| Discrete allocation | pfopt_allocation | Whole-share orders from target weights: latest prices from a price history or given, a portfolio value, greedy rounding or integer programming, long/short with a short ratio and optional reinvestment of short proceeds; the leftover cash and the error against the targets. | 1 |
| Portfolio analytics | pfopt_analytics | Performance of given weights: expected return, volatility, Sharpe, semideviation and Sortino, each asset’s risk contribution, and the value of every optimisation objective (variance, return, Sharpe, L2, quadratic utility, transaction cost, ex-ante and ex-post tracking error); cleaned weights. | 1 |
| Black-Litterman | pfopt_black_litterman | Black-Litterman allocation: a market-implied (or equal, estimated, given) prior of returns blended with absolute and relative views, view confidences (Idzorek), view uncertainty and tau into posterior returns and covariance; implied, max-Sharpe, min-volatility or max-utility weights; the market-implied risk aversion and prior returns from market caps. | 2 |
| Critical line algorithm | pfopt_cla | Markowitz’s critical line algorithm: the exact mean-variance frontier under per-asset bounds through its turning points, the max-Sharpe and min-volatility portfolios and the frontier curve. | 1 |
| Downside-risk optimisation | pfopt_downside | Portfolios that control losses instead of variance, from historical return scenarios: mean-semivariance (downside deviation below a threshold, Sortino ratio), mean-CVaR (expected shortfall at a confidence level) and mean-CDaR (conditional drawdown at risk, with the drawdown curve); minimum risk, target risk, target return and downside quadratic utility. | 3 |
| Return and risk estimates | pfopt_estimates | Annual expected returns (mean historical, exponentially weighted, CAPM) and covariance matrices (sample, semicovariance, exponential, minimum covariance determinant, manual, Ledoit-Wolf and oracle shrinkage), correlation, conversions between prices and returns, and positive-semidefinite repair. | 4 |
| Hierarchical risk parity | pfopt_hrp | Hierarchical risk parity: cluster the assets by correlation distance (single, complete, average, weighted, centroid, median or Ward linkage), order them along the tree and split risk by recursive bisection; returns the weights, performance, linkage, dendrogram and clustered correlation heatmap. | 1 |
| Mean-variance optimisation | pfopt_mean_variance | Efficient-frontier portfolios: max Sharpe (tangency), min volatility, max quadratic utility, max return for a target volatility and min volatility for a target return, long-only or long/short, market neutral, with per-asset, sector and linear constraints and L2, transaction-cost and tracking-error terms; the efficient frontier curve with random portfolios; custom convex and nonconvex objectives (log-barrier risk budgeting, index tracking, risk parity). | 4 |
