# American Institute of Mathematical Sciences

January  2018, 3: 5 doi: 10.1186/s41546-018-0031-1

## Zero covariation returns

 1. Robert H. Smith School of Business, University of Maryland, College Park 20742, MD, USA; 2. Department of Mathematics, K. U. Leuven, Leuven, Belgium

Received  November 26, 2017 Revised  May 07, 2018

Asset returns are modeled by locally bilateral gamma processes with zero covariations. Covariances are then observed to be consequences of randomness in variations. Support vector machine regressions on prices are employed to model the implied randomness. The contributions of support vector machine regressions are evaluated using reductions in the economic cost of exposure to prediction residuals. Both local and global mean reversion and momentum are represented by drift dependence on price levels. Optimal portfolios maximize conservative portfolio values calculated as distorted expectations of portfolio returns observed on simulated path spaces. They are also shown to outperform classical alternatives.
Citation: Dilip B. Madan, Wim Schoutens. Zero covariation returns. Probability, Uncertainty and Quantitative Risk, 2018, 3 (0) : 5-. doi: 10.1186/s41546-018-0031-1
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