Portfolio Optimization Methods
34 portfolio optimization methods 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 method is fully documented with mathematical formulation, advantages, limitations, and practical guidance for NSE and BSE equities.
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 - minimize variance for a target expected return on the efficient frontier.
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
Modern machine learning approaches that use hierarchical clustering to build robust portfolios without inverting the covariance matrix — particularly effective for Indian markets with correlated sector exposures.
Hierarchical Risk Parity (HRP)
Uses hierarchical clustering and graph theory for robust allocation without covariance matrix inversion.
HERC
Hierarchical Equal Risk Contribution - combines clustering with equal risk budgeting.
HERC2
Enhanced HERC with improved cluster-level risk budgeting and allocation.
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 - allocate risk across assets according to specified budgets and risk measures.
Inverse Volatility
Weight each asset inversely proportional to its standalone volatility - a closed-form, robust baseline.
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, statistical arbitrage pairs trading, and signal-based dividend allocations.
Equally Weighted (1/N)
The estimation-error-free baseline that often outperforms complex optimized portfolios.
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.
Dividend Optimizer
Entropy-based optimization for dividend income - balance yield, growth, and risk.