Methodology — Weights-Mode Return Synthesis

Transparency is a feature. This page explains what weights-mode return synthesis measures and why we compute it — in plain terms. The precise formulas and numeric conventions are documented in our internal methodology; the summary here is deliberate, not an omission.

A weights-mode portfolio has no shares or transactions — only target weights and the constituents' return series. Before we can report any performance or risk metric, we have to turn those pieces into a single portfolio return series, and that requires a rebalancing convention: an assumption about how often the portfolio is pulled back to its target mix. The convention is not cosmetic — it changes total return, volatility, drawdown and factor betas — so we make it explicit, default it to daily rebalancing, and test every mode. Weights are treated as capital fractions and are normalized first, so only the relative allocation matters.

Modes

Daily rebalance (default)

The portfolio is snapped back to its target weights every single period, so the mix never drifts. Each period's portfolio return is simply the target-weighted average of the constituent returns. This is the convention the stateless portfolio-analytics endpoint uses.

Buy and hold

The weights are set once at inception and then allowed to drift with performance — winners grow into a larger share of the portfolio and losers shrink, with no rebalancing. Because a past winner accumulates weight, subsequent returns tilt more toward it.

Periodic

A middle ground: the portfolio is rebalanced to its target on a fixed cadence and allowed to drift in between. Rebalancing every period is exactly daily rebalance; never rebalancing within the window is exactly buy and hold; anything in between interpolates the two.

Conventions

• Normalization: the weights are divided by their sum before use, so a portfolio specified with proportional weights gives the same result however it is scaled, and all three modes agree on the very first period.
• Frequency-agnostic: the synthesis works on a matrix of period returns and does not annualize anything itself. Whoever calls it chooses the period (daily, monthly) and the annualization downstream.

Edge cases

• There must be at least one asset and at least one period of returns; an empty input cannot produce a series.
• The number of weights must match the number of asset return rows; a mismatch is rejected rather than guessed at.
• If the weights sum to zero there is nothing to normalize, and if the portfolio value ever falls to zero or below (a total loss) a percentage return is undefined — both cases are flagged rather than reported as a misleading number.
• The periodic mode needs a valid, positive rebalancing cadence, and an unrecognized mode name is rejected.