Improved Portfolio Choice using Second-Order Stochastic Dominance

We examine the use of second-order stochastic dominance as both a way to measure performance and also as a technique for constructing portfolios. Using in-sample data, we construct portfolios such that their second-order stochastic dominance over a typical pension fund benchmark is most probable. The empirical results based on 21 years of daily data suggest that this portfolio choice technique significantly outperforms the benchmark portfolio out-of-sample. As a preference-free technique it will also suit any risk-averse investor in e.g. a pension fund. Moreover, its out-of-sample performance across eight different measures is superior to widely discussed portfolio choice approaches such as equal weights, mean variance, and minimum-variance methods.second-order stochastic dominance, portfolio choice, portfolio measurement

Portfolio optimisation models and properties of return distributions

Mean-risk models have been widely used in portfolio optimisation. However, such models may produce portfolios that are dominated with respect to second order stochastic dominance and therefore not optimal for rational and risk-averse investors. This paper considers the problem of constructing a portfolio which is nondominated with respect to second order stochastic dominance and whose return distribution has specified desirable properties. The problem is multi-objective and is transformed into a single objective problem by using the reference point method, in which target levels, known as aspiration points, are specified for the objective function values. A model is proposed in which the aspiration points relate to ordered return outcomes of the portfolio return. The model is extended by additionally specifying reservation points, which act pre-emptively in the optimisation. The theoretical properties of the models are studied. The performance of the models on real data drawn from the Hang Seng index is also investigated

Testing for Stochastic Dominance with Diversification Possibilities

We derive empirical tests for stochastic dominance that allow for diversification betweenchoice alternatives. The tests can be computed using straightforward linearprogramming. Bootstrapping techniques and asymptotic distribution theory canapproximate the sampling properties of the test results and allow for statistical inference.Our results could provide a stimulus to the further proliferation of stochastic dominancefor the problem of portfolio selection and evaluation (as well as other choice problemsunder uncertainty that involve diversification possibilities). An empirical application forUS stock market data illustrates our approach.stochastic dominance;portfolio selection;linear programming;portfolio diversification;portfolio evaluation

EVALUATION OF ALTERNATIVE RISK SPECIFICATIONS IN FARM PROGRAMMING MODELS

The use of alternative probability density functions to specify risk in farm programming models is explored and compared to a traditional specification using historical data. A method is described that compares risk efficient crop mixes using stochastic dominance techniques to examine impacts of different risk specifications on farm plans. Results indicate that a traditional method using historical farm data is as efficient for risk averse producers as two other methods of incorporating risk in farm programming models when evaluated using second degree stochastic dominance. Stochastic dominance with respect to a function further discriminates among the distributions, indicating that a density function based on the historic forecasting accuracy of the futures market results in a more risk-efficient crop mix for highly risk averse producers. Results also illustrate the need to validate alternative risk specifications perceived as improvements to traditional methods.Risk and Uncertainty,

Testing for Third-Order Stochastic Dominance with Diversification Possibilities

We derive an empirical test for third-order stochastic dominance that allows fordiversification between choice alternatives. The test can be computed usingstraightforward linear programming. Bootstrapping techniques and asymptoticdistribution theory can approximate the sampling properties of the test results and allowfor statistical inference. Our approach is illustrated using real-life US stock market data.efficiency;stochastic dominance;portfolio selection;linear programming;portfolio evaluation

Portfolio choice and estimation risk : a comparison of Bayesian approaches to resampled efficiency

Estimation risk is known to have a huge impact on mean/variance (MV) optimized portfolios, which is one of the primary reasons to make standard Markowitz optimization unfeasible in practice. Several approaches to incorporate estimation risk into portfolio selection are suggested in the earlier literature. These papers regularly discuss heuristic approaches (e.g., placing restrictions on portfolio weights) and Bayesian estimators. Among the Bayesian class of estimators, we will focus in this paper on the Bayes/Stein estimator developed by Jorion (1985, 1986), which is probably the most popular estimator. We will show that optimal portfolios based on the Bayes/Stein estimator correspond to portfolios on the original mean-variance efficient frontier with a higher risk aversion. We quantify this increase in risk aversion. Furthermore, we review a relatively new approach introduced by Michaud (1998), resampling efficiency. Michaud argues that the limitations of MV efficiency in practice generally derive from a lack of statistical understanding of MV optimization. He advocates a statistical view of MV optimization that leads to new procedures that can reduce estimation risk. Resampling efficiency has been contrasted to standard Markowitz portfolios until now, but not to other approaches which explicitly incorporate estimation risk. This paper attempts to fill this gap. Optimal portfolios based on the Bayes/Stein estimator and resampling efficiency are compared in an empirical out-of-sample study in terms of their Sharpe ratio and in terms of stochastic dominance

