Asset Returns and State-Dependent Risk Preferences

We propose a consumption-based capital asset pricing model in which the representative agent's preferences display state-dependent risk aversion. We obtain a valuation equation in which the vector of excess returns on equity includes both consumption risk as well as the risk associated with variations in preferences. We develop a simple model that can be estimated without specifying the functional form linking risk aversion with state variables. Our estimates are based on Markov chain Monte Carlo estimation of exact discrete-time parameterizations for linear diffusion processes. Since consumption risk is not forced to account for the entire risk premium, our results contrast sharply with estimates from models in which risk aversion is state-independent. We find that relaxing fixed risk preferences yields estimates for relative risk aversion that are (i) reasonable by usual standards, (ii) correlated with both consumption and returns and (iii) indicative of an additional preference risk of holding the assets. Nous suggérons un modèle d'équilibre de prix des actifs où les préférences de l'agent représentatif sont caractérisées par une aversion contingente au risque. Nous obtenons une équation de valorisation où la prime de risque dépend du risque de préférences en plus du risque de consommation habituel. Nous développons une application empirique qui ne nécessite pas une forme fonctionnelle reliant l'aversion non-observable à des variables économiques observables. Nos estimations sont basées sur une estimation en chaîne markovienne de Monte-Carlo pour des vraisemblances exactes de processus linéaires de diffusion appliquées aux données en temps discret. Puisque le risque de consommation n'a plus à justifier seul la forte prime de risque observée sur les fonds propres, nos estimations contrastent fortement avec celles obtenues dans le cas standard où l'aversion au risque est constante. En particulier, nous trouvons des estimés de l'aversion au risque qui sont (i) de niveau raisonnable, (ii) corrélés avec la consommation et les rendements et (iii) cohérents avec un risque additionnel de détention d'actifs.Asset Pricing Models, Bayesian Analysis, Continuous-time Econometric Models, Data Augmentation, Equity Premium Puzzle, Markov Chain Monte Carlo, Risk Aversion, State-Dependent Preferences, Wealth, Modèles de prix des actifs, analyse bayesienne, modèles économétriques en temps continu, augmentation de données, énigme de la prime de risque, chaîne markovienne de Monte Carlo, aversion au risque, préférences contingentes, richesse

Asset Returns and State-Dependent Risk Preferences

We propose a consumption-based capital asset pricing model in which the representative agent's preferences display state-dependent risk aversion. We obtain a valuation equation in which the vector of excess on equity includes both consumption risk as well as the risk associated with variations in preferences. We develop a simple model that can be estimated without specifying the functional form linking risk aversion with state variables. Our estimates are based on Markov chain Monte Carlo estimation of exact discrete-time parameterizations for linear diffusion processes. Since consumption risk is not forced to account for the entire risk premium, our results contrast sharply with estimates from models in which risk aversion is state-independent. We find that relaxing fixed risk preferences yields estimates for relative risk aversion that are (i) reasonable by usual standards, (ii) correlated with both consumption and returns and (iii) indicative of an additional preference risk of holding the asests.Asset pricing models, Bayesian analysis, continuous-time econometric models, data augmentation, equity premium puzzle, Markov chain Monte Carlo, risk aversion, state-dependent preferences, wealth

Metabolome-Informed Microbiome Analysis Refines Metadata Classifications and Reveals Unexpected Medication Transfer in Captive Cheetahs.

