Minimum Variance Strategy Research Articles

Portfolio Optimization Using Forward-Looking Information*

We develop a new family of estimators of the covariance matrix that relies solely on forward-looking information. It uses only current prices of plain-vanilla options. In an out-of-sample study, we show that a minimum variance strategy based on these fully-implied estimators outperforms several benchmark strategies, including various strategies based on historical estimates, index investing, and 1/N investing. The outperformance originates in crisis periods when information flow and information asymmetry are high. Although the historical benchmark strategies improve when more recent data are used, they never outperform fully-implied strategies. Thus, our results suggest that investors are better off relying on forward-looking information.

Restoring Value to Minimum Variance

A long-only investable minimum variance strategy outperformed the S&P 500 over the fourdecadesfromJanuary1973toDecember2012.Throughthelensofafactormodel, we show that this outperformance can be largely attributed to implicit style bets. Specifically, minimum variance has thrived by tilting toward stocks that have lower market capitalization and volatility, and a higher ratio of earnings to price. As funds have poured into minimum variance in the wake of the financial crisis, and plausibly as a consequence of this trend, the value tilt has disappeared and a momentum tilt has emerged. This suggests that the cost of entry to minimum variance is at a historic high. We show how the value tilt can be restored to minimum variance by targeting specific exposures, and that there was a substantial long-term benefit to the restoration at most recent points of entry to the strategy.

Understanding industry betas

Abstract This paper models and explains the dynamics of market betas for 30 US industry portfolios between 1970 and 2009. We use DCC–MIDAS and kernel regression techniques as alternatives to the standard ex-post measures. We find betas to exhibit substantial persistence, time variation, ranking variability, and heterogeneity in their business cycle exposure. While we find only a limited amount of structural breaks in the betas of individual industries, we do identify a common structural break in March 1998. We propose two practical applications to understand the economic significance of these results. We find the cross-sectional dispersion in industry betas to be countercyclical and negatively related to future market returns. We also find DCC–MIDAS betas to outperform other beta measures in terms of limiting the downside risk and ex-post market exposure of a market-neutral minimum-variance strategy.

On portfolio optimization: Imposing the right constraints

We reassess the recent finding that no established portfolio strategy outperforms the naively diversified portfolio, 1/N, by developing a constrained minimum-variance portfolio strategy on a shrinkage theory based framework. Our results show that our constrained minimum-variance portfolio yields significantly lower out-of-sample variances than many established minimum-variance portfolio strategies. Further, we observe that our portfolio strategy achieves higher Sharpe ratios than 1/N, amounting to an average Sharpe ratio increase of 32.5% across our six empirical datasets. We find that our constrained minimum-variance strategy is the only strategy that achieves the goal of improving the Sharpe ratio of 1/N consistently and significantly. At the same time, our developed portfolio strategy achieves a comparatively low turnover and exhibits no excessive short interest.

Understanding Industry Betas

This paper models and explains the dynamics of market betas for 30 US industry portfolios between 1970 and 2009. We use DCC-MIDAS and kernel regression techniques as alternatives to the standard ex-post measures. We find betas to exhibit substantial persistence, time variation, ranking variability, and heterogeneity in their business cycle exposure. While we find only a limited amount of structural breaks in the betas of individual industries, we do identify a common structural break in March 1998. We propose two practical applications to understand the economic significance of these results. We find the cross-sectional dispersion in industry betas to be countercyclical and negatively related to future market returns. We also find DCC-MIDAS betas to outperform other beta measures in terms of limiting the downside risk and ex-post market exposure of a market-neutral minimum-variance strategy.

