Nonparametric Sharpe Ratio Function Estimation in Heteroscedastic Regression Models via Convex Optimization
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Proceedings of the TwentyFirst International Conference on Artificial Intelligence and Statistics, PMLR 84:14951504, 2018.
Abstract
We consider maximum likelihood estimation (MLE) of heteroscedastic regression models based on a new “parametrization” of the likelihood in terms of the Sharpe ratio function, or the ratio of the mean and volatility functions. While with a standard parametrization the MLE problem is not convex and hence hard to solve globally, our parametrization leads to a functional that is jointly convex in the Sharpe ratio and inverse volatility functions. The major difficulty with the resulting infinitedimensional convex program is the shape constraint on the inverse volatility function. We propose to solve the problem by solving a sequence of finitedimensional convex programs with increasing dimensions, which can be done globally and efficiently. We demonstrate that, when the goal is to estimate the Sharpe ratio function directly, the finitesample performance of the proposed estimation method is superior to existing methods that estimate the mean and variance functions separately. When applied to a financial dataset, our method captures a wellknown covariatedependent effect on the Shape ratio.
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