Minimum Variance Strategy Research Articles

High-dimensional portfolio optimization based on tree-structured factor model

Certain characteristics are known to predict cross-sectional expected stock returns and risk exposures. We propose a novel portfolio optimization procedure to incorporate multiple characteristic information, which requires minimal parameters and no stringent assumptions. Instead of investing in individual stocks, we perform portfolio optimization on a large panel of characteristic portfolios generated by a tree-structured portfolio sorting method, which can capture the non-linearities and interactions among stock characteristics to help predict expected returns and covariances. Simulations show that our tree-structured Lasso-based mean–variance (MV) strategy has better out-of-sample Sharpe ratios than the three benchmark strategies: the stock-based MV strategy, the stock-based global minimum variance (GMV) strategy, and the double-sorted portfolio-based MV strategy. We use daily stock data from the Chinese A-share market from 2002-04-01 to 2022-12-31 to compare the out-of-sample performance of the tree-structured Lasso-MV with other classical strategies, such as GMV and equally weighted (EW) strategies, etc. The empirical results suggest that the tree-structured Lasso-MV strategy can achieve a higher Sharpe ratio, a smaller standard deviation, and a lower turnover. These results are robust to different levels of granularity.

Hedging cryptocurrency options

The cryptocurrency market is volatile, non-stationary and non-continuous. Together with liquid derivatives markets, this poses a unique opportunity to study risk management, especially the hedging of options, in a turbulent market. We study the hedge behaviour and effectiveness for the class of affine jump diffusion models and infinite activity Lévy processes. First, market data is calibrated to stochastic volatility inspired-implied volatility surfaces to price options. To cover a wide range of market dynamics, we generate Monte Carlo price paths using an stochastic volatility with correlated jumps model, a close-to-actual-market GARCH-filtered kernel density estimation as well as a historical backtest. In all three settings, options are dynamically hedged with Delta, Delta–Gamma, Delta–Vega and Minimum Variance strategies. Including a wide range of market models allows to understand the trade-off in the hedge performance between complete, but overly parsimonious models, and more complex, but incomplete models. The calibration results reveal a strong indication for stochastic volatility, low jump frequency and evidence of infinite activity. Short-dated options are less sensitive to volatility or Gamma hedges. For longer-dated options, tail risk is consistently reduced by multiple-instrument hedges, in particular by employing complete market models with stochastic volatility.

Robust self tuned AGC controller for wind energy penetrated power system

This paper presents the self-tuned Automatic Generation Control for an interconnected power system with dominant wind energy penetration. The uncertain behavior of wind power plant has random fluctuations on the frequency of the power system and optimum performance cannot be achieved by the fixed structure controller. Thus, the self-tuned controller can handle the load disturbances of varying nature efficiently, by generating control signal based on least square method and minimum variance strategy. A two-area interconnected power system model consists of thermal, hydro and doubly fed induction generator-based wind power plants with dominant participation factor and random power output is considered for the simulation study. The self-tuned AGC efficiently regulates the variation in area control error caused by load disturbance and wind fluctuation, by adjusting its parameter automatically based on least square algorithm. Moreover, controller parameters also adjust its parameters qualitatively based on equipment parameter under various operating condition.

An efficient robust optimized functional link broad learning system for solar irradiance prediction