An empirical study of the impact of skewness and kurtosis on hedging decisions

This study uses real price data rather than a simulation approach to investigate how hedging behaviours may change when hedgers consider skewness and excess kurtosis of hedging returns in their decision models. The study involves modelling the time-varying skewness and excess kurtosis of returns. The empirical results show that adding a preference for positively skewed returns to traditional mean-variance models may not lead to more speculative hedging/investment behaviours. Post-hedged return distributions suggest that the third moments of hedged portfolios have probably been well adjusted by mean-variance strategies, rendering three-moment decision models on a par with traditional mean-variance models. Additionally, considering the aversion to excess kurtosis will cause investors to hedge more. The research also provides empirical support for traditional minimum-variance strategies.

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 naive-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.

Portfolio Optimization Using Forward-Looking Information

In this paper we develop a new family of estimators of the covariance matrix that relies solely on forward-looking information. These estimators only use current price information from a cross-section of plain-vanilla options and employ different higher moments of the implied return distributions. In an out-of-sample study for US blue-chip stocks we show that a minimum-variance strategy based on these fully implied covariance estimators consistently outperforms a wide range of different benchmark strategies, including strategies based on historical estimates, index investing, and investing according to the 1/N rule. This result is very robust and holds with and without short-sales restrictions, with portfolios being rebalanced at different frequencies, and with transactions costs taken into account. The outperformance is particular strong in crisis periods when information flow and information asymmetry are high. The outperformance can only be reached using a fully implied approach; partially implied approaches that combine implied moments with historical ones might even perform worse than purely historical approaches. We further observe that covariance estimators based on implied second and fourth moments outperform estimators based on implied skewness. In conclusion, our results show that investors can better exploit possible diversification benefits by relying solely on forward-looking information from options markets.

Multiple tests for the performance of different investment strategies

In the context of modern portfolio theory, we compare the out-of-sample performance of eight investment strategies which are based on statistical methods with the out-of-sample performance of a family of trivial strategies. A wide range of approaches is considered in this work, including the traditional sample-based approach, several minimum-variance techniques, a shrinkage, and a minimax approach. In contrast to similar studies in the literature, we also consider short-selling constraints and a risk-free asset. We provide a way to extend the concept of minimum-variance strategies in the context of short-selling constraints. A main drawback of most empirical studies on that topic is the use of simple testing procedures which do not account for the effects of multiple testing. For that reason we conduct several hypothesis tests which are proposed in the multiple-testing literature. We test whether it is possible to beat a trivial strategy by at least one of the non-trivial strategies, whether the trivial strategy is better than every non-trivial strategy, and which of the non-trivial strategies is significantly outperformed by naive diversification. The empirical part of our study is conducted using US stock returns from the last four decades, obtained via the CRSP database.

Aging, visual information, and adaptation to task asymmetry in bimanual force coordination

This study investigated the coordination and control strategies that the elderly adopt during a redundant finger force coordination task and how the amount of visual information regulates the coordination patterns. Three age groups (20-24, 65-69, and 75-79 yr) performed a bimanual asymmetric force task. Task asymmetry was manipulated via imposing different coefficients on the finger forces such that the weighted sum of the two index finger forces equaled the total force. The amount of visual information was manipulated by changing the visual information gain of the total force output. Two hypotheses were tested: the reduced adaptability hypothesis predicts that the elderly show less degree of force asymmetry between hands compared with young adults in the asymmetric coefficient conditions, whereas the compensatory hypothesis predicts that the elderly exhibit more asymmetric force coordination patterns with asymmetric coefficients. Under the compensatory hypothesis, two contrasting directions of force sharing strategies (i.e., more efficient coordination strategy and minimum variance strategy) are expected. A deteriorated task performance (high performance error and force variability) was found in the two elderly groups, but enhanced visual information improved the task performance in all age groups. With low visual information gain, the elderly showed reduced adaptability (i.e., less asymmetric forces between hands) to the unequal weighting coefficients, which supported the reduced adaptability hypothesis; however, the elderly revealed the same degree of adaptation as the young group under high visual gain. The findings are consistent with the notion that the age-related reorganization of force coordination and control patterns is mediated by visual information and, more generally, the interactive influence of multiple categories of constraints.

