Mean-variance Optimization Research Articles

The optimal payoff for a Yaari investor

Yaari's dual theory of choice under risk is the natural counterpart of expected utility theory. While optimal payoff choice for an expected utility maximizer is well studied in the literature, less is known about the optimal payoff for a Yaari investor. We perform a fairly general analysis and derive optimal payoffs in a variety of relevant cases. As a main contribution, we provide the optimal payoff for a Yaari investor under a variance constraint; thus, extending mean–variance optimization to distorted expectation–variance optimization. We also derive the optimal payoff for an investor who aims to outperform an external benchmark under the requirement that the payoff stays in the neighbourhood of this benchmark.

An optimistic value iteration for mean–variance optimization in discounted Markov decision processes

This paper proposes an optimistic value iteration for steady-state mean–variance optimization in infinite-horizon discounted Markov decision processes (MDPs). The involved variance metric concerns reward variability in the long run, and future deviations are discounted to their present values. This mean–variance optimality criterion is time-inconsistent since its reward function depends on the mean, which renders traditional dynamic programming methods inapplicable. A family of policy/value iteration algorithms can be developed under a bilevel optimization algorithm framework, but there are still several problems to solve for a reinforcement learning (RL) extension. One problem is that in the value iteration, the inner optimization should achieve a near-optimal solution to ensure convergence before the outer update, which is required in every outer iteration. However, in an RL scenario, it is impractical to determine when the inner optimization should be stopped. To deal with this problem, we propose an optimistic value iteration, where the outer updates can be merged into the inner optimization with a learning rate. We prove the algorithm convergence and conduct a numerical experiment on portfolio management to validate the proposed algorithm.

An efficient portfolio approach towards ecosystem-based fisheries governance in EU

In the framework of multispecies fisheries governance, the main objective of this paper is to apply modern portfolio theory (MPT) to the North-East Atlantic European fisheries, including all the key commercial fish species subject to total allowable catches (TAC) and quota regimes within the EU. This is done, first, quantifying the inherent return and risk of the potential fish portfolios and, secondly, estimating an individual constrained financial efficient frontier (FEF) for each of the nine fishing countries in the North-East Atlantic. Unlike previous studies in the field of financial fisheries economics, and due to its major robustness under non-normality and the presence of fat tails, we are using Conditional Value-at-Risk (CVaR) instead of the conventional mean-variance optimization (MVO) as the method to solve the optimization problem of minimizing risk under a set of alternative constraints so as to obtain the respective FEFs. Our results show that changing the species portfolio distribution, it would be possible to improve efficiency, that is to say, to simultaneously get increasing returns and decreasing risk levels. Moreover, this efficiency gain would be compatible with specific quota transfers among fishing countries.

A Distributional Framework for Risk-Sensitive End-to-End Planning in Continuous MDPs

Recent advances in efficient planning in deterministic or stochastic high-dimensional domains with continuous action spaces leverage backpropagation through a model of the environment to directly optimize action sequences. However, existing methods typically do not take risk into account when optimizing in stochastic domains, which can be incorporated efficiently in MDPs by optimizing a nonlinear utility function of the return distribution. We bridge this gap by introducing Risk-Aware Planning using PyTorch (RAPTOR), a novel unified framework for risk-sensitive planning through end-to-end optimization of commonly-studied risk-sensitive utility functions such as entropic utility, mean-variance optimization and CVaR. A key technical difficulty of our approach is that direct optimization of general risk-sensitive utility functions by backpropagation is impossible due to the presence of environment stochasticity. The novelty of RAPTOR lies in leveraging reparameterization of the state distribution, leading to a unique distributional perspective of end-to-end planning where the return distribution is utilized for sampling as well as optimizing risk-aware objectives by backpropagation in a unified framework. We evaluate and compare RAPTOR on three highly stochastic MDPs, including nonlinear navigation, HVAC control, and linear reservoir control, demonstrating the ability of RAPTOR to manage risk in complex continuous domains according to different notions of risk-sensitive utility.

RISK DISTRIBUTION AMONG UNCORRELATED RISK FACTORS: DIVERSIFIED RISK PARITY

This paper aims to distribute the risk among equity risk, interest rate risk and inflation risk, in a portfolio to prevent a risk concentrated portfolio by employing diversified risk parity (DRP) strategy. Principal component analysis and minimum linear torsion models are used to obtain DRP strategies which are compared with other risk based models and tested on five different asset classes whose prices are collected between January 1988 and December 2017. For attaining a thorough analysis, we include mean-variance optimization whose results are compared with both risk-based and DRP strategies in the out-of-sample testing using Sharpe ratio and uncorrelated risk factors. The results demonstrate that DRP strategies have better performance than other models. Specifically, DRP based on the minimum linear torsion model yields the highest Sharpe and risk diversification ratios. Thus, this strategy may guide the investors to construct risk diversified portfolios, especially, during financial crises.

