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The quantitative path to macro information efficiency

Financial markets are not information efficient with respect to macroeconomic information because data are notoriously ‘dirty’, relevant economic research is expensive, and establishing stable relations between macro data and market performance is challenging. However, statistical programming and packages have prepared the ground for great advances in macro information efficiency. The quantitative path to macro information efficiency leads over three stages. The first is elaborate in-depth data wrangling that turns raw macro data (and even textual information) into clean and meaningful time series whose frequency and time stamps accord with market prices. The second stage is statistical learning, be it supervised (to validate logical hypotheses), or unsupervised (to detect patterns). The third stage is realistic backtesting to verify the value of the learning process and to assess the commercial viability of a macro trading strategy.

The below is a high-level summary linking a series of previous posts.

Macro information inefficiency

Macro information refers to public information that is relevant for financial asset and derivatives prices at the country, asset-class or sector level. It includes economic data, such as national accounts, business surveys, government balance sheets, market data, such as prices, carry and valuation metrics, and alternative data. Information efficiency of markets means that prices reflect available information. Efficient financial markets would produce and use macro research to the extent that incremental investment returns and social benefits exceed costs.

It is easy to understand why markets do not incorporate all macro information. Information is expensive and asset managers only invest in information as long as markets are sufficiently inefficient. What is less well understood is that barriers to using any kind of macro information in investment management are high (view summary here). This is so because macro data often have poor quality, require much additional research for interpretation, and relate to asset prices only indirectly. Compared to market concepts, such as trend and carry, economic information is further from the core business and understanding of portfolio managers. Even where institutions do employ macro researchers there is often a gap between economic views and actual investment strategies, reflecting lack of trust and lack of clear implications of the former for the latter.

Macro information inefficiency is consistent with the evidence of numerous behavioral biases of both retail and professional investors and the prevalence of simplistic trading rules in algorithmic strategies.

Statistical programming

The rise of statistical programming is enabling the expansion of data science for the macro trading space. Data science is simply a set of methods to extract knowledge from data. The methods do not necessarily have to be complicated and the datasets do not necessarily have to be “big”. Indeed, in the macroeconomic space data do not expand as rapidly as in other areas, because data frequency is typically low (often just monthly and quarterly), the set of relevant countries and currency areas is limited, and there is not much scope for adding data from experimental settings.

With modern tools it is easy for portfolio management to incorporate data science. It takes essentially three things: [1] API access to relevant economics and markets databases, such as Refinitiv, Macrobond, Bloomberg, Haver, Quandl, Trading Economics and so forth, [2] research into what the economic and market time series actually mean and how that should affect market prices, and [3] a suitable programming platform to work with the data. The latter typically calls for either R or Python:

  • The R project provides a programming language and work environment for statistical analysis. It is not just for programmers (view post here). Even with limited coding skills R outclasses Excel spreadsheets and boosts information efficiency. Like Excel, the R environment is built around data structures, albeit far more flexible ones. Operations on data are simple and efficient, particularly for import, wrangling, and complex transformations. Moreover, R is a functional programming language. This means that functions can use other functions as arguments, making code succinct and readable. Specialized “functions of functions” map elaborate coding subroutines to data structures. Finally, R users have access to a repository of almost 15,000 packages of function for all sorts of operations and analyses.
  • Python is an interpreted, object-oriented, high-level programming language, which is also highly convenient for data analysis through libraries such as Numpy (foundational package for scientific computing), SciPy (collection of packages for scientific computing), pandas (structures and functions to work with data), matplotlib (package for plots and other 2D data visualizations), and IPython (robust and productive environment for interactive and exploratory computing). Python is exceptionally popular among programmers. Unlike domain-specific programming languages, such as R, Python is not only suitable for research and prototyping but also for building the production systems.

N.B.: A newer open-source statistical programming language, Julia, has appeared in 2012. It distinguishes itself from R and Python through greater speed. However, it has not yet established itself in terms of community and packages to an extent that is comparable with R and Python.

Statistical wrangling

In order to be relevant for portfolio management, macro information must be relatable to market prices, both conceptually and in terms of timing. Alas relating macro and asset return data is often obstructed by many deficiencies in the former:

  • Short history: Many economic data series, particularly in emerging economies, have only 5-20 years of history, which does not allow assessing their impact across many business cycles. Often this necessitates combining them with older discontinued series or substitutes that market had followed in the more distant past.
  • Revisions: Most databases simply record economic time series in their recently revised state. However, initial and intermediate releases of many economic indicators, such as GDP or business surveys, may have looked significantly different. This means that the information recorded for the past actually is not the information that was available in the past.
  • Time inconsistency: Unlike for market data, time of reference and time of availability for economic data are not the same. The information for industrial production in January may only be available in late March. This information is typically not embedded in the databases of the main service providers.
  • Calendar effects: Many economic data series are strongly influenced by seasonal patterns, working day numbers, and school holiday schedules. While some series are calendar adjusted by the source, the adjustment is typically incomplete and not comparable across countries.
  • Distortions: Almost all economic data are at least temporarily distorted relative to the concept they are meant to measure. For example, inflation data are often affected by one-off tax changes and administered price hikes. Production and balance sheet data often display disruptions due to strikes or natural disasters and sudden breaks due to changes in methodology.

Therefore, in order to make economic data tradable, they require an in-depth elaborate process of data wrangling. Generally, data wrangling means the transformation of raw irregular data into a clean tidy data set. In many sciences, this simply requires reformatting and relabelling. For macroeconomics, data wrangling takes a lot more.

  • Common technical procedures include[1] splicing different series across time according to pre-set rules, [2] combining various revised versions of series into a single ‘available at the time’ series, and [3] assigning publication time stamps to the periodic updates of time series.
  • Additional statistical procedures for economic data include seasonal adjustment, working data adjustment, holiday adjustment, outlier adjustment and flexible filtering of volatile series. There are specialized packages in R and Python with functions that assist with these operations.