A new machine learning approach for forecasting short-termsolar irradiance is presented in this paper considering different weather conditions and time horizon in a microgrid environment. Using historical solar irradiance, a short-term forecasting model known as Robust optimized functional link broad learning system (FLBLS) is developed. Here the original input comprising delayed historical solar irradiance samples is initially expanded by exponential trigonometric functions and the expanded features are then used to create a large number of feature nodes using random weights and biases. Further the newly created features are fed as inputs to the enhancement nodes forming a broad learning system (BLS). This newly formed flat FLBLS facilitates incremental learning in fast remodelling of the network if needed for efficient performance without a retraining process unlike deep neural networks using several hidden layers and filters, etc. The proposed approach is designed on the basis of the standard random vector functional link network (RVFLN), however unlike the traditional RVFLN that applies inputs directly and set up the enhancement nodes, in our proposed approach, initially the inputs are expanded and map the expanded inputs to generate a set of mapped features. It reduces the lengthy process unlike deep neural networks that involves the back propagation algorithm for error minimization. The proposed FLBLS approach simplifies the learning process with the proper choice of feature nodes as it can be implemented to a flat network or a simpler network such as ELM that requires only the simple calculation of the output weight and obtain the final output where retraining is not required for adding extra feature nodes or enhancement nodes like deep neural architectures. Also, the minimum variance strategy with the training samples is useful in rejecting the effects of noise and outliers in the system and make the network robust which gets reflected in computing output weights using generalized least square. The minimum variance strategy further enhances the performance of the proposed system. To improve the prediction accuracy, the FLBLS parameters are optimized using an efficient metaheuristic chaotic firefly-sine cosine levy flight algorithm. Also, to reject the effects of noise and outliers and make the network robust a minimum variance strategy is used with the training samples that gets reflected in computing output weights using generalised least squares. The suggested method is experimented rigorously and analysed with different time frames designed for 30 min and 60 min ahead solar irradiance prediction. The obtained results from experiments confirm that the proposed FLBLS approach outperforms other randomized neural network forecasting methods as well many state-of-the-art methods using solar irradiance data of Hyderabad, India collected from National Renewable Energy Laboratory (NREL). This approach exhibits with the lowest errors in different case studies among all the compared methods. This FLBLS designed approach is an efficient approach for the purpose of solar irradiance prediction with highly nonlinear data.

Asymmetric multivariate HAR models for realized covariance matrix: A study based on volatility timing strategies

Forecasting high-dimensional covariance matrices is crucial for portfolio optimization and risk management. Recent studies focus on modelling the realized covariance matrices constructed with intraday prices using multivariate heterogeneous autoregressive (MHAR) models. Considering the mounting evidence of the asymmetric volatility phenomenon, this paper extends the literature by investigating whether volatility timing investors could achieve economic gains through incorporating asymmetry in the MHAR models. Empirical results in China's stock markets show that our proposed method of incorporating the asymmetric logistic smooth transition structure in the MHAR model achieves the highest economic values out-of-sample under various market conditions. Furthermore, we uncover that the most diversified portfolio strategy is more applicable when the market is in tranquil stage, while the global minimum variance strategy is more applicable during market turbulence.

Which clean energy sectors are attractive? A portfolio diversification perspective

Clean energy assets have opened up new investment opportunities for market participants. How to construct an efficient clean energy stock portfolio and how it would perform in comparison to traditional assets remain unclear. To fill this gap, this paper investigates optimal allocation within the clean energy stock market. Specifically, the risk and return characteristics of individual clean energy stock sub-sectors are examined. Optimization techniques are used to generate the desired clean energy stock allocation. The performance is compared to the equity market benchmark and dirty energy stocks. The results show that the risk and return on clean energy stock sub-sectors vary significantly. Clean energy stocks generally underperform the overall equity market but outperform dirty stocks. For investors looking to decarbonize their portfolios, the minimum-tail risk strategy is superior to the minimum-variance strategy. The index that tracks developers and operators of renewable energy projects provides the best risk-adjusted returns for investors with moderate risk tolerance and is effective at mitigating the volatility risk of dirty assets. The wind and energy storage indices, however, are the preferred options for reducing the tail risks of dirty assets. The findings shed light on the efficacy of clean energy portfolio optimization strategies and the heterogeneous diversification benefits across clean energy stock sub-sectors, which has important implications for investors constructing clean energy portfolios to meet investment objectives.