The optimal value-at-risk hedging strategy under bivariate regime switching ARCH framework

Unlike the majority of other hedging literatures in which variance is taken as the risk indicator, this article uses the Value-at-Risk (VaR) as the risk management tool of the hedged portfolio. This article adopts a bivariate Markov regime Switching Autoregressive Conditional Heteroscedastic (SWARCH) model to formulate the optimal VaR hedging strategy and then compares it with the other dynamic futures hedging strategies mentioned in the literature in hedging performance. Using Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX) futures data, the in-sample and out-of-sample results shows that when VaR is used as the criterion to measure the futures hedging effectiveness, the performance of the dynamic hedging strategy is superior to that of the static hedging strategy, and the performance of the optimal VaR hedging strategy is better than that of the minimum variance and mean-variance hedging strategies. Besides, from the standpoint that the volatility of hedge ratio and hedged portfolio variance decline, no matter what kind of hedging strategy is adopted, the regime switching model is better in in-sample and out-of-sample hedging effectiveness than the Generalized Autoregressive Conditional Heteroscedastic (GARCH) model.

Discrete-Time, Minimum-Variance Hedging of European Contingent Claims

This paper addresses minimum-variance hedging of European contingent claims (ECC) in the case where changes to the hedging portfolio can be made only at discrete, pre-decided times. A simple derivation of the minimum-variance hedging strategy is first given in a general setting. The strategy is then applied to a general class of European contingent claims written on an underlying asset whose price process is a martingale modeled by a geometric Brownian motion. A Wiener space setting is used to show that the minimum-variance strategy requires the asset holding to equal the ratio of conditional expectations of the changes in the ECC payoff and the underlying asset price that occur when sample paths of the Wiener process are modified in a certain manner. In the case of specific claims, the minimum-variance hedging strategy can be further expressed in terms of pricing functions. Unlike previous work, the results of this paper apply equally well to simple as well as path-dependent claims.

On Portfolio Optimization: Imposing the Right Constraints

We reassess the recent finding that no established portfolio strategy outperforms the naively diversified portfolio, 1/N, by developing a constrained minimum-variance portfolio strategy on a shrinkage theory based framework. Our results show that our constrained minimum-variance portfolio yields significantly lower out-of-sample variances than many established minimum-variance portfolio strategies. Further, we observe that our portfolio strategy achieves higher Sharpe ratios than 1/N, amounting to an average Sharpe ratio increase of 32.5% across our six empirical datasets. We find that our constrained minimum-variance strategy is the only strategy that achieves the goal of improving the Sharpe ratio of 1/N consistently and significantly. At the same time, our developed portfolio strategy achieves a comparatively low turnover and exhibits no excessive short interest.

Use of an artificial immune network optimization approach to tune the parameters of a discrete variable structure controller

Recently, the discrete variable structure controllers (VSCs) for nonlinear systems has received some attention. These VSCs are formulated for the systems with different kinds of uncertainties using switching or nonswitching types of techniques. The performance of these controllers depends not only on the control structure but also on the values of the controller’s parameters. In this context, an artificial immune system (AIS) can be useful to tune the VSCs’ parameters. AISs represent a field of biologically inspired computing that attempts to exploit theories, principles, and concepts of modern immunology to design immune system-based applications in science and engineering, mainly in learning and optimization applications. This paper presents an AIS approach applied to optimize the design of an incremental discrete VSC for minimizing the generalized minimum variance strategy. Control design and implementation tests are assessed in a reactor and a control valve.

05/00619 Processing and properties of a glass-ceramic from coal fly ash from a thermal power plant through an economic process

The application of an on-line self-tunina control algorithm based on a minimum variance strategy to thermal power plants is considered. In thermal power plants it is required to maintain the pressure of the steam turbine within certain limits while supplying the demanded power as fast as possible upon request. Basically, two control loops are involved in order to satisfy these conditions. Simulation of a thermal power plant is used to demonstrate the qualitative aspects of the suggested control scheme. The integrals of the squared error of both the boiler steam pressure and the turbine generated power are used to measure the effectiveness of this control scheme. The test results clearly indicate the advantages of the new self-tuningh controller over the conventional PI controller. The proposed self-tuning algorithm is simple and can be easily implemented locally on a microprocessor.

