Portfolio Optimization docs

Capital Asset Pricing Model (CAPM)

A model that describes the relationship between systematic risk and expected return for assets, particularly stocks.

Modern Portfolio Theory

A framework for constructing portfolios that maximize expected return for a given level of market risk.

Efficient Frontier

The set of optimal portfolios that offer the highest expected return for a defined level of risk.

Expected Returns

The anticipated return on an investment based on historical data or forward-looking estimates.

Volatility (σ)

A statistical measure of the dispersion of returns, usually measured using standard deviation.

The cornerstone of Modern Portfolio Theory that helps investors construct optimal portfolios balancing risk and return.

A portfolio optimization approach that focuses solely on minimizing risk without a specific return target.

Maximizes expected portfolio return minus a penalty for variance, balancing risk aversion with return expectations.

An algorithm developed by Harry Markowitz to trace the entire efficient frontier for portfolio optimization problems.

A modern portfolio optimization method that uses machine learning techniques to build diversified portfolios.

An extension of HRP that combines hierarchical clustering with equal risk contribution principles.

A hybrid approach that combines hierarchical clustering with traditional optimization techniques.

A simplified hierarchical approach that uses equal weights within clusters for portfolio construction.

A simple yet effective diversification approach that assigns equal weight to all assets in a portfolio.

A portfolio optimization method that minimizes the expected loss in the worst-case scenarios beyond the VaR threshold.

A portfolio optimization method that minimizes the maximum expected drawdown with a certain confidence level.

A signal-based optimization approach using cross-sectional z-scores of technical indicators combined through linear programming.

Maximize dividend yield while maintaining portfolio diversity using entropy-based optimization. Balances income generation with intelligent diversification.

Sharpe Ratio

A measure of risk-adjusted return that helps investors understand the return of an investment compared to its risk.

CAPM Beta (β)

A measure of systematic risk that represents how an asset moves relative to the overall market.

Rolling Beta (β)

A time-series analysis of beta that shows how an asset's relationship with the market changes over different periods.

Sortino Ratio

A modification of the Sharpe ratio that only penalizes returns falling below a specified target or required rate of return.

Skewness

A measure of the asymmetry of the probability distribution of returns about its mean.

Kurtosis

A measure of the "tailedness" of the probability distribution of returns, indicating the presence of extreme values.

Jensen's Alpha (α)

A risk-adjusted performance measure that represents the average return on a portfolio above or below CAPM predictions.

Treynor Ratio

A portfolio performance metric that measures returns earned in excess of the risk-free rate per unit of market risk (beta).

Value at Risk (VaR)

A statistical technique used to measure the level of financial risk within a portfolio over a specific time frame.

Conditional Value at Risk (CVaR)

Also known as Expected Shortfall, measures the expected loss in the worst-case scenarios beyond the VaR threshold.

Maximum Drawdown

A measure of the largest peak-to-trough decline in a portfolio's value, representing the worst-case scenario for an investment.

Blume Adjusted Beta

A modified beta calculation that adjusts for the tendency of betas to revert toward the market average over time.

Entropy

A measure of uncertainty or randomness in portfolio returns, indicating the level of unpredictability in the system.

Omega Ratio (Ω)

A performance measure that evaluates the probability-weighted ratio of gains versus losses for a threshold return.

Calmar Ratio

A performance measurement that uses the ratio of average annual compound rate of return to maximum drawdown.

Ulcer Index

A volatility measure that captures the depth and duration of drawdowns, focusing on downside movement.

Entropic Value at Risk (EVaR)

A coherent risk measure that provides tighter bounds on tail risk than traditional VaR or CVaR.

Gini Mean Difference

A measure of dispersion in returns that evaluates the average absolute difference between all pairs of observations.

Drawdown at Risk (DaR)

A risk metric representing the maximum expected drawdown that won't be exceeded with a certain confidence level.

Conditional Drawdown at Risk (CDaR)

The expected value of drawdown when exceeding the Drawdown at Risk threshold, measuring tail drawdown risk.

Upside Potential Ratio

A performance metric that evaluates upside potential relative to downside risk, focusing on beneficial asymmetry.

Modigliani Risk-Adjusted Performance (M²)

A measure that adjusts portfolio returns to match market volatility, allowing direct comparison with benchmark returns.

Information Ratio

A performance metric that evaluates active return per unit of risk relative to a benchmark index.

Sterling Ratio

A risk-adjusted return metric similar to Calmar but using average annual drawdown minus 10% in the denominator.

V2 Ratio

A relative performance metric that considers both outperformance versus the benchmark and the stability of that outperformance.

Welch Beta

A robust alternative to traditional beta that uses winsorization to reduce the impact of extreme returns.

Semi Beta

A downside beta that measures portfolio sensitivity to the benchmark only during down markets.

Coskewness

Measures the relationship between portfolio returns and squared market returns, indicating asymmetrical risk.

Cokurtosis

Measures the relationship between portfolio returns and cubed market returns, indicating tail dependency.

GARCH Beta

A time-varying measure of portfolio beta that accounts for volatility clustering using GARCH models.