The Market Measure of Carbon Risk and its Impact on the Minimum Variance Portfolio

Like environment, social, and governance investing, climate change is an important concern for asset managers and owners and a new challenge for portfolio construction. Until now, investors have mainly measured carbon risk using fundamental approaches, such as with carbon intensity metrics. Nevertheless, it has not been proven that asset prices are directly affected by these fundamental-based measures. In this article, the authors focus on another approach, which consists of measuring the sensitivity of stock prices with respect to a carbon risk factor. In the authors’ opinion, carbon betas are market-based measures that are complementary to carbon intensities or fundamental-based measures when managing investment portfolios; carbon betas may be viewed as an extension or forward-looking measure of the current carbon footprint. In particular, they show how this new metric can be used to build minimum variance strategies and how it affects portfolio construction. <b>TOPICS:</b>ESG investing, portfolio construction, tail risks, fundamental equity analysis <b>Key Findings</b> ▪ Measuring carbon risk is different if we consider a fundamental-based approach by using carbon intensity metrics or a market-based approach by using carbon betas. ▪ Managing relative carbon risk implies overweighting of green firms, whereas managing absolute carbon risk implies having zero exposure to the carbon risk factor. The first approach is an active management bet, whereas the second is an immunization investment strategy. ▪ Both specific and systematic carbon risks are important when building a minimum variance portfolio and justify combining fundamental and market approaches to carbon risk.

Minimum variance control of chaos in a hyperchaotic memristor based oscillator using online particle swarm optimization

This paper introduces a new hyperchaotic oscillator base on a new boundary-restricted Hewlett-Packard memristor model. Firstly, the complex system is designed based on a memristor-based hyperchaotic real system, and its properties are analyzed by means of Lyapunov exponents, Lyapunov dimension and phase portraits diagrams. Secondly, a simple feedback control based on the minimum variance control technique is designed to stabilize the hyperchaotic oscillator system, which is one of the new developed approaches for controlling the chaos in high-dimensional hyperchaotic systems. In this method, the time series variance is considered for designing and calculating the state feedback control gain. Furthermore, the state feedback control is designed so that to minimize the variance as a cost function, followed by developing an online optimization technique using the particle swarm optimization method in order to calculate the state feedback control based on the minimum variance strategy. Then, the application of this method is examined on a hyperchaotic memristor-based oscillator. Finally, the sensitivity of the proposed method is evaluated in different initial conditions that greatly influence the hyperchaotic dynamics. Considering that the optimization is online, simulation results show highly good effectiveness of the presented technique in controlling the chaos in high-dimensional hyperchaotic oscillators

The Market Measure of Carbon Risk and its Impact on the Minimum Variance Portfolio

Like ESG investing, climate change is an important concern for asset managers and owners, and a new challenge for portfolio construction. Until now, investors have mainly measured carbon risk using fundamental approaches, such as with carbon intensity metrics. Nevertheless, it has not been proven that asset prices are directly impacted by these fundamental-based measures. In this paper, we focus on another approach, which consists in measuring the sensitivity of stock prices with respect to a carbon risk factor. In our opinion, carbon betas are market-based measures that are complementary to carbon intensities or fundamental-based measures when managing investment portfolios, because carbon betas may be viewed as an extension or forward-looking measure of the current carbon footprint. In particular, we show how this new metric can be used to build minimum variance strategies and how they impact their portfolio construction.

Diversifying Estimation Errors: An Efficient Averaging Rule for Portfolio Optimization

We propose an averaging rule that combines established minimum-variance strategies to minimize the expected out-of-sample variance. Our rule overcomes the problem of selecting the “best” strategy ex-ante and diversifies remaining estimation errors of the single strategies included in the averaging. Extensive simulations show that the contributions of estimation errors to the out-of-sample variances are uncorrelated between the considered strategies. This implies that averaging over multiple strategies o˙ers sizable diversification benefits. Our rule leverages these benefits and compares favorably to eleven strategies in terms of out-of-sample variance on both simulated and empirical data sets. The Sharpe ratio is across all data sets at least 25% higher than for the 1/N portfolio.

The global minimum variance hedge

Abstract We explore futures hedging based on the global minimum variance strategy. As evidenced by using eleven of the world’s major stock market indexes and their corresponding futures contracts, the results show that the global minimum variance hedge may deviate statistically from the Ederington (J Finance 43(1):157–170, 1979) minimum variance hedge. We also present a regression approach to testing the hedge ratios and futures positions when the noise terms follow a normal distribution. In the illustration examined, we show that the global minimum variance hedge provides a more economically significant information ratio yield than that under the minimum variance hedge.