Neural control of turbogenerator systems

The application of neural networks to excitation control of a synchronous generator is considered here. A radial basis function (RBF) network was constructed using a hybrid training algorithm, combining linear optimization of the output layer weights with singular-value decomposition, and non-linear optimization of the centres and widths using second-order gradient descent BFGS. The Jacobian of the RBF network was calculated to provide instantaneous linear models of the plant, which were then used to form linear controllers. Generalized minimum variance, Kalman, and internal model control schemes were implemented on an industry-standard VME platform linked to a network of Inmos transputers, and the performance of the neural models and neural control schemes were investigated on a 3 kVA laboratory micromachine system. Comparison was made with a self-tuning regulator, employing a generalized minimum variance strategy. The results presented illustrate that not only is it possible to successfully implement neural controllers on a generator system, but also their performance is comparable with a benchmark self-tuning controller, while avoiding the significant supervisory code needed to ensure robust operation of the self-tuning controller.

Neural Modelling and Control of a Synchronous Generator

Neural network techniques have been applied to excitation control of a synchronous generator. A radial basis function network was constructed using a hybrid training algorithm, combining linear optimization of the output layer weights with singular value decomposition, and non-linear optimization of the basis function centres and widths using second-order gradient descent BFGS. The network Jacobian was subsequently calculated to provide instantaneous linear models of the plant. Using these models, internal model control, Kalman and generalized minimum variance schemes were implemented on an industry-standard VME platform. The performance of the neural models and neural control schemes was investigated on a laboratory micromachine, with comparisons being made with a self-tuning regulator, employing a generalized minimum variance strategy.

Dahlin minimum variance self-tuning controller

An alternative minimum variance self-tuning controller is presented. The proposed controller, which is designed to combine a minimum variance strategy with a Dahlin controller, overcomes the shortcomings of the original version of minimum variance control and is found to be competitive with the generalized minimum variance controller. It tracks set-point changes with the desired speed of response, penalizes the excessive control action, and can be applied to non-minimum phase systems. The control algorithm is also extended to multi-variable systems. Robust pole-assignment can be incorporated to enable closed-loop system stability characteristics to be readily specified. Simulated results are presented to indicate the advantages of the proposed controller.

Simulation study of self-tuning adaptive control for rougher flotation

The properties of different self-tuning algorithms are studied and evaluated using a phenomenological dynamic simulator of the flotation process. The problem of controlling a system with constant but unknown parameters is considered. In the beginning the analysis is restricted to discrete-time single input-single output systems. An explicit algorithm obtained by combining a least squares estimator with a minimum variance regulator computed from the estimated model is analyzed. The corresponding implicit generalized minimum variance algorithm is also tested. A multivariable self-tuning regulator based on the minimum variance strategy is represented. The conclusions are drawn upon these simulation results and on practical experience for the use of these algorithms in flotation control.

Self-tuning algorithm for automatic generation control in an interconnected power system

This paper describes a control scheme based on a generalized minimum variance strategy for the load frequency and tie-line power control of a multi-area interconnected thermal power system. Each control area in the interconnection is represented by a reduced-order stochastic AR-MAX model with parameters estimated using an extended least squares technique. The area generator corrective control is computed by a self-tuning algorithm derived from the minimization of a generalized cost function, which is defined in terms of the system output and the weighting on the control effort. The control algorithm is further coupled with a simple load accommodation routine to account for the non-zero mean component of the load disturbances. Simulation studies show that, compared with conventional methods, the proposed control strategies are more effective, especially when system non-linearities are taken into account.