Analysis of Life Extension Performance Metrics for Optimal Management of Offshore Wind Assets

Abstract The main objective of this study is to develop an optimal life extension management strategy for ageing offshore wind farms. Finding the appropriate performance metric for an operation is essential for a durable, reliable, and profitable offshore wind farm operation. To this end, the key metrics to evaluate the life extension performance of an offshore wind farm are investigated. The mean value and the standard deviation of each performance metric are calculated using a probabilistic techno-economic assessment framework for a single offshore wind asset, which is later extended to evaluate the whole offshore wind farm by the multi-asset portfolio optimization. In this regard, the Markowitz modern portfolio theory is applied to estimate a risk-adjusted return parameter, the Sharpe ratio of the overall portfolio of offshore wind assets. Later on, the key performance metrics are compared to identify the most suitable metrics at different stages of life extension, and a further discussion is given for different offshore wind farm sizes. Moreover, the optimal management strategy, which maximizes the Sharpe ratio of the overall offshore wind farm, is analyzed using one of the key performance metrics under optimistic, moderate, and pessimistic scenarios. Finally, the optimal allocation (portfolio) of offshore wind assets attained based on the mean-variance optimization is presented for the different stages of the life extension of the offshore wind farms accounting for the uncertainty propagation during the life extension.

Emerging Market Bonds: Expected Returns and Currency Impact

Optimizing in local currency or in currency-adjusted expected returns depends on the portfolio base currency. Currency unhedged portfolios are more suitable for EUR-based investors and much less for CHF-based portfolios. The appreciation of the portfolio base currency represents a serious risk. Emerging market bond portfolios gain from the absence of currency risk when the portfolio base currency is the US dollar. The empirical results reveal that traditional models such as mean-variance optimization (MVO), minimum-variance optimization (MinVo), and Sharpe ratio optimizations are suitable for portfolio allocation, using both local currency and currency-adjusted expected bond returns as inputs in the optimizations. However, network- and centrality-based allocations outperform traditional models.

Mean-Variance Optimization for Simulation of Order Flow

In this article, the authors propose an order flow simulator for meta orders such as those originating from the trading activity of buy-side firms. The simulator is designed with three key goals in mind. First, it should be simple to use and to integrate into different applications. Second, it must be computationally efficient to handle many securities. Third, the simulated order flow should possess statistical properties similar to those of observed order flow in the market. The authors provide two empirical examples. In addition to illustrating some statistical properties of the order flow simulator, they use the simulator to estimate the number of trades needed to determine whether order flow from a buy-side firm has alpha.

Statistical QoS-Guaranteed Traffic Rate Adaptation for Wireless Scalable Video Streaming

Provisioning multiple statistical QoS for real-time scalable video streaming over wireless fading channels is addressed in this article. A traffic rate adaptation (TRA) strategy is presented to minimize the video quality variation while keeping satisfactory average video quality by selectively delivering encoding layers of video streaming depending on dynamic channel conditions. The QoS-guaranteed TRA policy optimization is formulated based on Markov decision processes. A vector-composed policy gradient algorithm that combines gradient estimate and stochastic approximation is developed to solve the constrained mean-variance optimization problem online. It is attractive for online control and optimization with high computational efficiency and adaptability to unknown environments. Simulation results show the effectiveness of the presented strategy.

Computing optimal portfolios of multi-assets with tail risk: the case of bitcoin

ABSTRACT Assets with tail risk may produce a suboptimal portfolio under mean-variance optimization when asset returns are not normally distributed. We provide a new Monte Carlo simulation method for computing and attaching tails to observed empirical return distributions. We find that a combination of stochastic optimization and the new method for simulating tails in returns with expected shortfall utility function produces optimal portfolios that have better return and risk characteristics than those of mean-variance optimal portfolios. Results from this study suggest that bitcoin can be a diversifier in a multi-asset portfolio when optimization takes all moments of return into consideration.