Accessing the China A-Shares Market via Minimum-Variance Investing

As the China A-shares market is receiving more attention from international investors because of its expanding market size and improved access, means of accessing the market have become an important topic. The authors suggest the use of minimum variance investing as an alternative to the traditional market cap approach for accessing the China A-shares market. Their portfolio construction method takes into account the stock suspension features of the China A-shares market, and the simulated results show that China A-shares minimum variance investing is capable of achieving volatility reduction. The study also observes return enhancement from the minimum variance strategies for the 2007–2017 period. The authors compare minimum variance investing in different markets and find that the volatility reduction in the China A-shares market is lower compared with other major equity markets despite its superior historical return. This can be attributed to its smaller ex ante volatility reduction and forecastability of the ex post volatility. The authors investigate two methods of applying factor exposure control of the minimum variance portfolio. The results show that a value and quality factor overlay does not affect the volatility reduction capability and helps to enhance the return of the China A-shares minimum variance portfolio through the capture of factor risk premium.

The Diversification Benefits of Including Carbon Assets in Financial Portfolios

Carbon allowances traded in the EU-Emission Trading Scheme (EU-ETS) were initially designed as an economic motivation for efficiently curbing greenhouse as emissions, but now it mimics quite a few characteristics of financial assets, and have now been used as a candidate product in building financial portfolios. In this study, we examine the time-varying correlations between carbon allowance prices with other financial indices, during the third phase of EU-ETS. The results show that, at the beginning of this period, carbon price was still strongly corrected with other financial indices. However, this connection was weakened over time. Given the relative independence of carbon assets from other financial assets, we argue for the diversification benefits of including carbon assets in financial portfolios, and building such portfolios, respectively, with the traditional global minimum variance (GMV) strategy, the mean-variance-OGARCH (MV-OGARCH) strategy, and the dynamic conditional correlation (DCC) strategy. It is shown that the portfolio built with the MV-OGARCH strategy far out-performs the others and that including carbon assets in financial portfolios does help reduce investment risks.

Mean-variance versus naïve diversification: The role of mispricing

We compare the equal-weight naïve 1/N portfolio with mean-variance strategies from the perspective of mispricing (alpha) and provide three new findings. First, we analytically show that the 1/N rule approaches the ex ante mean-variance efficient portfolio in the absence of mispricing. With mispricings, mean-variance strategies can overcome the difficulty brought by the imprecise parameter estimates and outperform 1/N by exploiting the mispricing. Second, with mispricings the 1/N rule is unlikely to outperform mean-variance strategies even when N is large, since mean-variance strategies have more opportunities to exploit mispricings. Third, minimum-variance strategies do not exploit mispricings and underperform the 1/N rule.

Mean-Variance versus Naave Diversification: The Role of Mispricing

We compare the equal-weight naive 1/N portfolio with mean-variance strategies from the perspective of mispricing (alpha) and provide three new findings. First, we analytically show that the 1/N rule approaches the ex ante mean-variance efficient portfolio in the absence of mispricing. With mispricings, mean-variance strategies can overcome the difficulty brought by the imprecise parameter estimates and outperform 1/N by exploiting the mispricing. Second, with mispricings the 1/N rule is unlikely to outperform mean-variance strategies even when N is large, since mean-variance strategies have more opportunities to exploit mispricings. Third, minimum-variance strategies do not exploit mispricings and underperform the 1/N rule.

The Impact of Constraints on Minimum-Variance Portfolios

Optimized minimum-variance strategies tend to have low liquidity; high turnover; high tracking error; and concentrated stock, sector, and country positions. Minimum-variance index providers typically mitigate these implementation problems by imposing constraints. The authors construct minimum-variance portfolios for the United States, global developed markets, and emerging markets and apply commonly used constraints to determine their effect on simulated portfolio characteristics, performance, and trading costs. The constraints they test succeed in improving investability but shift portfolio characteristics toward those of the capitalization-weighted benchmark. In particular, each additional constraint increases volatility. Nonetheless, minimum-variance strategies are a valid choice for risk-averse investors.

