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A Practical Guide to Robust Portfolio Optimization
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... Recently, Yin et al. (2021) proposed a practical guide to robust portfolio optimization based on mean-variance formulations. They assumed that asset returns are uncertain and belong to either box or an ellipsoidal uncertainty sets. ...
This paper reviews recent advances in robust portfolio selection problems and their extensions, from both operational research and financial perspectives. A multi-dimensional classification of the models and methods proposed in the literature is presented, based on the types of financial problems, uncertainty sets, robust optimization approaches, and mathematical formulations. Several open questions and potential future research directions are identified.
... They show that when the uncertainty matrix is proportional to the asset covariance matrix then the robust MVO counterpart is equivalent to a standard MVO model based on the nominal mean estimates but with a larger risk aversion parameter. More recently, Yin et al. [71] make the case for the preference of quadratic uncertainty sets over the more restrictive box uncertainty. Furthermore, they provide evidence for a diagonal uncertainty structure based on asset variances and propose calibrating the level of uncertainty as a function of the underlying asset Sharpe ratios. ...
Mean-variance optimization (MVO) is known to be highly sensitive to estimation error in its inputs. Recently, norm penalization of MVO programs has proven to be an effective regularization technique that can help mitigate the adverse effects of estimation error. In this paper, we augment the standard MVO program with a convex combination of parameterized $L_1$ and $L_2$ norm penalty functions. The resulting program is a parameterized penalized quadratic program (PPQP) whose primal and dual form are shown to be constrained quadratic programs (QPs). We make use of recent advances in neural-network architecture for differentiable QPs and present a novel, data-driven stochastic optimization framework for optimizing parameterized regularization structures in the context of the final decision-based MVO problem. The framework is highly flexible and capable of jointly optimizing both prediction and regularization model parameters in a fully integrated manner. We provide several historical simulations using global futures data and highlight the benefits and flexibility of the stochastic optimization approach.
... The common way of modelling financial market is through normal distribution, having said that, this is prior the assumption that the data series follow a normal distribution. This is generally set to define uncertainty that is set for the portfolio optimization, as we choose the parameter estimator for the first two moments of the distribution as input parameters for the problem I-Chen Lu (2009). However, it is worth mentioning that normal distribution is not ideal when underlying assets return are violated, especially in fat tail and extreme edges. ...
This study analyzes the robustness and performance of the two common optimization models (classical mean-variance optimization and CVaR) in real world application compared with an alternative model that ignores the widely used mean-variance framework through robustness testing from 2013 to 2021 with the data being trained simultaneously from 1997-2012. A market indicator was built based on the risk environment model and was used as an input parameter for the optimization function of the alternative model. The results from the analysis of the performance of the three portfolios demonstrated that having a market view as input parameters incorporated into the optimization problem produces stable and higher returns under the mechanism of multi-period optimization. The alternative model solution was tested in case scenarios to target synthetic hedge fund strategies and proved to be efficient in optimizing the curve to meet the return expectation while considering the current market environment.
... Unlike mean-variance optimisation, robust optimisation takes into account the uncertainty in the asset return estimates and significantly reduces the sensitivity of the final portfolio to small changes in expected returns. The description of the framework based on robust optimisation can be found in our recent papers, e.g., Yin et al. (2021). Details about how the allocation of robust portfolios is constructed from the robust optimisation algorithm was explored in our paper by Perchet et al. (2016). ...
In this paper we introduce the notion of themes as an additional investment dimension beyond asset classes, regions, sectors and styles, and we propose a framework to allocate to thematic investments at a strategic asset allocation level. The goal of thematic investments is to provide the means to invest in assets that have their returns significantly impacted by the structural changes underlying the theme. Such changes come about through megatrends that shape societies: Demographic shifts, social or attitudinal changes, environmental impact, resource scarcity, economic imbalances, transfer of power, technological advances and regulatory or political changes. Allocating to themes requires discipline because thematic investments are not only exposed to the theme but also to the traditional risk factors. Our approach to allocating to thematic investments uses a framework based on robust portfolio optimisation, which takes into account the expected excess return derived from the exposure to the theme as well as exposures to traditional risk factors. As an illustration, we provide an example where thematic investments in energy transition, environmental sustainability, healthcare innovation, consumer innovation and disruptive tech are added to a traditional multi-asset portfolio.
... This yields positive definite correlation matrices, which are slightly different from the original correlation matrix, C. The size of the shock is also easily controlled by changing k. Before we move on to the experiment, we wish to add another trading strategy to the experiment, which is inspired by Robust Portfolio Optimization (see [12]). The idea (in our case) is to solve the problem in a way in which the trading strategy is not as dependent on the correlation matrix C. The way we do this is by training our ANN models on samples coming from a model with correlation ...