Markowitz Mean-Variance Portfolio Selection and Optimization under a Behavioral Spectacle: New Empirical Evidence

This paper investigates the robustness of the conventional mean-variance (MV) optimization model by making two adjustments within the MV formulation. First, the portfolio selection based on a behavioral decision-making theory that encapsulates the MV statistics and investors psychology. The second aspect involves capturing the portfolio asset dependence structure through copula. Using the behavioral MV (BMV) and the copula behavioral MV (CBMV), the results show that stocks with lower behavioral scores outperform counterpart portfolios with higher behavioral scores. On the other hand, in the Forex market, the reverse is observed for the BMV approach, while the CBMV remains consistent.

Risk Management for Crypto Assets: Towards Volume-Adjusted Metrics

Cryptocurrencies (or coins) have attracted a significant interest from amateur and professional investors alike. Those currencies are traded on specialized exchanges and are characterized by extreme price dynamics and pockets of significant volatility with liquidity risk being a major concern. The article studies 20 cryptocurrencies over the period Q4.2013-Q2.2021 to glean key stylized facts about their dynamics. We demonstrate that traditional risk metrics may be insufficient to fully evaluate their risk profiles and so propose to leverage a set of novel volume-adjusted metrics. Adjustments to the Sharpe ratio, the Value at Risk (VaR) and the Expected Tail Loss (ETL) measures are outlined so they better reflect the specifics of cryptocurrencies. This enhances the classical two-dimensional mean-variance optimization with a third dimension – volume traded, thus engendering a new three-dimensional asset map that can be used for improved risk management. This new framework is illustrated over the 20 major cryptocurrencies and corresponding adjusted metrics are calculated and interpreted.

OPTIMAL CROSS-CURRENCY MORTGAGE DECISIONS

In this paper, we study optimal mortgage decisions in a cross-currency setting. In particular, we address the question on how a household should optimally split its mortgage portfolio in a fixed rate mortgage in the domestic currency and an adjustable rate mortgage denominated in a foreign currency subject to some risk constraints. We propose an affine factor model which allows to jointly investigate the impact of variations in interest rates as well as of exchange rate fluctuations on mortgage decisions. As a case study, we apply our model to real data on Swiss and German mortgage markets and we estimate parameters using a quasi-Kalman filter approach. We then study the impact of different income splits, risk attitudes, and mortgage specifications on the household’s portfolio choice in a mean–variance optimization approach.

Is COVID-19 anticipating the future? Evidence from investors’ sustainable orientation

In this paper, we discuss the attractiveness of green and sustainable assets, from an investor perspective. Inspired by the current state of the art, with researchers positively (re)considering the added value of stocks associated with the fulfilment of sustainable development goals, we analyze whether such stocks demonstrated: (1) a different and (2) an outperforming dynamic during various stages of the COVID-19 pandemic. In particular, we examine sustainable-indexed assets and companies with a fully bio-based production system, against a counterfactual group of non-indexed activities operating in the same sectors. Asset connectivity is investigated by means of a correlation network, and portfolio optimization is applied to measure profitability. The results show: (1) fewer connections between bio-based assets and the “rest of the world,” suggesting that, given their potential long-term resilience, investors might consider them capable of mitigating COVID-19 systemic risk, and therefore a valid investment to hold; and (2) the effectiveness and profitability of bio-based assets in portfolios. Considering the latter finding, we document a switching effect after the hard lockdown phase, during which rational investors (seeking an optimal mean–variance) may have inferred the efficacy of capital re-allocation from simply sustainable assets to bio-based companies. Here, we discuss the potential role of the pandemic as an accelerator of the sustainable green transition, considering the welfare implications in terms of socio-economic wellbeing and reduction of negative environmental externalities deriving from the conversion of the traditional production and management system. The profitability of the returns investments might increase the attractiveness of sustainable management organizations, causing the diffusion of these virtuous systems to increase further.

Complete Neighbourhood Search Heuristic Algorithm for Portfolio Optimization

In portfolio optimization, the fundamental goal of an investor is to optimally allocate investments between different assets. Mean-variance optimization methods make unrealistic assumptions to solve the problem of optimal allocation. On the other hand, when realistic constraints like holding size and cardinality are introduced it leads to optimal asset allocation which differ from the mean variance optimization. The resulting optimization problem become quite complex as it exhibits multiple local extrema and discontinuities. Heuristic algorithms work well for the complex problem. Therefore, a heuristic algorithm is developed which is based on hill climbing complete (HC-C). It is utilized to solve the extended portfolio optimization problem. In order to validate its performance, the proposed HC-C is tested with standard portfolio optimization problem. Experimental results are benchmarked with the quadratic programming method and threshold accepting (TA) algorithm.