Evaluation of realized multi-power variations in minimum variance hedging

This study investigated the hedging performance of realized multi-power variations under minimum variance strategy. The minimum variance hedge ratios are estimated by the realized DCC-GARCH model, and the risk and utility metrics are used to evaluate the performances of long and short hedge. The empirical results derived from the S&P 500 index demonstrated that the realized DCC-GARCH model with realized tri-power variation outperforms others in reducing risks, and generates largest economic benefits. While considering transaction costs, the superiority of the realized DCC-GARCH model with realized multi-power variations persists and produced less rebalancing costs than the realized DCC-GARCH model with realized variance.

Tradability versus Performance: The Role of Liquidity in Minimum Variance Smart Beta Products

Low-volatility themed strategies have been among the most popular “smart beta” index products introduced in recent years, and minimum variance in particular has become a widely adopted approach to implementing low-volatility exposure. In the following analysis, we attempt to address the following questions: From a risk perspective, to what extent is the “theoretical” low risk of these strategies driven by illiquidity masquerading as low volatility? Do returns of minimum variance strategies encapsulate some form of liquidity premium in addition to the outperformance of low risk stocks? And, if there is a tendency to tilt towards smaller and less liquid stocks, what can be done to ensure tradability of minimum variance portfolios?

Task-driven imaging in cone-beam computed tomography.

Conventional workflow in interventional imaging often ignores a wealth of prior information of the patient anatomy and the imaging task. This work introduces a task-driven imaging framework that utilizes such information to prospectively design acquisition and reconstruction techniques for cone-beam CT (CBCT) in a manner that maximizes task-based performance in subsequent imaging procedures. The framework is employed in jointly optimizing tube current modulation, orbital tilt, and reconstruction parameters in filtered backprojection reconstruction for interventional imaging. Theoretical predictors of noise and resolution relates acquisition and reconstruction parameters to task-based detectability. Given a patient-specific prior image and specification of the imaging task, an optimization algorithm prospectively identifies the combination of imaging parameters that maximizes task-based detectability. Initial investigations were performed for a variety of imaging tasks in an elliptical phantom and an anthropomorphic head phantom. Optimization of tube current modulation and view-dependent reconstruction kernel was shown to have greatest benefits for a directional task (e.g., identification of device or tissue orientation). The task-driven approach yielded techniques in which the dose and sharp kernels were concentrated in views contributing the most to the signal power associated with the imaging task. For example, detectability of a line pair detection task was improved by at least three fold compared to conventional approaches. For radially symmetric tasks, the task-driven strategy yielded results similar to a minimum variance strategy in the absence of kernel modulation. Optimization of the orbital tilt successfully avoided highly attenuating structures that can confound the imaging task by introducing noise correlations masquerading at spatial frequencies of interest. This work demonstrated the potential of a task-driven imaging framework to improve image quality and reduce dose beyond that achievable with conventional imaging approaches.

Multi-asset portfolio optimization and out-of-sample performance: an evaluation of Black–Litterman, mean-variance, and naïve diversification approaches

The Black–Litterman model aims to enhance asset allocation decisions by overcoming the problems of mean-variance portfolio optimization. We propose a sample-based version of the Black–Litterman model and implement it on a multi-asset portfolio consisting of global stocks, bonds, and commodity indices, covering the period from January 1993 to December 2011. We test its out-of-sample performance relative to other asset allocation models and find that Black–Litterman optimized portfolios significantly outperform naïve-diversified portfolios (1/N rule and strategic weights), and consistently perform better than mean-variance, Bayes–Stein, and minimum-variance strategies in terms of out-of-sample Sharpe ratios, even after controlling for different levels of risk aversion, investment constraints, and transaction costs. The BL model generates portfolios with lower risk, less extreme asset allocations, and higher diversification across asset classes. Sensitivity analyses indicate that these advantages are due to more stable mixed return estimates that incorporate the reliability of return predictions, smaller estimation errors, and lower turnover.