Neural Networks and Value at Risk

Abstract

Inspired by Gu, Kelly & Xiu’s (GKX, 2020) advancement of the measurement of asset risk premia via the introduction of feed forward neural networks, we investigate, if machine learning can advance the process of ‘estimating Value at Risk (VaR) thresholds’. For this purpose, we compare simple (GKX’s feed forward) and advanced (convolutional, recurrent) neural networks with established approaches (Hidden Markov Model, Mean/Variance). Utilizing a generative regime switching framework, we perform Monte-Carlo simulations of asset returns for Value at Risk threshold estimation. Using equity markets and long term bonds as test assets in the global, US, Euro area and UK setting over an up to 1,250 weeks sample horizon ending in August 2018, we investigate neural networks along three design steps relating (i) to the initialization of the neural network, (ii) its incentive function according to which it has been trained and (iii) the amount of data we feed. First, we compare neural networks with random seeding with networks that are initialized via estimations from the best-established model (i.e. the Hidden Markov). We find latter to outperform in terms of the frequency of VaR breaches (i.e. the realized return falling short of the estimated VaR threshold). Second, we balance the incentive structure of the loss function of our networks by adding a second objective to the training instructions so that the neural networks optimize for accuracy while also aiming to stay in empirically realistic regime distributions (i.e. bull vs. bear market frequencies). In particular this design feature enables the balanced incentive recurrent neural network (RNN) to outperform the single incentive RNN as well as any other neural network or established approach by statistically and economically significant levels. Third, we half our training data set of 2,000 days. We find our networks when fed with substantially less data (i.e. 1,000 days) to perform significantly worse which highlights a crucial weakness of neural networks in their dependence on very large data sets. Hence, we conclude that well designed neural networks, i.e. a recurrent neural network initialized with best current evidence and balanced incentives – can potentially advance the protection offered to institutional investors by VaR thresholds through a reduction in threshold breaches. However, such advancements rely on the availability of a long data history, which may not always be available in practice when estimating asset management VaR thresholds.

Keywords: Asset Management, Downside Risk, Initialization, Loss Function, Machine Learning, Neural Networks

JEL Classification: C01, C57, C58, G01, G17