How Minerva Turns Signals Into Position Sizes

Minerva models decide whether a strategy wants to be long, short, or flat. A separate position-sizing method converts each accepted long or short signal into a dollar position and a whole number of shares. This explainer compares 100% of Equity with Fixed Risk, Kelly, Volatility Targeting, Signal Proportional, and ATR-Based sizing. The legacy names fixed_fractional and fixed are aliases for Fixed Risk, not separate methods.

Plain-English overview

The model decides what direction to trade; the sizing method decides how much of the strategy’s current equity to put into the trade. 100% of Equity targets position notional equal to current equity whenever a signal qualifies. Fixed Risk chooses a position intended to lose a specified percentage of current equity if the initial stop is reached. Kelly adjusts that risk percentage using the strategy’s completed-trade history. Volatility Targeting changes the position according to the instrument’s volatility and the forecast magnitude. Signal Proportional starts with a Fixed Risk position and deliberately scales it by signal strength. ATR-Based uses an ATR-derived price movement instead of the actual stop distance to calculate shares.

The calculated position is only the requested position. Minerva can still reduce an entry because of cash, leverage, maximum-position, minimum-size, whole-share, or market-participation constraints. Once a position is open, Minerva does not continually resize it as the price, stop, volatility, ATR, or signal strength changes.

Visual: what consecutive same-direction signals actually do

Because a position is sized only when it opens, firing the same-direction signal again while the trade is live does nothing. The size is recomputed only at the next entry, after an exit returns the strategy to flat, or on a reversal. This behavior holds for every one of the six methods.

Technical overview

Minerva separates signal generation from execution sizing. A model produces a direction and strength. The execution layer converts that output to a signed forecast, applies the entry threshold and any regime adjustment, and sizes an accepted order at the next eligible bar open. Each sizing method calculates a raw absolute integer quantity q0 from current equity E, entry price P, and its method-specific inputs. The common execution layer then applies, in order, the maximum-position-value cap, the long-cash cap, the maximum-leverage cap, the minimum-position-size rule, and entry participation limits to produce executed quantity q.

Fixed Risk, Kelly, and Signal Proportional use the initial fixed or trailing stop distance when calculating quantity. ATR-Based substitutes ATR × multiple as its sizing distance. Volatility Targeting uses estimated daily percentage volatility instead of a stop distance. 100% of Equity uses only current equity and entry price. Stops, gaps, commissions, slippage, and the daily circuit breaker operate after sizing, so realized losses can differ from a method’s modeled risk.

Numerical examples

Example 1: The same accepted signal under every method

Assume:

• Current equity: $100,000
• Entry price: $100
• Initial stop distance: 5%, or $5 per share
• Risk per trade: 0.5%, or $500
• Final forecast: 10 out of 20
• Signal Proportional scale range: 0.2 to 1.0
• Daily percentage volatility: 2%
• Target annual volatility: 20%
• Forecast scalar: 10
• Instrument diversification multiplier: 1.0
• Regime volatility multiplier: 1.0
• ATR: $2
• ATR multiple: 2
• Kelly example: applied Kelly risk fraction of 1%
• No cash, leverage, maximum-position, minimum-size, liquidity, or rounding constraint binds

Visual: Example 1 as a share of equity

The same accepted signal, sized by each method, drawn as a fraction of the $100,000 account. This is the “how much am I putting in” answer at the moment of entry.

Example 2: Why Fixed Risk does not imply a fixed dollar position

With $100,000 of equity and 0.5% risk per trade, the risk budget is always $500. The requested position changes when the initial stop distance changes:

At a constant 5% stop, Fixed Risk at 0.5% requests approximately 10% of current equity on every new entry. At a constant 1% stop, it requests approximately 50%.

Example 3: How gains and losses change the next order

Assume a $100 entry price, 0.5% Fixed Risk, a 5% stop, and no binding caps:

These quantities are recalculated only when a new position is opened. Neither method rebalances an existing position while it remains open.

Visual: how the position tracks equity over six consecutive trades

Run six trades in a row, each a fresh entry after the previous one closes. The colored bars are the dollars deployed at each entry; the grey line is total equity. Because every entry resizes from current equity, the bars rise and fall with the line while the fraction stays fixed. Switch scenarios to see growth versus drawdown, and note how each method's per-trade loss in the losing run is exactly its exposure × the 5% stop.

Example 4: How portfolio weighting changes the capital sleeve

Assume a $400,000 portfolio account assigns a 25% weight to one Minerva strategy:

How portfolio sleeves are formed

A portfolio sleeve is the portion of a larger portfolio account allocated to one strategy holding. “Sleeve” is appropriate here because the strategy is one component of a multi-strategy portfolio; it is not the preferred term for the capital in a standalone backtest.

