Portfolio Optimization Methods
33 reference pages on portfolio optimization for Indian equity markets, from classical Markowitz Mean-Variance to modern Hierarchical Risk Parity, regime-aware MVO, distributionally robust CVaR, and statistical-arbitrage pairs trading. Each page covers the mathematical formulation, advantages, limitations, and practical guidance for NSE and BSE equities.
The page count is not the method count. The API exposes 31 optimization methods, and the website picker offers 30 of them: Kalman Pairs Trading is reachable by API and MCP but is deliberately absent from the picker. Two pages here describe a technique rather than a selectable method, so they have no entry in either list: Maximum Sharpe Ratio is the objective the Mean-Variance method solves, and Risk Parity is the variance case of the framework that Risk Budgeting runs under CVaR.
Classical Methods
Foundational mean-variance optimization techniques and their modern extensions - including EWMA-conditioned moments, robust uncertainty sets, sample-resampled frontiers, sparse L1-regularised allocations, and Markov-switching regime conditioning.
Mean-Variance (MVO)
Classical Markowitz optimization, solved here as the tangency portfolio that maximizes the Sharpe ratio.
Minimum Variance
Construct the global minimum variance portfolio without requiring expected return estimates.
Maximum Sharpe Ratio
Find the tangency portfolio that maximizes risk-adjusted return on the efficient frontier.
Max Quadratic Utility
Balance expected return against variance scaled by a risk aversion parameter.
Critical Line Algorithm
Trace the exact efficient frontier analytically without numerical solvers.
Black-Litterman
Bayesian portfolio optimization blending equilibrium returns with entropy-tilted implicit views.
EWMA Mean-Variance
RiskMetrics-style mean-variance with exponentially weighted moments that adapt to volatility regimes.
Robust Mean-Variance
Ellipsoidal worst-case MVO that hedges against estimation error in expected returns.
Resampled Mean-Variance
Michaud-style resampled efficient frontier averaged across block-bootstrap samples.
Sparse Markowitz (L1)
Brodie et al. sparse mean-variance with an L1 penalty that yields concentrated portfolios.
HMM Regime MVO
Markov-switching regime-conditioned mean-variance optimization that adapts to bull/bear regimes.
Clustering-Based Methods
Methods that use hierarchical clustering of the correlation matrix to structure the allocation. HRP, HERC and HERC2 allocate capital down the cluster tree without inverting the covariance matrix; NCO solves a small optimization inside each cluster and then one across the clusters.
Hierarchical Risk Parity (HRP)
Uses hierarchical clustering and recursive bisection to allocate capital without inverting the covariance matrix.
HERC
Hierarchical Equal Risk Contribution - splits capital down the cluster tree by relative risk, with naive risk parity inside each cluster.
HERC2
The HERC descent with equal weights inside each cluster, CVaR as the risk measure, and Spearman codependence.
Nested Clustered (NCO)
Combines clustering with convex optimization to reduce estimation error.
Risk-Focused Methods
Optimization methods that prioritise risk control - equal risk contribution, risk budgeting across alternative measures (variance, CVaR, EVaR, EDaR), maximum diversification, and tail-risk minimisation including a distributionally robust formulation.
Risk Parity
Allocate weights so each asset contributes equally to total portfolio risk.
Risk Budgeting
Generalizes risk parity - here with equal budgets under CVaR, so each asset targets the same share of tail risk.
Inverse Volatility
Weight each asset inversely proportional to its standalone volatility - a closed-form baseline that ignores correlations.
Maximum Diversification
Maximize the diversification ratio - the weighted average asset volatility relative to portfolio volatility.
Maximum Decorrelation
Minimize the quadratic form of the correlation matrix to isolate pure diversification effects.
Minimum CVaR
Minimize Conditional Value at Risk for portfolios focused on controlling tail risk.
Minimum CDaR
Minimize Conditional Drawdown at Risk to build portfolios resilient to sustained losses.
Minimum Semivariance
Minimize the variance of downside returns only - penalize losses without penalizing upside.
Minimum EVaR
Minimize Entropic Value-at-Risk - a coherent measure that bounds CVaR from above.
Minimum EDaR
Minimize Entropic Drawdown-at-Risk - the entropic counterpart of CDaR for capital-preservation mandates.
Distributionally Robust CVaR
Worst-case CVaR over a Wasserstein ball of distributions - hedges against return-distribution misspecification.
Benchmark-Relative Methods
Methods designed for index-relative mandates - tracking-error constrained enhanced indexing and sparse subset replication of an index using only a small number of constituents.
Ensemble Methods
Methods that combine multiple base optimisers into a single allocation via a cross-validated meta-stage, diversifying model risk across different inductive biases.
Factor & Alternative Methods
Non-MVO approaches including the equal-weight baseline, factor-based quintile momentum, growth-optimal Kelly investing, and statistical arbitrage pairs trading.
Equally Weighted (1/N)
The estimation-error-free baseline against which DeMiguel, Garlappi and Uppal (2009) tested 14 optimized models.
Quintile Momentum
Rank assets by momentum and equal-weight the top quintile - the long-leg of the classical momentum factor.
Kelly Optimization
Long-only growth-optimal portfolio that maximizes the expected logarithm of wealth.
Kalman Pairs Trading
Stat-arb on cointegrated pairs with a Kalman-filtered time-varying hedge ratio.
Not investment advice. Past performance is not indicative of future results.