Optimal Statistics Capital Management

Quantitative Research in Markets, Information and Prediction

Optimal Statistics conducts applied research into the behaviour of financial markets, predictive models and complex information systems.

Our research focuses on a recurring question: how does useful information emerge, propagate and change across different scales, markets and trading environments?

Rather than treating market behaviour as a single homogeneous process, we examine the interaction between short-horizon market microstructure, longer-horizon information transmission and the systematic relationships traditionally captured by factor models.

Current Research

High-Frequency Market Microstructure

At very short horizons, prices are shaped by the mechanics of trading as well as by underlying information.

Our current research examines high-frequency market behaviour including:

• order-flow dynamics;
• bid–ask spreads and liquidity;
• short-horizon price formation;
• transaction and quote behaviour;
• temporary versus persistent price movements;
• interaction between liquidity conditions and predictive signals; and
• the stability of relationships as market conditions change.

A central objective is to distinguish genuine information from effects created by trading mechanics, execution costs, temporary imbalances and microstructure noise.

This is particularly important because relationships that appear statistically powerful at high frequency can disappear—or reverse—once realistic execution and changing liquidity are taken into account.

Scale-Variant Information Cascades

Information does not necessarily enter all markets simultaneously or propagate at a constant rate.

Optimal Statistics is investigating scale-variant information cascades: the transmission of information through markets over different time horizons and across related assets.

An information event may first appear as a localised change in order flow, subsequently influence related securities or markets, and eventually become incorporated into broader market pricing.

The research considers:

• the direction and speed of information transmission;
• lead–lag relationships between markets;
• whether transmission mechanisms differ across time scales;
• persistence and decay of predictive information;
• changes in information flow under different volatility and liquidity regimes;
• interaction between local market signals and broader global movements; and
• whether apparently separate predictive relationships are manifestations of the same underlying information process.

The aim is not simply to identify correlation, but to understand the structure through which information becomes incorporated into prices.

Information Cascades and Classical Factor Models

Classical factor models describe returns through relatively persistent common exposures such as market, value, size, momentum and other systematic effects.

Our research asks whether some of these apparently stable factor relationships can also be understood as the aggregate outcome of information propagating through markets at different speeds and scales.

This creates an interesting connection between two traditionally separate views of markets:

Questions include:

• whether conventional factor exposures vary systematically with the state of information transmission;
• whether short-horizon predictive relationships aggregate into longer-horizon factor behaviour;
• whether factor returns contain identifiable lead–lag structures;
• whether factor performance deteriorates when the underlying information cascade changes;
• whether apparent factor premia partly reflect delayed information absorption rather than permanent risk characteristics; and
• whether scale-dependent models can improve upon static factor specifications.

This work may help explain why apparently robust factors can perform very differently across market regimes.

Predictive Model Research

Optimal Statistics also develops and evaluates predictive models across financial and other complex datasets.

Our emphasis is not simply on maximising historical fit.

Models are examined for:

• out-of-sample predictive performance;
• calibration;
• parameter and feature stability;
• sensitivity to market regime;
• interactions between predictors;
• signal agreement and confluence;
• degradation through time;
• transaction-cost robustness; and
• performance relative to appropriate benchmarks.

A model that performs exceptionally in one period may be less valuable than a weaker model whose behaviour remains stable across changing conditions.

Understanding why a model works, when it stops working and which components are responsible is therefore an important part of the research process.

Statistical Methodology

Our market research draws on broader work in applied statistics, including:

From Statistical Relationship to Useful Information

Financial datasets contain enormous numbers of statistically observable relationships. Only a small fraction are economically useful.

Our research therefore places particular emphasis on the transition from:

observation → statistical relationship → predictive information → implementable decision

At each stage, apparent information can be lost through instability, changing market structure, transaction costs, model error or incorrect interpretation.

The objective is to identify relationships that remain useful after those effects are taken into account.

Research Philosophy

We regard markets as dynamic information systems rather than collections of independent price series.

That perspective naturally leads from high-frequency microstructure to information transmission between securities, sectors and markets, and ultimately to the systematic structures described by broader asset-pricing models.

The scales are different.

The underlying information process may not be.