Let:

• Eaccount,0 be the portfolio account’s starting equity.
• wi be holding i’s portfolio weight.
• Esleeve,i be holding i’s initial allocated capital.

Portfolio weights are positive and together exhaust the portfolio:

sum(wi) = 1

At portfolio launch, each holding’s initial sleeve is:

Esleeve,i = Eaccount,0 × wi

The launch weights and allocated-capital amounts are then frozen for the launched book. Each holding replays its tested strategy execution configuration inside its own allocated capital rather than sizing from the portfolio’s entire shared cash balance. As that holding makes or loses money, its strategy equity changes, and its next position is sized from that updated strategy equity.

How Minerva calculates portfolio weights

Except for Equal Weight, the methods begin with timestamp-aligned per-bar return histories for the strategy holdings. Correlation-aware methods use a denoised covariance matrix. A volatility floor prevents an unusually sparse strategy from appearing nearly riskless merely because most of its returns are zero, and a maximum-weight cap prevents one holding from dominating the book.

For three or more holdings, the default maximum holding weight is:

max_weight = min(100%, max(2 ÷ N, 40%))

The default volatility floor used for portfolio weighting is:

σfloor = 25% × median cross-sectional strategy volatility

These controls modify the raw portfolio-weighting solution before allocated capital is assigned.

How portfolio weighting and strategy sizing interact

Portfolio weighting and strategy sizing answer different questions:

• Portfolio weighting: What fraction of the portfolio account belongs to each strategy?
• Strategy sizing: What fraction of that strategy’s current equity should be deployed on this trade?

They operate sequentially and therefore multiply at portfolio launch:

initial holding position notional = portfolio starting equity × launch weight × strategy exposure fraction

Equivalently:

Ni,0 = Eaccount,0 × wi × xi,0

where xi is the position exposure produced by the strategy sizing method before shared caps.

At launch, the same multiplication determines modeled stop risk at the portfolio-account level:

• With 100% of Equity and a stop fraction s, modeled account risk from holding i is approximately wi × s.
• With Fixed Risk, modeled account risk from holding i is approximately wi × r.
• With Kelly, it is approximately wi × K.
• With Signal Proportional, it is approximately wi × m × r.
• With ATR-Based, actual stop risk depends on how the execution-stop distance compares with kATR × A.
• With Volatility Targeting, stop risk is an output of the chosen exposure and stop distance rather than the sizing target.

After launch, each holding compounds independently:

Esleeve,i,t = Esleeve,i,0 + cumulative net P&Li,t

Ni,t = Esleeve,i,t × xi,t

Because holdings earn different returns, their effective weights can drift away from the frozen launch weights:

weffective,i,t = Esleeve,i,t ÷ Eaccount,t

Portfolio weighting therefore does not replace strategy sizing, and strategy sizing does not replace portfolio weighting. The launch weight establishes the strategy’s initial capital boundary. The strategy sizing method determines how much of its current strategy equity is used for each accepted trade.

Portfolio interplay example

Consider a $300,000 portfolio containing three equally weighted strategies:

w1 = w2 = w3 = 1 ÷ 3

Each strategy receives:

$300,000 × 1 ÷ 3 = $100,000

The portfolio weights are identical in both rows. The difference comes entirely from the strategy sizing method used inside each allocated sleeve.

Formula notation

• E = current strategy equity when a new position is sized.
• P = entry price at the next eligible bar open.
• q0 = raw absolute shares before shared caps; q = final executed absolute shares.
• r = configured risk_per_trade fraction.
• D = initial stop-derived risk per share; Dexec = actual entry-to-execution-stop distance.
• s = initial stop-distance fraction, so D = P × s when a percentage stop controls sizing.
• F = absolute final adjusted forecast on Minerva’s 0–20 scale; Fs = volatility-targeting forecast scalar.
• p = causal win rate; b = average win divided by average loss.
• fK = fractional-Kelly multiplier; Kmax = maximum Kelly risk fraction; K = applied Kelly risk fraction.
• τ = target annual volatility; Mregime = regime volatility multiplier; IDM = instrument diversification multiplier.
• σd = estimated daily percentage volatility.
• A = ATR; kATR = ATR multiple.
• mmin and mmax = minimum and maximum Signal Proportional scales.
• L = maximum leverage; C = available cash; MPV = maximum position value.
• w = portfolio weight; Eaccount = total portfolio account equity.
• floor(x) = round down to a whole number of shares.

Complete comparison

The numerical rows in the detailed table use the assumptions from Example 1.