Machine Learning in Risk Measurement: Gaussian Process Regression for Value-at-Risk and Expected Shortfall

2018 ◽  
Author(s):  
Sascha Wilkens
Keyword(s):  
Machine Learning ◽  
At Risk ◽  
Gaussian Process ◽  
Value At Risk ◽  
Gaussian Process Regression ◽  
Expected Shortfall ◽  
Risk Measurement

Exchange Spin Coupling from Gaussian Process Regression

2020 ◽  
Author(s):  
Marc Philipp Bahlke ◽  
Natnael Mogos ◽  
Jonny Proppe ◽  
Carmen Herrmann
Keyword(s):  
Machine Learning ◽  
Gaussian Process ◽  
Gaussian Process Regression ◽  
Molecular Magnets ◽  
Molecular Structures ◽  
Spin Coupling ◽  
Structure Property ◽  
Data Set ◽  
Uncertainty Estimates

Heisenberg exchange spin coupling between metal centers is essential for describing and understanding the electronic structure of many molecular catalysts, metalloenzymes, and molecular magnets for potential application in information technology. We explore the machine-learnability of exchange spin coupling, which has not been studied yet. We employ Gaussian process regression since it can potentially deal with small training sets (as likely associated with the rather complex molecular structures required for exploring spin coupling) and since it provides uncertainty estimates (“error bars”) along with predicted values. We compare a range of descriptors and kernels for 257 small dicopper complexes and find that a simple descriptor based on chemical intuition, consisting only of copper-bridge angles and copper-copper distances, clearly outperforms several more sophisticated descriptors when it comes to extrapolating towards larger experimentally relevant complexes. Exchange spin coupling is similarly easy to learn as the polarizability, while learning dipole moments is much harder. The strength of the sophisticated descriptors lies in their ability to linearize structure-property relationships, to the point that a simple linear ridge regression performs just as well as the kernel-based machine-learning model for our small dicopper data set. The superior extrapolation performance of the simple descriptor is unique to exchange spin coupling, reinforcing the crucial role of choosing a suitable descriptor, and highlighting the interesting question of the role of chemical intuition vs. systematic or automated selection of features for machine learning in chemistry and material science.

scholarly journals Optimisation of Time-Varying Asset Pricing Models with Penetration of Value at Risk and Expected Shortfall

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 394
Author(s):  
Adeel Nasir ◽  
Kanwal Iqbal Khan ◽  
Mário Nuno Mata ◽  
Pedro Neves Mata ◽  
Jéssica Nunes Martins
Keyword(s):  
At Risk ◽  
Asset Pricing ◽  
Stock Returns ◽  
Value At Risk ◽  
Expected Shortfall ◽  
Time Varying ◽  
Pricing Models ◽  
Asset Pricing Model ◽  
Asset Pricing Models ◽  
Market Beta

This study aims to apply value at risk (VaR) and expected shortfall (ES) as time-varying systematic and idiosyncratic risk factors to address the downside risk anomaly of various asset pricing models currently existing in the Pakistan stock exchange. The study analyses the significance of high minus low VaR and ES portfolios as a systematic risk factor in one factor, three-factor, and five-factor asset pricing model. Furthermore, the study introduced the six-factor model, deploying VaR and ES as the idiosyncratic risk factor. The theoretical and empirical alteration of traditional asset pricing models is the study’s contributions. This study reported a strong positive relationship of traditional market beta, value at risk, and expected shortfall. Market beta pertains its superiority in estimating the time-varying stock returns. Furthermore, value at risk and expected shortfall strengthen the effects of traditional beta impact on stock returns, signifying the proposed six-factor asset pricing model. Investment and profitability factors are redundant in conventional asset pricing models.

EXPECTED SHORTFALL PADA PORTOFOLIO OPTIMAL DENGAN METODE SINGLE INDEX MODEL (Studi Kasus pada Saham IDX30)

2021 ◽  
Vol 10 (2) ◽  
pp. 269-278
Author(s):  
Eis Kartika Dewi ◽  
Dwi Ispriyanti ◽  
Agus Rusgiyono
Keyword(s):  
At Risk ◽  
Value At Risk ◽  
Market Price ◽  
Expected Shortfall ◽  
Optimal Portfolio ◽  
Share Price ◽  
Single Index ◽  
Index Model ◽  
Single Index Model ◽  
Stock Investment

Stock investment is a commitment to a number of funds in marketable securities which shows proof of ownership of a company with the aim of obtaining profits in the future. For obtaining optimal returns from stock investments, investors are expected to form optimal portfolios. The optimal portfolio formation using the Single Index Model is based on the observation that a stock fluctuates in the direction of the market price. It shows that most stocks tend to experience price increases if the market share price rises, and vice versa. Selection of optimal portfolio-forming stocks on IDX30 using the Single Index Model method produces 4 stocks, that are BRPT (Barito Pacific Tbk.) with weight 31.134%, ICBP (Indofood CBP Sukses Makmur Tbk.) 17.138%, BBCA (Bank Central Asia Tbk.) 51.331% and SMGR (Semen Indonesia (Persero) Tbk.) 0.397%. Every investment must have a risk, for that investors need to calculate the possible risks that occur before investing. To calculate risk, Expected Shortfall (ES) is used as a measure of risk that is better than Value at Risk (VaR) because ES fulfill the subadditivity. At the 95% confidence level, the ES value is 23.063% while the VaR value is 10.829%. This means that the biggest possible risk that an optimal portfolio investor will receive using the Single Index Model for the next five weeks is 23.063%.Keywords : Portfolio, Single Index Model, Expected Shortfall, Value at Risk.

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