Systematic equity allocation across countries for dollar-based investors

August 16, 2025

Jupyter Notebook

This post demonstrates that country allocation with macroeconomic factors can materially enhance the returns on international equity portfolios in dollar terms. We identify a range of economic developments that, according to standard theory and in conjunction with market inattention, should predict the outperformance of countries either through exchange rate appreciation or higher local-currency equity returns. These developments are captured in backtestable economic factor scores, built from point-in-time macro-quantamental indicators. To select and combine these factors into trading signals without hindsight bias, we employ sequential machine learning. Empirical evidence based on 19 international markets shows highly significant predictive power and consistent material value arising from cross-country allocation alone. A simulation of U.S. dollar-based cross-country allocation of real money investment also reveals material long-term outperformance relative to an equally-weighted international portfolio or a U.S. portfolio.

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Boosting macro trading signals

April 26, 2025

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Boosting is a machine learning ensemble method that combines the predictions of a chain of basic models, whereby each model seeks to address the shortcomings of the previous one. This post applies adaptive boosting (Adaboost) to trading signal optimisation. Signals are constructed with macro factors to guide positioning in a broad range of global FX forwards.
Boosting is beneficial for learning from a wide and heterogeneous set of markets over time, because it is well-suited for exploiting the diversity of experiences across countries and global economic states. Empirically, we generate machine learning-based signals that use regularized regression and random forest regression, and compare processes with and without adaptive boosting methods. For both regression types, machine learning prefers boosting as datasets get larger and, by doing so, creates more profitable signals.

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Macro trading signal optimization: basic statistical learning methods

March 15, 2025

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A key task of macro strategy development is condensing candidate factors into a single positioning signal. Statistical learning offers methods for selecting factors, combining them to a return prediction, and classifying the market state. These methods efficiently incorporate diverse information sets and allow running realistic backtests.
This post applies sequential statistical learning to optimal signal generation for interest rate swap positions. Sequential methods update, estimate, and select models over time, adapting to growing development data sets, and apply signals based on the latest optimal model each month. These methods require intelligent choices on model versions, hyperparameters, cross-validation splitters, and model quality criteria. Sequential statistical learning has generally done a good job in discarding irrelevant information and has produced greater accuracy and higher risk-adjusted returns than simple factor averages.

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Statistical learning for sectoral equity allocation

September 4, 2024

Jupyter Notebook of factor calculation Jupyter Notebook of statistical learning

There is sound reason and evidence for the predictive power of macro indicators for relative sectoral equity returns. However, the relations between economic information and equity sector performance can be complex. Considering the broad range of available point-in-time macro-categories that are now available, statistical learning has become a compelling method for discovering macro predictors and supporting prudent and realistic backtests of related strategies. This post shows a simple five-step method to use statistical learning to select and combine macro predictors from a broad set of categories for the 11 major equity sectors in 12 developed countries. The learning process produces signals based on changing models and factors per the statistical evidence. These signals have been positive predictors for relative returns of all sectors versus a broad basket. Combined into a single strategy, these signals create material and uncorrelated investor value through sectoral allocation alone.

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How “beta learning” improves macro trading strategies

June 1, 2024

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Macro beta is the sensitivity of a financial contract’s return to a broad economic or market factor. Macro betas broaden the traditional concept of equity market betas and can often be estimated using financial contract baskets. Macro sensitivities are endemic in trading strategies, diluting alpha, undermining portfolio diversification, and distorting backtests. However, it is possible to immunize strategies through “beta learning,” a statistical learning method that supports identifying appropriate models and hyperparameters and allows backtesting of hedged strategies without look-ahead bias. The process can be easily implemented with existing Python classes and methods. This post illustrates the powerful beneficial impact of macro beta estimation and its application on an emerging market FX carry strategy.

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FX trading signals with regression-based learning

April 23, 2024

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Regression-based statistical learning helps build trading signals from multiple candidate constituents. The method optimizes models and hyperparameters sequentially and produces point-in-time signals for backtesting and live trading. This post applies regression-based learning to macro trading factors for developed market FX trading, using a novel cross-validation method for expanding panel data. Sequentially optimized models consider nine theoretically valid macro trend indicators to predict FX forward returns. The learning process has delivered significant predictors of returns and consistent positive PnL generation for over 20 years. The most important macro-FX signals, in the long run, have been relative labor market trends, manufacturing business sentiment changes, relative inflation expectations, and terms of trade dynamics.

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Macroeconomic data and systematic trading strategies

April 23, 2024

While economic information undeniably wields a significant and widespread influence on financial markets, the systematic incorporation of macroeconomic data into trading strategies has thus far been limited. This reflects skepticism towards economic theory and serious data problems, such as revisions, distortions, calendar effects, and, generally, the lack of point-in-time formats. However, the emergence of industry-wide quantamental indicators and the rise of statistical learning methods in financial markets make macroeconomic information more practical and powerful. Successful demonstrations of statistical learning and macro-quantamental indicators have been achieved, with various machine learning techniques poised to further improve the utilization of economic information.

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Regression-based macro trading signals

February 24, 2024

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Regression is one method for combining macro indicators into a single trading signal. Specifically, statistical learning based on regression can optimize model parameters and hyperparameters sequentially and produce signals based on whatever model has predicted returns best up to a point in time. This method learns from growing datasets and produces valid point-in-time signals for backtesting. However, whether regression delivers good signals depends on managing the bias-variance trade-off of machine learning. This post provides guidance on pre-selecting the right regression models and hyperparameter grids based on theory and empirical evidence. It considers the advantages and disadvantages of various regression methods, including non-negative least squares, elastic net, weighted least squares, least absolute deviations, and nearest neighbors.

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Optimizing macro trading signals – A practical introduction

December 16, 2023

Jupyter Notebook

Based on theory and empirical evidence, point-in-time indicators of macroeconomic trends and states are strong candidates for trading signals. A key challenge is to select and condense them into a single signal. The simplest (and often successful) approach is conceptual risk parity, i.e., an equally weighted average of normalized scores. However, there is scope for optimization. Statistical learning offers methods for sequentially choosing the best model class and other hyperparameters for signal generation, thus supporting realistic backtests and automated operation of strategies.
This post and an attached Jupyter Notebook show implementations of sequential signal optimization with the scikit-learn package and some specialized extensions. In particular, the post applies statistical learning to sequential optimization of three important tasks: feature selection, return prediction, and market regime classification.

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How to measure the quality of a trading signal

October 7, 2023

The quality of a trading signal depends on its ability to predict future target returns and to generate material economic value when applied to positioning. Statistical metrics of these two properties are related but not identical. Empirical evidence must support both. Moreover, there are alternative criteria for predictive power and economic trading value, which are summarized in this post. The right choice depends on the characteristics of the trading signal and the objective of the strategy. Each strategy calls for a bespoke appropriate criterion function. This is particularly important for statistical learning that seeks to optimize hyperparameters of trading models and derive meaningful backtests.

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