Free lesson · Quant strategy development

02 / The variables that actually enter the decision

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Start with the idea

A feature is useful only after its timing, unit and role are defined. Normalising a predictor can make instruments comparable, but it can also erase economically useful level information or amplify tiny denominators.

Symbols, units & horizon

xᵢ,ₜ: feature of instrument i at time t
μ̂ᵢ,ₜ and σ̂ᵢ,ₜ: mean and SD estimated from permitted history
zᵢ,ₜ: dimensionless standardised feature
rₜ,ⱼ: within-period log return j
m: count of within-period intervals
RVₜ: square root of sum of squared returns, a realised-volatility measure for that period
Hat: estimate

When and why to use this

Use standardised features to compare signal strength and realised volatility to scale exposure. Record whether each variable predicts returns or merely constrains execution and risk.

Useful variables have a defined mechanism, timestamp, unit, and action. More inputs can make a backtest easier to fit while making the economic story harder to test. Distinguish predictors from risk controls, execution controls, and accounting variables; each has a different role.

Variable family	Examples / units	How it changes a bot
Return and trend	Lagged returns, moving-average gap, momentum / decimal return	Forecast direction and strength at a specified horizon
Relative value	Residual spread, valuation ratio, basis / price or standard deviations	Estimate deviation from a defensible relationship
Volatility and tails	Realised volatility, range, jump indicators / return units	Scale exposure, widen uncertainty, constrain losses
Liquidity and activity	Spread / bp; volume / shares; depth / units	Decide whether to trade and how much is executable
Order flow	Signed volume, imbalance, cancellations / normalised units	Short-horizon forecast and adverse-selection estimate
Carry and financing	Rates, dividends, borrow, funding / rate per period	Adjust expected holding return and feasibility
Fundamentals and events	Earnings surprise, revisions, issuance / timestamped values	Condition the forecast on newly available information
Cross-asset context	Market, sector, curve, credit, currency returns	Separate common exposure from instrument-specific information
Portfolio state	Positions, cash, beta, inventory, pending orders	Constrain new orders using total actual and potential exposure
Operational state	Quote age, feed gaps, rejects, reconciliation differences	Pause, reconcile, or escalate before further trading

z_{i, t} = \frac{x_{i, t} - {\hat{μ}}_{i, t}}{{\hat{σ}}_{i, t}}, {RV}_{t} = \sqrt{\sum_{j = 1}^{m} r_{t, j}^{2}}

Algebra and arithmetic

Standardise a feature and aggregate squared moves

Solve the scale-location representation $x = μ + σ z$ for z: subtract μ and divide by positive σ. Invert with $x = μ + σ z$ .
For intraperiod log returns, realised variance is the sum of their squares; take its square root for realised volatility. It is a quadratic-variation estimator with sampling and microstructure limitations.

Work it by hand

x=12, fitted mean=10, SD=2 gives z=1. Intraperiod returns .01,−.02,.01 give RV=√.0006=.024495, or 2.4495% for that observation interval.

A time-series z-score compares today’s feature with that instrument’s past, using a documented window available at the decision. A cross-sectional rank compares instruments at the same time. Do not confuse the two. Realised volatility above aggregates intraperiod squared log returns; annualisation and overnight moves require an explicit convention.

Python implementation

Self-contained teaching example. Python 3.10+; dependencies and input conventions are shown in the code and notation. Run in your own Python environment.

from math import sqrt

def z_score(value, training_mean, training_sd):
    if training_sd <= 0:
        raise ValueError("Positive training SD required")
    return (value-training_mean)/training_sd

def realized_volatility(intraperiod_log_returns):
    """No annualisation; microstructure noise and sampling choice matter."""
    return sqrt(sum(r*r for r in intraperiod_log_returns))

print(z_score(12,10,2), realized_volatility([.01,-.01]))

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