Large-scale Time-Varying Portfolio Optimisation using Graph Attention Networks

Apart from assessing individual asset performance, investors in financial markets also need to consider how a set of firms performs collectively as a portfolio. Whereas traditional Markowitz-based mean-variance portfolios are widespread, network-based optimisation techniques have built upon these developments. However, most studies do not contain firms at risk of default and remove any firms that drop off indices over a certain time. This is the first study to incorporate risky firms and use all the firms in portfolio optimisation. We propose and empirically test a novel method that leverages Graph Attention networks (GATs), a subclass of Graph Neural Networks (GNNs). GNNs, as deep learning-based models, can exploit network data to uncover nonlinear relationships. Their ability to handle high-dimensional features and accommodate customised layers for specific purposes makes them particularly appealing for large-scale problems such as mid- and small-cap portfolio optimization. This study utilises 30 years of data on mid-cap firms, creating graphs of firms using distance correlation and the Triangulated Maximally Filtered Graph approach. These graphs are the inputs to a GAT model that we train using custom layers which impose weight and allocation constraints and a loss function derived from the Sharpe ratio, thus directly maximising portfolio risk-adjusted returns. This new model is benchmarked against a network characteristic-based portfolio, a mean variance-based portfolio, and an equal-weighted portfolio. The results show that the portfolio produced by the GAT-based model outperforms all benchmarks and is consistently superior to other strategies over a long period while also being informative of market dynamics.

A Distributionally Robust Optimisation Approach to Fair Credit Scoring

Credit scoring has been catalogued by the European Commission and the Executive Office of the US President as a high-risk classification task, a key concern being the potential harms of making loan approval decisions based on models that would be biased against certain groups. To address this concern, recent credit scoring research has considered a range of fairness-enhancing techniques put forward by the machine learning community to reduce bias and unfair treatment in classification systems. While the definition of fairness or the approach they follow to impose it may vary, most of these techniques, however, disregard the robustness of the results. This can create situations where unfair treatment is effectively corrected in the training set, but when producing out-of-sample classifications, unfair treatment is incurred again. Instead, in this paper, we will investigate how to apply Distributionally Robust Optimisation (DRO) methods to credit scoring, thereby empirically evaluating how they perform in terms of fairness, ability to classify correctly, and the robustness of the solution against changes in the marginal proportions. In so doing, we find DRO methods to provide a substantial improvement in terms of fairness, with almost no loss in performance. These results thus indicate that DRO can improve fairness in credit scoring, provided that further advances are made in efficiently implementing these systems. In addition, our analysis suggests that many of the commonly used fairness metrics are unsuitable for a credit scoring setting, as they depend on the choice of classification threshold.

Attention-based Dynamic Multilayer Graph Neural Networks for Loan Default Prediction

Whereas traditional credit scoring tends to employ only individual borrower- or loan-level predictors, it has been acknowledged for some time that connections between borrowers may result in default risk propagating over a network. In this paper, we present a model for credit risk assessment leveraging a dynamic multilayer network built from a Graph Neural Network and a Recurrent Neural Network, each layer reflecting a different source of network connection. We test our methodology in a behavioural credit scoring context using a dataset provided by U.S. mortgage financier Freddie Mac, in which different types of connections arise from the geographical location of the borrower and their choice of mortgage provider. The proposed model considers both types of connections and the evolution of these connections over time. We enhance the model by using a custom attention mechanism that weights the different time snapshots according to their importance. After testing multiple configurations, a model with GAT, LSTM, and the attention mechanism provides the best results. Empirical results demonstrate that, when it comes to predicting probability of default for the borrowers, our proposed model brings both better results and novel insights for the analysis of the importance of connections and timestamps, compared to traditional methods.

Deep residential representations: Using unsupervised learning to unlock elevation data for geo-demographic prediction

LiDAR (short for "Light Detection And Ranging" or "Laser Imaging, Detection, And Ranging") technology can be used to provide detailed three-dimensional elevation maps of urban and rural landscapes. To date, airborne LiDAR imaging has been predominantly confined to the environmental and archaeological domains. However, the geographically granular and open-source nature of this data also lends itself to an array of societal, organizational and business applications where geo-demographic type data is utilised. Arguably, the complexity involved in processing this multi-dimensional data has thus far restricted its broader adoption. In this paper, we propose a series of convenient task-agnostic tile elevation embeddings to address this challenge, using recent advances from unsupervised Deep Learning. We test the potential of our embeddings by predicting seven English indices of deprivation (2019) for small geographies in the Greater London area. These indices cover a range of socio-economic outcomes and serve as a proxy for a wide variety of downstream tasks to which the embeddings can be applied. We consider the suitability of this data not just on its own but also as an auxiliary source of data in combination with demographic features, thus providing a realistic use case for the embeddings. Having trialled various model/embedding configurations, we find that our best performing embeddings lead to Root-Mean-Squared-Error (RMSE) improvements of up to 21% over using standard demographic features alone. We also demonstrate how our embedding pipeline, using Deep Learning combined with K-means clustering, produces coherent tile segments which allow the latent embedding features to be interpreted.

A transformer-based model for default prediction in mid-cap corporate markets

In this paper, we study mid-cap companies, i.e. publicly traded companies with less than US $10 billion in market capitalisation. Using a large dataset of US mid-cap companies observed over 30 years, we look to predict the default probability term structure over the medium term and understand which data sources (i.e. fundamental, market or pricing data) contribute most to the default risk. Whereas existing methods typically require that data from different time periods are first aggregated and turned into cross-sectional features, we frame the problem as a multi-label time-series classification problem. We adapt transformer models, a state-of-the-art deep learning model emanating from the natural language processing domain, to the credit risk modelling setting. We also interpret the predictions of these models using attention heat maps. To optimise the model further, we present a custom loss function for multi-label classification and a novel multi-channel architecture with differential training that gives the model the ability to use all input data efficiently. Our results show the proposed deep learning architecture's superior performance, resulting in a 13% improvement in AUC (Area Under the receiver operating characteristic Curve) over traditional models. We also demonstrate how to produce an importance ranking for the different data sources and the temporal relationships using a Shapley approach specific to these models.

The value of text for small business default prediction: A deep learning approach

Compared to consumer lending, Micro, Small and Medium Enterprise (mSME) credit risk modelling is particularly challenging, as, often, the same sources of information are not available. To mitigate limited data availability, it is standard policy for a loan officer to provide a textual loan assessment. In turn, this statement is analysed by a credit expert alongside any available standard credit data. In our paper, we exploit recent advances from the field of Deep Learning and Natural Language Processing (NLP), including the BERT (Bidirectional Encoder Representations from Transformers) model, to extract information from 60000+ textual assessments. We consider the performance in terms of AUC (Area Under the Curve) and Balanced Accuracy and find that the text alone is surprisingly effective for predicting default. Yet, when combined with traditional data, it yields no additional predictive capability. We do find, however, that deep learning with categorical embeddings is capable of producing a modest performance improvement when compared to alternative machine learning models. We explore how the loan assessments influence predictions, explaining why despite the text being predictive, no additional performance is gained. This exploration leads us to a series of recommendations on a new strategy for the collection of future mSME loan assessments.