Methodology — Risk-Based Portfolio Construction

Transparency is a feature. This page explains what these portfolio allocators do and why — in plain terms. The precise formulas and numeric conventions are documented in our internal methodology; the summary here is deliberate, not an omission.

These are three long-only allocators: each one takes a covariance matrix — the table describing how volatile each holding is and how the holdings move together — and turns it into a set of portfolio weights. Every weight is zero or positive (no short positions) and the weights always add up to the whole portfolio. What separates the three methods is how much of the risk picture each one uses: the first looks only at each asset's own volatility, the second uses the full web of co-movements, and the third deliberately balances how much risk each holding contributes.

Inverse-variance weights

This is the simplest, most correlation-blind approach: it gives each holding a weight in proportion to how calm it is on its own, so steadier assets get more capital and jumpier ones get less. It looks only at each asset's individual volatility and ignores how the assets move together, which makes it easy to read but naive about diversification. It needs a genuine, positive volatility for every holding to be defined.

Minimum-variance weights

This method uses the entire covariance picture — every asset's volatility and every pairwise co-movement — to find the single combination with the lowest possible overall portfolio volatility, the classic global minimum-variance portfolio. Because it exploits how holdings offset one another, it can lean heavily on assets that hedge the rest of the book. For the well-behaved inputs we use here the result comes out long-only, though in the general unconstrained case this recipe can call for short positions. It requires a covariance matrix that is not degenerate — if the assets are effectively redundant, the answer is undefined rather than guessed at.

Equal-risk-contribution (ERC / risk parity) weights

Also called risk parity, this allocator sizes each holding so that every asset contributes the same share of total portfolio risk — no single position quietly dominates the risk budget. For two assets there is a clean known result: the weights come out inversely proportional to volatility and, notably, do not depend on the correlation at all (Maillard, Roncalli & Teiletche). For three or more assets there is no tidy closed form, so we solve it numerically with an established iterative routine (the cyclical coordinate descent of Griveau-Billion, Richard & Roncalli) that starts from an inverse-volatility guess and refines it until the risk shares are equalized. The result is long-only and sums to the whole portfolio. It needs a positive volatility for every holding, and if the numerical search fails to settle we report that rather than return a half-converged answer.

Honest limits

• All three are driven entirely by a covariance matrix estimated from past returns — they inherit whatever is right or wrong about that estimate, and none of them uses any view on expected return.
• The inputs must form a proper square risk table; a malformed or mismatched matrix is rejected rather than patched over.
• These are risk-shaping tools, not return-maximizing ones: minimum-variance and risk parity aim to control volatility and concentration, not to chase the highest expected gain.