2,495 research outputs found
Bayesian Cointegrated Vector Autoregression models incorporating Alpha-stable noise for inter-day price movements via Approximate Bayesian Computation
We consider a statistical model for pairs of traded assets, based on a
Cointegrated Vector Auto Regression (CVAR) Model. We extend standard CVAR
models to incorporate estimation of model parameters in the presence of price
series level shifts which are not accurately modeled in the standard Gaussian
error correction model (ECM) framework. This involves developing a novel matrix
variate Bayesian CVAR mixture model comprised of Gaussian errors intra-day and
Alpha-stable errors inter-day in the ECM framework. To achieve this we derive a
novel conjugate posterior model for the Scaled Mixtures of Normals (SMiN CVAR)
representation of Alpha-stable inter-day innovations. These results are
generalized to asymmetric models for the innovation noise at inter-day
boundaries allowing for skewed Alpha-stable models.
Our proposed model and sampling methodology is general, incorporating the
current literature on Gaussian models as a special subclass and also allowing
for price series level shifts either at random estimated time points or known a
priori time points. We focus analysis on regularly observed non-Gaussian level
shifts that can have significant effect on estimation performance in
statistical models failing to account for such level shifts, such as at the
close and open of markets. We compare the estimation accuracy of our model and
estimation approach to standard frequentist and Bayesian procedures for CVAR
models when non-Gaussian price series level shifts are present in the
individual series, such as inter-day boundaries. We fit a bi-variate
Alpha-stable model to the inter-day jumps and model the effect of such jumps on
estimation of matrix-variate CVAR model parameters using the likelihood based
Johansen procedure and a Bayesian estimation. We illustrate our model and the
corresponding estimation procedures we develop on both synthetic and actual
data.Comment: 30 page
Model Averaging in Risk Management with an Application to Futures Markets
This paper considers the problem of model uncertainty in the case of multi-asset volatility models and discusses the use of model averaging techniques as a way of dealing with the risk of inadvertently using false models in portfolio management. Evaluation of volatility models is then considered and a simple Value-at-Risk (VaR) diagnostic test is proposed for individual as well as ‘average ’ models. The asymptotic as well as the exact finite-sample distribution of the test statistic, dealing with the possibility of parameter uncertainty, are established. The model averaging idea and the VaR diagnostic tests are illustrated by an application to portfolios of daily returns on six currencies, four equity indices, four ten year government bonds and four commodities over the period 1991-2007. The empirical evidence supports the use of ‘thick’ model averaging strategies over single models or Bayesian type model averaging procedures
Bayesian Inference of the Multi-Period Optimal Portfolio for an Exponential Utility
We consider the estimation of the multi-period optimal portfolio obtained by
maximizing an exponential utility. Employing Jeffreys' non-informative prior
and the conjugate informative prior, we derive stochastic representations for
the optimal portfolio weights at each time point of portfolio reallocation.
This provides a direct access not only to the posterior distribution of the
portfolio weights but also to their point estimates together with uncertainties
and their asymptotic distributions. Furthermore, we present the posterior
predictive distribution for the investor's wealth at each time point of the
investment period in terms of a stochastic representation for the future wealth
realization. This in turn makes it possible to use quantile-based risk measures
or to calculate the probability of default. We apply the suggested Bayesian
approach to assess the uncertainty in the multi-period optimal portfolio by
considering assets from the FTSE 100 in the weeks after the British referendum
to leave the European Union. The behaviour of the novel portfolio estimation
method in a precarious market situation is illustrated by calculating the
predictive wealth, the risk associated with the holding portfolio, and the
default probability in each period.Comment: 38 pages, 5 figure
Performance analysis and optimal selection of large mean-variance portfolios under estimation risk
We study the consistency of sample mean-variance portfolios of arbitrarily
high dimension that are based on Bayesian or shrinkage estimation of the input
parameters as well as weighted sampling. In an asymptotic setting where the
number of assets remains comparable in magnitude to the sample size, we provide
a characterization of the estimation risk by providing deterministic
equivalents of the portfolio out-of-sample performance in terms of the
underlying investment scenario. The previous estimates represent a means of
quantifying the amount of risk underestimation and return overestimation of
improved portfolio constructions beyond standard ones. Well-known for the
latter, if not corrected, these deviations lead to inaccurate and overly
optimistic Sharpe-based investment decisions. Our results are based on recent
contributions in the field of random matrix theory. Along with the asymptotic
analysis, the analytical framework allows us to find bias corrections improving
on the achieved out-of-sample performance of typical portfolio constructions.
Some numerical simulations validate our theoretical findings
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