Portfolio Optimization Methods

16 portfolio optimization methods for Indian equity markets, from classical Markowitz Mean-Variance to modern Hierarchical Risk Parity. 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 based on Modern Portfolio Theory, including the original Markowitz framework and its extensions.

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.

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 prioritize risk control, from equal risk contribution to tail-risk minimization using CVaR and CDaR.

Risk Parity

Allocate weights so each asset contributes equally to total portfolio risk.

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.

Alternative Methods

Non-traditional approaches including naive diversification, income optimization, and technical signal-based allocation.

Equally Weighted (1/N)

The estimation-error-free baseline that often outperforms complex optimized portfolios.

Dividend Optimizer

Entropy-based optimization for dividend income - balance yield, growth, and risk.

Technical Indicator

Combine momentum, trend, and volatility signals for allocation decisions.