Spotting co-movement breakdowns with neural networks

The co-movement of financial assets is a tricky thing to measure. It is dynamic and prone to significant shifts during market upheavals. One possible approach could be to use some form of principal component analysis (PCA), a statistical technique that reduces the dimensionality of a dataset while explaining much of its variability. But most market practitioners consider PCA unfit for this purpose.

“It only really works for linear Gaussian systems, which is as far from finance as you could imagine,” says Stephen Roberts, director of the Oxford-Man Institute of Quantitative Finance, and Man Group professor of machine learning at Oxford University.

Together with Bryan Lim, a researcher at the Oxford-Man Institute, and Stefan Zohren, a senior researcher at Man Group, Roberts proposes a solution that uses autoencoders, a type of artificial neural network that relies on a bottleneck structure to reduce the size of an input dataset to a few latent factors. They introduce an indicator – the autoencoder reconstruction ratio (ARR) – which is designed to capture assets’ co-movements in real time by measuring the so-called average reconstruction error. The reconstruction error measures how well the few latent factors generated by the autoencoder are able to reproduce the original dataset.

The basic idea is that when assets move more independently – that is, their co-movements decrease – the latent factors lose some of their explanatory power and will reconstruct the original data less accurately. As the average reconstruction error increases, so does the ARR – signalling a scenario where the market is more stable and diversification strategies are more effective.

Conversely, when the latent factors are able to reconstruct more of the original data, the reconstruction error is lower and the ARR goes down, indicating that co-movements have increased. Here, correlations shoot up to dangerous levels and markets could see a spike in volatility or a drawdown, resulting in a breakdown of diversification strategies.

The ARR can also be applied to improve forecasting of realised volatility and market crashes. Numerical tests suggest this is more effective with high-frequency data. The paper shows it performs better at a five-minute frequency than with daily market data. “Being able to forecast intraday volatility is obviously very important. The ARR improves the forecast and thus helps to effectively risk-manage your position,” says Zohren.

The technique could be used to improve volatility scaling for systematic trading strategies. “The ARR enables portfolios to respond rapidly to heightened levels of asset co-movements that historically have been indicators of wide-scale market stress,” says Anthony Ledford, chief scientist at Man AHL.

Importantly, the use of ARR is not bounded by the size of the dataset, but rather by computational power – an ever-growing resource. “There is no theoretical limit to the number of assets and asset classes this metric can handle simultaneously. The only limit is computational. [With] too many assets, the answer might take too long to arrive to be useful for trading purposes,” explains Roberts.

[PCA] only really works for linear Gaussian systems, which is as far from finance as you could imagine

Stephen Roberts, Oxford-Man Institute of Quantitative Finance

The idea to employ autoencoders came from Lim. “The insight Brian [Lim] had was to realise that you can use these autoencoders to form a kind of deep sparse compression of financial assets. And you can look to see how much you’ve managed to compress in this lower dimensional representation space,” explains Roberts.

The ARR is analogous to a real-time, non-linear version of the so-called absorption ratio, which measures co-movement changes by describing the portion of variance within a system that is explained by PCA. “What we’re trying to do here is inspired by this idea [of the absorption ratio] and turns it into a nonlinear model,” says Zohren. “Interesting features and dependencies, which you could only learn using machine learning methods, are captured by the encoder. The encoder effectively takes the returns and tries to encode them in the model, which is then used for reconstructing the returns.”

“In the reconstruction ratio, the autoencoder takes the place of the PCA,” he adds.

Autoencoders are not new in finance. They are designed to recognise patterns and identify exceptions, and have been widely used in fraud detection – and to some extent, to detect trading signals. In 2018, Alexei Kondratyev, global head of data analytics at Standard Chartered Bank, proposed using autoencoders to analyse yield curves.

Kondratyev sees Lim, Zohren and Roberts’s results as part of a wider and welcome trend in quant finance. “It’s yet another paper that shows how we should move beyond PCA and other simple linear models, towards more sophisticated nonlinear models,” he says. “Now we have computational power and decades of progress in machine learning. We have the tools that allow us to do more and better than just using PCA.”

There is room for further development. One avenue could be to connect the trading signals from the model to an execution system. “An interesting extension to this would be to expand it to tie in with trade execution algorithms,” says Roberts.