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Register a new userRobust and Adaptive Algorithms for Online Portfolio Selection
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Added by
Theodoros Tsagaris
Publication date
2010
fields
Financial
and research's language is
English
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We present an online approach to portfolio selection. The motivation is within the context of algorithmic trading, which demands fast and recursive updates of portfolio allocations, as new data arrives. In particular, we look at two online algorithms: Robust-Exponentially Weighted Least Squares (R-EWRLS) and a regularized Online minimum Variance algorithm (O-VAR). Our methods use simple ideas from signal processing and statistics, which are sometimes overlooked in the empirical financial literature. The two approaches are evaluated against benchmark allocation techniques using 4 real datasets. Our methods outperform the benchmark allocation techniques in these datasets, in terms of both computational demand and financial performance.
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We develop the idea of using Monte Carlo sampling of random portfolios to solve portfolio investment problems. In this first paper we explore the need for more general optimization tools, and consider the means by which constrained random portfolios may be generated. A practical scheme for the long-only fully-invested problem is developed and tested for the classic QP application. The advantage of Monte Carlo methods is that they may be extended to risk functions that are more complicated functions of the return distribution, and that the underlying return distribution may be computed without the classical Gaussian limitations. The optimization of quadratic risk-return functions, VaR, CVaR, may be handled in a similar manner to variability ratios such as Sortino and Omega, or mathematical constructions such as expected utility and its behavioural finance extensions. Robustification is also possible. Grid computing technology is an excellent platform for the development of such computations due to the intrinsically parallel nature of the computation, coupled to the requirement to transmit only small packets of data over the grid. We give some examples deploying GridMathematica, in which various investor risk preferences are optimized with differing multivariate distributions. Good comparisons with established results in Mean-Variance and CVaR optimization are obtained when ``edge-vertex-biased sampling methods are employed to create random portfolios. We also give an application to Omega optimization.
We study the optimal portfolio allocation problem from a Bayesian perspective using value at risk (VaR) and conditional value at risk (CVaR) as risk measures. By applying the posterior predictive distribution for the future portfolio return, we derive relevant quantiles needed in the computations of VaR and CVaR, and express the optimal portfolio weights in terms of observed data only. This is in contrast to the conventional method where the optimal solution is based on unobserved quantities which are estimated, leading to suboptimality. We also obtain the expressions for the weights of the global minimum VaR and CVaR portfolios, and specify conditions for their existence. It is shown that these portfolios may not exist if the confidence level used for the VaR or CVaR computation are too low. Moreover, analytical expressions for the mean-VaR and mean-CVaR efficient frontiers are presented and the extension of theoretical results to general coherent risk measures is provided. One of the main advantages of the suggested Bayesian approach is that the theoretical results are derived in the finite-sample case and thus they are exact and can be applied to large-dimensional portfolios. By using simulation and real market data, we compare the new Bayesian approach to the conventional method by studying the performance and existence of the global minimum VaR portfolio and by analysing the estimated efficient frontiers. It is concluded that the Bayesian approach outperforms the conventional one, in particular at predicting the out-of-sample VaR.
Financial markets are complex environments that produce enormous amounts of noisy and non-stationary data. One fundamental problem is online portfolio selection, the goal of which is to exploit this data to sequentially select portfolios of assets to achieve positive investment outcomes while managing risks. Various algorithms have been proposed for solving this problem in fields such as finance, statistics and machine learning, among others. Most of the methods have parameters that are estimated from backtests for good performance. Since these algorithms operate on non-stationary data that reflects the complexity of financial markets, we posit that adaptively tuning these parameters in an intelligent manner is a remedy for dealing with this complexity. In this paper, we model the mapping between the parameter space and the space of performance metrics using a Gaussian process prior. We then propose an oracle based on adaptive Bayesian optimization for automatically and adaptively configuring online portfolio selection methods. We test the efficacy of our solution on algorithms operating on equity and index data from various markets.
We study the Markowitz portfolio selection problem with unknown drift vector in the multidimensional framework. The prior belief on the uncertain expected rate of return is modeled by an arbitrary probability law, and a Bayesian approach from filtering theory is used to learn the posterior distribution about the drift given the observed market data of the assets. The Bayesian Markowitz problem is then embedded into an auxiliary standard control problem that we characterize by a dynamic programming method and prove the existence and uniqueness of a smooth solution to the related semi-linear partial differential equation (PDE). The optimal Markowitz portfolio strategy is explicitly computed in the case of a Gaussian prior distribution. Finally, we measure the quantitative impact of learning, updating the strategy from observed data, compared to non-learning, using a constant drift in an uncertain context, and analyze the sensitivity of the value of information w.r.t. various relevant parameters of our model.
We extend Relative Robust Portfolio Optimisation models to allow portfolios to optimise their distance to a set of benchmarks. Portfolio managers are also given the option of computing regret in a way which is more in line with market practices than other approaches suggested in the literature. In addition, they are given the choice of simply adding an extra constraint to their optimisation problem instead of outright changing the objective function, as is commonly suggested in the literature. We illustrate the benefits of this approach by applying it to equity portfolios in a variety of regions.
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