Stochastic Dominance Portfolio Analysis of Forestry Assets

We consider the forestry decision-making and harvesting problem from the perspective of financial portfolio management, where harvestable forest stands constitute one of the liquid assets of the portfolio. Using real data from Finnish mixed borealis forests and from the Helsinki stock exchange, we investigate the effect of trading the timber stock together with the forest land, or without the land (i.e., harvesting), on the portfolio efficiency. As our research methodology, we utilize the general Stochastic Dominance (SD) criteria, focusing on the recent theoretical advances in analyzing portfolio diversification within the SD framework. Our findings shed some further light on the question of how to model the forestry planning problem, and provide some comparative evidence of the applicability of the alternative SD test approaches.Forest Management, Portfolio Optimization, Stochastic Dominance, Diversification

MARKET IMPERFECTIONS, DISCOUNT FACTORS AND STOCHASTIC DOMINANCE: AN EMPIRICAL ANALYSIS WITH OIL-LINKED DERIVATIVES

Oil-linked derivatives are becoming very important in Modern Investment Theory. Accordingly, the analysis of Pricing Techniques and Portfolio Choice Problems involving these securities is a major topic for both managers and researchers. We focus on both the No-Arbitrage Approach and Stochastic Discount Factor (SDF) based methods in order to study oil-linked derivatives available at The New York Mercantile Exchange, Inc, one of the world's largest markets in energy and precious metals. First, we generalize some theoretical properties of the SDF in order to capture the effects induced by the bid-ask spread when analyzing dominated/efficient portfolios. Secondly, we apply our findings and empirically analyze the existence of dominated assets and portfolios in the oil derivatives market. Our results reveal the systematic presence of dominated prices, which should be taken into account by traders when composing their portfolios. Additionally, the test yields pricing and portfolio choice methods as well as new strategies that may allow brokers to outperform their service for their clients. It is worth to point out that the conclusions of the test have two important characteristics: On the one hand, they are very precise since we draw on perfectly synchronized bid/ask prices, as provided by Reuters. On the other hand, they are robust in the sense that they do not depend on any assumption about the underlying asset price dynamics. Finally, despite the empirical test focuses on oil derivatives, the methodology is general enough to apply to a broad range of markets.

Market imperfections, discount factors and stochastic dominance: an empirical analysis with oil-linked derivatives

Oil-linked derivatives are becoming very important in Modern Investment Theory. Accordingly, the analysis of Pricing Techniques and Portfolio Choice Problems involving these securities is a major topic for both managers and researchers. We focus on both the No-Arbitrage Approach and Stochastic Discount Factor (SDF) based methods in order to study oil-linked derivatives available at The New York Mercantile Exchange, Inc, one of the world's largest markets in energy and precious metals. First, we generalize some theoretical properties of the SDF in order to capture the effects induced by the bid-ask spread when analyzing dominated/efficient portfolios. Secondly, we apply our findings and empirically analyze the existence of dominated assets and portfolios in the oil derivatives market. Our results reveal the systematic presence of dominated prices, which should be taken into account by traders when composing their portfolios. Additionally, the test yields pricing and portfolio choice methods as well as new strategies that may allow brokers to outperform their service for their clients. It is worth to point out that the conclusions of the test have two important characteristics: On the one hand, they are very precise since we draw on perfectly synchronized bid/ask prices, as provided by Reuters. On the other hand, they are robust in the sense that they do not depend on any assumption about the underlying asset price dynamics. Finally, despite the empirical test focuses on oil derivatives, the methodology is general enough to apply to a broad range of markets

Finding common ground when experts disagree: robust portfolio decision analysis

We address the problem of decision making under “deep uncertainty,” introducing an approach we call Robust Portfolio Decision Analysis. We introduce the idea of Belief Dominance as a prescriptive operationalization of a concept that has appeared in the literature under a number of names. We use this concept to derive a set of non-dominated portfolios; and then identify robust individual alternatives from the non-dominated portfolios. The Belief Dominance concept allows us to synthesize multiple conflicting sources of information by uncovering the range of alternatives that are intelligent responses to the range of beliefs. This goes beyond solutions that are optimal for any specific set of beliefs to uncover defensible solutions that may not otherwise be revealed. We illustrate our approach using a problem in the climate change and energy policy context: choosing among clean energy technology R&D portfolios. We demonstrate how the Belief Dominance concept can uncover portfolios that would otherwise remain hidden and identify robust individual investments