8 Optimization Algorithms. One Architecture.

Finds the portfolio with the lowest possible volatility — the leftmost point on the efficient frontier. Pure risk minimization using only the covariance structure. SLSQP solver minimizes ½·w'Σw subject to full investment, long-only, position bounds, and bucket bounds. Uses analytical gradients (∇ = Σw) for fast convergence. Supports vol targeting via quadratic inequality constraint and turnover penalty via L1 regularization.

Best for: Capital preservation. Defensive allocation. The lowest-risk portfolio achievable within your constraint set.

Equalizes every asset's contribution to total portfolio risk. Each position carries the same marginal risk — true balance. The mathematical foundation of all-weather portfolios used by Bridgewater and other institutional allocators. Solves via Spinu's Cyclical Coordinate Descent on ½·x'Σx − Σ(1/N)·ln(x_i), then normalizes. High-volatility assets receive lower weight; low-volatility assets receive higher weight.

Best for: Balanced risk allocation. All-weather portfolios. Investors who believe risk balance matters more than return optimization.

Generalizes Risk Parity: where ERC sets all budgets equal, Risk Budgeting lets you choose the allocation of risk per asset class. Minimizes Σ_{i<j}(RC_i/b_i − RC_j/b_j)² so that risk contributions are exactly proportional to the chosen budgets. Key insight: a 60% equity risk budget does NOT produce 60% equity weight — because equities are more volatile, the engine allocates less weight to hit the 60% risk contribution target.

Best for: Custom risk profiles. Bucket-level risk control. Specifying how much risk comes from each asset class.

López de Prado's machine-learning-inspired allocation: cluster assets by correlation distance d = √(½·(1−ρ)), build a Ward-linkage dendrogram, quasi-diagonalize the covariance matrix, then allocate via recursive bisection weighted by inverse cluster variance. Works when Markowitz fails — never inverts the covariance matrix, so it's immune to the matrix instability that plagues classical methods on large universes.

Best for: Robust diversification. Unstable markets. Large universes where covariance matrix inversion is unreliable.

Maximizes the diversification ratio DR = (σ'w) / √(w'Σw) — the ratio of weighted average asset volatilities to total portfolio volatility. A higher ratio means more diversification benefit is captured. Equals 1.0 for a single-asset portfolio and increases as imperfectly correlated assets are combined. Assets with low correlation to the rest of the portfolio receive higher weight; highly correlated assets are consolidated.

Best for: Diversification-seeking allocation. Maximizing the structural benefit of combining imperfectly correlated assets.

Where volatility measures average dispersion, CVaR focuses on tail risk: the expected loss in the worst (1−β) fraction of historical scenarios. Default β=95%, so the engine minimizes the average loss conditional on being in the worst 5% of return outcomes. Uses the Rockafellar-Uryasev linear programming reformulation: minimize α + (1/(T·(1−β)))·Σ_t z_t with auxiliary loss variables. Directly targets catastrophic drawdowns rather than average volatility.

Best for: Tail risk protection. Drawdown minimization. Investors who care more about worst-case losses than average dispersion.

The only return-aware engine in the platform — and it's stabilized for a reason. Classical mean-variance fails out of sample because both inputs (returns and covariance) are noisy. Robust MV addresses both at the source. Σ is shrunk via Ledoit-Wolf Oracle Approximating Shrinkage toward a structured target; μ is shrunk via James-Stein toward the grand mean. The risk-aversion parameter λ (configurable 0.1–1.0) tunes how aggressively the engine seeks return versus minimizes variance. The result degrades gracefully when estimates are imprecise.

Best for: Growth-oriented allocation with statistical guardrails. Investors who want to target returns but distrust raw historical estimates.