In recent years, research in deep learning has intensified, and deep learning methods have been developed in all areas of finance. This thesis aims to combine deep learning-based market generators with deep hedging methods to create a model-and greek-free framework that finds risk optimal hedging strategies from observed price paths. First, we explain and test the deep hedging method using virtually unrestricted amounts of synthetic data from Black-Scholes and Heston models. We show that the deep hedging method can find reasonable hedging strategies for simple claims, path-dependent options with and without transaction costs. However, architecture and inputs (including processing) have significant impacts on performance. We also observe that the deep hedging method can yield unstable hedging strategies in multivariate models. Next, we explain and test data-driven market generators based on variational autoencoders. We observe that the market generators can produce paths with similar marginal distributions and correlation to a Black-Scholes model. The market generators struggle in the Heston model and when conditioning on initial instantaneous variance. We propose several moment regularization terms that partly alleviate these issues. Finally, we combine and test the market generators with the deep hedging methods when assuming that a Black-Scholes or Heston model drives the market. In a Black-Scholes model, we observe that the combined framework can learn reasonable hedging strategies for call and down-and-out call options from a modest number of observations. In a Heston model, we also observe that the framework can learn hedging strategies (conditioned on initial instantaneous variance) from a single path. Still, the framework struggles with high initial instantaneous variance. We also show that it is possible to improve performance by utilizing overlapping paths, which increase the number of training paths. The results are promising. However, the techniques still require refining and further development before it is feasible to use commercially.
Investment portfolio optimization (IPO) is one of the most important problems in the financial area. Also, one of the most important features of financial markets is their embedded uncertainty. Thus, it is essential to propose a novel IPO model that can be employed in the presence of uncertain data. Accordingly, the main goal of this paper is to propose a novel fuzzy multi-period multi-objective portfolio optimization (FMPMOPO) model that is capable to be used under data ambiguity and practical constraints including budget constraint, cardinality constraint, and bound constraint. It should be noted that three objectives including terminal wealth, risk, and liquidity as well as practical constraints are considered in proposed FMPMOPO model. Also, the alpha-cut method is employed to deal with fuzzy data. Finally, the proposed fuzzy multi-period wealth-risk-liquidity (FMPWRL) model is implemented in real-world case study from Tehran stock exchange (TSE). The experimental results show the applicability and efficacy of the proposed FMPWRL model for fuzzy multi-period multi-objective investment portfolio optimization problem under fuzzy environment.
The covariation among financial asset returns is often a key ingredient used in the construction of optimal portfolios. Estimating covariances from data, however, is challenging due to the potential influence of estimation error, specially in high-dimensional problems, which can impact negatively the performance of the resulting portfolios. We address this question by putting forward a simple approach to disentangle the role of variance and covariance information in the case of mean-variance efficient portfolios. Specifically, mean-variance portfolios can be represented as a two-fund rule: one fund is a fully invested portfolio that depends on diagonal covariance elements, whereas the other is a long-short, self financed portfolio associated with the presence of non-zero off-diagonal covariance elements. We characterize the contribution of each of these two components to the overall performance in terms of out-of-sample returns, risk, risk-adjusted returns and turnover. Finally, we provide an empirical illustration of the proposed portfolio decomposition using both simulated and real market data.
The indifference of many investment practitioners to mean-variance optimization technology, despite its theoretical appeal, is understandable in many cases. The major problem with MV optimization is its tendency to maximize the effects of errors in the input assumptions. Unconstrained MV optimization can yield results that are inferior to those of simple equal-weighting schemes. Nevertheless, MV optimization is superior to many ad hoc techniques in terms of integration of portfolio objectives with client constraints and efficient use of information. Its practical value may be enhanced by the sophisticated adjustment of inputs and the imposition of constraints based on fundamental investment considerations and the importance of priors. The operating principle should be that, to the extent that reliable information is available, it should be included as part of the definition of the optimization procedure.
This note corrects an error in the proof of Proposition 2 of “Risk Reduction in Large Portfolios: Why Imposing the Wrong Constraint Helps” that appeared in the Journal of Finance, August 2003.
This comprehensive reference delivers a toolkit for harvesting market rewards from a wide range of investments. Written by a world-renowned industry expert, the reference discusses how to forecast returns under different parameters. Expected returns of major asset classes, investment strategies, and the effects of underlying risk factors such as growth, inflation, liquidity, and different risk perspectives, are also explained. Judging expected returns requires balancing historical returns with both theoretical considerations and current market conditions. Expected Returns provides extensive empirical evidence, surveys of risk-based and behavioral theories, and practical insights.
As quantitative techniques have become commonplace in the investment industry, the mitigation of estimation and model risk in portfolio management has grown in importance. Robust optimization, which incorporates estimation error directly into the portfolio optimization process, is typically used with conventional robust statistical estimation methods. This perspective on the robust optimization approach reviews useful practical extensions and discusses potential applications for robust portfolio optimization.