Design and Evaluation of Robo-Advisors Using Index Fund and Alternative Assets of Cryptocurrency and Gold: Case of Indonesian Capital Market

Robo-advisor is one of the most prominent innovation in the wealth management industry, and its success in Indonesia has been evident in the case of Bibit. Therefore, wealth management companies need to employ Robo-Advisor to overcome their competition. This research aims to give recommendation on asset allocation method and asset class selection for Robo-Advisors in Indonesia using Sharpe Ratio Analysis. Then, the author will analyze the robo-advisor’s performance during equity market downturn. Finally, The Robo-Advisor’s actual performance will be tested in 2018, 2019, and 2020. The Sharpe ratio analysis result showed that Robo-Advisors seeking higher risk-adjusted return should choose mean-variance optimization over risk parity for asset allocation method, and the inclusion of gold and bitcoin in a portfolio of stock mutual fund and bond mutual fund increases the risk-adjusted return of the portfolio. The proposed robo-advisor’s portfolio protected investors from equity market downturn in 2011-2010 in 83,3% of the case. Finally, the proposed robo-advisor’s portfolio generated better return for the conservative, moderate and aggressive investor during 2018, 2019, and 2020 when compared to LQ45.

A combinatorial optimization approach to scenario filtering in portfolio selection

Recent studies stressed the fact that covariance matrices computed from empirical financial time series appear to contain a high amount of noise. This makes the classical Markowitz Mean–Variance Optimization model unable to correctly evaluate the performance associated to selected portfolios. Since the Markowitz model is still one of the most used practitioner-oriented tool, several filtering methods have been proposed in the literature to overcome the problem. Among them, the two most promising ones refer to the Random Matrix Theory and to the Power Mapping strategy. The basic idea of these methods is to transform the estimated correlation matrix before applying the Mean–Variance Optimization model. However, experimental analysis shows that these two strategies are not always effective when applied to real financial datasets.In this paper we propose a new filtering method based on Quadratic Programming. We develop a Mixed Integer Quadratic Programming model, which is able to filter those observations that may affect the performance of the selected portfolio. We discuss the properties of this new model and test it on some real financial datasets. We compare the out-of-sample performance of our portfolios with the one of the portfolios provided by the two above mentioned alternative filtering methods giving evidence that our method outperforms them. Although our model can be solved efficiently with standard optimization solvers, the computational burden increases for large datasets. To solve also these problems, we propose a heuristic procedure, which, on the basis of our empirical results, shows to be both efficient and effective.

Portfolio Constraints: An Empirical Analysis

Mean-variance optimization often leads to unreasonable asset allocations. This problem has forced scholars and practitioners alike to introduce portfolio constraints. The scope of our study is to verify which type of constraint is more suitable for achieving efficient performance. We have applied the main techniques developed by the financial community, including classical weight, flexible, norm-based, variance-based, tracking error volatility, and beta constraints. We employed panel data on the monthly returns of the sector indices forming the MSCI All Country World Index from January 1995 to December 2020. The assessment of each strategy was based on out-of-sample performance, measured using a rolling window method with annual rebalancing. We observed that the best strategies are those subject to constraints derived from the equal-weighted model. If the goal is the best compromise between absolute return, efficiency, total risk, economic sustainability, diversification, and ease of implementation, the best solution is a portfolio subject to no short selling and bound either to the equal weighting or to TEV limits. Overall, we found that constrained optimization models represent an efficient alternative to classic investment strategies that provide substantial advantages to investors.

Large-Scale Mean-Variance Optimization and Chunking Algorithm

Large-Scale Mean-Variance Optimization and Chunking Algorithm

Equilibrium reinsurance-investment strategy with a common shock under two kinds of premium principles

This paper investigates the optimal mean-variance reinsurance-investment problem for an insurer with a common shock dependence under two kinds of popular premium principles: the variance premium principle and the expected value premium principle. We formulate the optimization problem within a game theoretic framework and derive the closed-form expressions of the equilibrium reinsurance-investment strategy and equilibrium value function under the two different premium principles by solving the extended Hamilton–Jacobi–Bellman system of equations. We find that under the variance premium principle, the proportional reinsurance is the optimal reinsurance strategy for the optimal reinsurance-investment problem with a common shock, while under the expected value premium principle, the excess-of-loss reinsurance is the optimal reinsurance strategy. In addition, we illustrate the equilibrium reinsurance-investment strategy by numerical examples and discuss the impacts of model parameters on the equilibrium strategy.