: private API
        • Regime adjusted exp weighted variance: private API
        • Regime adjusted exp weighted covariance (a): private API
        • Regime adjusted exp weighted covariance (b): private API
        • Mahalanobis regime bias: private API
        • HAC row kernel: private API
        • Regime switches: private API
        • Estimated regime bias: private API
        • Estimated Mahalanobis bias: private API
        • Separate portfolio bias: private API
        • Mahalanobis level closure: private API
      • Higher-Moment Partial Fit: private API
        • Cross-Sectional Regression: private API
        • Cross-Sectional Weights: private API
        • Cross-Sectional Factor Model: private API
          • Base descriptor: private API
          • Panel Field Descriptors: private API
          • Lag Descriptors: private API
          • EW mean descriptors: private API
          • EW volatility descriptors: private API
          • EW beta descriptors (a): private API
          • EW beta descriptors (b): private API
          • Rolling Descriptors: private API
          • Base exposure: private API
          • Composite Exposure: private API
          • Derived Exposure: private API
          • One-Hot Exposure: private API
          • Constant Exposure: private API
          • Exposure Neutralisation: private API
          • Observed Exposure: private API
        • Factor Family Basis: private API
        • Factor Family Basis Transforms: private API
          • Base Return Forecast: private API
          • Descriptor Scores: private API
          • Custom Value Return Forecast: private API
          • Fixed Weighted Return Forecast: private API
          • Exp weighted Return Forecast: private API
          • Target Return Forecast: private API
          • Forecast Evaluation: private API
          • Forecast History: private API
          • Forecast Information Coefficient: private API
          • Forecast Portfolios: private API
          • Forecast Factor Correlation: private API
          • Forecast Forward Windows: private API
          • Forecast Calibration: private API
          • Forecast Summary: private API
          • Target Return Forecast Step: private API
        • Cross-Sectional Regression Diagnostics: private API
        • Cross-Sectional Exposure Diagnostics: private API
        • Factor Model Summary: private API
        • Cross-Sectional Idiosyncratic Diagnostics: private API
        • Cross-Sectional Exposure IC: private API
      • Coverage Universe: private API
      • Price-level expected returns: private API
      • Composite price-level statistics: private API
      • Rank-one covariance: private API
      • Geodesic shrinkage covariance: private API
      • Base Distance: private API
      • Distance: private API
      • Distance distance: private API
      • Similarity: private API
      • Feature Distance: private API
      • Feature distance active rows: private API
    • JuMP model optimisation: private API
      • Base Phylogeny: private API
      • Clusters: private API
      • Hierarchical: private API
      • Non hierarchical clustering: private API
      • Phylogeny: private API
        • DBHT: private API
        • PMFG: private API
        • Graph Traversal: private API
        • Clique Hierarchy: private API
        • Bubble Tree: private API
        • DBHT Dendrogram: private API
        • DBHT Clustering: private API
      • LoGo: private API
        • Minimum Spanning Tree: private API
        • Network Estimator: private API
        • Network Graph: private API
        • Separation: private API
        • Centrality: private API
        • Centrality Polarity: private API
        • Centrality Estimator: private API
        • Centrality Queries: private API
      • Phylogeny Clustering: private API
      • Phylogeny Matrix: private API
      • Asset Phylogeny: private API
      • Base Constraint Generation: private API
      • Linear constraint generation (a): private API
      • Linear constraint generation (b): private API
      • Risk budget constraint generation: private API
      • Phylogeny constraint generation: private API
      • Weight bounds constraint generation: private API
      • Asset sets matrix: private API
      • Threshold constraint generation: private API
      • Exposure constraint generation: private API
      • Cross-Sectional Factor Axis: private API
      • Base Prior: private API
      • Empirical Prior: private API
      • Factor Prior: private API
      • High Order Prior: private API
        • Black-Litterman Views Generation: private API
        • Black-Litterman Prior: private API
        • Bayesian Black-Litterman Prior: private API
        • Factor Black-Litterman Prior: private API
        • Augmented Black-Litterman Prior: private API
          • Entropy pooling algorithms: private API
          • Entropy pooling mean views: private API
          • Entropy pooling view types: private API
          • Entropy pooling solvers: private API
          • Entropy pooling moment views: private API
          • Entropy pooling tail view solve: private API
        • Meucci entropy pooling Prior: private API
        • Entropy pooling Prior (a): private API
        • Entropy pooling Prior (b): private API
        • Entropy pooling Prior (c): private API
      • Opinion pooling Prior: private API
      • High order factor Prior estimator: private API
      • Asset Panel Estimators: private API
      • Base cross-sectional factor Prior: private API
      • Cross-Sectional Factor Prior: private API
      • Prior partial fit: private API
      • Prior expected returns: private API
      • Low-dimension ensemble prior: private API
      • Cross-Sectional Prior Fold: private API
      • Cross-Sectional Forecast History Carry: private API
      • Cross-Sectional Calibration Rules: private API
      • Cross-Sectional Carry Histories: private API
      • Prior Scenarios: private API
      • Prior Returns Source: private API
      • Base Uncertainty Sets: private API
      • Delta Uncertainty Sets: private API
      • Normal Uncertainty Sets: private API
      • Bootstrap Uncertainty Sets: private API
      • L1 uncertainty sets: private API
      • Calibration Rules: private API
      • Compact Uncertainty Sets: private API
      • Norm-Ball Uncertainty Sets: private API
      • Orthogonal Uncertainty Sets: private API
      • Compact Radius Rules: private API
    • Turnover: private API