Market data are generally easier to wrangle than economic data, but also suffer from major deficiencies. The most common issue are missing or bad price data. There is – at present – no commercial database for a broad range of generic financial returns (as opposed to mere price series). Nor are there widely used packages of functions that specifically wrangle financial return data across asset classes.

News and comments are major drivers for asset prices, maybe more so than conventional price and economic data. Yet it is impossible for any financial professional to read and analyse the vast and growing flow of written information. This is becoming the domain of natural language processing; a technology that supports the quantitative evaluation of humans’ natural language (view post here). It delivers textual information in a structured form that makes it usable for financial market analysis. A range of useful tools is now available for extracting and analysing financial news and comments.

Statistical Learning

Statistical learning refers to a set of tools for modelling and understanding complex datasets. Understanding statistical learning is critical in modern financial markets, even for non-quants (view post here). That is because statistical learning provides guidance on how the experiences of investors in markets shape their future behaviour. Statistical learning works with complex datasets in order to forecast returns or to estimate the impact of specific events. Methods range from simple regression to complex machine learning. Simplicity can deliver superior returns if it avoids “overfitting”, i.e. gearing models to recent experiences. Success must be measured in “out-of-sample” predictive power after a model has been selected and estimated.

Machine learning is based on statistical learning methods but partly automates the construction of forecast models through the study of data patterns, the selection of best functional form for a given level of complexity and the selection of the best level of complexity for out of sample forecasting. Beyond speed and convenience, machine learning methods is highly useful for macro trading research because it enables backtests that are based on methods rather than on specific factors. Backtest of specific factors are mostly invalid because the factor choice is typically shaped by historical experiences.

Machine learning is conventionally divided into three main fields: supervised learning, unsupervised learning, and reinforcement learning.

  • In supervised learning the researcher posits input variables and output variables and uses an algorithm to learn which function maps the former to the latter. This principle underlies the majority of statistical learning applications in financial markets. A classic example is the assessment of what the change in interest rate differential between two countries means for the dynamics of their exchange rate.
    Supervised learning can be divided into regression, where the output variable is a real number, and classification, where the output variable is a category, such as “policy easing” or “policy tightening” for central bank decisions.
  • Unsupervised learning only knows input data. Its goal is to model the underlying structure or distribution of the data in order to learn previously unknown patterns. Application of unsupervised machine learning techniques includes clustering (partitioning the data set according to similarity), anomaly detection, association mining and dimension reduction (see below).
  • Reinforcement learning is a specialized application of (deep) machine learning that interacts with the environment and seeks to improve on the way it performs a task so as to maximize its reward (view post here). The computer employs trial and error. The model designer defines the reward but gives no clues as to how to solve the problem. Reinforcement learning holds potential for trading systems because markets are highly complex and quickly changing dynamic systems. Conventional forecasting models have been notoriously inadequate. A self-adaptive approach that can learn quickly from the outcome of actions may be more suitable.

Linear regression remains the most popular tool for supervised learning in financial markets (apart from informal chart and correlation analysis). It can be the appropriate model if it relates market returns to previous available information in a theoretically plausible functional form. However, regression is also often applied to concurrent data, i.e. observations of data series at the same point in time. Such regressions of contemporaneous data are very popular in the research of financial institutions but are rarely backed up by solid underlying theory for the presumed one-dimensional relation between dependent and explanatory variables.

Structural vector autoregression (SVAR) is a quite practical model class for empirical macroeconomics. It can also be employed for macro trading strategies, because it helps to identify specific market and macro shocks (view post here). For example, SVAR can identify short-term policy, growth or inflation expectation shocks. Once a shock is identified it can be used for trading in two ways. First, one can compare the type of shock implied by markets with the actual news flow and detect fundamental inconsistencies. Second, different types of shocks may entail different types of subsequent asset price dynamics and may form a basis for systematic strategies.

One important area of statistical learning for investment research is dimension reduction. This refers to methods that condense the bulk of the information of a vast multitude of macroeconomic time series into a smaller set that distills the relevant trends for investors. In macroeconomics there are many related data series that have only limited and highly correlated information content for markets. There are three types of statistical dimension reduction methods. The first type selects a subset of “best” explanatory variables (Elastic Net or Lasso, view post here). The second type selects a small set of latent background factors of all explanatory variables and then uses these background factors for prediction (Dynamic Factor Models). The third type generates a small set of functions of the original explanatory variables that historically would have retained their explanatory power and then deploys these for forecasting (Sufficient Dimension Reduction).


Backtesting is meant to assess how well a trading strategy idea would have worked in the past. Statistical programming makes it easy to backtest trading strategies. However, its computational power and convenience can also be corrosive the investment process due to its tendency to discover temporary patterns while data samples for cross-validation are limited. Moreover, the business of algorithmic trading strategies, unfortunately, provides strong incentives for overfitting models and embellishing backtests (view post here). Similarly, academic researchers in the field of trading factors often feel compelled to resort to data mining in order to produce publishable ‘significant’ empirical findings (view post here).

Good backtests require sound principles and integrity (view post here). Sound principles should include [1] formulating a logical economic theory upfront, [2] choosing sample data upfront, [3] keeping the model simple and intuitive, and [4] limiting try-outs when testing ideas. Realistic performance expectations of trading strategies should be based on a range of plausible versions of a strategy, not an optimized one. Bayesian inference works well for that approach, as it estimates both the performance parameters and their uncertainty. The most important principle of all is integrity: aiming to produce good research rather than good backtests and to communicate statistical findings honestly rather than selling them.


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