High-low Strategy of Portfolio Composition using Evolino RNN Ensembles

trategy of investment is important tool enabling better investor's decisions in uncertain finance market. Rules of portfolio selection help investors balance accepting some risk for the expectation of higher returns. The aim of the research is to propose strategy of constructing investment portfolios based on the composition of distributions obtained by using high–low data. The ensemble of 176 Evolino recurrent neural networks (RNN) trained in parallel investigated as an artificial intelligence solution, which applied in forecasting of financial markets. Predictions made by this tool twice a day with different historical data give two distributions of expected values, which reflect future dynamic exchange rates. Constructing the portfolio, according to the shape, parameters of distribution and the current value of the exchange rate allows the optimization of trading in daily exchange-rate fluctuations. Comparison of a high-low portfolio with a close-to-close portfolio shows the efficiency of the new forecasting tool and new proposed trading strategy

The fundamental nature of HARA utility

Many models in Economics assume a utility function belonging to the HARA family. This paper shows that HARA utility is more fundamental to economic analysis. The HARA functional form is the unique form which satisfies basic economic principles in an optimization context. Using HARA is therefore not just a matter of convenience or tractability but rather emerges from economic reasoning, i.e., it is inherent in the economic optimization problem. The paper applies Lie symmetries to the optimality equation of Merton’s (1969, 1971) widelyused intertemporal model of the consumer-investor in order to show the inherent nature of the HARA utility function. Lie symmetries derive the conditions whereby the optimal solution remains invariant under scale transformations of wealth. The latter arise as the result of growth over time or due to the effects of policy. The symmetries place restrictions on the model, with the key one being the use of HARA utility. We show that this scale invariance of agents’ wealth implies linear optimal solutions to consumption and portfolio allocation and linear risk tolerance (and vice versa). The results have broad implications, as the model studied is a fundamental one in Macroeconomics and Finance. The paper demonstrates the use of Lie symmetries as a powerful tool to deal with economic optimization problems

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