    • Fees: private API
    • Net returns drawdowns: private API
    • Tracking: private API
      • Base Risk Measures: private API
      • Variance: private API
      • Moment Risk Measures: private API
      • Kurtosis: private API
      • Negative Skewness: private API
        • X at Risk: private API
        • Conditional X at Risk: private API
        • Entropic X at Risk: private API
        • Relativistic X at Risk: private API
        • Power Norm X at Risk: private API
      • OWA risk measures (a): private API
      • OWA risk measures (b): private API
      • Average Drawdown: private API
      • Ulcer Index: private API
      • Maximum Drawdown: private API
      • Brownian Distance Variance: private API
      • Worst Realisation: private API
      • No Risk: private API
      • Range: private API
      • Turnover risk measure: private API
      • Tracking risk measure: private API
      • Variance Skew Kurtosis: private API
      • Generic Value at Risk Range: private API
      • Ratio Risk Measure: private API
      • Equal Risk Measure: private API
      • Median Absolute Deviation Risk: private API
      • Non-Optimisation Risk Measures: private API
      • Adjust Risk Contributions: private API
      • Expected Risk: private API
      • Risk Measure Tools: private API
        • Optimisation types: private API
        • Pipe routing: private API
        • Time-dependent: private API
        • Weight finalisers: private API
        • Investable universe: private API
        • Panel collapse: private API
        • Result investable view: private API
        • Base Cross Validation (a): private API
        • Base Cross Validation (b): private API
        • KFold: private API
        • Combinatorial: private API
        • WalkForward: private API
        • Multiple randomised: private API
        • Validation: private API
        • Scoring: private API
        • Optimisation Cross Validation: private API
        • Base search cross validation: private API
        • Grid search cross validation: private API
        • Randomised search cross validation: private API
        • Online fold loop: private API
        • Covariance Forecast Evaluation: private API
        • Covariance forecast summary: private API
        • Resume: private API
        • Log-wealth regret: private API
      • Naive optimisation: private API
        • Base clustering optimisation: private API
        • Hierarchical Risk Parity: private API
        • Schur Complement Hierarchical Risk Parity: private API
        • Hierarchical Equal Risk Contribution: private API
          • JuMP optimisation types: private API
          • JuMP model accessors: private API
          • JuMP model state: private API
          • Frontier sweep: private API
          • JuMP model setup: private API
          • MIP indicators: private API
            • Return estimators: private API
            • Objective functions: private API
            • Return constraints: private API
          • Budget Constraints: private API
          • Weight Constraints: private API
          • SDP Constraints: private API
          • Integer Phylogeny Constraints: private API
          • Cardinality Constraints: private API
          • Threshold Constraints: private API
          • Turnover Constraints: private API
          • Fees Constraints: private API
          • Tracking Error Constraints: private API
          • Regularisation Constraints: private API
          • Weight norm constraints: private API
        • JuMP Optimiser (a): private API
        • JuMP Optimiser (b): private API
        • Mean Risk: private API
        • Factor risk contribution: private API
        • Near optimal centering (a): private API
        • Near optimal centering (b): private API
        • Risk budgeting: private API
        • Relaxed risk budgeting: private API
          • Base Risk Constraints: private API
          • Variance Constraints: private API
          • Moment risk measure constraints: private API
          • Kurtosis Constraints: private API
          • Negative Skewness Constraints: private API
            • XatRisk Constraints: private API
            • Conditional XatRisk Constraints: private API
            • Entropic XatRisk Constraints: private API
            • Relativistic XatRisk Constraints: private API
            • Power-Norm XatRisk Constraints: private API
          • OWA risk measures constraints: private API
          • Average Drawdown Constraints: private API
          • Ulcer Index Constraints: private API
          • Maximum Drawdown Constraints: private API
          • Brownian Distance Variance Constraints: private API
          • Worst Realisation Constraints: private API
          • No Risk Constraints: private API
          • Range Constraints: private API
          • Turnover Risk Measure Constraints: private API
          • Tracking Risk Measure Constraints: private API
          • Variance Skew Kurtosis Constraints: private API
          • Generic Value at Risk Range Constraints: private API
        • Base meta optimisation: private API
        • Nested Clustered: private API
        • Stacking: private API
        • Subset resampling: private API
        • Base finite allocation: private API
        • Discrete finite allocation: private API
        • Greedy finite allocation: private API
      • Risk measure compatibility: private API
      • Online optimisation: private API
        • Base Online Portfolio Selection: private API
        • Online Selection Rules: private API
        • Online Portfolio Selection: private API
        • Programme Allocation Set: private API
        • Forecast rules: private API
        • Second set rules: private API
        • Mirror descent: private API
        • Follow the leader: private API
        • Adaptive optimistic: private API
        • Meta-learning: private API
        • Allocation risk ceiling: private API
        • Allocation Set programme: private API
        • Sparse portfolio algorithms: private API
      • Projection weight finalisers: private API
    • Expected Returns: private API
      • Factor attribution: private API
      • Factor attribution realised: private API
      • Factor attribution realised methods: private API
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  • Estimated Mahalanobis bias
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Estimated Mahalanobis bias

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