5,018 research outputs found
Portfolio choice and estimation risk : a comparison of Bayesian approaches to resampled efficiency
Estimation risk is known to have a huge impact on mean/variance (MV) optimized portfolios, which is one of the primary reasons to make standard Markowitz optimization unfeasible in practice. Several approaches to incorporate estimation risk into portfolio selection are suggested in the earlier literature. These papers regularly discuss heuristic approaches (e.g., placing restrictions on portfolio weights) and Bayesian estimators. Among the Bayesian class of estimators, we will focus in this paper on the Bayes/Stein estimator developed by Jorion (1985, 1986), which is probably the most popular estimator. We will show that optimal portfolios based on the Bayes/Stein estimator correspond to portfolios on the original mean-variance efficient frontier with a higher risk aversion. We quantify this increase in risk aversion. Furthermore, we review a relatively new approach introduced by Michaud (1998), resampling efficiency. Michaud argues that the limitations of MV efficiency in practice generally derive from a lack of statistical understanding of MV optimization. He advocates a statistical view of MV optimization that leads to new procedures that can reduce estimation risk. Resampling efficiency has been contrasted to standard Markowitz portfolios until now, but not to other approaches which explicitly incorporate estimation risk. This paper attempts to fill this gap. Optimal portfolios based on the Bayes/Stein estimator and resampling efficiency are compared in an empirical out-of-sample study in terms of their Sharpe ratio and in terms of stochastic dominance
Statistical inference for the EU portfolio in high dimensions
In this paper, using the shrinkage-based approach for portfolio weights and
modern results from random matrix theory we construct an effective procedure
for testing the efficiency of the expected utility (EU) portfolio and discuss
the asymptotic behavior of the proposed test statistic under the
high-dimensional asymptotic regime, namely when the number of assets
increases at the same rate as the sample size such that their ratio
approaches a positive constant as . We provide an
extensive simulation study where the power function and receiver operating
characteristic curves of the test are analyzed. In the empirical study, the
methodology is applied to the returns of S\&P 500 constituents.Comment: 27 pages, 5 figures, 2 table
Tracking Error and Active Portfolio Management
Persistent bear market conditions have led to a shift of focus in the tracking error literature. Until recently the portfolio allocation literature focused on tracking error minimization as a consequence of passive benckmark management under portfolio weights, transaction costs and short selling constraints. Abysmal benchmark performance shifted the literature's focus towards active portfolio strategies that aim at beating the benchmark while keeping tracking error within acceptable bounds. We investigate an active (dynamic) portfolio allocation strategy that exploits the predictability in the conditional variance-covariance matrix of asset returns. To illustrate our procedure we use Jorion's (2002) tracking error frontier methodology. We apply our model to a representative portfolio of Australian stocks over the period January 1999 through November 2002.
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1/N versus Mean-Variance
Mean-variance optimisation has been roundly criticised by financial economists and practitioners alike, leading many to advocate a simple 1/N weighting heuristic. We investigate the performance of the Markowitz technique conditional on investor forecasting ability. Using a novel analytical approach, we demonstrate that investors with a modicum of forecasting ability can employ mean-variance to significantly increase their ex ante utility, outperforming the 1/N rule
Dynamic modeling of mean-reverting spreads for statistical arbitrage
Statistical arbitrage strategies, such as pairs trading and its
generalizations, rely on the construction of mean-reverting spreads enjoying a
certain degree of predictability. Gaussian linear state-space processes have
recently been proposed as a model for such spreads under the assumption that
the observed process is a noisy realization of some hidden states. Real-time
estimation of the unobserved spread process can reveal temporary market
inefficiencies which can then be exploited to generate excess returns. Building
on previous work, we embrace the state-space framework for modeling spread
processes and extend this methodology along three different directions. First,
we introduce time-dependency in the model parameters, which allows for quick
adaptation to changes in the data generating process. Second, we provide an
on-line estimation algorithm that can be constantly run in real-time. Being
computationally fast, the algorithm is particularly suitable for building
aggressive trading strategies based on high-frequency data and may be used as a
monitoring device for mean-reversion. Finally, our framework naturally provides
informative uncertainty measures of all the estimated parameters. Experimental
results based on Monte Carlo simulations and historical equity data are
discussed, including a co-integration relationship involving two
exchange-traded funds.Comment: 34 pages, 6 figures. Submitte
In Defense of Portfolio Optimization: What If We Can Forecast?
We challenge academic consensus that estimation error makes mean-variance portfolio strategies inferior to passive equal-weighted approaches. We demonstrate analytically, via simulation and empirically that investors endowed with modest forecasting ability benefit substantially from an MV approach. An investor with some forecasting ability improves expected utility by increasing the number of assets considered. We frame our study realistically using budget constraints, transaction costs and out-of-sample testing for a wide range of investments. We derive practical decision rules to choose between passive and mean variance optimisation results and generate results consistent with much financial market practice and the original Markowitz formulation
Statistical Estimation for Covariance Structures with Tail Estimates using Nodewise Quantile Predictive Regression Models
This paper considers the specification of covariance structures with tail
estimates. We focus on two aspects: (i) the estimation of the VaR-CoVaR risk
matrix in the case of larger number of time series observations than assets in
a portfolio using quantile predictive regression models without assuming the
presence of nonstationary regressors and; (ii) the construction of a novel
variable selection algorithm, so-called, Feature Ordering by Centrality
Exclusion (FOCE), which is based on an assumption-lean regression framework,
has no tuning parameters and is proved to be consistent under general sparsity
assumptions. We illustrate the usefulness of our proposed methodology with
numerical studies of real and simulated datasets when modelling systemic risk
in a network
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