The Markowitz Category

We give an algebraic definition of a Markowitz market and classify markets up to isomorphism. Given this classification, the theory of portfolio optimization in Markowitz markets without short selling constraints becomes trivial. Conversely, this classification shows that, up to isomorphism, there is little that can be said about a Markowitz market that is not already detected by the theory of portfolio optimization. In particular, if one seeks to develop a simplified low-dimensional model of a large financial market using mean--variance analysis alone, the resulting model can be at most two-dimensional.Comment: 1 figur

Export diversification and resource-based industrialization: the case of natural gas

For resource-rich economies, primary commodity specialization has often been considered to be detrimental to growth. Accordingly, export diversification policies centered on resource-based industries have long been advocated as effective ways to moderate the large variability of export revenues. This paper discusses the applicability of a mean-variance portfolio approach to design these strategies and proposes some modifications aimed at capturing the key features of resource processing industries (presence of scale economies and investment lumpiness). These modifications help make the approach more plausible for use in resource-rich countries. An application to the case of natural gas is then discussed using data obtained from Monte Carlo simulations of a calibrated empirical model. Lastly, the proposed framework is put to work to evaluate the performances of the diversification strategies implemented in a set of nine gas-rich economies. These results are then used to formulate some policy recommendations

Environmental Risks and Benefits of Nano-Enabled Clean Energy Technologies

Engineered nanomaterials (ENMs) are increasingly incorporated into clean energy technologies due to observed improvement in technological and system performance. Though these materials could revolutionize many products and technologies, increased use of ENMs can also introduce uncertainty and risks that are difficult to predict. Increase in ENM use could significantly increase ENM releases to the environment across their life cycle, from material synthesis to end-of-life. To address knowledge gaps and uncertainties, this work assesses a portfolio of ENMs from a systems perspective. First, characterization and quantification methods were developed for three carbonaceous ENMs, fullerenes (C60, C70, and derivative PCBM), which have promising application in solar technologies. Empirical ecotoxicity assays and predation studies were performed to determine ecotoxicity and predation effects. Next, an integrated model predicted potential risks of ENM accumulation by estimating potential manufacturing locations, spatial concentrations, and potential ecological risks. This was followed by an adaption of portfolio optimization, a model traditionally used to optimize investment performance, to model potential environmental and economic risks and simultaneous performance benefits and inform safe nano-enabled design. Ecotoxicity findings demonstrate differences among fullerenes where organisms exposed to fullerenes also experienced significantly increased predation risk, underscoring the need to consider potential system-level effects. Based on manufacturing locations, potential ENM exposure may be within buffer distances of sensitive ecosystems. However, modeled ENM accumulation would only reach levels associated with ecotoxicity risk under extreme scenarios. Future ENM use-patterns can be informed by the portfolio optimization approach, where optimal portfolios are determined by the materials-mix that yielded the greatest overall performance return while minimizing the portfolio risks. These novel methods and tools contribute to the knowledge of the benefits and risks of ENMs, which will help to guide more responsible and proactive policy and planning around ENM development and use

Theory and Applications of Robust Optimization

In this paper we survey the primary research, both theoretical and applied, in the area of Robust Optimization (RO). Our focus is on the computational attractiveness of RO approaches, as well as the modeling power and broad applicability of the methodology. In addition to surveying prominent theoretical results of RO, we also present some recent results linking RO to adaptable models for multi-stage decision-making problems. Finally, we highlight applications of RO across a wide spectrum of domains, including finance, statistics, learning, and various areas of engineering.Comment: 50 page

Risk minimization and portfolio diversification

We consider the problem of minimizing capital at risk in the Black-Scholes setting. The portfolio problem is studied given the possibility that a correlation constraint between the portfolio and a financial index is imposed. The optimal portfolio is obtained in closed form. The effects of the correlation constraint are explored; it turns out that this portfolio constraint leads to a more diversified portfolio

Asset Allocation with Aversion to Parameter Uncertainty: A Minimax Regression Approach

This paper takes a minimax regression approach to incorporate aversion to parameter uncertainty into the mean-variance model. The uncertainty-averse minimax mean-variance portfolio is obtained by minimizing with respect to the unknown weights the upper bound of the usual quadratic risk function over a fuzzy ellipsoidal set. Beyond the existing approaches, our methodology offers three main advantages: first, the resulting optimal portfolio can be interpreted as a Bayesian mean-variance portfolio with the least favorable prior density, and this result allows for a comprehensive comparison with traditional uncertainty-neutral Bayesian mean-variance portfolios. Second, the minimax mean-variance portfolio has a shrinkage expression, but its performance does not necessarily lie within those of the two reference portfolios. Third, we provide closed form expressions for the standard errors of the minimax mean-variance portfolio weights and statistical significance of the optimal portfolio weights can be easily conducted. Empirical applications show that incorporating aversion to parameter uncertainty leads to more stable optimal portfolios that outperform traditional uncertainty-neutral Bayesian mean-variance portfolios.Asset allocation, estimation error, aversion to uncertainty, min-imax regression, Bayesian mean-variance portfolios, least favorable prior