Even high-quality collection and reporting of study metadata in microbiome studies can lead to various forms of inadvertently missing or mischaracterized information that can alter the interpretation or outcome of the studies, especially with nonmodel organisms. Metabolomic profiling of fecal microbiome samples can provide empirical insight into unanticipated confounding factors that are not possible to obtain even from detailed care records. We illustrate this point using data from cheetahs from the San Diego Zoo Safari Park. The metabolomic characterization indicated that one cheetah had to be moved from the non-antibiotic-exposed group to the antibiotic-exposed group. The detection of the antibiotic in this second cheetah was likely due to grooming interactions with the cheetah that was administered antibiotics. Similarly, because transit time for stool is variable, fecal samples within the first few days of antibiotic prescription do not all contain detected antibiotics, and the microbiome is not yet affected. These insights significantly altered the way the samples were grouped for analysis (antibiotic versus no antibiotic) and the subsequent understanding of the effect of the antibiotics on the cheetah microbiome. Metabolomics also revealed information about numerous other medications and provided unexpected dietary insights that in turn improved our understanding of the molecular patterns on the impact on the community microbial structure. These results suggest that untargeted metabolomic data provide empirical evidence to correct records and aid in the monitoring of the health of nonmodel organisms in captivity, although we also expect that these methods may be appropriate for other social animals, such as cats.IMPORTANCE Metabolome-informed analyses can enhance omics studies by enabling the correct partitioning of samples by identifying hidden confounders inadvertently misrepresented or omitted from carefully curated metadata. We demonstrate here the utility of metabolomics in a study characterizing the microbiome associated with liver disease in cheetahs. Metabolome-informed reinterpretation of metagenome and metabolome profiles factored in an unexpected transfer of antibiotics, preventing misinterpretation of the data. Our work suggests that untargeted metabolomics can be used to verify, augment, and correct sample metadata to support improved grouping of sample data for microbiome analyses, here for nonmodel organisms in captivity. However, the techniques also suggest a path forward for correcting clinical information in microbiome studies more broadly to enable higher-precision analyses

GOGGLES: Automatic Image Labeling with Affinity Coding

Generating large labeled training data is becoming the biggest bottleneck in building and deploying supervised machine learning models. Recently, the data programming paradigm has been proposed to reduce the human cost in labeling training data. However, data programming relies on designing labeling functions which still requires significant domain expertise. Also, it is prohibitively difficult to write labeling functions for image datasets as it is hard to express domain knowledge using raw features for images (pixels). We propose affinity coding, a new domain-agnostic paradigm for automated training data labeling. The core premise of affinity coding is that the affinity scores of instance pairs belonging to the same class on average should be higher than those of pairs belonging to different classes, according to some affinity functions. We build the GOGGLES system that implements affinity coding for labeling image datasets by designing a novel set of reusable affinity functions for images, and propose a novel hierarchical generative model for class inference using a small development set. We compare GOGGLES with existing data programming systems on 5 image labeling tasks from diverse domains. GOGGLES achieves labeling accuracies ranging from a minimum of 71% to a maximum of 98% without requiring any extensive human annotation. In terms of end-to-end performance, GOGGLES outperforms the state-of-the-art data programming system Snuba by 21% and a state-of-the-art few-shot learning technique by 5%, and is only 7% away from the fully supervised upper bound.Comment: Published at 2020 ACM SIGMOD International Conference on Management of Dat

EM Algorithms for Multivariate Skewed Variance Gamma Distribution with Unbounded Densities and Applications

The multivariate skewed variance gamma (VG) distribution is useful for modelling data with heavy-tails and high density around the location parameter. When the shape parameter is sufficiently small, the density function is unbounded at the location parameter. In this thesis, we proposed three modifications to appropriately bound the likelihood function so that the maximum is well-defined. These modified likelihoods are the capped, leave-one-out (LOO), and weighted LOO likelihoods. Moreover, we present expectation/conditional maximisation (ECM) algorithms to accurately estimate parameters of the VG distribution using its normal mean-variance mixture representation. Apart from parameter estimation, we also calculate standard errors (SEs) to assess the significance of the parameter estimates. However, this calculation requires the second order derivative of the log-likelihood function with respect to vector/matrices. We apply new matrix differentiation formulas to efficiently compute the observed and Fisher information matrices for the VG distribution. These SE calculations rely on asymptotic properties of the maximum likelihood estimator (MLE) which have been extensively studied under the smooth likelihood case. For the cusp/unbounded case, proving these asymptotic properties are a challenge as they do not satisfy the smoothness regularity condition. We numerically investigate these asymptotic properties for the location estimator when the likelihood function has cusp or unbounded points. We demonstrated its super-efficient rate of convergence and found the double generalised gamma distribution provides a good approximation to the asymptotic distribution of the location parameter. Lastly, the ECM algorithms are applied to the vector autoregressive moving average model with VG and Student's t innovations to capture serial correlation, leptokurtosis, skewness, and cross dependence of return data from high frequency stock indices and cryptocurrencies