Estimation of the value-at-risk (VaR) of a large portfolio of assets is an important task for financial institutions. As the joint log-returns of asset prices can often be projected to a latent space of a much smaller dimension, the use of a variational autoencoder (VAE) for estimating the VaR is a natural suggestion. To ensure the bottleneck structure of autoencoders when learning sequential data, we use a temporal VAE (TempVAE) that avoids the use of an autoregressive structure for the observation variables. However, the low signal-to-noise ratio of financial data in combination with the auto-pruning property of a VAE typically makes use of a VAE prone to posterior collapse. Therefore, we use annealing of the regularization to mitigate this effect. As a result, the auto-pruning of the TempVAE works properly, which also leads to excellent estimation results for the VaR that beat classical GARCH-type, multivariate versions of GARCH and historical simulation approaches when applied to real data.
We consider portfolio optimization in a regime‐switching market. The assets of the portfolio are modeled through a hidden Markov model (HMM) in discrete time, where drift and volatility of the single assets are allowed to switch between different states. We consider different parametrizations of the involved asset covariances: statewise uncorrelated assets (though linked through the common Markov chain), assets correlated in a state‐independent way, and assets where the correlation varies from state to state. As a benchmark, we also consider a model without regime switches. We utilize a filter‐based expectation‐maximization (EM) algorithm to obtain optimal parameter estimates within this multivariate HMM and present parameter estimators in all three HMM settings. We discuss the impact of these different models on the performance of several portfolio strategies. Our findings show that for simulated returns, our strategies in many settings outperform naïve investment strategies, like the equal weights strategy. Information criteria can be used to detect the best model for estimation as well as for portfolio optimization. A second study using real data confirms these findings.
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